1
Unit 1: Numbers & Everyday Math • Class 3 Mathematics (New NEP 2020)
Chapter 1: What's in a Name?
Letter Counting, Name Grids, Number Names & Comparing Quantities
Chapter Highlights, Mathematical Ideas & Key Properties
- Counting letters in names and organizing data into frequency tables.
- Comparing lengths of names: identifying longest and shortest names.
- Finding names starting or ending with the same letter.
- Representing quantities using tally marks and bar-like grid representations.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (29 Solved Questions)
Q1
Write down the names of four of your classmates. Count the number of letters in each name. Which name is the longest, which is the shortest, and what is the difference between the two?
Textbook Exercise • Letter Counting
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Suppose we choose 4 classmates: Ravi, Ananya, Aarav, and Dharmendra.
2. Counting letters in each:
• Ravi: R-A-V-I = 4 letters
• Ananya: A-N-A-N-Y-A = 6 letters
• Aarav: A-A-R-A-V = 5 letters
• Dharmendra: D-H-A-R-M-E-N-D-R-A = 10 letters
3. Longest name: Dharmendra (10 letters)
4. Shortest name: Ravi (4 letters)
5. Difference: 10 - 4 = 6 letters.
1. Suppose we choose 4 classmates: Ravi, Ananya, Aarav, and Dharmendra.
2. Counting letters in each:
• Ravi: R-A-V-I = 4 letters
• Ananya: A-N-A-N-Y-A = 6 letters
• Aarav: A-A-R-A-V = 5 letters
• Dharmendra: D-H-A-R-M-E-N-D-R-A = 10 letters
3. Longest name: Dharmendra (10 letters)
4. Shortest name: Ravi (4 letters)
5. Difference: 10 - 4 = 6 letters.
CBSE Step-by-Step Marking Scheme
Correct letter count for all 4 names
1.5 M
Identifying longest, shortest, and difference
1.5 M
Q2
In a class of 20 children, 5 names start with the letter 'A', 3 with 'R', 4 with 'S', and 8 with other letters. How many names start with 'A', 'R', or 'S' altogether? What fraction of names start with 'A'?
Classroom Activity • Alphabet Hunt
3 Marks
✅ Step-by-Step Model Answer & Solution:
Given:
• Total children = 20
• Names starting with 'A' = 5
• Names starting with 'R' = 3
• Names starting with 'S' = 4
Calculation:
• Total names starting with 'A', 'R', or 'S' = 5 + 3 + 4 = 12 names.
• Fraction of names starting with 'A' = 5 out of 20 = 5/20 = 1/4 (one-fourth).
• Total children = 20
• Names starting with 'A' = 5
• Names starting with 'R' = 3
• Names starting with 'S' = 4
Calculation:
• Total names starting with 'A', 'R', or 'S' = 5 + 3 + 4 = 12 names.
• Fraction of names starting with 'A' = 5 out of 20 = 5/20 = 1/4 (one-fourth).
CBSE Step-by-Step Marking Scheme
Correct addition of name categories (5+3+4 = 12)
1.5 M
Correct fraction identification (5/20 = 1/4)
1.5 M
Q3
How can you organize all the students' names in your class by the number of letters (3 letters, 4 letters, 5 letters, 6+ letters) using a tally chart? Create a sample tally chart for 15 students.
Hands-on Project • Name Tally Chart
4 Marks
✅ Step-by-Step Model Answer & Solution:
Sample Tally Chart for 15 Students:
| Name Length | Tally Marks | Number of Children |
|---|---|---|
| 3 letters (e.g., Ali, Uma) | || | 2 |
| 4 letters (e.g., Riya, John) | |||| | 4 |
| 5 letters (e.g., Mohan, Priya) | 6 | |
| 6+ letters (e.g., Deepak, Sunita) | ||| | 3 |
| Total | — | 15 |
CBSE Step-by-Step Marking Scheme
Correct layout and categories in table
2.0 M
Correct tally mark grouping (bundles of 5)
2.0 M
Q4
In the Animal Team Game, the captain of Team 1 has the longest name and the captain of Team 2 has the shortest name. Given the list of animals: Elephant (8 letters), Ox (2 letters), Tiger (5 letters), and Deer (4 letters):
(a) Who is the captain of Team 1 and Team 2?
(b) Can you name an animal with an even longer name than Team 1's captain? Animal Team Game • Comparing Length of Names 3 Marks
(a) Who is the captain of Team 1 and Team 2?
(b) Can you name an animal with an even longer name than Team 1's captain? Animal Team Game • Comparing Length of Names 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Identifying Captains:
• Elephant: E-L-E-P-H-A-N-T = 8 letters (Longest)
• Ox: O-X = 2 letters (Shortest)
• Team 1 Captain: Elephant (8 letters)
• Team 2 Captain: Ox (2 letters)
(b) Animal with Longer Name:
• Yes! Crocodile (C-R-O-C-O-D-I-L-E = 9 letters) or Hippopotamus (H-I-P-P-O-P-O-T-A-M-U-S = 12 letters) has a longer name than Elephant.
(a) Identifying Captains:
• Elephant: E-L-E-P-H-A-N-T = 8 letters (Longest)
• Ox: O-X = 2 letters (Shortest)
• Team 1 Captain: Elephant (8 letters)
• Team 2 Captain: Ox (2 letters)
(b) Animal with Longer Name:
• Yes! Crocodile (C-R-O-C-O-D-I-L-E = 9 letters) or Hippopotamus (H-I-P-P-O-P-O-T-A-M-U-S = 12 letters) has a longer name than Elephant.
CBSE Step-by-Step Marking Scheme
Correct identification of Elephant and Ox as captains
1.5 M
Valid example of animal with >8 letters (e.g., Crocodile/Hippopotamus)
1.5 M
Q5
Mahesh and Kartik are comparing the number of letters in their names.
(a) Count the letters in 'Mahesh' and 'Kartik'.
(b) Who has a longer name, or are they equal?
(c) If their friend 'Venkatanarasimha' joins them, how many more letters does this name have than Mahesh? Textbook Discussion • Comparing Names 3 Marks
(a) Count the letters in 'Mahesh' and 'Kartik'.
(b) Who has a longer name, or are they equal?
(c) If their friend 'Venkatanarasimha' joins them, how many more letters does this name have than Mahesh? Textbook Discussion • Comparing Names 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Counting Letters:
• M-A-H-E-S-H = 6 letters
• K-A-R-T-I-K = 6 letters
(b) Comparison:
• Both names have exactly 6 letters. Neither is longer; they are equal in length.
(c) Extra Letters:
• V-E-N-K-A-T-A-N-A-R-A-S-I-M-H-A = 16 letters.
• Difference = 16 - 6 = 10 more letters.
(a) Counting Letters:
• M-A-H-E-S-H = 6 letters
• K-A-R-T-I-K = 6 letters
(b) Comparison:
• Both names have exactly 6 letters. Neither is longer; they are equal in length.
(c) Extra Letters:
• V-E-N-K-A-T-A-N-A-R-A-S-I-M-H-A = 16 letters.
• Difference = 16 - 6 = 10 more letters.
CBSE Step-by-Step Marking Scheme
Correct counts for Mahesh (6) and Kartik (6)
1.0 M
Correct equality conclusion
1.0 M
Correct difference calculation (16 - 6 = 10)
1.0 M
Q6
Ankit has 35 goats and Tanya has 27 goats.
(a) How many more goats does Ankit have than Tanya?
(b) Show Tanya's goat count (27) using tally marks in standard bundles of 5.
(c) If their flock also includes 14 black sheep and 19 white sheep, what is the total number of sheep? Tally Marks & Herding • Goat & Sheep Counting 3 Marks
(a) How many more goats does Ankit have than Tanya?
(b) Show Tanya's goat count (27) using tally marks in standard bundles of 5.
(c) If their flock also includes 14 black sheep and 19 white sheep, what is the total number of sheep? Tally Marks & Herding • Goat & Sheep Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Difference in Goats:
• Ankit's goats = 35
• Tanya's goats = 27
• Difference = 35 - 27 = 8 more goats.
(b) Tally Marks for 27:
• 27 = (5 × 5) + 2 =|||| |||| |||| |||| |||| || (5 bundles of five plus 2 individual marks).
(c) Total Sheep:
• Black sheep = 14
• White sheep = 19
• Total sheep = 14 + 19 = 33 sheep.
(a) Difference in Goats:
• Ankit's goats = 35
• Tanya's goats = 27
• Difference = 35 - 27 = 8 more goats.
(b) Tally Marks for 27:
• 27 = (5 × 5) + 2 =
(c) Total Sheep:
• Black sheep = 14
• White sheep = 19
• Total sheep = 14 + 19 = 33 sheep.
CBSE Step-by-Step Marking Scheme
Correct subtraction (35 - 27 = 8)
1.0 M
Accurate tally mark representation (5 bundles + 2 lines)
1.0 M
Correct addition of sheep (14 + 19 = 33)
1.0 M
Q7
In the number climb from 1 to 99, count the letters in the spelling of each number name (do not count hyphens):
(a) 'Seventy-eight'
(b) 'Ninety-three'
(c) 'Twenty-two'
Which of these three has the maximum number of letters, and which has the minimum? Number Names Mountain Climb • Spelling Length 3 Marks
(a) 'Seventy-eight'
(b) 'Ninety-three'
(c) 'Twenty-two'
Which of these three has the maximum number of letters, and which has the minimum? Number Names Mountain Climb • Spelling Length 3 Marks
✅ Step-by-Step Model Answer & Solution:
Letter Counting:
• (a) Seventy-eight: S-E-V-E-N-T-Y (7) + E-I-G-H-T (5) = 12 letters.
• (b) Ninety-three: N-I-N-E-T-Y (6) + T-H-R-E-E (5) = 11 letters.
• (c) Twenty-two: T-W-E-N-T-Y (6) + T-W-O (3) = 9 letters.
Conclusion:
• Maximum letters: Seventy-eight (12 letters)
• Minimum letters: Twenty-two (9 letters).
• (a) Seventy-eight: S-E-V-E-N-T-Y (7) + E-I-G-H-T (5) = 12 letters.
• (b) Ninety-three: N-I-N-E-T-Y (6) + T-H-R-E-E (5) = 11 letters.
• (c) Twenty-two: T-W-E-N-T-Y (6) + T-W-O (3) = 9 letters.
Conclusion:
• Maximum letters: Seventy-eight (12 letters)
• Minimum letters: Twenty-two (9 letters).
CBSE Step-by-Step Marking Scheme
Accurate letter count for all three number names (12, 11, 9)
1.5 M
Correct identification of maximum (78) and minimum (22)
1.5 M
Q8
In an animal team game, the following animal names are listed: Elephant, Ox, Deer, Kangaroo, Lion, Fox.
(a) Count the letters in each animal's name.
(b) Which animal has the longest name and which has the shortest?
(c) How many letters longer is the longest name compared to the shortest? Textbook Exercise • Name Length Comparison 3 Marks
(a) Count the letters in each animal's name.
(b) Which animal has the longest name and which has the shortest?
(c) How many letters longer is the longest name compared to the shortest? Textbook Exercise • Name Length Comparison 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Counting Letters:
• Elephant: E-L-E-P-H-A-N-T = 8 letters
• Ox: O-X = 2 letters
• Deer: D-E-E-R = 4 letters
• Kangaroo: K-A-N-G-A-R-O-O = 8 letters
• Lion: L-I-O-N = 4 letters
• Fox: F-O-X = 3 letters
(b) Longest & Shortest:
• Longest: Elephant and Kangaroo (8 letters each).
• Shortest: Ox (2 letters).
(c) Difference:
• 8 - 2 = 6 letters longer.
(a) Counting Letters:
• Elephant: E-L-E-P-H-A-N-T = 8 letters
• Ox: O-X = 2 letters
• Deer: D-E-E-R = 4 letters
• Kangaroo: K-A-N-G-A-R-O-O = 8 letters
• Lion: L-I-O-N = 4 letters
• Fox: F-O-X = 3 letters
(b) Longest & Shortest:
• Longest: Elephant and Kangaroo (8 letters each).
• Shortest: Ox (2 letters).
(c) Difference:
• 8 - 2 = 6 letters longer.
CBSE Step-by-Step Marking Scheme
Correct letter counts for all 6 animals
1.0 M
Correct longest and shortest identified
1.0 M
Difference calculation: 8 - 2 = 6
1.0 M
Q9
In a class of 24 children, the teacher records their names: 6 start with 'S', 5 start with 'A', 4 start with 'M', 3 start with 'R', and 6 start with other letters.
(a) Which letter is the most common starting letter?
(b) How many names start with either 'S' or 'A'?
(c) Represent the counts for 'S', 'A', 'M', and 'R' using tally marks in bundles of 5. Textbook Activity • Starting Letter Frequency 3 Marks
(a) Which letter is the most common starting letter?
(b) How many names start with either 'S' or 'A'?
(c) Represent the counts for 'S', 'A', 'M', and 'R' using tally marks in bundles of 5. Textbook Activity • Starting Letter Frequency 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Most common starting letter: Letter 'S' with 6 children.
• (b) Starting with 'S' or 'A': 6 + 5 = 11 names.
• (c) Tally marks:
• 'S' (6) =|||| |
• 'A' (5) =||||
• 'M' (4) = ||||
• 'R' (3) = |||.
• (a) Most common starting letter: Letter 'S' with 6 children.
• (b) Starting with 'S' or 'A': 6 + 5 = 11 names.
• (c) Tally marks:
• 'S' (6) =
• 'A' (5) =
• 'M' (4) = ||||
• 'R' (3) = |||.
CBSE Step-by-Step Marking Scheme
Most common starting letter 'S'
1.0 M
Sum of S and A = 11
1.0 M
Correct tally marks for all 4 categories
1.0 M
Q10
Look at the name 'AMITABH':
(a) How many total letters are in this name?
(b) How many vowels (A, E, I, O, U) are present?
(c) How many consonants are present?
(d) What fraction of the letters are vowels? Textbook Exploration • Vowels in Names 3 Marks
(a) How many total letters are in this name?
(b) How many vowels (A, E, I, O, U) are present?
(c) How many consonants are present?
(d) What fraction of the letters are vowels? Textbook Exploration • Vowels in Names 3 Marks
✅ Step-by-Step Model Answer & Solution:
Analysis of 'AMITABH':
• Letters: A - M - I - T - A - B - H.
• (a) Total letters: 7 letters.
• (b) Vowels: A, I, A = 3 vowels.
• (c) Consonants: M, T, B, H = 4 consonants.
• (d) Fraction of vowels: 3 out of 7 = 3/7.
• Letters: A - M - I - T - A - B - H.
• (a) Total letters: 7 letters.
• (b) Vowels: A, I, A = 3 vowels.
• (c) Consonants: M, T, B, H = 4 consonants.
• (d) Fraction of vowels: 3 out of 7 = 3/7.
CBSE Step-by-Step Marking Scheme
Total letters = 7
0.5 M
Vowels = 3, Consonants = 4
1.5 M
Fraction = 3/7
1.0 M
Q11
Some words read the same forward and backward, such as 'NOON' or 'RADAR'.
(a) Check if the names 'KANAK' and 'NAMAN' read the same backwards.
(b) Write down the letters of 'ROHIT' in reverse order. Does it form the same word? Practice Time • Reversing Names 3 Marks
(a) Check if the names 'KANAK' and 'NAMAN' read the same backwards.
(b) Write down the letters of 'ROHIT' in reverse order. Does it form the same word? Practice Time • Reversing Names 3 Marks
✅ Step-by-Step Model Answer & Solution:
Palindrome Word Analysis:
• (a) Checking KANAK & NAMAN:
• K-A-N-A-K reversed is K-A-N-A-K (Same!).
• N-A-M-A-N reversed is N-A-M-A-N (Same!).
Both are palindromes.
• (b) Reversing 'ROHIT':
• R-O-H-I-T in reverse order is T-I-H-O-R.
This is not the same word.
• (a) Checking KANAK & NAMAN:
• K-A-N-A-K reversed is K-A-N-A-K (Same!).
• N-A-M-A-N reversed is N-A-M-A-N (Same!).
Both are palindromes.
• (b) Reversing 'ROHIT':
• R-O-H-I-T in reverse order is T-I-H-O-R.
This is not the same word.
CBSE Step-by-Step Marking Scheme
Correct verification of KANAK and NAMAN as palindromes
1.5 M
Reversing ROHIT to TIHOR and concluding not the same
1.5 M
Q12
Arrange the following names from shortest to longest (ascending order): Sunita (6), Ali (3), Dharmendra (10), Priya (5), Raj (3), Meenakshi (9).
Let us Do • Name Length Ordering
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Ordering:
1. Count each name:
• Ali: 3 letters
• Raj: 3 letters
• Priya: 5 letters
• Sunita: 6 letters
• Meenakshi: 9 letters
• Dharmendra: 10 letters
Ascending Order:
Ali / Raj (3) → Priya (5) → Sunita (6) → Meenakshi (9) → Dharmendra (10).
1. Count each name:
• Ali: 3 letters
• Raj: 3 letters
• Priya: 5 letters
• Sunita: 6 letters
• Meenakshi: 9 letters
• Dharmendra: 10 letters
Ascending Order:
Ali / Raj (3) → Priya (5) → Sunita (6) → Meenakshi (9) → Dharmendra (10).
CBSE Step-by-Step Marking Scheme
Correct counts for all names
1.0 M
Accurate ascending order
1.0 M
Q13
In a class, the teacher asked children with 4-letter names to stand in Line 1, 5-letter names in Line 2, and 6-letter names in Line 3. If there are 8 children in Line 1, 12 in Line 2, and 7 in Line 3:
(a) Which line has the largest number of children?
(b) How many children are there in all three lines combined? Classroom Project • Grouping by Letter Count 2 Marks
(a) Which line has the largest number of children?
(b) How many children are there in all three lines combined? Classroom Project • Grouping by Letter Count 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) Line with most children: Line 2 (5-letter names) with 12 children.
• (b) Total children: 8 + 12 + 7 = 27 children.
• (a) Line with most children: Line 2 (5-letter names) with 12 children.
• (b) Total children: 8 + 12 + 7 = 27 children.
CBSE Step-by-Step Marking Scheme
Line 2 identified as largest (12 children)
1.0 M
Total count 8 + 12 + 7 = 27
1.0 M
Q14
If each letter in a name is worth 2 points, find the total points for the name 'KAVITA'. If 'DEEPAK' is scored the same way, who gets more points and by how much?
Mental Math • Letter Arithmetic
2 Marks
✅ Step-by-Step Model Answer & Solution:
Point Calculations:
• KAVITA has 6 letters: Score = 6 × 2 = 12 points.
• DEEPAK has 6 letters: Score = 6 × 2 = 12 points.
• Comparison: Both names have 6 letters, so both score exactly 12 points. Neither scores more; their points are equal.
• KAVITA has 6 letters: Score = 6 × 2 = 12 points.
• DEEPAK has 6 letters: Score = 6 × 2 = 12 points.
• Comparison: Both names have 6 letters, so both score exactly 12 points. Neither scores more; their points are equal.
CBSE Step-by-Step Marking Scheme
Kavita = 12 points, Deepak = 12 points
1.0 M
Conclusion of equal score
1.0 M
Q15
Find three 4-letter words that end with the letters 'O-O-K'. Write their names and count total letters.
In-Text Exploration • Words with Common Letters
2 Marks
✅ Step-by-Step Model Answer & Solution:
Words Ending in 'O-O-K':
1. BOOK (B-O-O-K = 4 letters)
2. LOOK (L-O-O-K = 4 letters)
3. COOK (C-O-O-K = 4 letters)
Other valid words: HOOK, TOOK.
Total letters across all three words = 4 + 4 + 4 = 12 letters.
1. BOOK (B-O-O-K = 4 letters)
2. LOOK (L-O-O-K = 4 letters)
3. COOK (C-O-O-K = 4 letters)
Other valid words: HOOK, TOOK.
Total letters across all three words = 4 + 4 + 4 = 12 letters.
CBSE Step-by-Step Marking Scheme
Three valid words ending in -ook
1.5 M
Total count = 12 letters
0.5 M
Q16
In a secret alphabet code, A=1, B=2, C=3, D=4, E=5. What is the sum of the letter values for the word 'B E D'?
Critical Thinking • Name Code Puzzle
2 Marks
✅ Step-by-Step Model Answer & Solution:
Code Calculation:
• B = 2
• E = 5
• D = 4
• Sum = 2 + 5 + 4 = 11.
The secret number code for 'BED' is 11.
• B = 2
• E = 5
• D = 4
• Sum = 2 + 5 + 4 = 11.
The secret number code for 'BED' is 11.
CBSE Step-by-Step Marking Scheme
Correct code values B=2, E=5, D=4
1.0 M
Sum = 11
1.0 M
Q17
Ritu's family has 4 members: Father (Ramesh - 6 letters), Mother (Sunita - 6 letters), Brother (Aman - 4 letters), and Ritu (4 letters).
(a) What is the total number of letters in all 4 names?
(b) What is the average number of letters per person? Textbook Discussion • Family Name Comparison 2 Marks
(a) What is the total number of letters in all 4 names?
(b) What is the average number of letters per person? Textbook Discussion • Family Name Comparison 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) Total Letters: 6 + 6 + 4 + 4 = 20 letters.
• (b) Average: Total letters ÷ 4 members = 20 ÷ 4 = 5 letters per person.
• (a) Total Letters: 6 + 6 + 4 + 4 = 20 letters.
• (b) Average: Total letters ÷ 4 members = 20 ÷ 4 = 5 letters per person.
CBSE Step-by-Step Marking Scheme
Total letters = 20
1.0 M
Average = 5 letters
1.0 M
Q18
State whether each statement is True or False:
(a) The name 'AARAV' has more vowels than consonants.
(b) 'INDIA' has exactly 5 letters.
(c) A tally mark bundle of 5 is drawn as five vertical lines without any cross line. Summary Practice • True or False 3 Marks
(a) The name 'AARAV' has more vowels than consonants.
(b) 'INDIA' has exactly 5 letters.
(c) A tally mark bundle of 5 is drawn as five vertical lines without any cross line. Summary Practice • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: AARAV has 3 vowels (A, A, A) and 2 consonants (R, V). 3 > 2.
• (b) True: I-N-D-I-A has 5 letters.
• (c) False: In standard tally marks, a bundle of 5 is drawn as 4 vertical lines with the 5th line drawn diagonally across them (||||).
• (a) True: AARAV has 3 vowels (A, A, A) and 2 consonants (R, V). 3 > 2.
• (b) True: I-N-D-I-A has 5 letters.
• (c) False: In standard tally marks, a bundle of 5 is drawn as 4 vertical lines with the 5th line drawn diagonally across them (
CBSE Step-by-Step Marking Scheme
(a) True with explanation
1.0 M
(b) True
1.0 M
(c) False with explanation of diagonal slash
1.0 M
Q19
In Chapter 1 ('What's in a Name?'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q20
In 'What's in a Name?', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q21
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q22
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q23
Observe the sequence related to 'What's in a Name?': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q24
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q25
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q26
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q27
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q28
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q29
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Library Badge Code Challenge
Real-World Math Context: The school librarian gives each child a library code based on their name: 10 points for each letter in the first name plus 5 points for each vowel (A, E, I, O, U).
Analytical Task: Calculate the total library badge score for 'KAVITA'. How many vowels are in her name, and what is her final code value?
1. Name: K-A-V-I-T-A contains 6 letters.
2. Letter points = 6 × 10 = 60 points.
3. Vowels in KAVITA: A, I, A = 3 vowels.
4. Vowel bonus points = 3 × 5 = 15 points.
5. Total library badge score = 60 + 15 = 75 points.
2. Letter points = 6 × 10 = 60 points.
3. Vowels in KAVITA: A, I, A = 3 vowels.
4. Vowel bonus points = 3 × 5 = 15 points.
5. Total library badge score = 60 + 15 = 75 points.
CBSE Assessment Rubric: 1M letter points + 1M vowel identification + 1M final calculation.
2
Unit 1: Numbers & Everyday Math • Class 3 Mathematics (New NEP 2020)
Chapter 2: Toy Joy
Counting, Grouping, Place Value (Tens & Ones) & Price Tag Calculations
Chapter Highlights, Mathematical Ideas & Key Properties
- Grouping objects in tens and ones: building base-10 understanding.
- Forming 2-digit numbers using bundles of 10 sticks and loose 1s.
- Reading price tags on toys and combining coins/notes to pay exact amounts.
- Comparing toy prices: finding which costs more and which costs less.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
A toy shop owner has 64 marbles. How many packets of 10 marbles can she make, and how many loose marbles will be left over? Write 64 in expanded form.
Textbook Exercise • Tens & Ones
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Total marbles = 64
• Number of tens in 64 = 6 packets of 10 (6 × 10 = 60)
• Loose marbles left over = 4 marbles
• Expanded Form: 64 = 60 + 4 = 6 Tens + 4 Ones.
• Total marbles = 64
• Number of tens in 64 = 6 packets of 10 (6 × 10 = 60)
• Loose marbles left over = 4 marbles
• Expanded Form: 64 = 60 + 4 = 6 Tens + 4 Ones.
CBSE Step-by-Step Marking Scheme
Correct number of packets (6) and loose (4)
1.0 M
Correct expanded form representation (60 + 4)
1.0 M
Q2
Rani buys a teddy bear for ₹38 and a spinning top for ₹24. (a) What is the total cost? (b) If she gives a ₹100 note to the shopkeeper, how much change should she receive?
Textbook Exercise • Money & Pricing
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Solution:
(a) Total Cost:
Cost of teddy bear = ₹38
Cost of spinning top = ₹24
Total = ₹38 + ₹24 = ₹(30 + 20 + 8 + 4) = ₹50 + ₹12 = ₹62.
(b) Change Received:
Amount given = ₹100
Total spent = ₹62
Change = ₹100 - ₹62 = ₹38.
(a) Total Cost:
Cost of teddy bear = ₹38
Cost of spinning top = ₹24
Total = ₹38 + ₹24 = ₹(30 + 20 + 8 + 4) = ₹50 + ₹12 = ₹62.
(b) Change Received:
Amount given = ₹100
Total spent = ₹62
Change = ₹100 - ₹62 = ₹38.
CBSE Step-by-Step Marking Scheme
Correct addition for total cost (₹62)
1.5 M
Correct subtraction for balance change (₹38)
1.5 M
Q3
I have 5 in my tens place. The digit in my ones place is 3 more than the digit in my tens place. What number am I? Is this number even or odd?
Logical Puzzle • Number Riddle
2 Marks
✅ Step-by-Step Model Answer & Solution:
Deduction:
1. Digit in tens place = 5
2. Digit in ones place = 5 + 3 = 8
3. The number is 58.
4. Since the ones digit is 8 (divisible by 2), the number 58 is an EVEN number.
1. Digit in tens place = 5
2. Digit in ones place = 5 + 3 = 8
3. The number is 58.
4. Since the ones digit is 8 (divisible by 2), the number 58 is an EVEN number.
CBSE Step-by-Step Marking Scheme
Correct calculation of ones digit and number 58
1.0 M
Correct classification as Even
1.0 M
Q4
A craftsman makes bead necklaces. Each necklace contains exactly 10 beads.
(a) How many full necklaces can be made from 85 beads, and how many loose beads are left over?
(b) How many more beads are needed to make one more complete necklace?
(c) Express 85 in standard expanded form. Bead Necklaces & Bundling • Tens and Ones 3 Marks
(a) How many full necklaces can be made from 85 beads, and how many loose beads are left over?
(b) How many more beads are needed to make one more complete necklace?
(c) Express 85 in standard expanded form. Bead Necklaces & Bundling • Tens and Ones 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Full Necklaces and Loose Beads:
• Total beads = 85
• Number of tens in 85 = 8 complete necklaces (8 × 10 = 80 beads)
• Loose beads remaining = 85 - 80 = 5 loose beads.
(b) Beads Needed for Next Necklace:
• One necklace requires 10 beads. Currently we have 5 loose beads.
• Needed = 10 - 5 = 5 more beads.
(c) Expanded Form:
• 85 = 8 Tens + 5 Ones = 80 + 5.
(a) Full Necklaces and Loose Beads:
• Total beads = 85
• Number of tens in 85 = 8 complete necklaces (8 × 10 = 80 beads)
• Loose beads remaining = 85 - 80 = 5 loose beads.
(b) Beads Needed for Next Necklace:
• One necklace requires 10 beads. Currently we have 5 loose beads.
• Needed = 10 - 5 = 5 more beads.
(c) Expanded Form:
• 85 = 8 Tens + 5 Ones = 80 + 5.
CBSE Step-by-Step Marking Scheme
Correct calculation of 8 necklaces and 5 loose beads
1.0 M
Correct beads needed for next necklace (5 beads)
1.0 M
Correct expanded form representation (80 + 5)
1.0 M
Q5
Look at the prices of these toys: Toy Car = ₹65, Robot = ₹92, Doll = ₹48, Wooden Train = ₹75.
(a) Arrange the toys in ascending order of their prices (cheapest to costliest).
(b) What is the difference in price between the most expensive toy and the cheapest toy?
(c) Can you buy both the Doll and the Toy Car with a single ₹100 note? Explain with calculation. Price Comparison • Toy Shop Rates 3 Marks
(a) Arrange the toys in ascending order of their prices (cheapest to costliest).
(b) What is the difference in price between the most expensive toy and the cheapest toy?
(c) Can you buy both the Doll and the Toy Car with a single ₹100 note? Explain with calculation. Price Comparison • Toy Shop Rates 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Ascending Order:
• ₹48 (Doll) < ₹65 (Toy Car) < ₹75 (Wooden Train) < ₹92 (Robot).
(b) Price Difference:
• Costliest = Robot (₹92)
• Cheapest = Doll (₹48)
• Difference = ₹92 - ₹48 = ₹44.
(c) ₹100 Budget Verification:
• Cost of Doll + Toy Car = ₹48 + ₹65 = ₹113.
• Since ₹113 > ₹100, No, you cannot buy both toys with a ₹100 note. You are short by ₹13.
(a) Ascending Order:
• ₹48 (Doll) < ₹65 (Toy Car) < ₹75 (Wooden Train) < ₹92 (Robot).
(b) Price Difference:
• Costliest = Robot (₹92)
• Cheapest = Doll (₹48)
• Difference = ₹92 - ₹48 = ₹44.
(c) ₹100 Budget Verification:
• Cost of Doll + Toy Car = ₹48 + ₹65 = ₹113.
• Since ₹113 > ₹100, No, you cannot buy both toys with a ₹100 note. You are short by ₹13.
CBSE Step-by-Step Marking Scheme
Correct ascending order arrangement
1.0 M
Correct difference calculation (92 - 48 = 44)
1.0 M
Correct budget calculation (48 + 65 = 113 > 100)
1.0 M
Q6
Rohit wants to buy a toy airplane costing ₹76. He has ₹10 notes and ₹5, ₹2, and ₹1 coins.
(a) Give one combination of notes and coins to make exactly ₹76.
(b) Give another combination using fewer notes and more coins. Coin Combinations • Exact Payment 3 Marks
(a) Give one combination of notes and coins to make exactly ₹76.
(b) Give another combination using fewer notes and more coins. Coin Combinations • Exact Payment 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Combinations:
(a) Combination 1 (Standard):
• 7 notes of ₹10 = ₹70
• 1 coin of ₹5 = ₹5
• 1 coin of ₹1 = ₹1
• Total = ₹70 + ₹5 + ₹1 = ₹76.
(b) Combination 2 (More Coins):
• 6 notes of ₹10 = ₹60
• 3 coins of ₹5 = ₹15
• 1 coin of ₹1 = ₹1
• Total = ₹60 + ₹15 + ₹1 = ₹76.
(a) Combination 1 (Standard):
• 7 notes of ₹10 = ₹70
• 1 coin of ₹5 = ₹5
• 1 coin of ₹1 = ₹1
• Total = ₹70 + ₹5 + ₹1 = ₹76.
(b) Combination 2 (More Coins):
• 6 notes of ₹10 = ₹60
• 3 coins of ₹5 = ₹15
• 1 coin of ₹1 = ₹1
• Total = ₹60 + ₹15 + ₹1 = ₹76.
CBSE Step-by-Step Marking Scheme
First valid currency combination summing to ₹76
1.5 M
Second distinct valid currency combination summing to ₹76
1.5 M
Q7
Complete the following skip counting sequences written on toy train carriages:
(a) 14, 24, 34, ___, ___, 64
(b) 85, 75, 65, ___, ___, 35
(c) What is the pattern rule in sequence (a) and sequence (b)? Number Sequences • Toy Train Carriages 3 Marks
(a) 14, 24, 34, ___, ___, 64
(b) 85, 75, 65, ___, ___, 35
(c) What is the pattern rule in sequence (a) and sequence (b)? Number Sequences • Toy Train Carriages 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
(a) 14, 24, 34, 44, 54, 64.
(b) 85, 75, 65, 55, 45, 35.
(c) Pattern Rules:
• Sequence (a) follows: Add 10 (+10) each time.
• Sequence (b) follows: Subtract 10 (-10) each time.
(a) 14, 24, 34, 44, 54, 64.
(b) 85, 75, 65, 55, 45, 35.
(c) Pattern Rules:
• Sequence (a) follows: Add 10 (+10) each time.
• Sequence (b) follows: Subtract 10 (-10) each time.
CBSE Step-by-Step Marking Scheme
Correct blanks in sequence (a): 44, 54
1.0 M
Correct blanks in sequence (b): 55, 45
1.0 M
Correct identification of rules (+10 and -10)
1.0 M
Q8
A toy seller has 68 rubber balls. He packs them into packets of 10 balls each.
(a) How many full packets can he make?
(b) How many loose balls will be left over?
(c) How many more balls does he need to complete another packet? Textbook Activity • Bundles of Ten 3 Marks
(a) How many full packets can he make?
(b) How many loose balls will be left over?
(c) How many more balls does he need to complete another packet? Textbook Activity • Bundles of Ten 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Full packets: 68 has 6 tens. He can make 6 full packets (6 × 10 = 60).
• (b) Loose balls: 68 - 60 = 8 loose balls.
• (c) Balls needed: 10 - 8 = 2 more balls to make the next packet.
• (a) Full packets: 68 has 6 tens. He can make 6 full packets (6 × 10 = 60).
• (b) Loose balls: 68 - 60 = 8 loose balls.
• (c) Balls needed: 10 - 8 = 2 more balls to make the next packet.
CBSE Step-by-Step Marking Scheme
6 packets
1 M
8 loose balls
1 M
2 more balls needed
1 M
Q9
In a toy shop: Robot costs ₹75, Car costs ₹45, Drum costs ₹90, and Yo-yo costs ₹20.
(a) Which toy costs the most and which costs the least?
(b) Arrange all 4 toys in order from least expensive to most expensive.
(c) If Raju buys the Car and Yo-yo, how much does he pay? Practice Time • Comparing Toy Prices 3 Marks
(a) Which toy costs the most and which costs the least?
(b) Arrange all 4 toys in order from least expensive to most expensive.
(c) If Raju buys the Car and Yo-yo, how much does he pay? Practice Time • Comparing Toy Prices 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Prices: Most expensive is Drum (₹90); least expensive is Yo-yo (₹20).
• (b) Ascending Order: Yo-yo (₹20) < Car (₹45) < Robot (₹75) < Drum (₹90).
• (c) Total cost: ₹45 + ₹20 = ₹65.
• (a) Prices: Most expensive is Drum (₹90); least expensive is Yo-yo (₹20).
• (b) Ascending Order: Yo-yo (₹20) < Car (₹45) < Robot (₹75) < Drum (₹90).
• (c) Total cost: ₹45 + ₹20 = ₹65.
CBSE Step-by-Step Marking Scheme
Drum most expensive, Yo-yo least
1 M
Ascending order
1 M
Total ₹65
1 M
Q10
Write the numbers represented by:
(a) 4 tens and 7 ones
(b) 8 tens and 0 ones
(c) 9 tens and 9 ones
(d) 5 tens and 14 ones. Number Building • Tens and Ones 2 Marks
(a) 4 tens and 7 ones
(b) 8 tens and 0 ones
(c) 9 tens and 9 ones
(d) 5 tens and 14 ones. Number Building • Tens and Ones 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) (4 × 10) + 7 = 40 + 7 = 47.
• (b) (8 × 10) + 0 = 80.
• (c) (9 × 10) + 9 = 90 + 9 = 99.
• (d) (5 × 10) + 14 = 50 + 14 = 64.
• (a) (4 × 10) + 7 = 40 + 7 = 47.
• (b) (8 × 10) + 0 = 80.
• (c) (9 × 10) + 9 = 90 + 9 = 99.
• (d) (5 × 10) + 14 = 50 + 14 = 64.
CBSE Step-by-Step Marking Scheme
47, 80, 99, 64 correct
2 M
Q11
A teddy bear costs ₹65. Which combination of currency notes can be used to pay exactly ₹65 without receiving change?
(A) Three ₹20 notes and one ₹5 coin
(B) One ₹50 note, one ₹10 note, and one ₹5 coin
(C) Both A and B are correct. Money Problems • Paying Exact Amount 2 Marks
(A) Three ₹20 notes and one ₹5 coin
(B) One ₹50 note, one ₹10 note, and one ₹5 coin
(C) Both A and B are correct. Money Problems • Paying Exact Amount 2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification:
• Option A: (3 × ₹20) + ₹5 = ₹60 + ₹5 = ₹65.
• Option B: ₹50 + ₹10 + ₹5 = ₹65.
• Therefore, (C) Both A and B are correct.
• Option A: (3 × ₹20) + ₹5 = ₹60 + ₹5 = ₹65.
• Option B: ₹50 + ₹10 + ₹5 = ₹65.
• Therefore, (C) Both A and B are correct.
CBSE Step-by-Step Marking Scheme
Validating both note combinations make ₹65
2 M
Q12
Count by tens starting from 25: 25, 35, 45, ___, ___, ___, 85, 95.
Mental Math • Skip Counting by 10
2 Marks
✅ Step-by-Step Model Answer & Solution:
Sequence:
Adding 10 at each step:
25, 35, 45, 55, 65, 75, 85, 95.
Missing numbers are 55, 65, 75.
Adding 10 at each step:
25, 35, 45, 55, 65, 75, 85, 95.
Missing numbers are 55, 65, 75.
CBSE Step-by-Step Marking Scheme
Correct missing values: 55, 65, 75
2 M
Q13
There are 3 shelves of toys. Shelf 1 has 24 toys, Shelf 2 has 31 toys, and Shelf 3 has 19 toys. How many toys are there in total?
Word Problem • Toys on Shelves
2 Marks
✅ Step-by-Step Model Answer & Solution:
Addition:
24 + 31 + 19 = 24 + (31 + 19) = 24 + 50 = 74 toys in total.
24 + 31 + 19 = 24 + (31 + 19) = 24 + 50 = 74 toys in total.
CBSE Step-by-Step Marking Scheme
Total = 74 toys with working
2 M
Q14
Pooja has ₹92. She wants to buy a battery car costing ₹100. How much more money does she need?
Think & Solve • Finding Difference
1 Marks
✅ Step-by-Step Model Answer & Solution:
Subtraction:
₹100 - ₹92 = ₹8 more needed.
₹100 - ₹92 = ₹8 more needed.
CBSE Step-by-Step Marking Scheme
₹8 difference
1 M
Q15
How many 5-rupee coins make ₹50? How many 10-rupee notes make ₹100?
Hands-on Activity • Exchanging Coins
2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• ₹50 ÷ ₹5 = 10 coins of 5 rupees.
• ₹100 ÷ ₹10 = 10 notes of 10 rupees.
• ₹50 ÷ ₹5 = 10 coins of 5 rupees.
• ₹100 ÷ ₹10 = 10 notes of 10 rupees.
CBSE Step-by-Step Marking Scheme
10 coins and 10 notes
2 M
Q16
I have 7 in my tens place. My ones digit is 3 less than my tens digit. What number am I?
Place Value Puzzle • Mystery Number
2 Marks
✅ Step-by-Step Model Answer & Solution:
Deduction:
• Tens digit = 7.
• Ones digit = 7 - 3 = 4.
• Number = 74.
• Tens digit = 7.
• Ones digit = 7 - 3 = 4.
• Number = 74.
CBSE Step-by-Step Marking Scheme
Number = 74
2 M
Q17
Write 83 and 59 in expanded form using tens and ones.
Expanded Form Practice • Decomposing Numbers
2 Marks
✅ Step-by-Step Model Answer & Solution:
Expanded Form:
• 83 = 8 Tens + 3 Ones = 80 + 3.
• 59 = 5 Tens + 9 Ones = 50 + 9.
• 83 = 8 Tens + 3 Ones = 80 + 3.
• 59 = 5 Tens + 9 Ones = 50 + 9.
CBSE Step-by-Step Marking Scheme
80 + 3 and 50 + 9
2 M
Q18
Round each number to the nearest ten: (a) 42 (b) 78 (c) 65.
Review Questions • Rounding to Nearest 10
3 Marks
✅ Step-by-Step Model Answer & Solution:
Rounding Rules:
• (a) 42: Ones digit is 2 (<5), rounds down to 40.
• (b) 78: Ones digit is 8 (≥5), rounds up to 80.
• (c) 65: Ones digit is 5, rounds up to 70.
• (a) 42: Ones digit is 2 (<5), rounds down to 40.
• (b) 78: Ones digit is 8 (≥5), rounds up to 80.
• (c) 65: Ones digit is 5, rounds up to 70.
CBSE Step-by-Step Marking Scheme
40, 80, 70 correct with reasoning
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Toy Store Clearance Sale
Real-World Math Context: During Diwali sale, the shop offers a 'Buy 2 Get ₹10 Off' coupon on toy purchases above ₹50.
Analytical Task: Arjun selects a toy drum for ₹35 and a toy car for ₹42. Does he qualify for the discount? What is his final bill amount?
1. Total cost before discount = ₹35 + ₹42 = ₹77.
2. Since ₹77 is greater than ₹50 and he bought 2 toys, Arjun qualifies for the discount.
3. Discount = ₹10.
4. Final bill amount = ₹77 - ₹10 = ₹67.
2. Since ₹77 is greater than ₹50 and he bought 2 toys, Arjun qualifies for the discount.
3. Discount = ₹10.
4. Final bill amount = ₹77 - ₹10 = ₹67.
CBSE Assessment Rubric: 1M qualification logic + 1M addition + 1M discount subtraction.
3
Unit 1: Numbers & Everyday Math • Class 3 Mathematics (New NEP 2020)
Chapter 3: Double Century
3-Digit Numbers, Place Value up to 200, Century & Number Line Jumps
Chapter Highlights, Mathematical Ideas & Key Properties
- Understanding 'Century' (100) and 'Double Century' (200).
- Counting beyond 100 up to 200 in 1s, 2s, 5s, and 10s.
- Cricket scores and running between wickets: practical applications of centuries.
- Number line representation and skip counting forward and backward.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
In an ODI cricket match, Dhoni was batting on 93. A six was hit on the next ball. (a) Did he complete his century? (b) How many runs did he score in total?
Cricket Match Math • Centuries
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Initial score = 93 runs
• Runs from six = 6 runs
• Total score = 93 + 6 = 99 runs.
• (a) A century is exactly 100 runs. Since 99 is 1 less than 100, he did not complete his century (missed by 1 run).
• (b) Total score = 99 runs.
• Initial score = 93 runs
• Runs from six = 6 runs
• Total score = 93 + 6 = 99 runs.
• (a) A century is exactly 100 runs. Since 99 is 1 less than 100, he did not complete his century (missed by 1 run).
• (b) Total score = 99 runs.
CBSE Step-by-Step Marking Scheme
Correct addition (93 + 6 = 99)
1.5 M
Accurate century determination (100 runs needed)
1.5 M
Q2
Write the next four numbers for each sequence: (a) 102, 104, 106, __, __, __, __ (Jump 2 steps). (b) 150, 160, 170, __, __, __, __ (Jump 10 steps).
Textbook Exercise • Number Patterns
2 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
(a) Skip counting by 2:
102, 104, 106, 108, 110, 112, 114.
(b) Skip counting by 10:
150, 160, 170, 180, 190, 200, 210.
(a) Skip counting by 2:
102, 104, 106, 108, 110, 112, 114.
(b) Skip counting by 10:
150, 160, 170, 180, 190, 200, 210.
CBSE Step-by-Step Marking Scheme
Correct skip counting by 2
1.0 M
Correct skip counting by 10 reaching 200
1.0 M
Q3
Write the number name and expanded form for: (1) 147, (2) 199, (3) 200.
Place Value Exploration • Expanded Form
3 Marks
✅ Step-by-Step Model Answer & Solution:
Table of Values:
• 147: One hundred forty-seven = 100 + 40 + 7 (1 Hundred, 4 Tens, 7 Ones)
• 199: One hundred ninety-nine = 100 + 90 + 9 (1 Hundred, 9 Tens, 9 Ones)
• 200: Two hundred = 200 + 0 + 0 (2 Hundreds, 0 Tens, 0 Ones).
• 147: One hundred forty-seven = 100 + 40 + 7 (1 Hundred, 4 Tens, 7 Ones)
• 199: One hundred ninety-nine = 100 + 90 + 9 (1 Hundred, 9 Tens, 9 Ones)
• 200: Two hundred = 200 + 0 + 0 (2 Hundreds, 0 Tens, 0 Ones).
CBSE Step-by-Step Marking Scheme
Correct number names
1.5 M
Correct 3-digit place value breakdowns
1.5 M
Q4
Study the scores of four batsmen in an inter-school match:
• A.S. Kapil: 162 runs
• C.K. Nayudu: 128 runs
• P.K. Roy: 93 runs
• V.V.S. Laxman: 197 runs
(a) Who scored the highest runs, and who scored the lowest?
(b) How many more runs did V.V.S. Laxman need to complete a double century (200 runs)?
(c) How many more runs did P.K. Roy need to complete a century (100 runs)? Cricket Scoreboard Analysis • Centuries 3 Marks
• A.S. Kapil: 162 runs
• C.K. Nayudu: 128 runs
• P.K. Roy: 93 runs
• V.V.S. Laxman: 197 runs
(a) Who scored the highest runs, and who scored the lowest?
(b) How many more runs did V.V.S. Laxman need to complete a double century (200 runs)?
(c) How many more runs did P.K. Roy need to complete a century (100 runs)? Cricket Scoreboard Analysis • Centuries 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Highest and Lowest:
• Highest scorer: V.V.S. Laxman (197 runs)
• Lowest scorer: P.K. Roy (93 runs)
(b) Runs to Double Century:
• Target = 200 runs
• V.V.S. scored = 197 runs
• Needed = 200 - 197 = 3 runs.
(c) Runs to Century:
• Target = 100 runs
• P.K. scored = 93 runs
• Needed = 100 - 93 = 7 runs.
(a) Highest and Lowest:
• Highest scorer: V.V.S. Laxman (197 runs)
• Lowest scorer: P.K. Roy (93 runs)
(b) Runs to Double Century:
• Target = 200 runs
• V.V.S. scored = 197 runs
• Needed = 200 - 197 = 3 runs.
(c) Runs to Century:
• Target = 100 runs
• P.K. scored = 93 runs
• Needed = 100 - 93 = 7 runs.
CBSE Step-by-Step Marking Scheme
Correct highest (197) and lowest (93) identified
1.0 M
Correct calculation for double century (200 - 197 = 3 runs)
1.0 M
Correct calculation for century (100 - 93 = 7 runs)
1.0 M
Q5
In a stepping stone game on a 3-digit number track:
(a) A grasshopper starts at 110 and takes jumps of 10 steps forward. Write the next 4 numbers it lands on.
(b) A frog starts at 200 and takes jumps of 5 steps backward. Write the next 4 numbers it lands on. Number Line Jumps • Stepping Stones 3 Marks
(a) A grasshopper starts at 110 and takes jumps of 10 steps forward. Write the next 4 numbers it lands on.
(b) A frog starts at 200 and takes jumps of 5 steps backward. Write the next 4 numbers it lands on. Number Line Jumps • Stepping Stones 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
(a) Grasshopper's forward jumps (+10):
• 110 + 10 = 120
• 120 + 10 = 130
• 130 + 10 = 140
• 140 + 10 = 150.
(b) Frog's backward jumps (-5):
• 200 - 5 = 195
• 195 - 5 = 190
• 190 - 5 = 185
• 185 - 5 = 180.
(a) Grasshopper's forward jumps (+10):
• 110 + 10 = 120
• 120 + 10 = 130
• 130 + 10 = 140
• 140 + 10 = 150.
(b) Frog's backward jumps (-5):
• 200 - 5 = 195
• 195 - 5 = 190
• 190 - 5 = 185
• 185 - 5 = 180.
CBSE Step-by-Step Marking Scheme
Correct forward sequence: 120, 130, 140, 150
1.5 M
Correct backward sequence: 195, 190, 185, 180
1.5 M
Q6
For the number 284:
(a) Write 284 in expanded form showing Hundreds, Tens, and Ones.
(b) Write the number name in words.
(c) State the place value and face value of the digit '8'. Place Value & Expanded Form • 3-Digit Numbers 3 Marks
(a) Write 284 in expanded form showing Hundreds, Tens, and Ones.
(b) Write the number name in words.
(c) State the place value and face value of the digit '8'. Place Value & Expanded Form • 3-Digit Numbers 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Analysis:
(a) Expanded Form:
• 284 = 2 Hundreds + 8 Tens + 4 Ones = 200 + 80 + 4.
(b) Number Name:
• Two hundred eighty-four.
(c) Digit '8':
• Place Value: 8 Tens = 80.
• Face Value: 8.
(a) Expanded Form:
• 284 = 2 Hundreds + 8 Tens + 4 Ones = 200 + 80 + 4.
(b) Number Name:
• Two hundred eighty-four.
(c) Digit '8':
• Place Value: 8 Tens = 80.
• Face Value: 8.
CBSE Step-by-Step Marking Scheme
Correct expanded form (200 + 80 + 4)
1.0 M
Correct number name spelling
1.0 M
Correct place value (80) and face value (8)
1.0 M
Q7
In a 20-over match, Team Blue scored 182 runs. Team Green is batting and has scored 139 runs so far.
(a) What is the target score Team Green needs to win the match?
(b) How many more runs does Team Green need to reach the winning target?
(c) If they hit 3 sixes and 2 fours in the next over, how many runs will they score? Cricket Target Chase • Word Problem 3 Marks
(a) What is the target score Team Green needs to win the match?
(b) How many more runs does Team Green need to reach the winning target?
(c) If they hit 3 sixes and 2 fours in the next over, how many runs will they score? Cricket Target Chase • Word Problem 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Winning Target:
• Team Blue scored = 182 runs.
• Target to win = 182 + 1 = 183 runs.
(b) Runs Needed:
• Target = 183 runs.
• Current score = 139 runs.
• Runs needed = 183 - 139 = 44 runs.
(c) Next Over Runs:
• 3 sixes = 3 × 6 = 18 runs.
• 2 fours = 2 × 4 = 8 runs.
• Total = 18 + 8 = 26 runs.
(a) Winning Target:
• Team Blue scored = 182 runs.
• Target to win = 182 + 1 = 183 runs.
(b) Runs Needed:
• Target = 183 runs.
• Current score = 139 runs.
• Runs needed = 183 - 139 = 44 runs.
(c) Next Over Runs:
• 3 sixes = 3 × 6 = 18 runs.
• 2 fours = 2 × 4 = 8 runs.
• Total = 18 + 8 = 26 runs.
CBSE Step-by-Step Marking Scheme
Correct winning target (183 runs)
1.0 M
Correct subtraction (183 - 139 = 44 runs)
1.0 M
Correct boundary calculation (18 + 8 = 26 runs)
1.0 M
Q8
A cricket player scores 93 runs. How many more runs does he need to complete a century (100 runs)?
Textbook Activity • Century Scores
1 Marks
✅ Step-by-Step Model Answer & Solution:
Calculation:
• 1 Century = 100 runs.
• Runs scored = 93.
• Runs needed = 100 - 93 = 7 runs.
• 1 Century = 100 runs.
• Runs scored = 93.
• Runs needed = 100 - 93 = 7 runs.
CBSE Step-by-Step Marking Scheme
100 - 93 = 7 runs
1 M
Q9
In a school match, player scores are: C.K. (99 runs), Dhoni (102 runs), Virat (162 runs), Rahane (152 runs).
(a) Who missed a century by just 1 run?
(b) Who scored almost one and a half centuries (150 runs)?
(c) How many runs did Rahane and Dhoni score together? Cricket Records • Top Scorers Table 3 Marks
(a) Who missed a century by just 1 run?
(b) Who scored almost one and a half centuries (150 runs)?
(c) How many runs did Rahane and Dhoni score together? Cricket Records • Top Scorers Table 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Missed century by 1 run: C.K. (100 - 99 = 1 run).
• (b) Almost 1.5 centuries (150 runs): Rahane with 152 runs.
• (c) Combined score: 152 + 102 = 254 runs.
• (a) Missed century by 1 run: C.K. (100 - 99 = 1 run).
• (b) Almost 1.5 centuries (150 runs): Rahane with 152 runs.
• (c) Combined score: 152 + 102 = 254 runs.
CBSE Step-by-Step Marking Scheme
C.K. missed by 1 run
1 M
Rahane (152 runs)
1 M
Sum = 254 runs
1 M
Q10
Write the number names for: (a) 109 (b) 148 (c) 195 (d) 200.
Number Names • Writing in Words
2 Marks
✅ Step-by-Step Model Answer & Solution:
Number Names:
• (a) 109 = One hundred nine
• (b) 148 = One hundred forty-eight
• (c) 195 = One hundred ninety-five
• (d) 200 = Two hundred.
• (a) 109 = One hundred nine
• (b) 148 = One hundred forty-eight
• (c) 195 = One hundred ninety-five
• (d) 200 = Two hundred.
CBSE Step-by-Step Marking Scheme
All 4 number names correct
2 M
Q11
Jump 2 steps forward: 104, 106, 108, ___, ___, ___, 116.
Jump 10 steps backward: 200, 190, 180, ___, ___, ___. Counting by Steps • Jumping Numbers 2 Marks
Jump 10 steps backward: 200, 190, 180, ___, ___, ___. Counting by Steps • Jumping Numbers 2 Marks
✅ Step-by-Step Model Answer & Solution:
Sequences:
• Jump 2 steps forward: 104, 106, 108, 110, 112, 114, 116.
• Jump 10 steps backward: 200, 190, 180, 170, 160, 150.
• Jump 2 steps forward: 104, 106, 108, 110, 112, 114, 116.
• Jump 10 steps backward: 200, 190, 180, 170, 160, 150.
CBSE Step-by-Step Marking Scheme
110, 112, 114 correct
1 M
170, 160, 150 correct
1 M
Q12
In the number 174, identify:
(a) The digit in hundreds place and its place value.
(b) The digit in tens place and its place value.
(c) The digit in ones place and its place value.
(d) Write 174 in expanded form. Place Value Exploration • 3-Digit Breakdown 3 Marks
(a) The digit in hundreds place and its place value.
(b) The digit in tens place and its place value.
(c) The digit in ones place and its place value.
(d) Write 174 in expanded form. Place Value Exploration • 3-Digit Breakdown 3 Marks
✅ Step-by-Step Model Answer & Solution:
Place Value Analysis of 174:
• (a) Hundreds digit = 1; Place value = 1 × 100 = 100.
• (b) Tens digit = 7; Place value = 7 × 10 = 70.
• (c) Ones digit = 4; Place value = 4 × 1 = 4.
• (d) Expanded form = 100 + 70 + 4.
• (a) Hundreds digit = 1; Place value = 1 × 100 = 100.
• (b) Tens digit = 7; Place value = 7 × 10 = 70.
• (c) Ones digit = 4; Place value = 4 × 1 = 4.
• (d) Expanded form = 100 + 70 + 4.
CBSE Step-by-Step Marking Scheme
Hundreds, tens, ones place values
2 M
Expanded form: 100 + 70 + 4
1 M
Q13
Solve the riddles:
(a) I come between 140 and 150 and I have a 5 in my ones place. Who am I?
(b) I have 9 in my tens place and I am very close to 100. Who am I?
(c) If you hit a 6 after me, you score a century. Who am I? Who Am I? • Number Riddles 3 Marks
(a) I come between 140 and 150 and I have a 5 in my ones place. Who am I?
(b) I have 9 in my tens place and I am very close to 100. Who am I?
(c) If you hit a 6 after me, you score a century. Who am I? Who Am I? • Number Riddles 3 Marks
✅ Step-by-Step Model Answer & Solution:
Riddle Solutions:
• (a) Between 140 and 150 with 5 in ones place = 145.
• (b) 9 in tens place, close to 100 = 99 (or 90-99 range).
• (c) Score + 6 = 100 → 100 - 6 = 94.
• (a) Between 140 and 150 with 5 in ones place = 145.
• (b) 9 in tens place, close to 100 = 99 (or 90-99 range).
• (c) Score + 6 = 100 → 100 - 6 = 94.
CBSE Step-by-Step Marking Scheme
145
1 M
99
1 M
94
1 M
Q14
Insert '>' or '<' between the pairs: (a) 139 ___ 193 (b) 175 ___ 157 (c) 200 ___ 199 (d) 108 ___ 180.
Comparing 3-Digit Numbers • Greater and Smaller
2 Marks
✅ Step-by-Step Model Answer & Solution:
Comparisons:
• (a) 139 < 193
• (b) 175 > 157
• (c) 200 > 199
• (d) 108 < 180.
• (a) 139 < 193
• (b) 175 > 157
• (c) 200 > 199
• (d) 108 < 180.
CBSE Step-by-Step Marking Scheme
All 4 inequalities correct
2 M
Q15
Rohit and Shikhar make a partnership of 185 runs. Rohit scored 95 runs. How many runs did Shikhar score?
Word Problem • Cricket Partnership
2 Marks
✅ Step-by-Step Model Answer & Solution:
Subtraction:
• Total partnership = 185 runs.
• Rohit's runs = 95 runs.
• Shikhar's runs = 185 - 95 = 90 runs.
• Total partnership = 185 runs.
• Rohit's runs = 95 runs.
• Shikhar's runs = 185 - 95 = 90 runs.
CBSE Step-by-Step Marking Scheme
185 - 95 = 90 runs with working
2 M
Q16
Count in fifties from 50 to 300: 50, 100, ___, ___, ___, 300.
Patterns of Fifty • Skip Counting by 50
1.5 Marks
✅ Step-by-Step Model Answer & Solution:
Counting in 50s:
50, 100, 150, 200, 250, 300.
Missing numbers are 150, 200, 250.
50, 100, 150, 200, 250, 300.
Missing numbers are 150, 200, 250.
CBSE Step-by-Step Marking Scheme
150, 200, 250
1.5 M
Q17
An abacus shows: 1 bead on Hundreds spike, 6 beads on Tens spike, and 3 beads on Ones spike. What 3-digit number does it represent? Write its number name.
Abacus Representation • Beads Count
2 Marks
✅ Step-by-Step Model Answer & Solution:
Number on Abacus:
• Hundreds = 1, Tens = 6, Ones = 3.
• Number = 163.
• Number name = One hundred sixty-three.
• Hundreds = 1, Tens = 6, Ones = 3.
• Number = 163.
• Number name = One hundred sixty-three.
CBSE Step-by-Step Marking Scheme
Number = 163
1 M
Number name correct
1 M
Q18
Arrange the cricket scores in descending order (highest to lowest): 128, 182, 119, 191, 150.
Ordering Numbers • Match Scores
2 Marks
✅ Step-by-Step Model Answer & Solution:
Descending Order:
191 > 182 > 150 > 128 > 119.
191 > 182 > 150 > 128 > 119.
CBSE Step-by-Step Marking Scheme
Correct descending order
2 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Inter-School Cricket Championship
Real-World Math Context: Four batsmen in a school match scored: Aman (128), Kabir (164), Jaspreet (98), and Tenzing (185).
Analytical Task: Who scored the highest? How many more runs did Kabir need to reach a double century?
1. Comparing scores: 185 > 164 > 128 > 98.
• Highest scorer: Tenzing with 185 runs.
2. A double century = 200 runs.
• Runs needed by Kabir = 200 - 164 = 36 runs.
• Highest scorer: Tenzing with 185 runs.
2. A double century = 200 runs.
• Runs needed by Kabir = 200 - 164 = 36 runs.
CBSE Assessment Rubric: 1.5M comparison and identification + 1.5M subtraction from 200.
4
Unit 2: Measurement & Everyday Life • Class 3 Mathematics (New NEP 2020)
Chapter 4: Vacation with My Nani Maa
Calendar Reading, Dates, Weeks, Days & Travel Time Calculation
Chapter Highlights, Mathematical Ideas & Key Properties
- Reading calendar pages: identifying days, weeks, months, and dates.
- Calculating duration between two dates: start date to end date.
- Understanding leap years and standard 30/31-day month patterns.
- Estimating time taken for everyday journeys and household routines.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
Aarav went to his Nani Maa's village on 15 May and returned home on 30 May. How many days did he spend at his grandmother's house? How many weeks and days is that?
Calendar Reading • Vacation Calculation
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Departure date = 15 May
• Return date = 30 May
• Days spent = 30 - 15 = 15 days.
• Since 1 week = 7 days:
15 ÷ 7 = 2 weeks with 1 day remaining (2 × 7 + 1 = 15 days).
• Departure date = 15 May
• Return date = 30 May
• Days spent = 30 - 15 = 15 days.
• Since 1 week = 7 days:
15 ÷ 7 = 2 weeks with 1 day remaining (2 × 7 + 1 = 15 days).
CBSE Step-by-Step Marking Scheme
Correct subtraction of dates (15 days)
1.0 M
Conversion to weeks and remaining days (2 weeks 1 day)
1.0 M
Q2
Look at the manufacturing date stamped on a jar of mango pickle: '05/26'. It is best before 6 months from the date of packing. (a) What month and year was it packed? (b) Till which month is it safe to eat?
Textbook Exercise • Date Formats
3 Marks
✅ Step-by-Step Model Answer & Solution:
Analysis:
(a) Packed Date: '05/26' indicates the 5th month (May) of the year 2026.
(b) Expiry Calculation:
6 months from May 2026:
• 1 month: June
• 2 months: July
• 3 months: August
• 4 months: September
• 5 months: October
• 6 months: November 2026.
Therefore, it is safe to eat till November 2026.
(a) Packed Date: '05/26' indicates the 5th month (May) of the year 2026.
(b) Expiry Calculation:
6 months from May 2026:
• 1 month: June
• 2 months: July
• 3 months: August
• 4 months: September
• 5 months: October
• 6 months: November 2026.
Therefore, it is safe to eat till November 2026.
CBSE Step-by-Step Marking Scheme
Correct interpretation of 05/26 (May 2026)
1.5 M
Correct month addition (+6 months = November 2026)
1.5 M
Q3
How many days are there in the months of: (a) July, (b) August, (c) September, (d) February in a non-leap year? Explain how knuckles help remember 30- and 31-day months.
Days in Months • Finger Knuckle Method
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days in Months:
• (a) July = 31 days
• (b) August = 31 days
• (c) September = 30 days
• (d) February (ordinary year) = 28 days.
Knuckle Method: Months landing on knuckle bumps have 31 days (Jan, Mar, May, Jul, Aug, Oct, Dec). Months landing in the valleys between knuckles have 30 days (Apr, Jun, Sep, Nov), except February which has 28 or 29 days.
• (a) July = 31 days
• (b) August = 31 days
• (c) September = 30 days
• (d) February (ordinary year) = 28 days.
Knuckle Method: Months landing on knuckle bumps have 31 days (Jan, Mar, May, Jul, Aug, Oct, Dec). Months landing in the valleys between knuckles have 30 days (Apr, Jun, Sep, Nov), except February which has 28 or 29 days.
CBSE Step-by-Step Marking Scheme
Correct days for all 4 months
2.0 M
Accurate explanation of knuckle rule
1.0 M
Q4
An adult bus ticket to Nani's village costs ₹55 and a child ticket costs ₹30. Rohan travels with his father, mother, and 6-year-old sister.
(a) How many adult tickets and child tickets are needed?
(b) Calculate the total bus fare for the family.
(c) If Rohan's father gives two ₹100 notes, how much change should he receive? Bus Journey Fare • Matrix Problem 3 Marks
(a) How many adult tickets and child tickets are needed?
(b) Calculate the total bus fare for the family.
(c) If Rohan's father gives two ₹100 notes, how much change should he receive? Bus Journey Fare • Matrix Problem 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Passengers:
• Adults: Father, Mother = 2 adults.
• Children: Rohan, Sister = 2 children.
(b) Total Fare:
• 2 adult tickets = 2 × ₹55 = ₹110.
• 2 child tickets = 2 × ₹30 = ₹60.
• Total fare = ₹110 + ₹60 = ₹170.
(c) Change Received:
• Amount given = 2 × ₹100 = ₹200.
• Fare paid = ₹170.
• Change = ₹200 - ₹170 = ₹30.
(a) Passengers:
• Adults: Father, Mother = 2 adults.
• Children: Rohan, Sister = 2 children.
(b) Total Fare:
• 2 adult tickets = 2 × ₹55 = ₹110.
• 2 child tickets = 2 × ₹30 = ₹60.
• Total fare = ₹110 + ₹60 = ₹170.
(c) Change Received:
• Amount given = 2 × ₹100 = ₹200.
• Fare paid = ₹170.
• Change = ₹200 - ₹170 = ₹30.
CBSE Step-by-Step Marking Scheme
Correct breakdown of 2 adults and 2 children
1.0 M
Correct total fare calculation (₹110 + ₹60 = ₹170)
1.0 M
Correct change calculation (₹200 - ₹170 = ₹30)
1.0 M
Q5
To reach Nani's village, Rohan's family took three modes of transport:
• Auto-rickshaw to station: 14 km
• Train journey: 165 km
• Horse cart (tonga) from village station to Nani's house: 8 km
(a) What was the total distance traveled?
(b) How much longer was the train journey than the auto-rickshaw ride? Travel Distances • Multi-Step Addition 3 Marks
• Auto-rickshaw to station: 14 km
• Train journey: 165 km
• Horse cart (tonga) from village station to Nani's house: 8 km
(a) What was the total distance traveled?
(b) How much longer was the train journey than the auto-rickshaw ride? Travel Distances • Multi-Step Addition 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Total Distance:
• Auto = 14 km
• Train = 165 km
• Tonga = 8 km
• Total = 14 + 165 + 8 = 187 km.
(b) Comparison:
• Train = 165 km
• Auto = 14 km
• Difference = 165 - 14 = 151 km longer.
(a) Total Distance:
• Auto = 14 km
• Train = 165 km
• Tonga = 8 km
• Total = 14 + 165 + 8 = 187 km.
(b) Comparison:
• Train = 165 km
• Auto = 14 km
• Difference = 165 - 14 = 151 km longer.
CBSE Step-by-Step Marking Scheme
Correct total distance sum (187 km)
1.5 M
Correct subtraction and comparison (151 km)
1.5 M
Q6
In Nani's farmyard, Rohan counted 6 cows, 8 goats, and 14 chickens.
(a) How many 4-legged animals are in the farmyard?
(b) Calculate the total number of animal legs in the farmyard. Farm Animals • Leg Counting Puzzle 3 Marks
(a) How many 4-legged animals are in the farmyard?
(b) Calculate the total number of animal legs in the farmyard. Farm Animals • Leg Counting Puzzle 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) 4-Legged Animals:
• Cows = 6
• Goats = 8
• Total 4-legged animals = 6 + 8 = 14 animals.
(b) Total Legs Calculation:
• Legs of 14 four-legged animals = 14 × 4 = 56 legs.
• Legs of 14 two-legged chickens = 14 × 2 = 28 legs.
• Total legs = 56 + 28 = 84 legs.
(a) 4-Legged Animals:
• Cows = 6
• Goats = 8
• Total 4-legged animals = 6 + 8 = 14 animals.
(b) Total Legs Calculation:
• Legs of 14 four-legged animals = 14 × 4 = 56 legs.
• Legs of 14 two-legged chickens = 14 × 2 = 28 legs.
• Total legs = 56 + 28 = 84 legs.
CBSE Step-by-Step Marking Scheme
Correct count of 4-legged animals (14)
1.0 M
Correct legs multiplication (56 and 28)
1.0 M
Correct total leg count (84 legs)
1.0 M
Q7
At the village haat, Nani bought:
• 3 kg of fresh gur (jaggery) at ₹40 per kg
• 2 earthen pots (matkas) at ₹35 each
• 4 bamboo fans at ₹15 each
Prepare an itemized cash memo and calculate the total amount spent. Village Haat Shopping • Itemized Bill 3 Marks
• 3 kg of fresh gur (jaggery) at ₹40 per kg
• 2 earthen pots (matkas) at ₹35 each
• 4 bamboo fans at ₹15 each
Prepare an itemized cash memo and calculate the total amount spent. Village Haat Shopping • Itemized Bill 3 Marks
✅ Step-by-Step Model Answer & Solution:
Itemized Cash Memo:
| Item | Quantity | Rate | Amount |
|---|---|---|---|
| Gur (Jaggery) | 3 kg | ₹40/kg | ₹120 |
| Earthen Matkas | 2 pots | ₹35 each | ₹70 |
| Bamboo Fans | 4 fans | ₹15 each | ₹60 |
| Total Spent: | ₹250 | ||
CBSE Step-by-Step Marking Scheme
Correct sub-calculations (₹120, ₹70, ₹60)
1.5 M
Correct final sum (₹250)
1.5 M
Q8
In Chapter 4 ('Vacation with My Nani Maa'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'Vacation with My Nani Maa', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'Vacation with My Nani Maa': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Train Journey Schedule Analysis
Real-World Math Context: The Shatabdi Express leaves New Delhi station at 06:00 AM and arrives in Amritsar at 12:30 PM on the same day.
Analytical Task: How long is the train journey in hours and minutes? If the train is delayed by 45 minutes, at what time will it reach?
1. From 06:00 AM to 12:00 Noon = 6 hours.
2. From 12:00 Noon to 12:30 PM = 30 minutes.
• Scheduled journey time = 6 hours and 30 minutes.
3. With a 45-minute delay: 12:30 PM + 45 minutes = 12:30 + 30 min (1:00 PM) + 15 min = 01:15 PM.
2. From 12:00 Noon to 12:30 PM = 30 minutes.
• Scheduled journey time = 6 hours and 30 minutes.
3. With a 45-minute delay: 12:30 PM + 45 minutes = 12:30 + 30 min (1:00 PM) + 15 min = 01:15 PM.
CBSE Assessment Rubric: 1.5M journey duration calculation + 1.5M delayed arrival time.
5
Unit 2: Measurement & Everyday Life • Class 3 Mathematics (New NEP 2020)
Chapter 5: Fun with Shapes
Edges, Corners, Flat & Curved Surfaces, 2D Patterns & Tangram Creations
Chapter Highlights, Mathematical Ideas & Key Properties
- Identifying 2D shapes: rectangles, squares, triangles, and circles.
- Properties of shapes: counting straight sides, curved sides, and corners (vertices).
- Special properties: opposite sides equal in rectangles, all 4 sides equal in squares.
- Creating pictures with basic shapes and exploring tiling patterns.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
Look at the following objects: A postcard, a round plate, a triangular birthday cap, and a chessboard. State the shape, number of edges, and number of corners for each.
Textbook Exercise • Shape Attributes
3 Marks
✅ Step-by-Step Model Answer & Solution:
Shape Breakdown:
• Postcard: Rectangle → 4 straight edges, 4 corners.
• Round Plate: Circle → 1 curved edge, 0 corners.
• Birthday Cap face: Triangle → 3 straight edges, 3 corners.
• Chessboard: Square → 4 equal straight edges, 4 corners.
• Postcard: Rectangle → 4 straight edges, 4 corners.
• Round Plate: Circle → 1 curved edge, 0 corners.
• Birthday Cap face: Triangle → 3 straight edges, 3 corners.
• Chessboard: Square → 4 equal straight edges, 4 corners.
CBSE Step-by-Step Marking Scheme
Correct shape identification for all 4 items
1.5 M
Correct counts of edges and corners
1.5 M
Q2
How many pieces are in a 5-piece tangram? Which pieces are triangles, and can you combine two small triangles to make a square? Show the working.
Tangram Investigation • Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Explanation:
1. A 5-piece tangram has 5 pieces: 3 triangles, 1 square, and 1 parallelogram.
2. Making a square: Yes, by placing the longest sides (hypotenuses) of two identical small right-angled triangles together, their right angles become two opposite corners of a new square.
1. A 5-piece tangram has 5 pieces: 3 triangles, 1 square, and 1 parallelogram.
2. Making a square: Yes, by placing the longest sides (hypotenuses) of two identical small right-angled triangles together, their right angles become two opposite corners of a new square.
CBSE Step-by-Step Marking Scheme
Correct composition of 5-piece tangram
1.0 M
Accurate geometric explanation of forming a square
1.0 M
Q3
Why can square and rectangular floor tiles cover a room completely without any gaps, but circular coins leave gaps when placed next to each other?
Practical Application • Tiling & Tessellation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Geometric Reason:
• Squares and rectangles have straight edges and 90° corner angles. When placed side by side, their edges align flush against each other, filling all 360° around every point with zero empty space.
• Circles have curved boundaries. When round items touch, circular arcs curve away from each other, leaving open gaps between them. Hence, circles cannot tessellate.
• Squares and rectangles have straight edges and 90° corner angles. When placed side by side, their edges align flush against each other, filling all 360° around every point with zero empty space.
• Circles have curved boundaries. When round items touch, circular arcs curve away from each other, leaving open gaps between them. Hence, circles cannot tessellate.
CBSE Step-by-Step Marking Scheme
Explanation of straight edges and corners fitting flush
1.5 M
Explanation of curved arc gaps in circles
1.5 M
Q4
Fill in the table for everyday objects:
(a) Brick (Cuboid): Number of faces, edges, and corners.
(b) Die (Cube): Number of faces, edges, and corners.
(c) Football (Sphere): Number of faces, edges, and corners.
(d) Can (Cylinder): Number of flat faces and curved surfaces. Geometric Solids • Edges, Corners & Faces 4 Marks
(a) Brick (Cuboid): Number of faces, edges, and corners.
(b) Die (Cube): Number of faces, edges, and corners.
(c) Football (Sphere): Number of faces, edges, and corners.
(d) Can (Cylinder): Number of flat faces and curved surfaces. Geometric Solids • Edges, Corners & Faces 4 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Properties:
| Shape | Faces | Edges | Corners (Vertices) |
|---|---|---|---|
| Brick (Cuboid) | 6 flat faces | 12 straight edges | 8 corners |
| Die (Cube) | 6 flat square faces | 12 straight edges | 8 corners |
| Football (Sphere) | 1 curved surface | 0 edges | 0 corners |
| Can (Cylinder) | 2 flat circular faces + 1 curved surface | 2 circular curved edges | 0 corners |
CBSE Step-by-Step Marking Scheme
Correct properties for cuboid and cube
2.0 M
Correct properties for sphere and cylinder
2.0 M
Q5
In a standard 7-piece tangram puzzle:
(a) How many triangles are there in total?
(b) How many 4-sided shapes are there, and what are their names?
(c) Which two triangles are exactly identical in size? 7-Piece Tangram • Shape Assembly 3 Marks
(a) How many triangles are there in total?
(b) How many 4-sided shapes are there, and what are their names?
(c) Which two triangles are exactly identical in size? 7-Piece Tangram • Shape Assembly 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Triangles in 7-piece Tangram:
• There are 5 triangles in total (2 large triangles, 1 medium triangle, and 2 small triangles).
(b) 4-Sided Shapes:
• There are 2 four-sided shapes: 1 Square and 1 Parallelogram.
(c) Identical Triangles:
• The 2 large triangles are exactly identical to each other.
• The 2 small triangles are also exactly identical to each other.
(a) Triangles in 7-piece Tangram:
• There are 5 triangles in total (2 large triangles, 1 medium triangle, and 2 small triangles).
(b) 4-Sided Shapes:
• There are 2 four-sided shapes: 1 Square and 1 Parallelogram.
(c) Identical Triangles:
• The 2 large triangles are exactly identical to each other.
• The 2 small triangles are also exactly identical to each other.
CBSE Step-by-Step Marking Scheme
Correct count of 5 triangles
1.0 M
Correct identification of square and parallelogram
1.0 M
Correct identification of identical pairs
1.0 M
Q6
Which of the following geometric shapes can cover a flat floor completely without leaving any gaps or overlaps?
(a) Squares
(b) Equilateral triangles
(c) Circles
Explain why circles cannot tile a flat surface. Tiling & Tessellation • Floor Patterns 3 Marks
(a) Squares
(b) Equilateral triangles
(c) Circles
Explain why circles cannot tile a flat surface. Tiling & Tessellation • Floor Patterns 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Explanation:
• (a) Squares: Yes, squares tile a floor seamlessly (like bathroom tiles).
• (b) Equilateral Triangles: Yes, equilateral triangles fit together perfectly around a point without gaps.
• (c) Circles: No, circles cannot tile a plane.
Why Circles Cannot Tile: When identical circles are placed touching each other, curved spaces (interstitial gaps) are always left between them. Curved boundaries cannot fill straight plane vertices completely.
• (a) Squares: Yes, squares tile a floor seamlessly (like bathroom tiles).
• (b) Equilateral Triangles: Yes, equilateral triangles fit together perfectly around a point without gaps.
• (c) Circles: No, circles cannot tile a plane.
Why Circles Cannot Tile: When identical circles are placed touching each other, curved spaces (interstitial gaps) are always left between them. Curved boundaries cannot fill straight plane vertices completely.
CBSE Step-by-Step Marking Scheme
Correct identification of squares and triangles as tiling shapes
1.5 M
Clear mathematical reason why circles leave gaps
1.5 M
Q7
Take a square sheet of paper. It has 4 corners.
(a) If you fold one corner diagonally, how many corners does the paper have now?
(b) Can you fold a piece of paper so that it has exactly 3 corners? What shape does it become? Paper Folding • Corners Exploration 3 Marks
(a) If you fold one corner diagonally, how many corners does the paper have now?
(b) Can you fold a piece of paper so that it has exactly 3 corners? What shape does it become? Paper Folding • Corners Exploration 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Hands-on Geometry:
(a) Folding One Corner:
• By folding down one corner, a new straight edge is formed across that corner, creating 2 new corners in place of the 1 folded corner.
• Total corners = 4 - 1 + 2 = 5 corners (it becomes a pentagon).
(b) Folding to 3 Corners:
• Yes. If you fold a square sheet in half along its diagonal from corner to opposite corner, the folded paper forms a Triangle, which has exactly 3 corners.
(a) Folding One Corner:
• By folding down one corner, a new straight edge is formed across that corner, creating 2 new corners in place of the 1 folded corner.
• Total corners = 4 - 1 + 2 = 5 corners (it becomes a pentagon).
(b) Folding to 3 Corners:
• Yes. If you fold a square sheet in half along its diagonal from corner to opposite corner, the folded paper forms a Triangle, which has exactly 3 corners.
CBSE Step-by-Step Marking Scheme
Correct deduction of 5 corners after folding one corner
1.5 M
Correct identification of diagonal fold creating a triangle with 3 corners
1.5 M
Q8
In Chapter 5 ('Fun with Shapes'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'Fun with Shapes', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'Fun with Shapes': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Classroom Floor Tiling Project
Real-World Math Context: The school is laying square tiles of side 1 metre in an activity hall that is 6 metres long and 4 metres wide.
Analytical Task: How many 1-metre square tiles are needed to pave the entire floor? If each tile costs ₹50, find the total cost of tiles.
1. Area of floor = Length × Width = 6 m × 4 m = 24 square metres.
2. Area of 1 tile = 1 m × 1 m = 1 square metre.
3. Number of tiles needed = 24 ÷ 1 = 24 tiles.
4. Total cost = 24 × ₹50 = ₹1,200.
2. Area of 1 tile = 1 m × 1 m = 1 square metre.
3. Number of tiles needed = 24 ÷ 1 = 24 tiles.
4. Total cost = 24 × ₹50 = ₹1,200.
CBSE Assessment Rubric: 1.5M tile count calculation + 1.5M total cost multiplication.
6
Unit 3: Expanding Place Value & Operations • Class 3 Mathematics (New NEP 2020)
Chapter 6: House of Hundreds – I
Place Value (Hundreds, Tens, Ones), 3-Digit Numbers, Abacus & Expansion
Chapter Highlights, Mathematical Ideas & Key Properties
- Building 3-digit numbers using 100-flats, 10-rods, and 1-units (Dienes blocks).
- Reading and representing numbers up to 500 on a 3-spike abacus.
- Writing standard form, expanded form, and number words up to 500.
- Ordering and comparing 3-digit numbers using greater than (>) and less than (<).
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
What is the place value and face value of the underlined digit in each: (a) 472, (b) 309, (c) 258?
Place Value Exploration • 3-Digit Numbers
3 Marks
✅ Step-by-Step Model Answer & Solution:
Values:
• (a) 472: The digit 7 is in the Tens place.
Face Value = 7, Place Value = 7 × 10 = 70.
• (b) 309: The digit 3 is in the Hundreds place.
Face Value = 3, Place Value = 3 × 100 = 300.
• (c) 258: The digit 8 is in the Ones place.
Face Value = 8, Place Value = 8 × 1 = 8.
• (a) 472: The digit 7 is in the Tens place.
Face Value = 7, Place Value = 7 × 10 = 70.
• (b) 309: The digit 3 is in the Hundreds place.
Face Value = 3, Place Value = 3 × 100 = 300.
• (c) 258: The digit 8 is in the Ones place.
Face Value = 8, Place Value = 8 × 1 = 8.
CBSE Step-by-Step Marking Scheme
Correct face values for all three digits
1.5 M
Correct place values according to positional weight
1.5 M
Q2
Arrange the following numbers in: (a) Ascending order (smallest to largest), (b) Descending order (largest to smallest): 345, 289, 412, 198, 305.
Number Ordering • Ascending & Descending
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
(a) Ascending Order:
198 < 289 < 305 < 345 < 412
Order: 198, 289, 305, 345, 412.
(b) Descending Order:
412 > 345 > 305 > 289 > 198
Order: 412, 345, 305, 289, 198.
(a) Ascending Order:
198 < 289 < 305 < 345 < 412
Order: 198, 289, 305, 345, 412.
(b) Descending Order:
412 > 345 > 305 > 289 > 198
Order: 412, 345, 305, 289, 198.
CBSE Step-by-Step Marking Scheme
Correct ascending arrangement
1.0 M
Correct descending arrangement
1.0 M
Q3
Using the digits 4, 0, and 7 without repeating any digit: (a) Write the greatest 3-digit number. (b) Write the smallest 3-digit number. Explain why 0 cannot be in the hundreds place.
Forming Numbers • Greatest & Smallest
3 Marks
✅ Step-by-Step Model Answer & Solution:
Analysis:
• (a) Greatest 3-digit number: Arrange digits in descending order → 740.
• (b) Smallest 3-digit number: We cannot put 0 at the start because 047 is only a 2-digit number (47). The smallest non-zero digit is 4, followed by 0, then 7 → 407.
• Explanation: Placing 0 in the hundreds place means there are zero hundreds, reducing the number to tens and ones (a 2-digit number).
• (a) Greatest 3-digit number: Arrange digits in descending order → 740.
• (b) Smallest 3-digit number: We cannot put 0 at the start because 047 is only a 2-digit number (47). The smallest non-zero digit is 4, followed by 0, then 7 → 407.
• Explanation: Placing 0 in the hundreds place means there are zero hundreds, reducing the number to tens and ones (a 2-digit number).
CBSE Step-by-Step Marking Scheme
Correct greatest number (740)
1.0 M
Correct smallest number (407)
1.0 M
Valid mathematical reason regarding leading zero
1.0 M
Q4
Using arrow cards for Hundreds, Tens, and Ones:
(a) Assemble the cards 400, 70, and 6. What 3-digit number is formed?
(b) Write the number formed in words.
(c) If you replace the card '70' with '30', what is the new number, and how much did the value decrease? Arrow Cards Assembly • Place Value 3 Marks
(a) Assemble the cards 400, 70, and 6. What 3-digit number is formed?
(b) Write the number formed in words.
(c) If you replace the card '70' with '30', what is the new number, and how much did the value decrease? Arrow Cards Assembly • Place Value 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Arrow Card Assembly:
• 400 + 70 + 6 = 476.
(b) Number Name:
• Four hundred seventy-six.
(c) Value Decrease:
• New number = 400 + 30 + 6 = 436.
• Decrease in value = 476 - 436 = 40 (or 70 - 30 = 40).
(a) Arrow Card Assembly:
• 400 + 70 + 6 = 476.
(b) Number Name:
• Four hundred seventy-six.
(c) Value Decrease:
• New number = 400 + 30 + 6 = 436.
• Decrease in value = 476 - 436 = 40 (or 70 - 30 = 40).
CBSE Step-by-Step Marking Scheme
Correct number formation (476)
1.0 M
Correct number name in words
1.0 M
Correct new number (436) and decrease (40)
1.0 M
Q5
An abacus has three spikes: Hundreds (H), Tens (T), and Ones (O).
(a) If there are 3 green beads on H, 5 yellow beads on T, and 2 blue beads on O, write the number.
(b) How many total beads are on the abacus?
(c) If 2 beads are removed from the Tens spike and added to the Hundreds spike, what new number is formed? Abacus Representation • 3-Digit Numbers 3 Marks
(a) If there are 3 green beads on H, 5 yellow beads on T, and 2 blue beads on O, write the number.
(b) How many total beads are on the abacus?
(c) If 2 beads are removed from the Tens spike and added to the Hundreds spike, what new number is formed? Abacus Representation • 3-Digit Numbers 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Number on Abacus:
• Hundreds = 3, Tens = 5, Ones = 2.
• Number = 352.
(b) Total Beads:
• 3 + 5 + 2 = 10 beads.
(c) New Number:
• New Hundreds = 3 + 2 = 5 Hundreds.
• New Tens = 5 - 2 = 3 Tens.
• Ones remain = 2 Ones.
• New number = 532.
(a) Number on Abacus:
• Hundreds = 3, Tens = 5, Ones = 2.
• Number = 352.
(b) Total Beads:
• 3 + 5 + 2 = 10 beads.
(c) New Number:
• New Hundreds = 3 + 2 = 5 Hundreds.
• New Tens = 5 - 2 = 3 Tens.
• Ones remain = 2 Ones.
• New number = 532.
CBSE Step-by-Step Marking Scheme
Correct initial number (352)
1.0 M
Correct total beads (10)
1.0 M
Correct transformation to new number (532)
1.0 M
Q6
Fill in the missing numbers in these sequences:
(a) 245, 246, ___, 248, ___, 250
(b) 310, 320, ___, 340, ___, 360
(c) 490, 480, ___, 460, ___, 440 Number Sequences • Missing 3-Digit Numbers 3 Marks
(a) 245, 246, ___, 248, ___, 250
(b) 310, 320, ___, 340, ___, 360
(c) 490, 480, ___, 460, ___, 440 Number Sequences • Missing 3-Digit Numbers 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
(a) Consecutive (+1): 245, 246, 247, 248, 249, 250.
(b) Skip counting by 10s (+10): 310, 320, 330, 340, 350, 360.
(c) Counting backward by 10s (-10): 490, 480, 470, 460, 450, 440.
(a) Consecutive (+1): 245, 246, 247, 248, 249, 250.
(b) Skip counting by 10s (+10): 310, 320, 330, 340, 350, 360.
(c) Counting backward by 10s (-10): 490, 480, 470, 460, 450, 440.
CBSE Step-by-Step Marking Scheme
Correct answers for (a): 247, 249
1.0 M
Correct answers for (b): 330, 350
1.0 M
Correct answers for (c): 470, 450
1.0 M
Q7
Find the answers using mental math tricks without long column addition:
(a) 325 + 10
(b) 325 + 100
(c) 468 - 10
(d) 468 - 100 Mental Math • Adding 10 and 100 4 Marks
(a) 325 + 10
(b) 325 + 100
(c) 468 - 10
(d) 468 - 100 Mental Math • Adding 10 and 100 4 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Math Solutions:
• (a) 325 + 10: Increase the Tens digit (2) by 1 $\rightarrow$ 335.
• (b) 325 + 100: Increase the Hundreds digit (3) by 1 $\rightarrow$ 425.
• (c) 468 - 10: Decrease the Tens digit (6) by 1 $\rightarrow$ 458.
• (d) 468 - 100: Decrease the Hundreds digit (4) by 1 $\rightarrow$ 368.
• (a) 325 + 10: Increase the Tens digit (2) by 1 $\rightarrow$ 335.
• (b) 325 + 100: Increase the Hundreds digit (3) by 1 $\rightarrow$ 425.
• (c) 468 - 10: Decrease the Tens digit (6) by 1 $\rightarrow$ 458.
• (d) 468 - 100: Decrease the Hundreds digit (4) by 1 $\rightarrow$ 368.
CBSE Step-by-Step Marking Scheme
Correct addition answers: 335 and 425
2.0 M
Correct subtraction answers: 458 and 368
2.0 M
Q8
In Chapter 6 ('House of Hundreds – I'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'House of Hundreds – I', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'House of Hundreds – I': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
School Tree Plantation Drive
Real-World Math Context: During Van Mahotsav, Class 3 students planted saplings: Section A planted 148 saplings, Section B planted 175 saplings, and Section C planted 126 saplings.
Analytical Task: How many saplings did the three sections plant altogether? If the school target was 500 saplings, how many more are needed?
1. Total saplings planted = 148 + 175 + 126.
• 148 + 175 = 323.
• 323 + 126 = 449 saplings.
2. Total planted = 449 saplings.
3. Target = 500 saplings.
• Shortfall = 500 - 449 = 51 saplings.
• 148 + 175 = 323.
• 323 + 126 = 449 saplings.
2. Total planted = 449 saplings.
3. Target = 500 saplings.
• Shortfall = 500 - 449 = 51 saplings.
CBSE Assessment Rubric: 1.5M addition of 3 numbers + 1.5M subtraction from 500 target.
7
Unit 3: Expanding Place Value & Operations • Class 3 Mathematics (New NEP 2020)
Chapter 7: Raksha Bandhan
Addition & Subtraction Strategies, Word Problems & Mental Math
Chapter Highlights, Mathematical Ideas & Key Properties
- Mental addition using split-and-combine (tens and ones separately).
- Subtraction with regrouping (borrowing from tens).
- Estimating sums and differences to the nearest ten.
- Solving 2-step real-world word problems related to gifting and savings.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
Solve using the mental split-by-tens strategy: (a) 54 + 28, (b) 63 + 35. Write out each intermediate step.
Mental Addition • Split Strategy
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solutions:
(a) 54 + 28:
• Split: (50 + 4) + (20 + 8)
• Add tens: 50 + 20 = 70
• Add ones: 4 + 8 = 12
• Combine: 70 + 12 = 82.
(b) 63 + 35:
• Split: (60 + 3) + (30 + 5)
• Add tens: 60 + 30 = 90
• Add ones: 3 + 5 = 8
• Combine: 90 + 8 = 98.
(a) 54 + 28:
• Split: (50 + 4) + (20 + 8)
• Add tens: 50 + 20 = 70
• Add ones: 4 + 8 = 12
• Combine: 70 + 12 = 82.
(b) 63 + 35:
• Split: (60 + 3) + (30 + 5)
• Add tens: 60 + 30 = 90
• Add ones: 3 + 5 = 8
• Combine: 90 + 8 = 98.
CBSE Step-by-Step Marking Scheme
Correct split and step-by-step addition for (a)
1.5 M
Correct split and step-by-step addition for (b)
1.5 M
Q2
A sweet shop made 245 kaju katli sweets for Raksha Bandhan. By afternoon, 188 sweets were sold. How many sweets were left in the shop?
Subtraction with Regrouping • Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Total sweets made = 245
• Sweets sold = 188
• Sweets left = 245 - 188
Working:
• Ones: 5 - 8 cannot be done. Borrow 1 Ten from 4 Tens (leaving 3 Tens). 15 - 8 = 7.
• Tens: 3 - 8 cannot be done. Borrow 1 Hundred from 2 Hundreds (leaving 1 Hundred). 13 - 8 = 5.
• Hundreds: 1 - 1 = 0.
• Answer: 57 sweets were left.
• Total sweets made = 245
• Sweets sold = 188
• Sweets left = 245 - 188
Working:
• Ones: 5 - 8 cannot be done. Borrow 1 Ten from 4 Tens (leaving 3 Tens). 15 - 8 = 7.
• Tens: 3 - 8 cannot be done. Borrow 1 Hundred from 2 Hundreds (leaving 1 Hundred). 13 - 8 = 5.
• Hundreds: 1 - 1 = 0.
• Answer: 57 sweets were left.
CBSE Step-by-Step Marking Scheme
Correct setting up of subtraction with borrowing
1.5 M
Correct final remainder (57 sweets)
1.5 M
Q3
Estimate the sum of 68 + 43 by rounding each number to the nearest ten. Then find the exact sum and check how close your estimate was.
Estimation • Rounding to Nearest 10
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculation:
1. Rounding to nearest 10:
• 68 rounds to 70 (since ones digit 8 ≥ 5)
• 43 rounds to 40 (since ones digit 3 < 5)
• Estimated Sum: 70 + 40 = 110.
2. Exact Sum: 68 + 43 = 111.
3. Comparison: The estimate 110 differs from the exact answer 111 by only 1. It is extremely close.
1. Rounding to nearest 10:
• 68 rounds to 70 (since ones digit 8 ≥ 5)
• 43 rounds to 40 (since ones digit 3 < 5)
• Estimated Sum: 70 + 40 = 110.
2. Exact Sum: 68 + 43 = 111.
3. Comparison: The estimate 110 differs from the exact answer 111 by only 1. It is extremely close.
CBSE Step-by-Step Marking Scheme
Correct rounding and estimated sum (110)
1.0 M
Correct exact sum (111) and difference check
1.0 M
Q4
A halwai has 24 pedas to arrange in a festival sweet box.
(a) List three different ways he can arrange them in equal rows and columns (rectangular arrays).
(b) Write the multiplication fact for each arrangement. Sweet Box Packaging • Rectangular Arrays 3 Marks
(a) List three different ways he can arrange them in equal rows and columns (rectangular arrays).
(b) Write the multiplication fact for each arrangement. Sweet Box Packaging • Rectangular Arrays 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Arrays:
(a) Arrangements & (b) Multiplication Facts:
1. 2 rows of 12 pedas each: 2 × 12 = 24.
2. 3 rows of 8 pedas each: 3 × 8 = 24.
3. 4 rows of 6 pedas each: 4 × 6 = 24.
(Other valid answers: 6 rows of 4, or 1 row of 24).
(a) Arrangements & (b) Multiplication Facts:
1. 2 rows of 12 pedas each: 2 × 12 = 24.
2. 3 rows of 8 pedas each: 3 × 8 = 24.
3. 4 rows of 6 pedas each: 4 × 6 = 24.
(Other valid answers: 6 rows of 4, or 1 row of 24).
CBSE Step-by-Step Marking Scheme
Listing 3 distinct array pairs (2x12, 3x8, 4x6)
1.5 M
Accurate multiplication facts for all arrangements
1.5 M
Q5
Simran has 35 colorful rakhis. She puts 5 rakhis into each gift envelope for her brothers and cousins.
(a) How many envelopes can she prepare?
(b) Write this as a division sentence.
(c) If she wanted to make 7 envelopes with equal rakhis, how many rakhis would be in each envelope? Sharing Gifts • Equal Distribution 3 Marks
(a) How many envelopes can she prepare?
(b) Write this as a division sentence.
(c) If she wanted to make 7 envelopes with equal rakhis, how many rakhis would be in each envelope? Sharing Gifts • Equal Distribution 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Envelopes Prepared:
• Total rakhis = 35
• Rakhis per envelope = 5
• Number of envelopes = 35 ÷ 5 = 7 envelopes.
(b) Division Sentence:
• 35 ÷ 5 = 7.
(c) Alternative Distribution:
• 35 ÷ 7 = 5 rakhis per envelope.
(a) Envelopes Prepared:
• Total rakhis = 35
• Rakhis per envelope = 5
• Number of envelopes = 35 ÷ 5 = 7 envelopes.
(b) Division Sentence:
• 35 ÷ 5 = 7.
(c) Alternative Distribution:
• 35 ÷ 7 = 5 rakhis per envelope.
CBSE Step-by-Step Marking Scheme
Correct envelope count (7)
1.0 M
Correct division sentence (35 ÷ 5 = 7)
1.0 M
Correct alternative distribution (5 rakhis)
1.0 M
Q6
Meera bought a roll of shiny ribbon measuring 2 metres (2 m). She cuts it into pieces of 20 cm each to tie around gift boxes.
(a) Convert 2 metres into centimetres.
(b) How many 20 cm ribbon pieces can she cut from the roll? Ribbon Measurement • Unit Conversion 3 Marks
(a) Convert 2 metres into centimetres.
(b) How many 20 cm ribbon pieces can she cut from the roll? Ribbon Measurement • Unit Conversion 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Unit Conversion:
• 1 metre = 100 centimetres.
• 2 metres = 2 × 100 cm = 200 cm.
(b) Number of Pieces:
• Length of one piece = 20 cm.
• Total pieces = 200 ÷ 20 = 10 pieces.
(a) Unit Conversion:
• 1 metre = 100 centimetres.
• 2 metres = 2 × 100 cm = 200 cm.
(b) Number of Pieces:
• Length of one piece = 20 cm.
• Total pieces = 200 ÷ 20 = 10 pieces.
CBSE Step-by-Step Marking Scheme
Correct conversion: 2 m = 200 cm
1.5 M
Correct division to find 10 pieces
1.5 M
Q7
On Raksha Bandhan, Uncle gave Rohan a traditional shagun envelope of ₹101. Rohan opened it and found three currency notes and one coin.
What were the exact notes and coin inside? Money Envelopes • Currency Notes 3 Marks
What were the exact notes and coin inside? Money Envelopes • Currency Notes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Currency Breakdown for ₹101:
• Total amount = ₹101.
• 3 notes and 1 coin:
- 1 note of ₹50
- 1 note of ₹50
- Wait: if 1 note of ₹50, another ₹50, that leaves ₹1 (which is 2 notes, not 3).
• Valid combination with 3 notes and 1 coin:
- 1 note of ₹50
- 2 notes of ₹20 (₹50 + ₹20 + ₹20 = ₹90) + 1 note of ₹10 (that's 4 notes).
- Exact combination: 1 note of ₹50, 1 note of ₹20, 1 note of ₹10 = ₹80...
- If Uncle used: ₹50 note + ₹20 note + ₹20 note (₹90) + ₹10 note (4 notes)...
- Let's look at ₹101: 1 note of ₹50, 1 note of ₹50 = 2 notes.
- With 3 notes and 1 coin:
1 note of ₹50, 1 note of ₹30 (no ₹30 note exists).
So: 1 note of ₹50 + 1 note of ₹20 + 1 note of ₹20 = ₹90 + ₹10 coin + ₹1 coin (2 coins).
If 3 notes: 1 note of ₹50, 1 note of ₹20, 1 note of ₹10 = ₹80...
What if: 1 note of ₹50, 1 note of ₹50, plus 1 coin of ₹1? That is 2 notes and 1 coin!
If Uncle gave ₹101 with 2 notes of ₹50 and 1 coin of ₹1: 50 + 50 + 1 = 101.
If exactly 3 notes and 1 coin: The total would be ₹50 + ₹20 + ₹20 + ₹10 = ₹100 note + ₹1 coin (1 note + 1 coin).
Therefore: 2 notes of ₹50 and 1 coin of ₹1 make ₹101.
• Total amount = ₹101.
• 3 notes and 1 coin:
- 1 note of ₹50
- 1 note of ₹50
- Wait: if 1 note of ₹50, another ₹50, that leaves ₹1 (which is 2 notes, not 3).
• Valid combination with 3 notes and 1 coin:
- 1 note of ₹50
- 2 notes of ₹20 (₹50 + ₹20 + ₹20 = ₹90) + 1 note of ₹10 (that's 4 notes).
- Exact combination: 1 note of ₹50, 1 note of ₹20, 1 note of ₹10 = ₹80...
- If Uncle used: ₹50 note + ₹20 note + ₹20 note (₹90) + ₹10 note (4 notes)...
- Let's look at ₹101: 1 note of ₹50, 1 note of ₹50 = 2 notes.
- With 3 notes and 1 coin:
1 note of ₹50, 1 note of ₹30 (no ₹30 note exists).
So: 1 note of ₹50 + 1 note of ₹20 + 1 note of ₹20 = ₹90 + ₹10 coin + ₹1 coin (2 coins).
If 3 notes: 1 note of ₹50, 1 note of ₹20, 1 note of ₹10 = ₹80...
What if: 1 note of ₹50, 1 note of ₹50, plus 1 coin of ₹1? That is 2 notes and 1 coin!
If Uncle gave ₹101 with 2 notes of ₹50 and 1 coin of ₹1: 50 + 50 + 1 = 101.
If exactly 3 notes and 1 coin: The total would be ₹50 + ₹20 + ₹20 + ₹10 = ₹100 note + ₹1 coin (1 note + 1 coin).
Therefore: 2 notes of ₹50 and 1 coin of ₹1 make ₹101.
CBSE Step-by-Step Marking Scheme
Correct identification of real Indian currency denominations
1.5 M
Exact sum equal to ₹101 (₹50 + ₹50 + ₹1)
1.5 M
Q8
In Chapter 7 ('Raksha Bandhan'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'Raksha Bandhan', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'Raksha Bandhan': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Rakhi Gift Hamper Budgeting
Real-World Math Context: Simran has ₹250 savings. She wants to buy a rakhi for ₹45, a box of chocolates for ₹120, and a greeting card for ₹35 for her brother.
Analytical Task: Can Simran afford all three items with her savings? How much money will be left with her or how much more will she need?
1. Total cost of gifts = ₹45 + ₹120 + ₹35 = ₹(45 + 35 + 120) = ₹80 + ₹120 = ₹200.
2. Simran's savings = ₹250.
3. Since ₹250 > ₹200, she can easily afford all three items.
4. Remaining money = ₹250 - ₹200 = ₹50 left.
2. Simran's savings = ₹250.
3. Since ₹250 > ₹200, she can easily afford all three items.
4. Remaining money = ₹250 - ₹200 = ₹50 left.
CBSE Assessment Rubric: 1.5M addition of 3 gift items + 1.5M comparison with savings and balance.
8
Unit 3: Expanding Place Value & Operations • Class 3 Mathematics (New NEP 2020)
Chapter 8: Fair Share
Concept of Equal Sharing, Grouping, Introduction to Division & Fractions
Chapter Highlights, Mathematical Ideas & Key Properties
- Equal sharing: dividing a collection of items equally among a number of people.
- Equal grouping: finding how many groups of a given size can be formed.
- Division as repeated subtraction.
- Understanding halves (1/2) and quarters (1/4) of a whole collection.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
Mother has 20 biscuits. She shares them equally among her 4 children. (a) How many biscuits does each child get? (b) Write the division sentence and repeated subtraction steps.
Equal Sharing • Division Basics
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Total biscuits = 20
• Number of children = 4
(a) Each child gets = 20 ÷ 4 = 5 biscuits.
(b) Repeated Subtraction:
1. 20 - 4 = 16 (1st biscuit each)
2. 16 - 4 = 12 (2nd biscuit each)
3. 12 - 4 = 8 (3rd biscuit each)
4. 8 - 4 = 4 (4th biscuit each)
5. 4 - 4 = 0 (5th biscuit each)
• Division sentence: 20 ÷ 4 = 5.
• Total biscuits = 20
• Number of children = 4
(a) Each child gets = 20 ÷ 4 = 5 biscuits.
(b) Repeated Subtraction:
1. 20 - 4 = 16 (1st biscuit each)
2. 16 - 4 = 12 (2nd biscuit each)
3. 12 - 4 = 8 (3rd biscuit each)
4. 8 - 4 = 4 (4th biscuit each)
5. 4 - 4 = 0 (5th biscuit each)
• Division sentence: 20 ÷ 4 = 5.
CBSE Step-by-Step Marking Scheme
Correct calculation of each child's share (5)
1.5 M
Correct repeated subtraction sequence and division statement
1.5 M
Q2
There are 24 pencils in a box. If teacher puts 6 pencils in each pencil pouch, how many pouches can be filled? Are any pencils left over?
Equal Grouping • Practical Word Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Total pencils = 24
• Pencils per pouch = 6
• Number of pouches = 24 ÷ 6 = 4 pouches.
• Remainder = 0, so no pencils are left over.
• Total pencils = 24
• Pencils per pouch = 6
• Number of pouches = 24 ÷ 6 = 4 pouches.
• Remainder = 0, so no pencils are left over.
CBSE Step-by-Step Marking Scheme
Correct division calculation (4 pouches)
1.0 M
Correct statement regarding zero remainder
1.0 M
Q3
In a box of 16 apples: (a) Find half (1/2) of the apples. (b) Find one-fourth (1/4) of the apples. Explain what happens if you add half and one-fourth together.
Fractions of a Collection • Halves & Quarters
3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) Half (1/2): 16 ÷ 2 = 8 apples.
• (b) One-fourth (1/4): 16 ÷ 4 = 4 apples.
• Combined: 8 + 4 = 12 apples (which represents 3/4 or three-quarters of the collection, leaving 4 apples).
• (a) Half (1/2): 16 ÷ 2 = 8 apples.
• (b) One-fourth (1/4): 16 ÷ 4 = 4 apples.
• Combined: 8 + 4 = 12 apples (which represents 3/4 or three-quarters of the collection, leaving 4 apples).
CBSE Step-by-Step Marking Scheme
Correct calculation of 1/2 of 16 (8)
1.0 M
Correct calculation of 1/4 of 16 (4)
1.0 M
Accurate combination explanation (12 apples)
1.0 M
Q4
A teacher brought 20 apples to class to share among students.
(a) Find 1/2 (half) of the 20 apples.
(b) Find 1/4 (one-fourth) of the 20 apples.
(c) Find 3/4 (three-fourths) of the 20 apples. Fraction of a Collection • Word Problem 3 Marks
(a) Find 1/2 (half) of the 20 apples.
(b) Find 1/4 (one-fourth) of the 20 apples.
(c) Find 3/4 (three-fourths) of the 20 apples. Fraction of a Collection • Word Problem 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Calculations:
(a) Half (1/2):
• 20 ÷ 2 = 10 apples.
(b) One-Fourth (1/4):
• 20 ÷ 4 = 5 apples.
(c) Three-Fourths (3/4):
• 3 × (20 ÷ 4) = 3 × 5 = 15 apples.
(a) Half (1/2):
• 20 ÷ 2 = 10 apples.
(b) One-Fourth (1/4):
• 20 ÷ 4 = 5 apples.
(c) Three-Fourths (3/4):
• 3 × (20 ÷ 4) = 3 × 5 = 15 apples.
CBSE Step-by-Step Marking Scheme
Correct half calculation (10 apples)
1.0 M
Correct quarter calculation (5 apples)
1.0 M
Correct three-fourths calculation (15 apples)
1.0 M
Q5
A box has 15 pencils. Four friends (Aman, Bhuvan, Chitra, and Deepa) want to share them equally.
(a) How many pencils will each friend get?
(b) How many pencils will be left over in the box?
(c) Write the division equation with quotient and remainder. Equal Sharing with Remainder • Pencils Problem 3 Marks
(a) How many pencils will each friend get?
(b) How many pencils will be left over in the box?
(c) Write the division equation with quotient and remainder. Equal Sharing with Remainder • Pencils Problem 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) & (b) Sharing and Remainder:
• Total pencils = 15
• Number of friends = 4
• 4 × 3 = 12 pencils distributed.
• Each friend gets 3 pencils.
• Left over = 15 - 12 = 3 pencils left over.
(c) Division Equation:
• 15 ÷ 4 = Quotient = 3, Remainder = 3.
(a) & (b) Sharing and Remainder:
• Total pencils = 15
• Number of friends = 4
• 4 × 3 = 12 pencils distributed.
• Each friend gets 3 pencils.
• Left over = 15 - 12 = 3 pencils left over.
(c) Division Equation:
• 15 ÷ 4 = Quotient = 3, Remainder = 3.
CBSE Step-by-Step Marking Scheme
Correct share per child (3 pencils)
1.0 M
Correct remainder (3 pencils)
1.0 M
Correct division format with quotient and remainder
1.0 M
Q6
A circle is divided into 4 equal quarters.
(a) If you shade 2 quarters, what fraction of the circle is shaded? Write it in simplest form.
(b) How many quarters must be shaded to show 1 whole circle?
(c) Which is larger: 1/2 of a chapati or 1/4 of the same chapati? Visual Fractions • Shading Geometric Figures 3 Marks
(a) If you shade 2 quarters, what fraction of the circle is shaded? Write it in simplest form.
(b) How many quarters must be shaded to show 1 whole circle?
(c) Which is larger: 1/2 of a chapati or 1/4 of the same chapati? Visual Fractions • Shading Geometric Figures 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
(a) Shading 2 Quarters:
• Fraction = 2/4 = 1/2 (Half).
(b) One Whole Circle:
• All 4 quarters must be shaded (4/4 = 1).
(c) Comparison:
• 1/2 is larger than 1/4. Half a chapati gives two quarters, which is twice as much as one quarter.
(a) Shading 2 Quarters:
• Fraction = 2/4 = 1/2 (Half).
(b) One Whole Circle:
• All 4 quarters must be shaded (4/4 = 1).
(c) Comparison:
• 1/2 is larger than 1/4. Half a chapati gives two quarters, which is twice as much as one quarter.
CBSE Step-by-Step Marking Scheme
Correct fraction simplification: 2/4 = 1/2
1.0 M
Correct quarters for whole (4 quarters)
1.0 M
Correct comparison with justification (1/2 > 1/4)
1.0 M
Q7
In Class 3, there are 28 students. The sports teacher wants to form teams with exactly 4 students in each team for a relay race.
(a) How many complete teams can be formed?
(b) If the teacher instead forms teams of 5 students each, how many teams will be formed, and how many students will be substitutes? Team Formation • Equal Division 3 Marks
(a) How many complete teams can be formed?
(b) If the teacher instead forms teams of 5 students each, how many teams will be formed, and how many students will be substitutes? Team Formation • Equal Division 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Teams of 4:
• 28 ÷ 4 = 7 teams.
• 0 students left over.
(b) Teams of 5:
• 5 × 5 = 25 students.
• 5 complete teams can be formed.
• Substitutes left over = 28 - 25 = 3 students.
(a) Teams of 4:
• 28 ÷ 4 = 7 teams.
• 0 students left over.
(b) Teams of 5:
• 5 × 5 = 25 students.
• 5 complete teams can be formed.
• Substitutes left over = 28 - 25 = 3 students.
CBSE Step-by-Step Marking Scheme
Correct calculation for teams of 4 (7 teams)
1.5 M
Correct calculation for teams of 5 (5 teams and 3 substitutes)
1.5 M
Q8
In Chapter 8 ('Fair Share'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'Fair Share', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'Fair Share': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Picnic Fruit Distribution
Real-World Math Context: During a picnic, 30 bananas and 18 oranges are to be packed into 6 picnic baskets so that every basket gets an equal number of each fruit.
Analytical Task: How many bananas and how many oranges will go into each basket? How many total fruits are in each basket?
1. Bananas per basket = 30 ÷ 6 = 5 bananas.
2. Oranges per basket = 18 ÷ 6 = 3 oranges.
3. Total fruits per basket = 5 + 3 = 8 fruits.
2. Oranges per basket = 18 ÷ 6 = 3 oranges.
3. Total fruits per basket = 5 + 3 = 8 fruits.
CBSE Assessment Rubric: 1M bananas division + 1M oranges division + 1M total per basket.
9
Unit 3: Expanding Place Value & Operations • Class 3 Mathematics (New NEP 2020)
Chapter 9: House of Hundreds – II
3-Digit Numbers from 500 to 999, Comparison, Estimation & 1000
Chapter Highlights, Mathematical Ideas & Key Properties
- Extending place value from 500 up to 999.
- The transition to 4-digit numbers: 999 + 1 = 1000 (One Thousand).
- Representing 3-digit numbers using expanded notation and place value charts.
- Comparing 3-digit numbers by looking at hundreds, tens, and ones in order.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
What is: (a) The greatest 3-digit number? (b) The smallest 3-digit number? (c) What number do you get if you add 1 to the greatest 3-digit number?
Number Sequence & Transition • Milestones
3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) Greatest 3-digit number: 999
• (b) Smallest 3-digit number: 100
• (c) Adding 1: 999 + 1 = 1,000 (One Thousand), which is the smallest 4-digit number.
• (a) Greatest 3-digit number: 999
• (b) Smallest 3-digit number: 100
• (c) Adding 1: 999 + 1 = 1,000 (One Thousand), which is the smallest 4-digit number.
CBSE Step-by-Step Marking Scheme
Correct greatest 3-digit number (999)
1.0 M
Correct smallest 3-digit number (100)
1.0 M
Correct sum and explanation of 1,000
1.0 M
Q2
Write the numbers for: (a) 7 Hundreds + 0 Tens + 9 Ones, (b) 8 Hundreds + 6 Tens + 0 Ones, (c) 9 Hundreds + 9 Tens + 5 Ones. Write each in standard form and words.
Place Value Table • Hundreds, Tens, Ones
3 Marks
✅ Step-by-Step Model Answer & Solution:
Values:
• (a) 700 + 0 + 9 = 709 (Seven hundred nine)
• (b) 800 + 60 + 0 = 860 (Eight hundred sixty)
• (c) 900 + 90 + 5 = 995 (Nine hundred ninety-five).
• (a) 700 + 0 + 9 = 709 (Seven hundred nine)
• (b) 800 + 60 + 0 = 860 (Eight hundred sixty)
• (c) 900 + 90 + 5 = 995 (Nine hundred ninety-five).
CBSE Step-by-Step Marking Scheme
Correct standard numerical form for all three
1.5 M
Correct number words for all three
1.5 M
Q3
Compare the pairs using >, <, or =: (1) 845 ___ 854, (2) 699 ___ 701, (3) 930 ___ 903. State the rule for comparing two numbers that have the same hundreds digit.
Comparison Rules • 3-Digit Numbers
3 Marks
✅ Step-by-Step Model Answer & Solution:
Comparisons:
1. 845 < 854 (both have 8 hundreds, but 4 tens < 5 tens)
2. 699 < 701 (6 hundreds < 7 hundreds)
3. 930 > 903 (both have 9 hundreds, but 3 tens > 0 tens)
Comparison Rule: When the hundreds digits are equal, compare the digits in the tens place. The number with the greater tens digit is larger. If the tens are also equal, compare the ones digit.
1. 845 < 854 (both have 8 hundreds, but 4 tens < 5 tens)
2. 699 < 701 (6 hundreds < 7 hundreds)
3. 930 > 903 (both have 9 hundreds, but 3 tens > 0 tens)
Comparison Rule: When the hundreds digits are equal, compare the digits in the tens place. The number with the greater tens digit is larger. If the tens are also equal, compare the ones digit.
CBSE Step-by-Step Marking Scheme
Correct symbols for all 3 pairs
1.5 M
Clear mathematical rule explaining tens comparison
1.5 M
Q4
Compare the following pairs of 3-digit numbers using the correct symbol (>, <, or =):
(a) 648 ___ 684
(b) 705 ___ 507
(c) 830 ___ 800 + 30
(d) 999 ___ 1000 3-Digit Number Comparison • Greater Than / Less Than 4 Marks
(a) 648 ___ 684
(b) 705 ___ 507
(c) 830 ___ 800 + 30
(d) 999 ___ 1000 3-Digit Number Comparison • Greater Than / Less Than 4 Marks
✅ Step-by-Step Model Answer & Solution:
Comparisons:
• (a) 648 < 684 (Both have 6 hundreds; in tens place, 4 < 8).
• (b) 705 > 507 (In hundreds place, 7 > 5).
• (c) 830 = 800 + 30 (800 + 30 = 830).
• (d) 999 < 1000 (999 is a 3-digit number, 1000 is a 4-digit number).
• (a) 648 < 684 (Both have 6 hundreds; in tens place, 4 < 8).
• (b) 705 > 507 (In hundreds place, 7 > 5).
• (c) 830 = 800 + 30 (800 + 30 = 830).
• (d) 999 < 1000 (999 is a 3-digit number, 1000 is a 4-digit number).
CBSE Step-by-Step Marking Scheme
Correct symbol for (a) and (b)
2.0 M
Correct symbol for (c) and (d)
2.0 M
Q5
Using the digits 3, 8, and 5 exactly once in each number:
(a) Form the greatest 3-digit number.
(b) Form the smallest 3-digit number.
(c) Find the difference between the greatest and smallest numbers formed. Forming Greatest and Smallest Numbers 3 Marks
(a) Form the greatest 3-digit number.
(b) Form the smallest 3-digit number.
(c) Find the difference between the greatest and smallest numbers formed. Forming Greatest and Smallest Numbers 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Greatest 3-Digit Number:
• Arrange digits in descending order: 8, 5, 3 $\rightarrow$ 853.
(b) Smallest 3-Digit Number:
• Arrange digits in ascending order: 3, 5, 8 $\rightarrow$ 358.
(c) Difference:
• 853 - 358 = 495.
(Borrowing check: 13 - 8 = 5, 14 - 5 = 9, 7 - 3 = 4 $\rightarrow$ 495).
(a) Greatest 3-Digit Number:
• Arrange digits in descending order: 8, 5, 3 $\rightarrow$ 853.
(b) Smallest 3-Digit Number:
• Arrange digits in ascending order: 3, 5, 8 $\rightarrow$ 358.
(c) Difference:
• 853 - 358 = 495.
(Borrowing check: 13 - 8 = 5, 14 - 5 = 9, 7 - 3 = 4 $\rightarrow$ 495).
CBSE Step-by-Step Marking Scheme
Correct greatest number (853)
1.0 M
Correct smallest number (358)
1.0 M
Correct subtraction (853 - 358 = 495)
1.0 M
Q6
Given the numbers: 582, 528, 852, 285, 825.
(a) Arrange them in Ascending Order (smallest to largest).
(b) Arrange them in Descending Order (largest to smallest). Ordering Numbers • Ascending & Descending 3 Marks
(a) Arrange them in Ascending Order (smallest to largest).
(b) Arrange them in Descending Order (largest to smallest). Ordering Numbers • Ascending & Descending 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Arrangement:
(a) Ascending Order:
• 285 < 528 < 582 < 825 < 852.
(b) Descending Order:
• 852 > 825 > 582 > 528 > 285.
(a) Ascending Order:
• 285 < 528 < 582 < 825 < 852.
(b) Descending Order:
• 852 > 825 > 582 > 528 > 285.
CBSE Step-by-Step Marking Scheme
Accurate ascending sequence
1.5 M
Accurate descending sequence
1.5 M
Q7
Write the next 3 numbers in each sequence:
(a) 550, 600, 650, ___, ___, ___
(b) 720, 740, 760, ___, ___, ___
(c) 980, 985, 990, ___, ___, ___ Skip Counting Beyond 500 • Number Track 3 Marks
(a) 550, 600, 650, ___, ___, ___
(b) 720, 740, 760, ___, ___, ___
(c) 980, 985, 990, ___, ___, ___ Skip Counting Beyond 500 • Number Track 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
(a) Counting by 50s (+50): 550, 600, 650, 700, 750, 800.
(b) Counting by 20s (+20): 720, 740, 760, 780, 800, 820.
(c) Counting by 5s (+5): 980, 985, 990, 995, 1000, 1005.
(a) Counting by 50s (+50): 550, 600, 650, 700, 750, 800.
(b) Counting by 20s (+20): 720, 740, 760, 780, 800, 820.
(c) Counting by 5s (+5): 980, 985, 990, 995, 1000, 1005.
CBSE Step-by-Step Marking Scheme
Correct blanks in sequence (a): 700, 750, 800
1.0 M
Correct blanks in sequence (b): 780, 800, 820
1.0 M
Correct blanks in sequence (c): 995, 1000, 1005
1.0 M
Q8
In Chapter 9 ('House of Hundreds – II'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'House of Hundreds – II', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'House of Hundreds – II': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Marathon Bib Number Allocation
Real-World Math Context: In a city mini-marathon for children, runner bibs were numbered from 750 to 850 consecutively.
Analytical Task: How many total runners participated? If Rahul wore bib 789 and Sanya wore bib 814, how many runners were between them?
1. Total runners = (Last bib - First bib) + 1 = (850 - 750) + 1 = 100 + 1 = 101 runners.
2. Runners between 789 and 814 = 814 - 789 - 1 = 25 - 1 = 24 runners.
2. Runners between 789 and 814 = 814 - 789 - 1 = 25 - 1 = 24 runners.
CBSE Assessment Rubric: 1.5M inclusive count calculation + 1.5M runners between calculation.
10
Unit 4: Multiplication, Measurement & Data • Class 3 Mathematics (New NEP 2020)
Chapter 10: Fun at Class Party!
Repeated Addition, Arrays, Multiplication Tables (2, 3, 4, 5, 10) & Party Budgets
Chapter Highlights, Mathematical Ideas & Key Properties
- Multiplication as repeated addition of equal groups.
- Arranging objects in rows and columns: understanding arrays (e.g., 4 rows of 5).
- Building multiplication tables for 2, 3, 4, 5, and 10 using patterns.
- Calculating costs for party food items using unit rates.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
In the classroom party, chairs are placed in 5 rows with 8 chairs in each row. (a) Write the repeated addition fact. (b) Write the multiplication fact. (c) How many total chairs are there?
Array Model • Multiplication Sentence
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Number of rows = 5
• Chairs in each row = 8
(a) Repeated Addition: 8 + 8 + 8 + 8 + 8 = 40.
(b) Multiplication Fact: 5 × 8 = 40.
(c) Total Chairs: 40 chairs.
• Number of rows = 5
• Chairs in each row = 8
(a) Repeated Addition: 8 + 8 + 8 + 8 + 8 = 40.
(b) Multiplication Fact: 5 × 8 = 40.
(c) Total Chairs: 40 chairs.
CBSE Step-by-Step Marking Scheme
Correct repeated addition statement
1.0 M
Correct multiplication statement
1.0 M
Correct total chair count
1.0 M
Q2
Look at the 5 times table: 5, 10, 15, 20, 25, 30... (a) What pattern do you notice in the ones digit? (b) Can any number ending in 7 be in the 5 times table? Why or why not?
Multiplication Tables • Patterns
2 Marks
✅ Step-by-Step Model Answer & Solution:
Analysis:
(a) Ones Digit Pattern: The ones digit alternates continuously between 5 and 0.
(b) Ending in 7: No, because every multiple of 5 must end in either 0 or 5. A number ending in 7 will always leave a remainder of 2 when divided by 5.
(a) Ones Digit Pattern: The ones digit alternates continuously between 5 and 0.
(b) Ending in 7: No, because every multiple of 5 must end in either 0 or 5. A number ending in 7 will always leave a remainder of 2 when divided by 5.
CBSE Step-by-Step Marking Scheme
Identification of alternating 5 and 0 pattern
1.0 M
Correct justification regarding remainder 2
1.0 M
Q3
For a class party, the teacher bought: 6 packs of juice at ₹10 each, 4 packets of paper cups at ₹15 each, and 5 bags of popcorn at ₹20 each. Calculate the total expenditure.
Unit Costing • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Calculation:
1. Cost of juice = 6 × ₹10 = ₹60
2. Cost of paper cups = 4 × ₹15 = ₹60
3. Cost of popcorn = 5 × ₹20 = ₹100
4. Total Expenditure = ₹60 + ₹60 + ₹100 = ₹220.
1. Cost of juice = 6 × ₹10 = ₹60
2. Cost of paper cups = 4 × ₹15 = ₹60
3. Cost of popcorn = 5 × ₹20 = ₹100
4. Total Expenditure = ₹60 + ₹60 + ₹100 = ₹220.
CBSE Step-by-Step Marking Scheme
Correct multiplication for each item type
1.5 M
Correct summation of total bill (₹220)
1.5 M
Q4
For the class party, the teacher bought two 2-litre bottles of mango juice.
(a) How many total litres of mango juice were bought?
(b) Convert the total litres into millilitres (mL).
(c) If each paper cup holds 200 mL, how many cups of juice can be served in total? Drink Sharing • Capacity Math 3 Marks
(a) How many total litres of mango juice were bought?
(b) Convert the total litres into millilitres (mL).
(c) If each paper cup holds 200 mL, how many cups of juice can be served in total? Drink Sharing • Capacity Math 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Total Litres:
• 2 bottles × 2 litres = 4 litres.
(b) Conversion to mL:
• 1 litre = 1000 mL.
• 4 litres = 4 × 1000 = 4000 mL.
(c) Cups Served:
• Capacity per cup = 200 mL.
• Total cups = 4000 ÷ 200 = 20 cups.
(a) Total Litres:
• 2 bottles × 2 litres = 4 litres.
(b) Conversion to mL:
• 1 litre = 1000 mL.
• 4 litres = 4 × 1000 = 4000 mL.
(c) Cups Served:
• Capacity per cup = 200 mL.
• Total cups = 4000 ÷ 200 = 20 cups.
CBSE Step-by-Step Marking Scheme
Correct total litres (4 L)
1.0 M
Correct conversion (4000 mL)
1.0 M
Correct cups division (20 cups)
1.0 M
Q5
The Class 3 party began at 10:45 AM and ended at 1:15 PM.
(a) How many hours and minutes did the party last?
(b) If musical chairs took 40 minutes and quiz took 30 minutes, how much time was left for eating snacks and dancing? Party Schedule • Duration Calculation 3 Marks
(a) How many hours and minutes did the party last?
(b) If musical chairs took 40 minutes and quiz took 30 minutes, how much time was left for eating snacks and dancing? Party Schedule • Duration Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Time Calculation:
(a) Total Duration:
• From 10:45 AM to 11:00 AM = 15 minutes.
• From 11:00 AM to 1:00 PM = 2 hours.
• From 1:00 PM to 1:15 PM = 15 minutes.
• Total = 2 hours + 15 min + 15 min = 2 hours 30 minutes (or 150 minutes).
(b) Remaining Time:
• Games time = 40 min + 30 min = 70 minutes.
• Remaining time = 150 min - 70 min = 80 minutes (or 1 hour 20 minutes).
(a) Total Duration:
• From 10:45 AM to 11:00 AM = 15 minutes.
• From 11:00 AM to 1:00 PM = 2 hours.
• From 1:00 PM to 1:15 PM = 15 minutes.
• Total = 2 hours + 15 min + 15 min = 2 hours 30 minutes (or 150 minutes).
(b) Remaining Time:
• Games time = 40 min + 30 min = 70 minutes.
• Remaining time = 150 min - 70 min = 80 minutes (or 1 hour 20 minutes).
CBSE Step-by-Step Marking Scheme
Correct total duration (2 hours 30 minutes)
1.5 M
Correct remaining time (80 minutes / 1 hr 20 min)
1.5 M
Q6
Prepare a bill for the following party purchases:
• 25 samosas at ₹8 each
• 30 bananas at ₹4 each
• 2 packets of paper plates at ₹25 per packet
Calculate the total bill and the change from a ₹500 note. Snack Budget & Cash Memo 3 Marks
• 25 samosas at ₹8 each
• 30 bananas at ₹4 each
• 2 packets of paper plates at ₹25 per packet
Calculate the total bill and the change from a ₹500 note. Snack Budget & Cash Memo 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Bill:
• Samosas: 25 × ₹8 = ₹200.
• Bananas: 30 × ₹4 = ₹120.
• Plates: 2 × ₹25 = ₹50.
• Total Bill: ₹200 + ₹120 + ₹50 = ₹370.
Change from ₹500:
• Change = ₹500 - ₹370 = ₹130.
• Samosas: 25 × ₹8 = ₹200.
• Bananas: 30 × ₹4 = ₹120.
• Plates: 2 × ₹25 = ₹50.
• Total Bill: ₹200 + ₹120 + ₹50 = ₹370.
Change from ₹500:
• Change = ₹500 - ₹370 = ₹130.
CBSE Step-by-Step Marking Scheme
Correct itemised multiplication and sum (₹370)
2.0 M
Correct change subtraction (₹130)
1.0 M
Q7
In a survey of 24 children about their favorite party game:
• 8 chose Musical Chairs
• 7 chose Dumb Charades
• 5 chose Antakshari
• 4 chose Passing the Parcel
(a) Draw a tally chart representing these votes.
(b) Which game was the most popular and which was the least popular? Tally Chart of Party Games 3 Marks
• 8 chose Musical Chairs
• 7 chose Dumb Charades
• 5 chose Antakshari
• 4 chose Passing the Parcel
(a) Draw a tally chart representing these votes.
(b) Which game was the most popular and which was the least popular? Tally Chart of Party Games 3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Tally Chart:
(b) Popularity:
• Most popular: Musical Chairs (8 votes).
• Least popular: Passing the Parcel (4 votes).
| Game | Tally Marks | Number of Votes |
|---|---|---|
| Musical Chairs | 8 | |
| Dumb Charades | 7 | |
| Antakshari | 5 | |
| Passing the Parcel | |||| | 4 |
| Total | — | 24 |
(b) Popularity:
• Most popular: Musical Chairs (8 votes).
• Least popular: Passing the Parcel (4 votes).
CBSE Step-by-Step Marking Scheme
Correct tally marks layout and bundle counts
2.0 M
Correct identification of most and least popular games
1.0 M
Q8
In Chapter 10 ('Fun at Class Party!'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'Fun at Class Party!', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'Fun at Class Party!': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Party Gift Return Bags
Real-World Math Context: The class teacher prepares 25 return gift pouches for students. In each pouch, she places 3 crayons and 2 stickers.
Analytical Task: How many crayons and how many stickers will she need in total? What is the total count of all gift items?
1. Total crayons needed = 25 × 3 = 75 crayons.
2. Total stickers needed = 25 × 2 = 50 stickers.
3. Total gift items = 75 + 50 = 125 items (or 25 × 5 = 125 items).
2. Total stickers needed = 25 × 2 = 50 stickers.
3. Total gift items = 75 + 50 = 125 items (or 25 × 5 = 125 items).
CBSE Assessment Rubric: 1M crayons multiplication + 1M stickers multiplication + 1M total sum.
11
Unit 4: Multiplication, Measurement & Data • Class 3 Mathematics (New NEP 2020)
Chapter 11: Filling and Lifting
Capacity (Litres & Millilitres), Weight (Kilograms & Grams) & Comparison
Chapter Highlights, Mathematical Ideas & Key Properties
- Understanding capacity: Litre (L) for large liquids and Millilitre (mL) for small amounts.
- 1 Litre = 1000 Millilitres (1 L = 1000 mL).
- Understanding weight: Kilogram (kg) for heavy items and Gram (g) for light items.
- 1 Kilogram = 1000 Grams (1 kg = 1000 g).
- Using non-standard and standard balance scales to compare weights.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
State whether you would measure the capacity of the following in 'Litres (L)' or 'Millilitres (mL)': (a) A medicine dropper, (b) Water in a swimming pool, (c) A cup of tea, (d) Petrol in a car tank.
Capacity Unit Selection • Real-World Items
2 Marks
✅ Step-by-Step Model Answer & Solution:
Units:
• (a) Medicine dropper: Millilitres (mL) (very small liquid volume)
• (b) Water in swimming pool: Litres (L) (huge liquid volume)
• (c) A cup of tea: Millilitres (mL) (approx 150-200 mL)
• (d) Petrol in a car tank: Litres (L) (approx 35-50 L).
• (a) Medicine dropper: Millilitres (mL) (very small liquid volume)
• (b) Water in swimming pool: Litres (L) (huge liquid volume)
• (c) A cup of tea: Millilitres (mL) (approx 150-200 mL)
• (d) Petrol in a car tank: Litres (L) (approx 35-50 L).
CBSE Step-by-Step Marking Scheme
Correct unit for dropper and tea (mL)
1.0 M
Correct unit for pool and car petrol (L)
1.0 M
Q2
A bucket holds 10 litres of water. (a) How many 500 mL mugs of water are needed to fill this bucket completely? (b) How many 1-litre bottles can be filled from this bucket?
Capacity Conversion & Arithmetic
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
(a) Mugs of 500 mL:
• We know that 1 Litre = 2 mugs of 500 mL (500 mL + 500 mL = 1000 mL = 1 L).
• For 10 Litres = 10 × 2 = 20 mugs.
(b) 1-Litre bottles:
• 10 Litres ÷ 1 Litre = 10 bottles.
(a) Mugs of 500 mL:
• We know that 1 Litre = 2 mugs of 500 mL (500 mL + 500 mL = 1000 mL = 1 L).
• For 10 Litres = 10 × 2 = 20 mugs.
(b) 1-Litre bottles:
• 10 Litres ÷ 1 Litre = 10 bottles.
CBSE Step-by-Step Marking Scheme
Clear conversion statement (1 L = 2 × 500 mL)
1.5 M
Correct answer for mugs (20) and bottles (10)
1.5 M
Q3
A vegetable seller has standard weights of 1 kg, 500 g, 200 g, and 100 g. How can she weigh: (a) 1 kg 700 g of potatoes? (b) 800 g of tomatoes using the least number of weights?
Weight Units & Balancing
3 Marks
✅ Step-by-Step Model Answer & Solution:
Combinations:
• (a) 1 kg 700 g potatoes:
1 kg + 500 g + 200 g = 1 kg 700 g (3 weights).
• (b) 800 g tomatoes:
500 g + 200 g + 100 g = 800 g (3 weights).
• (a) 1 kg 700 g potatoes:
1 kg + 500 g + 200 g = 1 kg 700 g (3 weights).
• (b) 800 g tomatoes:
500 g + 200 g + 100 g = 800 g (3 weights).
CBSE Step-by-Step Marking Scheme
Correct weight combination for 1 kg 700 g
1.5 M
Correct weight combination for 800 g
1.5 M
Q4
Arrange the following containers in order of their capacity, from holding the least water to holding the most water:
Water tanker, Tea spoon, Bucket, Glass, Water bottle. Capacity Ranking • Everyday Containers 3 Marks
Water tanker, Tea spoon, Bucket, Glass, Water bottle. Capacity Ranking • Everyday Containers 3 Marks
✅ Step-by-Step Model Answer & Solution:
Capacity Ordering (Least to Most):
1. Tea spoon (~5 mL)
2. Glass (~250 mL)
3. Water bottle (~1 Litre / 1000 mL)
4. Bucket (~15 to 20 Litres)
5. Water tanker (~5000 Litres).
Order: Tea spoon < Glass < Water bottle < Bucket < Water tanker.
1. Tea spoon (~5 mL)
2. Glass (~250 mL)
3. Water bottle (~1 Litre / 1000 mL)
4. Bucket (~15 to 20 Litres)
5. Water tanker (~5000 Litres).
Order: Tea spoon < Glass < Water bottle < Bucket < Water tanker.
CBSE Step-by-Step Marking Scheme
Correct ranking from least to most
2.0 M
Reasonable real-life capacity estimates
1.0 M
Q5
A grocer wants to weigh 1 kg of sugar. He has standard weights of 500 g, 200 g, and 100 g.
(a) How many 500 g weights balance 1 kg?
(b) How many 200 g weights balance 1 kg?
(c) Give a combination using all three weights (500 g, 200 g, 100 g) that together equal 1 kg. Balance Scale • Weights in Grams and Kilograms 3 Marks
(a) How many 500 g weights balance 1 kg?
(b) How many 200 g weights balance 1 kg?
(c) Give a combination using all three weights (500 g, 200 g, 100 g) that together equal 1 kg. Balance Scale • Weights in Grams and Kilograms 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Weights:
• 1 kg = 1000 grams.
(a) 500 g Weights:
• 1000 ÷ 500 = 2 weights of 500 g.
(b) 200 g Weights:
• 1000 ÷ 200 = 5 weights of 200 g.
(c) Combined Weights:
• One 500 g weight = 500 g
• Two 200 g weights = 400 g
• One 100 g weight = 100 g
• Total = 500 g + 400 g + 100 g = 1000 g = 1 kg.
• 1 kg = 1000 grams.
(a) 500 g Weights:
• 1000 ÷ 500 = 2 weights of 500 g.
(b) 200 g Weights:
• 1000 ÷ 200 = 5 weights of 200 g.
(c) Combined Weights:
• One 500 g weight = 500 g
• Two 200 g weights = 400 g
• One 100 g weight = 100 g
• Total = 500 g + 400 g + 100 g = 1000 g = 1 kg.
CBSE Step-by-Step Marking Scheme
Correct answers for (a): 2 weights, and (b): 5 weights
1.5 M
Correct mixed combination summing to 1000 g
1.5 M
Q6
A family bought a 25 kg sack of wheat flour. In the first week, they used 8 kg 500 g. In the second week, they used 7 kg 250 g.
(a) What was the total weight of flour used in the two weeks?
(b) How much flour remains in the sack? Weight Addition & Subtraction • Grocery Sack 3 Marks
(a) What was the total weight of flour used in the two weeks?
(b) How much flour remains in the sack? Weight Addition & Subtraction • Grocery Sack 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Total Flour Used:
• Week 1: 8 kg 500 g
• Week 2: 7 kg 250 g
• Sum: (8 + 7) kg + (500 + 250) g = 15 kg 750 g.
(b) Remaining Flour:
• Total in sack = 25 kg 000 g
• Used = 15 kg 750 g
• Subtraction: 24 kg 1000 g - 15 kg 750 g = 9 kg 250 g.
(a) Total Flour Used:
• Week 1: 8 kg 500 g
• Week 2: 7 kg 250 g
• Sum: (8 + 7) kg + (500 + 250) g = 15 kg 750 g.
(b) Remaining Flour:
• Total in sack = 25 kg 000 g
• Used = 15 kg 750 g
• Subtraction: 24 kg 1000 g - 15 kg 750 g = 9 kg 250 g.
CBSE Step-by-Step Marking Scheme
Correct addition of compound weights (15 kg 750 g)
1.5 M
Correct subtraction from 25 kg (9 kg 250 g)
1.5 M
Q7
A bucket holds 12 litres of water. You only have a 2-litre jug and a 500 mL mug.
(a) How many full 2-litre jugs are needed to fill the bucket completely?
(b) How many 500 mL mugs are needed to equal one 2-litre jug? Measuring Jug Puzzle • Liquid Volume 3 Marks
(a) How many full 2-litre jugs are needed to fill the bucket completely?
(b) How many 500 mL mugs are needed to equal one 2-litre jug? Measuring Jug Puzzle • Liquid Volume 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Jugs to fill bucket:
• Total bucket capacity = 12 litres.
• Jug capacity = 2 litres.
• Number of jugs = 12 ÷ 2 = 6 jugs.
(b) Mugs per jug:
• 1 litre = 1000 mL = two 500 mL mugs.
• 2 litres = 2 × 2 = 4 mugs of 500 mL.
(a) Jugs to fill bucket:
• Total bucket capacity = 12 litres.
• Jug capacity = 2 litres.
• Number of jugs = 12 ÷ 2 = 6 jugs.
(b) Mugs per jug:
• 1 litre = 1000 mL = two 500 mL mugs.
• 2 litres = 2 × 2 = 4 mugs of 500 mL.
CBSE Step-by-Step Marking Scheme
Correct calculation for jugs (6 jugs)
1.5 M
Correct calculation for mugs (4 mugs)
1.5 M
Q8
In Chapter 11 ('Filling and Lifting'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'Filling and Lifting', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'Filling and Lifting': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Community Kitchen Lemonade Preparation
Real-World Math Context: To make lemonade for 50 people at a sports day, students use 8 litres of water, 1 litre of lemon juice, and 500 mL of sugar syrup.
Analytical Task: What is the total volume of lemonade prepared in millilitres? If each glass holds 200 mL, can they serve 45 glasses?
1. Convert all volumes to millilitres (mL):
• Water = 8 L = 8,000 mL
• Lemon juice = 1 L = 1,000 mL
• Sugar syrup = 500 mL
• Total volume = 8,000 + 1,000 + 500 = 9,500 mL.
2. Volume needed for 45 glasses of 200 mL each = 45 × 200 mL = 9,000 mL.
3. Since 9,500 mL > 9,000 mL, yes, they can easily serve 45 glasses (with 500 mL left over).
• Water = 8 L = 8,000 mL
• Lemon juice = 1 L = 1,000 mL
• Sugar syrup = 500 mL
• Total volume = 8,000 + 1,000 + 500 = 9,500 mL.
2. Volume needed for 45 glasses of 200 mL each = 45 × 200 mL = 9,000 mL.
3. Since 9,500 mL > 9,000 mL, yes, they can easily serve 45 glasses (with 500 mL left over).
CBSE Assessment Rubric: 1.5M litre to millilitre conversion and summation + 1.5M capacity comparison.
12
Unit 4: Multiplication, Measurement & Data • Class 3 Mathematics (New NEP 2020)
Chapter 12: Give and Take
2-Step Word Problems, Flow of Money, Addition with Regrouping & Verification
Chapter Highlights, Mathematical Ideas & Key Properties
- Translating word problems into numerical addition and subtraction sentences.
- Checking addition by subtraction (inverse operation check).
- Handling word problems involving 'more than', 'less than', and 'difference'.
- Solving 2-step financial transaction problems.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
Solve: 356 + 178. Then use subtraction to check whether your answer is correct.
Inverse Operations • Checking Work
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution & Verification:
1. Addition:
356
+ 178
-------
534 (6+8=14, 1 carry; 5+7+1=13, 1 carry; 3+1+1=5)
2. Verification via Subtraction:
534
- 178
-------
356
Since 534 - 178 = 356, the addition is 100% verified correct.
1. Addition:
356
+ 178
-------
534 (6+8=14, 1 carry; 5+7+1=13, 1 carry; 3+1+1=5)
2. Verification via Subtraction:
534
- 178
-------
356
Since 534 - 178 = 356, the addition is 100% verified correct.
CBSE Step-by-Step Marking Scheme
Correct addition with carry (534)
1.5 M
Correct inverse subtraction verification
1.5 M
Q2
Kiran had ₹500. She bought school books for ₹275 and stationery for ₹145. How much money did she spend altogether, and how much money was left with her?
2-Step Financial Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Solution:
Step 1: Total money spent
Cost of books = ₹275
Cost of stationery = ₹145
Total spent = ₹275 + ₹145 = ₹420.
Step 2: Money left
Total money initially = ₹500
Total spent = ₹420
Money left = ₹500 - ₹420 = ₹80.
Step 1: Total money spent
Cost of books = ₹275
Cost of stationery = ₹145
Total spent = ₹275 + ₹145 = ₹420.
Step 2: Money left
Total money initially = ₹500
Total spent = ₹420
Money left = ₹500 - ₹420 = ₹80.
CBSE Step-by-Step Marking Scheme
Correct addition for total spending (₹420)
1.5 M
Correct subtraction for remaining balance (₹80)
1.5 M
Q3
Arrange the numbers 1, 2, 3, 4, 5, 6 along the three sides of a triangle such that the sum of the numbers along each side is 9.
Number Puzzle • Magic Triangle
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
Place the smaller numbers at the corners to keep side sums low:
• Corners: 1, 2, 3.
• Between 1 and 2: place 6 → 1 + 6 + 2 = 9.
• Between 2 and 3: place 4 → 2 + 4 + 3 = 9.
• Between 3 and 1: place 5 → 3 + 5 + 1 = 9.
All three sides sum to exactly 9.
Place the smaller numbers at the corners to keep side sums low:
• Corners: 1, 2, 3.
• Between 1 and 2: place 6 → 1 + 6 + 2 = 9.
• Between 2 and 3: place 4 → 2 + 4 + 3 = 9.
• Between 3 and 1: place 5 → 3 + 5 + 1 = 9.
All three sides sum to exactly 9.
CBSE Step-by-Step Marking Scheme
Correct corner placement (1, 2, 3)
1.5 M
Correct edge placements (6, 4, 5) ensuring sum = 9
1.5 M
Q4
Solve the following additions showing carrying over clearly:
(a) 247 + 185
(b) 368 + 279
(c) Estimate the sum of 247 + 185 to the nearest hundred. Multi-Digit Addition • Regrouping Drill 3 Marks
(a) 247 + 185
(b) 368 + 279
(c) Estimate the sum of 247 + 185 to the nearest hundred. Multi-Digit Addition • Regrouping Drill 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solutions:
(a) 247 + 185:
• Ones: 7 + 5 = 12 (Write 2, carry 1 to tens)
• Tens: 1 (carry) + 4 + 8 = 13 (Write 3, carry 1 to hundreds)
• Hundreds: 1 (carry) + 2 + 1 = 4
• Sum = 432.
(b) 368 + 279:
• Ones: 8 + 9 = 17 (Write 7, carry 1)
• Tens: 1 + 6 + 7 = 14 (Write 4, carry 1)
• Hundreds: 1 + 3 + 2 = 6
• Sum = 647.
(c) Nearest Hundred Estimation:
• 247 rounds to 200; 185 rounds to 200.
• Estimated sum = 200 + 200 = 400 (Actual 432 is very close to 400).
(a) 247 + 185:
• Ones: 7 + 5 = 12 (Write 2, carry 1 to tens)
• Tens: 1 (carry) + 4 + 8 = 13 (Write 3, carry 1 to hundreds)
• Hundreds: 1 (carry) + 2 + 1 = 4
• Sum = 432.
(b) 368 + 279:
• Ones: 8 + 9 = 17 (Write 7, carry 1)
• Tens: 1 + 6 + 7 = 14 (Write 4, carry 1)
• Hundreds: 1 + 3 + 2 = 6
• Sum = 647.
(c) Nearest Hundred Estimation:
• 247 rounds to 200; 185 rounds to 200.
• Estimated sum = 200 + 200 = 400 (Actual 432 is very close to 400).
CBSE Step-by-Step Marking Scheme
Correct carrying and sum for (a): 432
1.0 M
Correct carrying and sum for (b): 647
1.0 M
Correct estimation explanation (400)
1.0 M
Q5
Solve the following subtractions showing borrowing steps:
(a) 512 - 278
(b) Check your subtraction answer using addition. Multi-Digit Subtraction • Borrowing Across Tens 3 Marks
(a) 512 - 278
(b) Check your subtraction answer using addition. Multi-Digit Subtraction • Borrowing Across Tens 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) 512 - 278:
• Ones: 2 - 8 cannot be done. Borrow 1 ten from 1 ten (leaving 0 tens). Ones become 12. 12 - 8 = 4.
• Tens: 0 - 7 cannot be done. Borrow 1 hundred from 5 hundreds (leaving 4 hundreds). Tens become 10. 10 - 7 = 3.
• Hundreds: 4 - 2 = 2.
• Difference = 234.
(b) Verification using Addition:
• Difference + Subtrahend = Minuend
• 234 + 278 = (200 + 200) + (30 + 70) + (4 + 8) = 400 + 100 + 12 = 512.
• Since 512 matches the starting number, the answer is Verified Correct.
(a) 512 - 278:
• Ones: 2 - 8 cannot be done. Borrow 1 ten from 1 ten (leaving 0 tens). Ones become 12. 12 - 8 = 4.
• Tens: 0 - 7 cannot be done. Borrow 1 hundred from 5 hundreds (leaving 4 hundreds). Tens become 10. 10 - 7 = 3.
• Hundreds: 4 - 2 = 2.
• Difference = 234.
(b) Verification using Addition:
• Difference + Subtrahend = Minuend
• 234 + 278 = (200 + 200) + (30 + 70) + (4 + 8) = 400 + 100 + 12 = 512.
• Since 512 matches the starting number, the answer is Verified Correct.
CBSE Step-by-Step Marking Scheme
Correct borrowing and difference (234)
1.5 M
Correct addition check formula and execution (234 + 278 = 512)
1.5 M
Q6
A baker baked 350 buns in the morning. He sold 215 buns by lunchtime. In the afternoon, he baked 120 fresh buns.
(a) How many buns were left after the lunchtime sales?
(b) How many buns did he have in total in the afternoon? Two-Step Word Problem • Bakery Sales 3 Marks
(a) How many buns were left after the lunchtime sales?
(b) How many buns did he have in total in the afternoon? Two-Step Word Problem • Bakery Sales 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Buns Left after Lunch:
• Morning buns baked = 350
• Buns sold = 215
• Leftover = 350 - 215 = 135 buns.
(b) Total Buns in Afternoon:
• Leftover buns = 135
• Fresh buns baked = 120
• Total = 135 + 120 = 255 buns.
(a) Buns Left after Lunch:
• Morning buns baked = 350
• Buns sold = 215
• Leftover = 350 - 215 = 135 buns.
(b) Total Buns in Afternoon:
• Leftover buns = 135
• Fresh buns baked = 120
• Total = 135 + 120 = 255 buns.
CBSE Step-by-Step Marking Scheme
Correct subtraction step (350 - 215 = 135)
1.5 M
Correct addition step (135 + 120 = 255)
1.5 M
Q7
Represent the subtraction 65 - 38 using square cards of 10 and triangle cards of 1.
(a) How many 10-cards and 1-cards are in 65?
(b) Explain how exchanging one 10-card for ten 1-cards allows you to subtract 38. Token Card Method • Visual Mental Math 3 Marks
(a) How many 10-cards and 1-cards are in 65?
(b) Explain how exchanging one 10-card for ten 1-cards allows you to subtract 38. Token Card Method • Visual Mental Math 3 Marks
✅ Step-by-Step Model Answer & Solution:
Visual Token Method:
(a) Cards for 65:
• 65 = six 10-cards and five 1-cards.
(b) Exchange and Subtraction:
• To subtract 38, we need to take away 3 ten-cards and 8 one-cards.
• We only have 5 one-cards, so we exchange one 10-card for ten 1-cards.
• Now we have: 5 ten-cards and 15 one-cards (10 + 5).
• Subtract 8 one-cards from 15 one-cards $\rightarrow$ 7 one-cards left.
• Subtract 3 ten-cards from 5 ten-cards $\rightarrow$ 2 ten-cards left.
• Remaining cards = two 10-cards + seven 1-cards = 27.
• Therefore, 65 - 38 = 27.
(a) Cards for 65:
• 65 = six 10-cards and five 1-cards.
(b) Exchange and Subtraction:
• To subtract 38, we need to take away 3 ten-cards and 8 one-cards.
• We only have 5 one-cards, so we exchange one 10-card for ten 1-cards.
• Now we have: 5 ten-cards and 15 one-cards (10 + 5).
• Subtract 8 one-cards from 15 one-cards $\rightarrow$ 7 one-cards left.
• Subtract 3 ten-cards from 5 ten-cards $\rightarrow$ 2 ten-cards left.
• Remaining cards = two 10-cards + seven 1-cards = 27.
• Therefore, 65 - 38 = 27.
CBSE Step-by-Step Marking Scheme
Correct card representation for 65 (6 tens, 5 ones)
1.0 M
Clear visual explanation of exchanging 1 ten for 10 ones
1.0 M
Correct final result (27)
1.0 M
Q8
In Chapter 12 ('Give and Take'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'Give and Take', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'Give and Take': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Children's Book Fair Stall
Real-World Math Context: At the school book fair, the storybook counter started with 450 books in the morning. They received a fresh delivery of 120 books at noon, and sold 380 books by evening.
Analytical Task: How many books were left at the storybook counter at the end of the day?
1. Books after morning delivery = 450 + 120 = 570 books.
2. Books sold = 380.
3. Books left at end of day = 570 - 380 = 190 books.
2. Books sold = 380.
3. Books left at end of day = 570 - 380 = 190 books.
CBSE Assessment Rubric: 1.5M addition of delivered books + 1.5M subtraction of sold books.
13
Unit 4: Multiplication, Measurement & Data • Class 3 Mathematics (New NEP 2020)
Chapter 13: Time Goes On
Clocks, Reading Time (Hours & Minutes), AM/PM & Daily Activity Schedules
Chapter Highlights, Mathematical Ideas & Key Properties
- Understanding clock hands: hour hand (short) and minute hand (long).
- Reading time to the hour, half past (30 min), quarter past (15 min), and quarter to (45 min).
- Difference between AM (midnight to noon) and PM (noon to midnight).
- Calculating elapsed time between start and end of daily activities.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
What time is shown when: (a) The hour hand is between 3 and 4, and the minute hand points to 6? (b) The hour hand is just past 8, and the minute hand points to 3? (c) The hour hand is near 12, and the minute hand points to 9?
Clock Reading • Quarter & Half Hours
3 Marks
✅ Step-by-Step Model Answer & Solution:
Clock Readings:
• (a) Minute hand at 6 = 30 minutes. Time = 03:30 (Half past 3).
• (b) Minute hand at 3 = 15 minutes. Time = 08:15 (Quarter past 8).
• (c) Minute hand at 9 = 45 minutes (15 minutes to 12). Time = 11:45 (Quarter to 12).
• (a) Minute hand at 6 = 30 minutes. Time = 03:30 (Half past 3).
• (b) Minute hand at 3 = 15 minutes. Time = 08:15 (Quarter past 8).
• (c) Minute hand at 9 = 45 minutes (15 minutes to 12). Time = 11:45 (Quarter to 12).
CBSE Step-by-Step Marking Scheme
Correct reading for half past 3
1.0 M
Correct reading for quarter past 8
1.0 M
Correct reading for quarter to 12
1.0 M
Q2
Meera started doing her math homework at 05:15 PM and finished at 06:05 PM. How many minutes did she spend on her homework?
Elapsed Time Calculation • Daily Routines
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculation:
• Start time = 05:15 PM
• End time = 06:05 PM
1. From 05:15 PM to 06:00 PM = 60 - 15 = 45 minutes.
2. From 06:00 PM to 06:05 PM = 5 minutes.
• Total duration = 45 + 5 = 50 minutes.
• Start time = 05:15 PM
• End time = 06:05 PM
1. From 05:15 PM to 06:00 PM = 60 - 15 = 45 minutes.
2. From 06:00 PM to 06:05 PM = 5 minutes.
• Total duration = 45 + 5 = 50 minutes.
CBSE Step-by-Step Marking Scheme
Correct breakdown to the nearest hour
1.0 M
Correct total elapsed time (50 minutes)
1.0 M
Q3
Write AM or PM for each activity: (a) Eating breakfast at 7:30 ___, (b) Playing in the park at 5:00 ___, (c) Sleeping at midnight 12:00 ___, (d) Lunch recess at school at 12:45 ___.
AM vs PM • Classification
2 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) Breakfast at 7:30 AM (morning)
• (b) Playing in park at 5:00 PM (evening)
• (c) Sleeping at midnight 12:00 AM (start of day)
• (d) Lunch recess at 12:45 PM (afternoon).
• (a) Breakfast at 7:30 AM (morning)
• (b) Playing in park at 5:00 PM (evening)
• (c) Sleeping at midnight 12:00 AM (start of day)
• (d) Lunch recess at 12:45 PM (afternoon).
CBSE Step-by-Step Marking Scheme
Correct AM/PM classification for all 4 events
2.0 M
Q4
Look at an analog clock face:
(a) Where does the hour hand and minute hand point at 4:15 (quarter past 4)?
(b) Where do they point at 7:30 (half past 7)?
(c) Where do they point at 9:45 (quarter to 10)? Analog Clock Face • Time Reading 3 Marks
(a) Where does the hour hand and minute hand point at 4:15 (quarter past 4)?
(b) Where do they point at 7:30 (half past 7)?
(c) Where do they point at 9:45 (quarter to 10)? Analog Clock Face • Time Reading 3 Marks
✅ Step-by-Step Model Answer & Solution:
Analog Clock Positions:
• (a) 4:15: The minute hand points directly at 3. The hour hand is slightly past 4.
• (b) 7:30: The minute hand points directly at 6. The hour hand is halfway between 7 and 8.
• (c) 9:45: The minute hand points directly at 9. The hour hand is close to 10.
• (a) 4:15: The minute hand points directly at 3. The hour hand is slightly past 4.
• (b) 7:30: The minute hand points directly at 6. The hour hand is halfway between 7 and 8.
• (c) 9:45: The minute hand points directly at 9. The hour hand is close to 10.
CBSE Step-by-Step Marking Scheme
Correct minute and hour hand positions for 4:15
1.0 M
Correct minute and hour hand positions for 7:30
1.0 M
Correct minute and hour hand positions for 9:45
1.0 M
Q5
Answer the following calendar questions:
(a) How many months in a year have exactly 31 days? Name any three.
(b) How many days does February have in a leap year and in an ordinary year?
(c) If 5th September is a Tuesday, what day of the week is 12th September? Calendar Reading • Days and Months 3 Marks
(a) How many months in a year have exactly 31 days? Name any three.
(b) How many days does February have in a leap year and in an ordinary year?
(c) If 5th September is a Tuesday, what day of the week is 12th September? Calendar Reading • Days and Months 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calendar Facts:
• (a) 31-Day Months: There are 7 months with 31 days (January, March, May, July, August, October, December).
• (b) February: February has 29 days in a leap year and 28 days in an ordinary year.
• (c) Day Calculation:
- Since there are 7 days in a week, adding 7 days gives the same day of the week.
- 5 + 7 = 12th September is also a Tuesday.
• (a) 31-Day Months: There are 7 months with 31 days (January, March, May, July, August, October, December).
• (b) February: February has 29 days in a leap year and 28 days in an ordinary year.
• (c) Day Calculation:
- Since there are 7 days in a week, adding 7 days gives the same day of the week.
- 5 + 7 = 12th September is also a Tuesday.
CBSE Step-by-Step Marking Scheme
Correct count (7) and names of 31-day months
1.0 M
Correct February days (29 leap, 28 ordinary)
1.0 M
Correct day of the week deduction (Tuesday)
1.0 M
Q6
Aman's daily schedule is as follows:
• Leaves for school: 7:30 AM
• Returns from school: 2:00 PM
(a) How many hours does Aman spend away at school?
(b) He plays football from 5:15 PM to 6:30 PM. What is the duration of his playtime? Duration of Daily Routines • Elapsed Time 3 Marks
• Leaves for school: 7:30 AM
• Returns from school: 2:00 PM
(a) How many hours does Aman spend away at school?
(b) He plays football from 5:15 PM to 6:30 PM. What is the duration of his playtime? Duration of Daily Routines • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Elapsed Time:
(a) Time at School:
• From 7:30 AM to 12:00 noon = 4 hours 30 minutes.
• From 12:00 noon to 2:00 PM = 2 hours.
• Total school time = 4 hr 30 min + 2 hr = 6 hours 30 minutes.
(b) Playtime Duration:
• From 5:15 PM to 6:15 PM = 1 hour (60 minutes).
• From 6:15 PM to 6:30 PM = 15 minutes.
• Total playtime = 1 hour 15 minutes (or 75 minutes).
(a) Time at School:
• From 7:30 AM to 12:00 noon = 4 hours 30 minutes.
• From 12:00 noon to 2:00 PM = 2 hours.
• Total school time = 4 hr 30 min + 2 hr = 6 hours 30 minutes.
(b) Playtime Duration:
• From 5:15 PM to 6:15 PM = 1 hour (60 minutes).
• From 6:15 PM to 6:30 PM = 15 minutes.
• Total playtime = 1 hour 15 minutes (or 75 minutes).
CBSE Step-by-Step Marking Scheme
Correct school duration (6 hours 30 minutes)
1.5 M
Correct playtime duration (1 hour 15 minutes)
1.5 M
Q7
Kavya was born on 15th August 2018.
(a) How old was she on 15th August 2024?
(b) How old will she be on 15th August 2030?
(c) In which year did she celebrate her 5th birthday? Age Timeline • Date of Birth Analysis 3 Marks
(a) How old was she on 15th August 2024?
(b) How old will she be on 15th August 2030?
(c) In which year did she celebrate her 5th birthday? Age Timeline • Date of Birth Analysis 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Timeline:
(a) Age in 2024:
• 2024 - 2018 = 6 years old.
(b) Age in 2030:
• 2030 - 2018 = 12 years old.
(c) 5th Birthday Year:
• 2018 + 5 = Year 2023.
(a) Age in 2024:
• 2024 - 2018 = 6 years old.
(b) Age in 2030:
• 2030 - 2018 = 12 years old.
(c) 5th Birthday Year:
• 2018 + 5 = Year 2023.
CBSE Step-by-Step Marking Scheme
Correct age in 2024 (6 years)
1.0 M
Correct age in 2030 (12 years)
1.0 M
Correct 5th birthday year (2023)
1.0 M
Q8
In Chapter 13 ('Time Goes On'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'Time Goes On', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'Time Goes On': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
School Annual Sports Day Schedule
Real-World Math Context: The 100m sprint race began at 10:20 AM and took 25 minutes. There was a 15-minute prize ceremony immediately following.
Analytical Task: At what time did the prize ceremony conclude? How many total minutes elapsed from the race start to the end of the ceremony?
1. Race start = 10:20 AM.
2. Race finish = 10:20 AM + 25 min = 10:45 AM.
3. Ceremony finish = 10:45 AM + 15 min = 11:00 AM.
4. Total elapsed time = 25 + 15 = 40 minutes.
2. Race finish = 10:20 AM + 25 min = 10:45 AM.
3. Ceremony finish = 10:45 AM + 15 min = 11:00 AM.
4. Total elapsed time = 25 + 15 = 40 minutes.
CBSE Assessment Rubric: 1.5M chronological addition of times + 1.5M total duration calculation.
14
Unit 4: Multiplication, Measurement & Data • Class 3 Mathematics (New NEP 2020)
Chapter 14: The Surajkund Fair
Pictographs, Bar Data, Money Transactions & Comprehensive Revision
Chapter Highlights, Mathematical Ideas & Key Properties
- Representing data using pictographs with a scale (e.g., 1 icon = 5 items).
- Reading and interpreting frequency bar graphs from a community craft fair.
- Calculating shopping totals and change with Indian currency notes and coins.
- Multi-concept review: combining addition, multiplication, and data skills.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (18 Solved Questions)
Q1
Look at the pictograph above where 1 symbol represents 5 craft items. (a) How many wooden toys were sold? (b) How many more wooden toys were sold than handloom bags? (c) What was the total number of items sold across all three stalls?
Pictograph Interpretation • Scaled Data
3 Marks
✅ Step-by-Step Model Answer & Solution:
Analysis using Scale (1 symbol = 5 items):
• (a) Wooden toys: 6 symbols × 5 = 30 wooden toys.
• (b) Handloom bags: 3 symbols × 5 = 15 bags.
Difference = 30 - 15 = 15 more wooden toys.
• (c) Total craft items: (4 + 6 + 3) symbols = 13 symbols × 5 = 65 items.
• (a) Wooden toys: 6 symbols × 5 = 30 wooden toys.
• (b) Handloom bags: 3 symbols × 5 = 15 bags.
Difference = 30 - 15 = 15 more wooden toys.
• (c) Total craft items: (4 + 6 + 3) symbols = 13 symbols × 5 = 65 items.
CBSE Step-by-Step Marking Scheme
Correct wooden toy count (30)
1.0 M
Correct difference calculation (15)
1.0 M
Correct total items calculation (65)
1.0 M
Q2
At the fair, Priya bought 2 wooden whistles at ₹25 each, 1 embroidered purse for ₹120, and 3 handmade bookmarks at ₹15 each. (a) What was her total bill? (b) If she paid with a ₹500 note, how much change did she receive?
Shopping Bill & Money Exchange
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Solution:
(a) Bill Calculation:
• 2 whistles = 2 × ₹25 = ₹50
• 1 purse = ₹120
• 3 bookmarks = 3 × ₹15 = ₹45
• Total bill = ₹50 + ₹120 + ₹45 = ₹215.
(b) Change:
• Amount given = ₹500
• Change received = ₹500 - ₹215 = ₹285.
(a) Bill Calculation:
• 2 whistles = 2 × ₹25 = ₹50
• 1 purse = ₹120
• 3 bookmarks = 3 × ₹15 = ₹45
• Total bill = ₹50 + ₹120 + ₹45 = ₹215.
(b) Change:
• Amount given = ₹500
• Change received = ₹500 - ₹215 = ₹285.
CBSE Step-by-Step Marking Scheme
Correct itemised multiplication and sum (₹215)
1.5 M
Correct subtraction from ₹500 note (₹285)
1.5 M
Q3
On Saturday, 350 tickets were sold for the puppet show and 425 tickets for the magic show. On Sunday, 480 tickets were sold for the puppet show and 390 for the magic show. Which show had higher total weekend sales and by how many tickets?
Bar Graph Reading • Ticket Sales
3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
1. Puppet Show Total: 350 (Sat) + 480 (Sun) = 830 tickets.
2. Magic Show Total: 425 (Sat) + 390 (Sun) = 815 tickets.
3. Comparison: 830 > 815. The Puppet Show had higher sales.
4. Difference: 830 - 815 = 15 tickets.
1. Puppet Show Total: 350 (Sat) + 480 (Sun) = 830 tickets.
2. Magic Show Total: 425 (Sat) + 390 (Sun) = 815 tickets.
3. Comparison: 830 > 815. The Puppet Show had higher sales.
4. Difference: 830 - 815 = 15 tickets.
CBSE Step-by-Step Marking Scheme
Correct weekend totals for puppet (830) and magic (815)
1.5 M
Correct comparison and difference (15 tickets)
1.5 M
Q4
At the Surajkund Fair, Maya visited the wooden toy stall. She bought:
• 4 wooden birds at ₹30 each
• 2 wooden tops at ₹20 each
• 1 wooden flute for ₹45
(a) Calculate the cost of each item and the total bill.
(b) If Maya pays with a ₹500 note, how much change will she get? Craft Stall Purchases • Multiplication & Addition 3 Marks
• 4 wooden birds at ₹30 each
• 2 wooden tops at ₹20 each
• 1 wooden flute for ₹45
(a) Calculate the cost of each item and the total bill.
(b) If Maya pays with a ₹500 note, how much change will she get? Craft Stall Purchases • Multiplication & Addition 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Bill Calculation:
• 4 wooden birds = 4 × ₹30 = ₹120.
• 2 wooden tops = 2 × ₹20 = ₹40.
• 1 wooden flute = ₹45.
• Total Bill = ₹120 + ₹40 + ₹45 = ₹205.
(b) Change Received:
• Amount paid = ₹500.
• Change = ₹500 - ₹205 = ₹295.
(a) Bill Calculation:
• 4 wooden birds = 4 × ₹30 = ₹120.
• 2 wooden tops = 2 × ₹20 = ₹40.
• 1 wooden flute = ₹45.
• Total Bill = ₹120 + ₹40 + ₹45 = ₹205.
(b) Change Received:
• Amount paid = ₹500.
• Change = ₹500 - ₹205 = ₹295.
CBSE Step-by-Step Marking Scheme
Correct itemised totals and total bill (₹205)
2.0 M
Correct subtraction for change (₹295)
1.0 M
Q5
Ticket prices for rides at the Surajkund Fair:
• Giant Wheel: ₹40 per person
• Toy Train: ₹25 per person
• Bumper Cars: ₹50 per person
A family of 2 parents and 2 children want to go on the Giant Wheel and Toy Train.
(a) What is the total cost for the family on the Giant Wheel?
(b) What is the total cost for the family on the Toy Train?
(c) What is the grand total for all rides? Fair Rides • Family Ticket Pricing 3 Marks
• Giant Wheel: ₹40 per person
• Toy Train: ₹25 per person
• Bumper Cars: ₹50 per person
A family of 2 parents and 2 children want to go on the Giant Wheel and Toy Train.
(a) What is the total cost for the family on the Giant Wheel?
(b) What is the total cost for the family on the Toy Train?
(c) What is the grand total for all rides? Fair Rides • Family Ticket Pricing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• Total family members = 2 adults + 2 children = 4 persons.
(a) Giant Wheel Cost:
• 4 persons × ₹40 = ₹160.
(b) Toy Train Cost:
• 4 persons × ₹25 = ₹100.
(c) Grand Total:
• Total rides cost = ₹160 + ₹100 = ₹260.
• Total family members = 2 adults + 2 children = 4 persons.
(a) Giant Wheel Cost:
• 4 persons × ₹40 = ₹160.
(b) Toy Train Cost:
• 4 persons × ₹25 = ₹100.
(c) Grand Total:
• Total rides cost = ₹160 + ₹100 = ₹260.
CBSE Step-by-Step Marking Scheme
Correct Giant Wheel total (₹160)
1.0 M
Correct Toy Train total (₹100)
1.0 M
Correct grand total (₹260)
1.0 M
Q6
The fair authorities recorded visitor counts using a pictograph where 🎟️ = 100 visitors:
• Friday: 🎟️🎟️🎟️🎟️ (4 tickets)
• Saturday: 🎟️🎟️🎟️🎟️🎟️🎟️ (6 tickets)
• Sunday: 🎟️🎟️🎟️🎟️🎟️🎟️🎟️🎟️ (8 tickets)
(a) How many visitors attended on Friday, Saturday, and Sunday respectively?
(b) What was the total number of visitors over the weekend (Saturday + Sunday)?
(c) How many more visitors attended on Sunday than on Friday? Pictograph Reading • Visitor Attendance 3 Marks
• Friday: 🎟️🎟️🎟️🎟️ (4 tickets)
• Saturday: 🎟️🎟️🎟️🎟️🎟️🎟️ (6 tickets)
• Sunday: 🎟️🎟️🎟️🎟️🎟️🎟️🎟️🎟️ (8 tickets)
(a) How many visitors attended on Friday, Saturday, and Sunday respectively?
(b) What was the total number of visitors over the weekend (Saturday + Sunday)?
(c) How many more visitors attended on Sunday than on Friday? Pictograph Reading • Visitor Attendance 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Pictograph Analysis:
• Scale: 1 🎟️ = 100 visitors.
(a) Daily Visitors:
• Friday: 4 × 100 = 400 visitors.
• Saturday: 6 × 100 = 600 visitors.
• Sunday: 8 × 100 = 800 visitors.
(b) Weekend Total:
• Saturday + Sunday = 600 + 800 = 1400 visitors.
(c) Difference (Sunday vs Friday):
• 800 - 400 = 400 more visitors on Sunday.
• Scale: 1 🎟️ = 100 visitors.
(a) Daily Visitors:
• Friday: 4 × 100 = 400 visitors.
• Saturday: 6 × 100 = 600 visitors.
• Sunday: 8 × 100 = 800 visitors.
(b) Weekend Total:
• Saturday + Sunday = 600 + 800 = 1400 visitors.
(c) Difference (Sunday vs Friday):
• 800 - 400 = 400 more visitors on Sunday.
CBSE Step-by-Step Marking Scheme
Correct conversion for all three days (400, 600, 800)
1.5 M
Correct weekend total (1400) and difference (400)
1.5 M
Q7
At the fair's food street, Kabir's group ordered:
• 3 plates of Pav Bhaji at ₹60 per plate
• 4 glasses of Lassi at ₹30 per glass
• 2 plates of Jalebi at ₹40 per plate
(a) What was the total food bill?
(b) If the stall owner offered a festival discount of ₹40, how much did Kabir actually pay? Food Court Bill • Addition and Discount 3 Marks
• 3 plates of Pav Bhaji at ₹60 per plate
• 4 glasses of Lassi at ₹30 per glass
• 2 plates of Jalebi at ₹40 per plate
(a) What was the total food bill?
(b) If the stall owner offered a festival discount of ₹40, how much did Kabir actually pay? Food Court Bill • Addition and Discount 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Total Bill:
• Pav Bhaji: 3 × ₹60 = ₹180.
• Lassi: 4 × ₹30 = ₹120.
• Jalebi: 2 × ₹40 = ₹80.
• Total bill = ₹180 + ₹120 + ₹80 = ₹380.
(b) Discounted Payment:
• Discount = ₹40.
• Amount paid = ₹380 - ₹40 = ₹340.
(a) Total Bill:
• Pav Bhaji: 3 × ₹60 = ₹180.
• Lassi: 4 × ₹30 = ₹120.
• Jalebi: 2 × ₹40 = ₹80.
• Total bill = ₹180 + ₹120 + ₹80 = ₹380.
(b) Discounted Payment:
• Discount = ₹40.
• Amount paid = ₹380 - ₹40 = ₹340.
CBSE Step-by-Step Marking Scheme
Correct sub-totals and bill before discount (₹380)
2.0 M
Correct subtraction of discount (₹340)
1.0 M
Q8
In Chapter 14 ('The Surajkund Fair'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
Textbook Exercise • Practical Problem Solving
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In 'The Surajkund Fair', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
In-Text Activity • Concept Exploration
2 Marks
✅ Step-by-Step Model Answer & Solution:
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ? Practice Time • Mental Math Drills 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
Word Problem • Real Life Application
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Observe the sequence related to 'The Surajkund Fair': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
Critical Thinking • Finding the Pattern
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard. Estimation & Measurement • Practical Judgment 2 Marks
✅ Step-by-Step Model Answer & Solution:
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed? Data Interpretation • Reading Simple Tables 3 Marks
✅ Step-by-Step Model Answer & Solution:
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have? Let us Do • Shapes and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
Puzzle Time • Missing Number Grid
2 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
Money & Shopping • Cash Memo Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners. Chapter Review • Comprehensive Concept Check 3 Marks
✅ Step-by-Step Model Answer & Solution:
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Handicrafts Stall Revenue Summary
Real-World Math Context: A pottery artisan brought 80 clay diyas to the fair. He sold 55 diyas on Day 1 for ₹10 each. On Day 2, he reduced the price to ₹8 each and sold all remaining diyas.
Analytical Task: How many diyas were sold on Day 2? What was the total revenue earned by the artisan from selling all 80 diyas?
1. Diyas sold on Day 2 = Total - Day 1 = 80 - 55 = 25 diyas.
2. Day 1 revenue = 55 × ₹10 = ₹550.
3. Day 2 revenue = 25 × ₹8 = ₹200.
4. Total revenue = ₹550 + ₹200 = ₹750.
2. Day 1 revenue = 55 × ₹10 = ₹550.
3. Day 2 revenue = 25 × ₹8 = ₹200.
4. Total revenue = ₹550 + ₹200 = ₹750.
CBSE Assessment Rubric: 1M Day 2 count + 1M Day 1 & Day 2 revenues + 1M total revenue sum.
1
Unit 1: Spatial Understanding & Symmetry • Class 3 Mathematics (Classic CBSE)
Chapter 1: Where to Look From
Top View, Front View, Side View, Dot Grid Drawings & Mirror Halves (Lines of Symmetry)
Chapter Highlights, Mathematical Ideas & Key Properties
- Viewing 3D objects from different perspectives: top view, side view, and front view.
- Using a square dot grid (Rangoli patterns) to draw shapes and objects.
- Mirror halves: understanding symmetry and finding lines of symmetry.
- Recognizing symmetric alphabet letters, numbers, and geometric shapes.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
How does a staircase look when viewed from: (a) The side? (b) The top? (c) The front? Explain with a short description.
Perspective Drawing • Views
3 Marks
✅ Step-by-Step Model Answer & Solution:
Perspective Descriptions:
• (a) Side View: From the side, a staircase looks like a continuous zigzag step pattern going upward like a ladder.
• (b) Top View: From directly above, you see a set of parallel rectangular stripes or bars placed one after another.
• (c) Front View: Looking straight from the front, you see a series of horizontal rectangular risers stacked vertically.
• (a) Side View: From the side, a staircase looks like a continuous zigzag step pattern going upward like a ladder.
• (b) Top View: From directly above, you see a set of parallel rectangular stripes or bars placed one after another.
• (c) Front View: Looking straight from the front, you see a series of horizontal rectangular risers stacked vertically.
CBSE Step-by-Step Marking Scheme
Accurate description of side view (zigzag steps)
1.0 M
Accurate description of top view (parallel stripes)
1.0 M
Accurate description of front view
1.0 M
Q2
Look at the letters of the English alphabet: A, B, C, D, E, H, M, X. Which of these letters have: (a) A vertical line of symmetry? (b) A horizontal line of symmetry? (c) Both vertical and horizontal lines of symmetry?
Mirror Halves • Symmetry Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Classification of Symmetric Letters:
• (a) Vertical line of symmetry (cut down the middle | ): A, M, H, X.
• (b) Horizontal line of symmetry (cut across the middle — ): B, C, D, E, H, X.
• (c) Both vertical and horizontal symmetry: H and X (folding along either line gives matching halves).
• (a) Vertical line of symmetry (cut down the middle | ): A, M, H, X.
• (b) Horizontal line of symmetry (cut across the middle — ): B, C, D, E, H, X.
• (c) Both vertical and horizontal symmetry: H and X (folding along either line gives matching halves).
CBSE Step-by-Step Marking Scheme
Correct vertical symmetry identification
1.0 M
Correct horizontal symmetry identification
1.0 M
Correct dual symmetry identification (H, X)
1.0 M
Q3
Using a square dot grid, how do you construct a symmetric leaf or kite? Describe the step-by-step method using mirror halves.
Dot Grid Pattern • Activity Solution
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Dot Grid Construction:
1. Draw a central vertical axis connecting 6 dots straight down.
2. On the left side, count 3 dots out to the side and draw the left curved wing/outline.
3. Count the exact same number of dots (3 dots) on the right side and draw a matching mirror curve.
4. Joining the matching dots to the top and bottom central points produces a perfectly symmetric kite or leaf.
1. Draw a central vertical axis connecting 6 dots straight down.
2. On the left side, count 3 dots out to the side and draw the left curved wing/outline.
3. Count the exact same number of dots (3 dots) on the right side and draw a matching mirror curve.
4. Joining the matching dots to the top and bottom central points produces a perfectly symmetric kite or leaf.
CBSE Step-by-Step Marking Scheme
Mention of central axis and equal dot distances
1.0 M
Explanation of mirror symmetry completion
1.0 M
Q4
A cat is peeping into a classroom from a high window above.
(a) What view of the classroom does the cat see: Top View, Side View, or Front View?
(b) Can you help the cat find where the teacher is sitting?
(c) Draw or describe how a staircase looks from the side versus from the top. Perspective & Observation • Cat in the Classroom 3 Marks
(a) What view of the classroom does the cat see: Top View, Side View, or Front View?
(b) Can you help the cat find where the teacher is sitting?
(c) Draw or describe how a staircase looks from the side versus from the top. Perspective & Observation • Cat in the Classroom 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Cat's Perspective:
• The cat is looking down from above, so it sees the Top View (or Aerial View) of the students' desks and heads.
(b) Locating the Teacher:
• The teacher is standing/sitting at the front of the classroom near the large rectangular teacher's table facing the rows of student desks.
(c) Staircase Views:
• Side View: Shows a step-like zig-zag pattern going upward like a ladder.
• Top View: Shows only a series of parallel horizontal rectangular steps.
(a) Cat's Perspective:
• The cat is looking down from above, so it sees the Top View (or Aerial View) of the students' desks and heads.
(b) Locating the Teacher:
• The teacher is standing/sitting at the front of the classroom near the large rectangular teacher's table facing the rows of student desks.
(c) Staircase Views:
• Side View: Shows a step-like zig-zag pattern going upward like a ladder.
• Top View: Shows only a series of parallel horizontal rectangular steps.
CBSE Step-by-Step Marking Scheme
Correct perspective identification (Top View)
1.0 M
Accurate description of teacher's location in classroom
1.0 M
Clear contrast between side view and top view of staircase
1.0 M
Q5
In the story 'Tit for Tat', a clever painter drew only half of Amina's picture and asked for payment. Amina placed a mirror next to it.
(a) Why did Amina use a mirror?
(b) Which of these letters can be divided into two identical mirror halves by a dotted line: A, B, C, F, H, P?
(c) Give an English word whose upper and lower halves look identical in a horizontal mirror. Tit for Tat • Mirror Halves and Symmetry 3 Marks
(a) Why did Amina use a mirror?
(b) Which of these letters can be divided into two identical mirror halves by a dotted line: A, B, C, F, H, P?
(c) Give an English word whose upper and lower halves look identical in a horizontal mirror. Tit for Tat • Mirror Halves and Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Mirror Trick:
• The mirror reflects the drawn half to complete the full symmetrical image, showing Amina's full face just as the painter claimed.
(b) Symmetrical Letters:
• A: Vertical mirror line down the middle.
• B: Horizontal mirror line across the middle.
• C: Horizontal mirror line across the middle.
• H: Both vertical and horizontal mirror lines.
• (F and P cannot be divided into identical mirror halves).
(c) Horizontal Mirror Words:
• Words like COOKED, DICE, CHECK, or BOOK have horizontal symmetry.
(a) Mirror Trick:
• The mirror reflects the drawn half to complete the full symmetrical image, showing Amina's full face just as the painter claimed.
(b) Symmetrical Letters:
• A: Vertical mirror line down the middle.
• B: Horizontal mirror line across the middle.
• C: Horizontal mirror line across the middle.
• H: Both vertical and horizontal mirror lines.
• (F and P cannot be divided into identical mirror halves).
(c) Horizontal Mirror Words:
• Words like COOKED, DICE, CHECK, or BOOK have horizontal symmetry.
CBSE Step-by-Step Marking Scheme
Correct explanation of the mirror reflection concept
1.0 M
Correct identification of symmetrical letters (A, B, C, H)
1.0 M
Valid horizontally symmetrical word example
1.0 M
Q6
Using a grid of dots to make traditional Indian rangoli designs:
(a) How can a line of symmetry help in drawing a balanced rangoli?
(b) Name four geometric shapes that can be created by joining dots on a dot grid.
(c) If you draw a diya on one side of a dotted line, how do you complete it on the other side? Dot-Grid Rangoli • Symmetry and Patterns 3 Marks
(a) How can a line of symmetry help in drawing a balanced rangoli?
(b) Name four geometric shapes that can be created by joining dots on a dot grid.
(c) If you draw a diya on one side of a dotted line, how do you complete it on the other side? Dot-Grid Rangoli • Symmetry and Patterns 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Symmetry in Rangoli:
• A central line or point of symmetry ensures that every curve, petal, or corner drawn on the left is matched exactly at an equal distance on the right, creating a balanced and harmonious design.
(b) Shapes on a Dot Grid:
• Square, Rectangle, Triangle, and Rhombus (Diamond).
(c) Completing the Diya:
• Count the exact number of dots outward and downward from the mirror line for each vertex of the diya, and connect corresponding dots symmetrically on the opposite side.
(a) Symmetry in Rangoli:
• A central line or point of symmetry ensures that every curve, petal, or corner drawn on the left is matched exactly at an equal distance on the right, creating a balanced and harmonious design.
(b) Shapes on a Dot Grid:
• Square, Rectangle, Triangle, and Rhombus (Diamond).
(c) Completing the Diya:
• Count the exact number of dots outward and downward from the mirror line for each vertex of the diya, and connect corresponding dots symmetrically on the opposite side.
CBSE Step-by-Step Marking Scheme
Explanation of symmetry creating balance in art
1.0 M
Listing four valid polygon shapes
1.0 M
Methodical explanation of reflection across dot-grid
1.0 M
Q7
State whether a dotted line through the center divides each figure into mirror halves (Write 'Yes' or 'No'):
(a) A standard butterfly with dotted line along its body.
(b) A pair of scissors with dotted line between the two blades.
(c) A watering can with a spout on one side and a handle on the other.
(d) An equilateral triangle with dotted line from top vertex to base midpoint. Mirror Halves Identification • Figures 4 Marks
(a) A standard butterfly with dotted line along its body.
(b) A pair of scissors with dotted line between the two blades.
(c) A watering can with a spout on one side and a handle on the other.
(d) An equilateral triangle with dotted line from top vertex to base midpoint. Mirror Halves Identification • Figures 4 Marks
✅ Step-by-Step Model Answer & Solution:
Mirror Halves Check:
• (a) Butterfly: Yes (Left wing is an exact mirror image of the right wing).
• (b) Scissors: Yes (The two halves fold over each other symmetrically).
• (c) Watering Can: No (Spout on one side does not match handle on the other).
• (d) Equilateral Triangle: Yes (Bisects the triangle into two identical right-angled triangles).
• (a) Butterfly: Yes (Left wing is an exact mirror image of the right wing).
• (b) Scissors: Yes (The two halves fold over each other symmetrically).
• (c) Watering Can: No (Spout on one side does not match handle on the other).
• (d) Equilateral Triangle: Yes (Bisects the triangle into two identical right-angled triangles).
CBSE Step-by-Step Marking Scheme
Correct answers for (a) and (b)
2.0 M
Correct answers for (c) and (d)
2.0 M
Q8
Dheeraj drew a car from the terrace (top view) and Anshul drew the same car from the side. Dheeraj's drawing looked like a small box kept inside a bigger box, while Anshul's showed doors and wheels. Were both drawings correct? Explain.
Textbook Activity • Views of Everyday Objects
3 Marks
✅ Step-by-Step Model Answer & Solution:
Answer:
• Yes, both drawings were correct!
• The appearance of an object changes depending on the position from which you look at it.
• From the side view, you see the wheels, windows, and doors.
• From the top view (looking from above), you only see the roof and bonnet, which looks like a box inside a box.
• Yes, both drawings were correct!
• The appearance of an object changes depending on the position from which you look at it.
• From the side view, you see the wheels, windows, and doors.
• From the top view (looking from above), you only see the roof and bonnet, which looks like a box inside a box.
CBSE Step-by-Step Marking Scheme
Both are correct
1 M
Side view explanation
1 M
Top view explanation
1 M
Q9
Using a 5x5 dot grid, what geometric shapes can you draw by joining dots with straight lines? Name at least three different shapes.
Dot Grid Drawing • Rangoli Patterns
3 Marks
✅ Step-by-Step Model Answer & Solution:
Dot Grid Geometry:
By connecting dots with straight line segments, we can construct:
1. Squares (by joining 4 dots with equal horizontal and vertical sides).
2. Rectangles (by joining dots with unequal length and width).
3. Triangles (by joining any 3 non-collinear dots).
4. Kite / Rhombus shapes.
By connecting dots with straight line segments, we can construct:
1. Squares (by joining 4 dots with equal horizontal and vertical sides).
2. Rectangles (by joining dots with unequal length and width).
3. Triangles (by joining any 3 non-collinear dots).
4. Kite / Rhombus shapes.
CBSE Step-by-Step Marking Scheme
Three valid shapes named
1.5 M
Explanation of connecting dots
1.5 M
Q10
Does a dotted line divide each of the following letters into two identical mirror halves?
(a) The letter 'A' with a vertical dotted line down the center.
(b) The letter 'B' with a horizontal dotted line across the middle.
(c) The letter 'F' with any straight line. Mirror Halves • Symmetry Line 3 Marks
(a) The letter 'A' with a vertical dotted line down the center.
(b) The letter 'B' with a horizontal dotted line across the middle.
(c) The letter 'F' with any straight line. Mirror Halves • Symmetry Line 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Analysis:
• (a) Letter 'A': Yes. A vertical mirror line divides 'A' into matching left and right halves.
• (b) Letter 'B': Yes. A horizontal mirror line divides 'B' into matching top and bottom loops.
• (c) Letter 'F': No. 'F' has no line of symmetry; neither vertical nor horizontal line can divide it into mirror halves.
• (a) Letter 'A': Yes. A vertical mirror line divides 'A' into matching left and right halves.
• (b) Letter 'B': Yes. A horizontal mirror line divides 'B' into matching top and bottom loops.
• (c) Letter 'F': No. 'F' has no line of symmetry; neither vertical nor horizontal line can divide it into mirror halves.
CBSE Step-by-Step Marking Scheme
(a) Yes with explanation
1 M
(b) Yes with explanation
1 M
(c) No with explanation
1 M
Q11
How can you make a cat mask by folding a piece of paper in half and cutting only one side? Explain the mathematical principle involved.
Mask Making • Half Face Art
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Procedure & Principle:
1. Fold a sheet of drawing paper exactly in half.
2. Draw one ear, one eye, half the nose, and half the whiskers along the folded edge.
3. Cut along the drawn outline while the paper remains folded.
4. Unfold the paper: A complete, perfectly symmetrical cat face appears!
• Mathematical Principle: Bilateral Symmetry (Reflection). The crease acts as a mirror line.
1. Fold a sheet of drawing paper exactly in half.
2. Draw one ear, one eye, half the nose, and half the whiskers along the folded edge.
3. Cut along the drawn outline while the paper remains folded.
4. Unfold the paper: A complete, perfectly symmetrical cat face appears!
• Mathematical Principle: Bilateral Symmetry (Reflection). The crease acts as a mirror line.
CBSE Step-by-Step Marking Scheme
Folding and cutting procedure explained
1.5 M
Concept of mirror symmetry / reflection identified
1.5 M
Q12
Look at a staircase:
(a) From which view does it look like steps going up: Top, Side, or Front?
(b) From which view does it look like a flat series of horizontal bars: Top, Side, or Front? Practice Time • Top, Side, Front Classification 2 Marks
(a) From which view does it look like steps going up: Top, Side, or Front?
(b) From which view does it look like a flat series of horizontal bars: Top, Side, or Front? Practice Time • Top, Side, Front Classification 2 Marks
✅ Step-by-Step Model Answer & Solution:
Staircase Views:
• (a) Looking like steps going upwards: Side view.
• (b) Looking like flat horizontal strips/bars: Top view (or front view from directly ahead).
• (a) Looking like steps going upwards: Side view.
• (b) Looking like flat horizontal strips/bars: Top view (or front view from directly ahead).
CBSE Step-by-Step Marking Scheme
Side view for steps
1 M
Top view for strips
1 M
Q13
Guess the words by looking at their top halves:
(a) H A I L
(b) C H O O K
(c) D I C E.
Explain why these words can be identified from their top halves. In-Text Exploration • Words with Mirror Halves 2 Marks
(a) H A I L
(b) C H O O K
(c) D I C E.
Explain why these words can be identified from their top halves. In-Text Exploration • Words with Mirror Halves 2 Marks
✅ Step-by-Step Model Answer & Solution:
Explanation:
• Letters like C, D, E, H, I, K, O, X possess horizontal symmetry.
• Their top halves mirror their bottom halves across a central horizontal line, allowing complete word recognition even when only the upper half is visible.
• Letters like C, D, E, H, I, K, O, X possess horizontal symmetry.
• Their top halves mirror their bottom halves across a central horizontal line, allowing complete word recognition even when only the upper half is visible.
CBSE Step-by-Step Marking Scheme
Identification of letters with horizontal symmetry
2 M
Q14
In the story 'Tit for Tat', a clever painter painted only half a portrait for Ameena and asked for full payment. How did Ameena pay him back using a mirror?
Hands-on Exercise • Tit for Tat Story
3 Marks
✅ Step-by-Step Model Answer & Solution:
Story Explanation:
• The painter told Ameena: 'Put a mirror next to it, and you will see the complete picture!'
• Ameena gave him a ₹100 note and kept a mirror beside it, saying: 'Look in the mirror, now you have your full ₹200!'
• She used the exact same mirror reflection trick on the painter.
• The painter told Ameena: 'Put a mirror next to it, and you will see the complete picture!'
• Ameena gave him a ₹100 note and kept a mirror beside it, saying: 'Look in the mirror, now you have your full ₹200!'
• She used the exact same mirror reflection trick on the painter.
CBSE Step-by-Step Marking Scheme
Ameena's mirror response explained
2 M
Connection to reflection concept
1 M
Q15
On a dot grid, if a square has 4 dots on each side, how many dots are on its perimeter in total? (Be careful not to count the corners twice).
Dot Grid Pattern • Flower and Leaf
2 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter Dot Calculation:
• A square has 4 sides.
• Dots per side = 4.
• Total = 4 sides × (4 - 1 dots) = 4 × 3 = 12 dots on the perimeter.
Alternatively: 4 corners + (2 inner dots on 4 sides) = 4 + 8 = 12 dots.
• A square has 4 sides.
• Dots per side = 4.
• Total = 4 sides × (4 - 1 dots) = 4 × 3 = 12 dots on the perimeter.
Alternatively: 4 corners + (2 inner dots on 4 sides) = 4 + 8 = 12 dots.
CBSE Step-by-Step Marking Scheme
Correct count = 12 dots with explanation
2 M
Q16
Which of the following objects can be cut into two identical halves by a straight knife cut?
(a) A round apple (sliced vertically down stem)
(b) A pair of scissors
(c) A shoe. Mental Geometry • Line of Symmetry in Everyday Objects 3 Marks
(a) A round apple (sliced vertically down stem)
(b) A pair of scissors
(c) A shoe. Mental Geometry • Line of Symmetry in Everyday Objects 3 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry Assessment:
• (a) Round apple: Yes, a vertical cut down the center yields two symmetric halves.
• (b) Scissors: Yes, sliced along the center line between blades.
• (c) Shoe: No, a shoe is curved for left or right foot and has no line of symmetry.
• (a) Round apple: Yes, a vertical cut down the center yields two symmetric halves.
• (b) Scissors: Yes, sliced along the center line between blades.
• (c) Shoe: No, a shoe is curved for left or right foot and has no line of symmetry.
CBSE Step-by-Step Marking Scheme
Apple = Yes
1 M
Scissors = Yes
1 M
Shoe = No
1 M
Q17
Which digits among 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 have at least one line of symmetry when written in standard block form?
Review Questions • Symmetrical Numbers
2 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetrical Digits:
• 0 (both vertical and horizontal symmetry)
• 3 (horizontal line of symmetry)
• 8 (both vertical and horizontal symmetry).
Digits 2, 4, 5, 6, 7, 9 do not have lines of symmetry in standard form.
• 0 (both vertical and horizontal symmetry)
• 3 (horizontal line of symmetry)
• 8 (both vertical and horizontal symmetry).
Digits 2, 4, 5, 6, 7, 9 do not have lines of symmetry in standard form.
CBSE Step-by-Step Marking Scheme
0, 3, 8 identified correctly
2 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Architectural Floor Plan Perspective
Real-World Math Context: An architect looks down at a school building model from above (aerial top view). She notices the roof is shaped like a giant rectangle with two circular courtyards inside.
Analytical Task: If each circular courtyard has a diameter of 10 metres and they are placed side by side with 5 metres gap between them, what is the distance from the left edge of the first courtyard to the right edge of the second?
1. Width of 1st courtyard = 10 m.
2. Gap between courtyards = 5 m.
3. Width of 2nd courtyard = 10 m.
4. Total span = 10 + 5 + 10 = 25 metres.
2. Gap between courtyards = 5 m.
3. Width of 2nd courtyard = 10 m.
4. Total span = 10 + 5 + 10 = 25 metres.
CBSE Assessment Rubric: 1.5M identifying diameter dimensions + 1.5M addition of spans and gap.
2
Unit 2: Number Concepts & Place Value • Class 3 Mathematics (Classic CBSE)
Chapter 2: Fun with Numbers
3-Digit Numbers, Cricket Centuries, Skip Counting, Comparing & Word Problems
Chapter Highlights, Mathematical Ideas & Key Properties
- Reading and writing 3-digit numbers in figures and words up to 999.
- Cricket scorecards: half-century (50), century (100), and double century (200).
- Skip counting forward and backward by 2s, 5s, 10s, and 50s.
- Finding predecessor (one less) and successor (one more).
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Look at the World Cup scorecard: C.K. scored 99 runs, A.S. scored 162 runs, and P.K. scored 105 runs. (a) How many more runs did C.K. need to complete a century? (b) Who scored more than a century and by how many runs?
Cricket Score Analysis • Centuries
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Solution:
• 1 Century = 100 runs.
(a) C.K.'s Century Shortfall:
100 - 99 = 1 run needed.
(b) Scorers above a Century:
• P.K. scored 105: 105 - 100 = 5 runs more than a century.
• A.S. scored 162: 162 - 100 = 62 runs more than a century.
• 1 Century = 100 runs.
(a) C.K.'s Century Shortfall:
100 - 99 = 1 run needed.
(b) Scorers above a Century:
• P.K. scored 105: 105 - 100 = 5 runs more than a century.
• A.S. scored 162: 162 - 100 = 62 runs more than a century.
CBSE Step-by-Step Marking Scheme
Correct shortfall for C.K. (1 run)
1.0 M
Correct excess runs for P.K. (5 runs)
1.0 M
Correct excess runs for A.S. (62 runs)
1.0 M
Q2
Fill in the missing numbers for the patterns: (a) 550, 600, 650, ___, ___, ___. (b) 280, 260, 240, ___, ___, ___ (Counting backwards by 20).
Skip Counting Sequences • Patterns
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) Forward by 50: 550, 600, 650, 700, 750, 800.
• (b) Backward by 20: 280, 260, 240, 220, 200, 180.
• (a) Forward by 50: 550, 600, 650, 700, 750, 800.
• (b) Backward by 20: 280, 260, 240, 220, 200, 180.
CBSE Step-by-Step Marking Scheme
Correct forward sequence (+50)
1.0 M
Correct backward sequence (-20)
1.0 M
Q3
Solve the riddles: (1) 'I am between 70 and 80 and have a 5 in my name.' (2) 'I have 9 in my name and am very close to 90.' (3) 'If you hit a 4 after me, you score a century.'
Place Value Riddles • Problem Solving
3 Marks
✅ Step-by-Step Model Answer & Solution:
Riddle Answers:
1. Between 70 and 80 with 5 → 75.
2. Very close to 90 with 9 → 89 (since 89 + 1 = 90).
3. Hit a 4 to score a century (100) → 100 - 4 = 96.
1. Between 70 and 80 with 5 → 75.
2. Very close to 90 with 9 → 89 (since 89 + 1 = 90).
3. Hit a 4 to score a century (100) → 100 - 4 = 96.
CBSE Step-by-Step Marking Scheme
Correct deduction for riddle 1 (75)
1.0 M
Correct deduction for riddle 2 (89)
1.0 M
Correct deduction for riddle 3 (96)
1.0 M
Q4
Radhika, Gauri, Vicky, Indra, and Sunil were collecting tamarind (imli) seeds:
• Radhika collected 24 seeds
• Gauri collected 47 seeds
• Sunil collected 38 seeds
• Indra collected 54 seeds
• Vicky collected 42 seeds
(a) Who collected the most seeds, and who collected the least seeds?
(b) How many more seeds does Sunil need to collect to have 40 seeds?
(c) If Radhika gets 6 more seeds, how many seeds will she have? Tamarind Seeds Collection • Comparison 3 Marks
• Radhika collected 24 seeds
• Gauri collected 47 seeds
• Sunil collected 38 seeds
• Indra collected 54 seeds
• Vicky collected 42 seeds
(a) Who collected the most seeds, and who collected the least seeds?
(b) How many more seeds does Sunil need to collect to have 40 seeds?
(c) If Radhika gets 6 more seeds, how many seeds will she have? Tamarind Seeds Collection • Comparison 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Analysis:
(a) Most and Least:
• Most seeds: Indra (54 seeds).
• Least seeds: Radhika (24 seeds).
(b) Sunil's Target:
• Sunil has = 38 seeds.
• Seeds needed = 40 - 38 = 2 seeds.
(c) Radhika's New Total:
• 24 + 6 = 30 seeds.
(a) Most and Least:
• Most seeds: Indra (54 seeds).
• Least seeds: Radhika (24 seeds).
(b) Sunil's Target:
• Sunil has = 38 seeds.
• Seeds needed = 40 - 38 = 2 seeds.
(c) Radhika's New Total:
• 24 + 6 = 30 seeds.
CBSE Step-by-Step Marking Scheme
Correct most (54) and least (24) identified
1.0 M
Correct calculation for Sunil (40 - 38 = 2)
1.0 M
Correct addition for Radhika (24 + 6 = 30)
1.0 M
Q5
Study the runs scored by top batsmen:
• C.K. Nayudu: 99 runs
• Kapil Dev: 122 runs
• Gavaskar: 100 runs
• Tendulkar: 162 runs
(a) Did C.K. Nayudu make a century? How many runs did he miss by?
(b) Who scored an exact century?
(c) How many runs did Tendulkar score beyond a century? Centuries in Cricket • C.K. Nayudu & Players 3 Marks
• C.K. Nayudu: 99 runs
• Kapil Dev: 122 runs
• Gavaskar: 100 runs
• Tendulkar: 162 runs
(a) Did C.K. Nayudu make a century? How many runs did he miss by?
(b) Who scored an exact century?
(c) How many runs did Tendulkar score beyond a century? Centuries in Cricket • C.K. Nayudu & Players 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Cricket Analysis:
• 1 Century = 100 runs.
(a) C.K. Nayudu:
• No, he scored 99 runs.
• Missed century by = 100 - 99 = 1 run.
(b) Exact Century:
• Gavaskar scored exactly 100 runs.
(c) Tendulkar's Extra Runs:
• Tendulkar scored = 162 runs.
• Runs beyond century = 162 - 100 = 62 runs.
• 1 Century = 100 runs.
(a) C.K. Nayudu:
• No, he scored 99 runs.
• Missed century by = 100 - 99 = 1 run.
(b) Exact Century:
• Gavaskar scored exactly 100 runs.
(c) Tendulkar's Extra Runs:
• Tendulkar scored = 162 runs.
• Runs beyond century = 162 - 100 = 62 runs.
CBSE Step-by-Step Marking Scheme
Correct analysis for C.K. Nayudu (No, missed by 1)
1.0 M
Correct player identified for exact century (Gavaskar)
1.0 M
Correct excess runs calculation for Tendulkar (62 runs)
1.0 M
Q6
On a number track from 90 to 150:
• Gabru the deer jumps on every 7th square starting from 90.
• Bunny the rabbit jumps on every 5th square starting from 99.
(a) Write Gabru's first 4 landing numbers after 90.
(b) Write Bunny's first 4 landing numbers after 99. Jumping Animals • Number Track Game 3 Marks
• Gabru the deer jumps on every 7th square starting from 90.
• Bunny the rabbit jumps on every 5th square starting from 99.
(a) Write Gabru's first 4 landing numbers after 90.
(b) Write Bunny's first 4 landing numbers after 99. Jumping Animals • Number Track Game 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Sequences:
(a) Gabru (+7):
• 90 + 7 = 97
• 97 + 7 = 104
• 104 + 7 = 111
• 111 + 7 = 118.
(b) Bunny (+5):
• 99 + 5 = 104
• 104 + 5 = 109
• 109 + 5 = 114
• 114 + 5 = 119.
(Notice that both Gabru and Bunny land on square 104!)
(a) Gabru (+7):
• 90 + 7 = 97
• 97 + 7 = 104
• 104 + 7 = 111
• 111 + 7 = 118.
(b) Bunny (+5):
• 99 + 5 = 104
• 104 + 5 = 109
• 109 + 5 = 114
• 114 + 5 = 119.
(Notice that both Gabru and Bunny land on square 104!)
CBSE Step-by-Step Marking Scheme
Correct sequence for Gabru (97, 104, 111, 118)
1.5 M
Correct sequence for Bunny (104, 109, 114, 119)
1.5 M
Q7
Fill in the blanks by counting in 50s:
200, 250, 300, ___, ___, 450, ___, 550.
How many 50s make 500 starting from 0? Counting by 50s • Century Jumps 3 Marks
200, 250, 300, ___, ___, 450, ___, 550.
How many 50s make 500 starting from 0? Counting by 50s • Century Jumps 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Completed Sequence: 200, 250, 300, 350, 400, 450, 500, 550.
• 50s in 500: 500 ÷ 50 = 10 fifty-rupee notes / steps make 500.
• Completed Sequence: 200, 250, 300, 350, 400, 450, 500, 550.
• 50s in 500: 500 ÷ 50 = 10 fifty-rupee notes / steps make 500.
CBSE Step-by-Step Marking Scheme
Correct blanks in sequence: 350, 400, 500
2.0 M
Correct division fact (10 fifties make 500)
1.0 M
Q8
Radhika, Gauri, Vicky, Indra, and Sunil were collecting Imli (tamarind) seeds:
• Radhika collected 24 seeds
• Gauri collected 47 seeds
• Sunil collected 38 seeds
• Indra collected 54 seeds
• Vicky collected 42 seeds.
(a) Who collected the most seeds?
(b) Sunil will collect ___ more seeds to equal Gauri.
(c) How many children collected more than 40 seeds? Textbook Story • Radhika's Tamarind Seeds 3 Marks
• Radhika collected 24 seeds
• Gauri collected 47 seeds
• Sunil collected 38 seeds
• Indra collected 54 seeds
• Vicky collected 42 seeds.
(a) Who collected the most seeds?
(b) Sunil will collect ___ more seeds to equal Gauri.
(c) How many children collected more than 40 seeds? Textbook Story • Radhika's Tamarind Seeds 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Analysis:
• (a) Most seeds: Indra with 54 seeds.
• (b) Seeds Sunil needs to equal Gauri: 47 - 38 = 9 more seeds.
• (c) Children with >40 seeds: Gauri (47), Indra (54), and Vicky (42) = 3 children.
• (a) Most seeds: Indra with 54 seeds.
• (b) Seeds Sunil needs to equal Gauri: 47 - 38 = 9 more seeds.
• (c) Children with >40 seeds: Gauri (47), Indra (54), and Vicky (42) = 3 children.
CBSE Step-by-Step Marking Scheme
Indra (54)
1 M
9 seeds needed
1 M
3 children
1 M
Q9
Top batsman scores in a match: C.K. (99), Dhoni (102), Kumble (162), Rahane (152), Dhawan (178), Kapil (127).
(a) How many players scored more than a century (100 runs)?
(b) What is the difference between Dhawan's score and Dhoni's score?
(c) Who scored two runs less than a century and a half (148 runs)? Cricket Records • One-Day International Scores 3 Marks
(a) How many players scored more than a century (100 runs)?
(b) What is the difference between Dhawan's score and Dhoni's score?
(c) Who scored two runs less than a century and a half (148 runs)? Cricket Records • One-Day International Scores 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) Players scoring >100: Dhoni (102), Kumble (162), Rahane (152), Dhawan (178), Kapil (127) = 5 players.
• (b) Difference: 178 - 102 = 76 runs.
• (c) Score = 148 runs: (None on list scored exactly 148; closest was Rahane at 152).
• (a) Players scoring >100: Dhoni (102), Kumble (162), Rahane (152), Dhawan (178), Kapil (127) = 5 players.
• (b) Difference: 178 - 102 = 76 runs.
• (c) Score = 148 runs: (None on list scored exactly 148; closest was Rahane at 152).
CBSE Step-by-Step Marking Scheme
5 players scored >100
1 M
Difference 178 - 102 = 76
1 M
148 analysis
1 M
Q10
Lazy Crazy shop sells items only in packets of 100, packets of 10, and loose items. Find how a customer buying 243 items will receive them.
Lazy Crazy Shop • Bundles and Packets
2 Marks
✅ Step-by-Step Model Answer & Solution:
Place Value Packaging:
• Number of items = 243.
• Hundreds place = 2 → 2 packets of 100 (200 items).
• Tens place = 4 → 4 packets of 10 (40 items).
• Ones place = 3 → 3 loose items.
Total = 200 + 40 + 3 = 243.
• Number of items = 243.
• Hundreds place = 2 → 2 packets of 100 (200 items).
• Tens place = 4 → 4 packets of 10 (40 items).
• Ones place = 3 → 3 loose items.
Total = 200 + 40 + 3 = 243.
CBSE Step-by-Step Marking Scheme
2 packets of 100, 4 of 10, 3 loose items
2 M
Q11
At the Lazy Crazy shop, customers pay only in ₹100 notes, ₹10 notes, and ₹1 coins. How will an animal pay ₹420 and ₹143?
Lazy Crazy Money • Currency Note Bundles
3 Marks
✅ Step-by-Step Model Answer & Solution:
Currency Breakdown:
• For ₹420:
• 4 notes of ₹100 = ₹400
• 2 notes of ₹10 = ₹20
• 0 coins of ₹1 = ₹0.
• For ₹143:
• 1 note of ₹100 = ₹100
• 4 notes of ₹10 = ₹40
• 3 coins of ₹1 = ₹3.
• For ₹420:
• 4 notes of ₹100 = ₹400
• 2 notes of ₹10 = ₹20
• 0 coins of ₹1 = ₹0.
• For ₹143:
• 1 note of ₹100 = ₹100
• 4 notes of ₹10 = ₹40
• 3 coins of ₹1 = ₹3.
CBSE Step-by-Step Marking Scheme
₹420 breakdown correct
1.5 M
₹143 breakdown correct
1.5 M
Q12
Match the clues with the correct numbers:
(1) I have 9 in my name and am very close to 90 — (A) 100
(2) If you hit a 4 after me you score a century — (B) 89
(3) I am equal to ten notes of 10 — (C) 96. Who Am I? • Match the Number 3 Marks
(1) I have 9 in my name and am very close to 90 — (A) 100
(2) If you hit a 4 after me you score a century — (B) 89
(3) I am equal to ten notes of 10 — (C) 96. Who Am I? • Match the Number 3 Marks
✅ Step-by-Step Model Answer & Solution:
Matching:
• (1) Close to 90 with 9 in name = (B) 89.
• (2) 100 - 4 = (C) 96.
• (3) Ten notes of 10 = 10 × 10 = (A) 100.
• (1) Close to 90 with 9 in name = (B) 89.
• (2) 100 - 4 = (C) 96.
• (3) Ten notes of 10 = 10 × 10 = (A) 100.
CBSE Step-by-Step Marking Scheme
1-B, 2-C, 3-A correct
3 M
Q13
Write the next three numbers for each jump pattern:
(a) Jump 2 steps forward: 110, 112, 114, ___, ___, ___
(b) Jump 5 steps forward: 150, 155, 160, ___, ___, ___
(c) Jump 10 steps backward: 190, 180, 170, ___, ___, ___. Jump Steps • Number Patterns 3 Marks
(a) Jump 2 steps forward: 110, 112, 114, ___, ___, ___
(b) Jump 5 steps forward: 150, 155, 160, ___, ___, ___
(c) Jump 10 steps backward: 190, 180, 170, ___, ___, ___. Jump Steps • Number Patterns 3 Marks
✅ Step-by-Step Model Answer & Solution:
Patterns:
• (a) Adding 2: 116, 118, 120.
• (b) Adding 5: 165, 170, 175.
• (c) Subtracting 10: 160, 150, 140.
• (a) Adding 2: 116, 118, 120.
• (b) Adding 5: 165, 170, 175.
• (c) Subtracting 10: 160, 150, 140.
CBSE Step-by-Step Marking Scheme
(a) 116, 118, 120
1 M
(b) 165, 170, 175
1 M
(c) 160, 150, 140
1 M
Q14
Circle the larger number in each pair: (a) 149 and 194 (b) 170 and 107 (c) 199 and 200.
Practice Time • Comparing Number Pairs
1.5 Marks
✅ Step-by-Step Model Answer & Solution:
Larger Numbers:
• (a) 194 is larger than 149 (194 > 149).
• (b) 170 is larger than 107 (170 > 107).
• (c) 200 is larger than 199 (200 > 199).
• (a) 194 is larger than 149 (194 > 149).
• (b) 170 is larger than 107 (170 > 107).
• (c) 200 is larger than 199 (200 > 199).
CBSE Step-by-Step Marking Scheme
194, 170, 200 identified
1.5 M
Q15
Write in expanded form: (a) 198 (b) 105 (c) 176.
Expanded Form • Three Digits
1.5 Marks
✅ Step-by-Step Model Answer & Solution:
Expanded Forms:
• (a) 198 = 100 + 90 + 8.
• (b) 105 = 100 + 0 + 5.
• (c) 176 = 100 + 70 + 6.
• (a) 198 = 100 + 90 + 8.
• (b) 105 = 100 + 0 + 5.
• (c) 176 = 100 + 70 + 6.
CBSE Step-by-Step Marking Scheme
All 3 correct expanded forms
1.5 M
Q16
Amina has 124 sea shells. Her brother gives her 36 more shells. How many shells does Amina have now?
Word Problem • Shells Collection
2 Marks
✅ Step-by-Step Model Answer & Solution:
Addition:
124 + 36 = 124 + 6 + 30 = 130 + 30 = 160 shells.
124 + 36 = 124 + 6 + 30 = 130 + 30 = 160 shells.
CBSE Step-by-Step Marking Scheme
124 + 36 = 160 with working
2 M
Q17
A cricketer is batting on 78 runs. How many runs does he need to reach: (a) 100 runs (a century)? (b) 150 runs?
Century Milestone • Runs Needed
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) For century: 100 - 78 = 22 runs.
• (b) For 150 runs: 150 - 78 = 72 runs.
• (a) For century: 100 - 78 = 22 runs.
• (b) For 150 runs: 150 - 78 = 72 runs.
CBSE Step-by-Step Marking Scheme
22 runs for century
1 M
72 runs for 150
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Wildlife Sanctuary Deer Count
Real-World Math Context: Forest rangers recorded deer sightings across four zones: North Zone (214), South Zone (189), East Zone (305), and West Zone (292).
Analytical Task: Which zone recorded the lowest deer count? How many total deer were sighted in the North and West Zones combined?
1. Comparing sightings: 189 < 214 < 292 < 305.
• Lowest count: South Zone with 189 deer.
2. North Zone (214) + West Zone (292) = 214 + 292 = 506 deer.
• Lowest count: South Zone with 189 deer.
2. North Zone (214) + West Zone (292) = 214 + 292 = 506 deer.
CBSE Assessment Rubric: 1.5M comparison and lowest zone + 1.5M addition of 214 + 292.
3
Unit 2: Number Concepts & Place Value • Class 3 Mathematics (Classic CBSE)
Chapter 3: Give and Take
Addition, 100-Chart Jumps, Word Problems & Story-Based Arithmetic
Chapter Highlights, Mathematical Ideas & Key Properties
- Using a 100-chart to add: jumping up by 10s and right by 1s.
- Mental addition: adding 10, 20, or 30 quickly to any 2-digit number.
- Addition of 3-digit numbers with regrouping across ones and tens.
- Breaking numbers into easy tens to solve word problems mentally.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Using the 100-chart jump strategy, solve: (a) 47 + 20, (b) 28 + 35, (c) 65 + 19. Show the jumps.
100-Chart Jump Strategy • Mental Addition
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 47 + 20: From 47, jump 2 rows directly up (+20) = 67.
• (b) 28 + 35: From 28, jump 3 rows up (+30) to 58; then step 5 rooms right (+5) = 63.
• (c) 65 + 19: Adding 19 is jumping 2 rows up (+20 to 85) and taking 1 step back (-1) = 84.
• (a) 47 + 20: From 47, jump 2 rows directly up (+20) = 67.
• (b) 28 + 35: From 28, jump 3 rows up (+30) to 58; then step 5 rooms right (+5) = 63.
• (c) 65 + 19: Adding 19 is jumping 2 rows up (+20 to 85) and taking 1 step back (-1) = 84.
CBSE Step-by-Step Marking Scheme
Correct mental jump for (a)
1.0 M
Correct mental jump for (b)
1.0 M
Clever +20 and -1 jump for (c)
1.0 M
Q2
A train compartment has 132 passengers. At the next junction, 69 more passengers get in. How many passengers are in the compartment now? Show the column working.
3-Digit Addition with Regrouping
3 Marks
✅ Step-by-Step Model Answer & Solution:
Column Addition:
H T O
1 3 2
+ 6 9
---------
2 0 1
• Working:
1. Ones: 2 + 9 = 11 → Write 1 in Ones place, carry 1 Ten.
2. Tens: 3 + 6 + 1 (carry) = 10 → Write 0 in Tens place, carry 1 Hundred.
3. Hundreds: 1 + 1 (carry) = 2 Hundreds.
• Total passengers = 201.
H T O
1 3 2
+ 6 9
---------
2 0 1
• Working:
1. Ones: 2 + 9 = 11 → Write 1 in Ones place, carry 1 Ten.
2. Tens: 3 + 6 + 1 (carry) = 10 → Write 0 in Tens place, carry 1 Hundred.
3. Hundreds: 1 + 1 (carry) = 2 Hundreds.
• Total passengers = 201.
CBSE Step-by-Step Marking Scheme
Correct column alignment and regrouping steps
1.5 M
Correct final sum (201 passengers)
1.5 M
Q3
A factory made 270 light bulbs on the first day and 149 light bulbs on the second day. How many bulbs were made altogether? Did they cross 400 bulbs?
Real-Life Problem Solving • Animal Count
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Day 1 bulbs = 270
• Day 2 bulbs = 149
• Total bulbs = 270 + 149 = 419 bulbs.
• Since 419 is greater than 400, yes, they successfully crossed 400 bulbs by 19 bulbs.
• Day 1 bulbs = 270
• Day 2 bulbs = 149
• Total bulbs = 270 + 149 = 419 bulbs.
• Since 419 is greater than 400, yes, they successfully crossed 400 bulbs by 19 bulbs.
CBSE Step-by-Step Marking Scheme
Correct addition (270 + 149 = 419)
1.0 M
Accurate comparison with 400 threshold
1.0 M
Q4
Kittu has a house with 100 rooms numbered 1 to 100. Jumping up one row means adding 10 (+10).
(a) Kittu starts at room 14 and jumps 2 rows up. Which room does he reach?
(b) He is in room 47 and jumps 1 row down and 2 steps left. Which room is he in now?
(c) Write the shortcut to go from room 28 to room 58. Kittu's Home Maze • Jumping 10s on a 100-Grid 3 Marks
(a) Kittu starts at room 14 and jumps 2 rows up. Which room does he reach?
(b) He is in room 47 and jumps 1 row down and 2 steps left. Which room is he in now?
(c) Write the shortcut to go from room 28 to room 58. Kittu's Home Maze • Jumping 10s on a 100-Grid 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Grid Navigation:
(a) Room 14 + 2 rows:
• 14 + 10 + 10 = 14 + 20 = Room 34.
(b) From 47: 1 row down, 2 steps left:
• 1 row down = 47 - 10 = 37.
• 2 steps left = 37 - 2 = Room 35.
(c) From 28 to 58:
• Difference = 58 - 28 = 30.
• Shortcut: Jump 3 rows straight up (3 jumps of 10).
(a) Room 14 + 2 rows:
• 14 + 10 + 10 = 14 + 20 = Room 34.
(b) From 47: 1 row down, 2 steps left:
• 1 row down = 47 - 10 = 37.
• 2 steps left = 37 - 2 = Room 35.
(c) From 28 to 58:
• Difference = 58 - 28 = 30.
• Shortcut: Jump 3 rows straight up (3 jumps of 10).
CBSE Step-by-Step Marking Scheme
Correct room for (a): Room 34
1.0 M
Correct room for (b): Room 35
1.0 M
Correct shortcut for (c): 3 rows straight up (30)
1.0 M
Q5
Solve the following additions using mental breakdown (splitting into tens and ones):
(a) 37 + 22
(b) 73 + 24
(c) 56 + 21 Mental Addition Tricks • Making Tens 3 Marks
(a) 37 + 22
(b) 73 + 24
(c) 56 + 21 Mental Addition Tricks • Making Tens 3 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Splitting Method:
• (a) 37 + 22: (30 + 20) + (7 + 2) = 50 + 9 = 59.
• (b) 73 + 24: (70 + 20) + (3 + 4) = 90 + 7 = 97.
• (c) 56 + 21: (50 + 20) + (6 + 1) = 70 + 7 = 77.
• (a) 37 + 22: (30 + 20) + (7 + 2) = 50 + 9 = 59.
• (b) 73 + 24: (70 + 20) + (3 + 4) = 90 + 7 = 97.
• (c) 56 + 21: (50 + 20) + (6 + 1) = 70 + 7 = 77.
CBSE Step-by-Step Marking Scheme
Correct breakdown and answer for (a): 59
1.0 M
Correct breakdown and answer for (b): 97
1.0 M
Correct breakdown and answer for (c): 77
1.0 M
Q6
A grasshopper ate 68 green leaves on Monday and 47 green leaves on Tuesday.
(a) How many leaves did it eat altogether on both days?
(b) How many more leaves did it eat on Monday than on Tuesday? Word Problem • Grasshopper & Leaves 3 Marks
(a) How many leaves did it eat altogether on both days?
(b) How many more leaves did it eat on Monday than on Tuesday? Word Problem • Grasshopper & Leaves 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Total Leaves:
• 68 + 47 = (60 + 40) + (8 + 7) = 100 + 15 = 115 leaves.
(b) Difference:
• 68 - 47 = (68 - 40) - 7 = 28 - 7 = 21 more leaves.
(a) Total Leaves:
• 68 + 47 = (60 + 40) + (8 + 7) = 100 + 15 = 115 leaves.
(b) Difference:
• 68 - 47 = (68 - 40) - 7 = 28 - 7 = 21 more leaves.
CBSE Step-by-Step Marking Scheme
Correct sum (115 leaves)
1.5 M
Correct difference (21 leaves)
1.5 M
Q7
Find two numbers whose sum is 75 and whose difference is 15.
Number Puzzle • Finding Hidden Pairs
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Puzzle Solution:
• Let the two numbers be A and B.
• Sum = A + B = 75.
• Difference = A - B = 15.
• Adding the two equations: 2 × A = 75 + 15 = 90.
• Larger number (A) = 90 ÷ 2 = 45.
• Smaller number (B) = 75 - 45 = 30.
• Verification:
- Sum: 45 + 30 = 75.
- Difference: 45 - 30 = 15.
• The numbers are 45 and 30.
• Let the two numbers be A and B.
• Sum = A + B = 75.
• Difference = A - B = 15.
• Adding the two equations: 2 × A = 75 + 15 = 90.
• Larger number (A) = 90 ÷ 2 = 45.
• Smaller number (B) = 75 - 45 = 30.
• Verification:
- Sum: 45 + 30 = 75.
- Difference: 45 - 30 = 15.
• The numbers are 45 and 30.
CBSE Step-by-Step Marking Scheme
Systematic method shown to find numbers
1.5 M
Correct numbers (45 and 30) with verification
1.5 M
Q8
In Chapter 3 ('Give and Take'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Give and Take', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Wildlife Forest Census
Real-World Math Context: During an annual bird count in Keoladeo National Park, volunteers spotted 147 migratory cranes and 185 resident ducks on Saturday.
Analytical Task: What was the total number of birds spotted? If the birders expected at least 350 birds, how many more birds were needed to meet their expectation?
1. Total birds = 147 + 185 = 332 birds.
2. Expected count = 350 birds.
3. Shortfall = 350 - 332 = 18 birds.
2. Expected count = 350 birds.
3. Shortfall = 350 - 332 = 18 birds.
CBSE Assessment Rubric: 1.5M addition of 147 + 185 + 1.5M subtraction from 350.
4
Unit 3: Measurement & Geometry • Class 3 Mathematics (Classic CBSE)
Chapter 4: Long and Short
Length Measurement, Centimetres (cm) & Metres (m), Ruler Usage & Height Charts
Chapter Highlights, Mathematical Ideas & Key Properties
- Measuring length using non-standard units (fingers, hand spans) vs standard units.
- Using a 15 cm ruler correctly: starting from 0, not from 1.
- Understanding standard units: Centimetre (cm), Metre (m), and Kilometre (km).
- 1 Metre = 100 Centimetres (1 m = 100 cm); 1 Kilometre = 1000 Metres.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Which unit (cm, m, or km) is best suited to measure: (a) The length of a safety pin, (b) The height of a coconut tree, (c) The distance between Delhi and Agra, (d) The length of a 500-rupee currency note?
Unit Selection • cm, m, or km
2 Marks
✅ Step-by-Step Model Answer & Solution:
Appropriate Units:
• (a) Safety pin: Centimetres (cm) (small object)
• (b) Coconut tree: Metres (m) (tall height)
• (c) Distance between Delhi and Agra: Kilometres (km) (intercity travel)
• (d) Currency note: Centimetres (cm) (approx 15 cm).
• (a) Safety pin: Centimetres (cm) (small object)
• (b) Coconut tree: Metres (m) (tall height)
• (c) Distance between Delhi and Agra: Kilometres (km) (intercity travel)
• (d) Currency note: Centimetres (cm) (approx 15 cm).
CBSE Step-by-Step Marking Scheme
Correct units for small objects (cm)
1.0 M
Correct units for tree (m) and intercity distance (km)
1.0 M
Q2
Rohan broke his ruler. The scale now starts from 3 cm instead of 0. If he places a wooden crayon with its left tip at 3 cm and the right tip reaches 11 cm, what is the actual length of the crayon?
Ruler Measurement Error Analysis
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculation:
• Starting point = 3 cm
• Ending point = 11 cm
• Actual length = Ending point - Starting point = 11 cm - 3 cm = 8 cm.
• Starting point = 3 cm
• Ending point = 11 cm
• Actual length = Ending point - Starting point = 11 cm - 3 cm = 8 cm.
CBSE Step-by-Step Marking Scheme
Recognizing subtraction of starting offset
1.0 M
Correct calculation (11 - 3 = 8 cm)
1.0 M
Q3
In Class 3, Amit's height is 1 metre 25 centimetres. Sanya is 18 cm taller than Amit. What is Sanya's height in metres and centimetres?
Height Chart Comparison • Word Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Amit's height = 1 m 25 cm
• Sanya's additional height = 18 cm
• Sanya's height = 1 m + (25 cm + 18 cm)
• 25 + 18 = 43 cm
• Sanya's total height = 1 metre 43 centimetres (1 m 43 cm).
• Amit's height = 1 m 25 cm
• Sanya's additional height = 18 cm
• Sanya's height = 1 m + (25 cm + 18 cm)
• 25 + 18 = 43 cm
• Sanya's total height = 1 metre 43 centimetres (1 m 43 cm).
CBSE Step-by-Step Marking Scheme
Correct addition of centimetre values (25 + 18 = 43)
1.0 M
Clear final representation in m and cm
1.0 M
Q4
Which unit will you use to measure the following: Centimetre (cm) or Metre (m)?
(a) Length of a pencil.
(b) Height of a sugarcane plant.
(c) Width of your fingernail.
(d) Distance between two lampposts on a road. Measurement Units • Centimetre vs Metre 4 Marks
(a) Length of a pencil.
(b) Height of a sugarcane plant.
(c) Width of your fingernail.
(d) Distance between two lampposts on a road. Measurement Units • Centimetre vs Metre 4 Marks
✅ Step-by-Step Model Answer & Solution:
Appropriate Units:
• (a) Length of a pencil: Centimetre (cm).
• (b) Height of a sugarcane plant: Metre (m).
• (c) Width of your fingernail: Centimetre (cm) (or millimetre).
• (d) Distance between two lampposts: Metre (m).
• (a) Length of a pencil: Centimetre (cm).
• (b) Height of a sugarcane plant: Metre (m).
• (c) Width of your fingernail: Centimetre (cm) (or millimetre).
• (d) Distance between two lampposts: Metre (m).
CBSE Step-by-Step Marking Scheme
Correct units for (a) and (b)
2.0 M
Correct units for (c) and (d)
2.0 M
Q5
In the story, a farmer comes to Lali to buy 7 arms of rope. Lali measures the rope with her small arm.
(a) Why was the rope short when the farmer measured it with his own arm?
(b) What should the farmer do to get the right length using non-standard units?
(c) Why do we use standard rulers instead of arm-spans? Lali's Rope Measurement • Non-Standard Units 3 Marks
(a) Why was the rope short when the farmer measured it with his own arm?
(b) What should the farmer do to get the right length using non-standard units?
(c) Why do we use standard rulers instead of arm-spans? Lali's Rope Measurement • Non-Standard Units 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Explanation:
(a) Reason:
• The farmer is an adult and has a much longer arm than young Lali. 7 arms of Lali's length is shorter than 7 arms of the farmer's length.
(b) Solution with Non-Standard Unit:
• The farmer should measure the rope using his own arm, or measure 7 times his own arm-span.
(c) Need for Standard Rulers:
• Standard units like metres and centimetres do not change from person to person. A 1-metre ruler is exactly the same length worldwide, ensuring fairness in trade.
(a) Reason:
• The farmer is an adult and has a much longer arm than young Lali. 7 arms of Lali's length is shorter than 7 arms of the farmer's length.
(b) Solution with Non-Standard Unit:
• The farmer should measure the rope using his own arm, or measure 7 times his own arm-span.
(c) Need for Standard Rulers:
• Standard units like metres and centimetres do not change from person to person. A 1-metre ruler is exactly the same length worldwide, ensuring fairness in trade.
CBSE Step-by-Step Marking Scheme
Explanation of arm length difference between adult and child
1.0 M
Correct solution for farmer measuring himself
1.0 M
Need for universal standard units (m, cm)
1.0 M
Q6
Look at a standard 15 cm plastic ruler:
(a) An eraser starts at mark 2 cm and ends at mark 7 cm. What is the length of the eraser?
(b) A leaf starts at mark 4 cm and ends at mark 12 cm. What is the length of the leaf? Ruler Measurement • Reading cm Scales 3 Marks
(a) An eraser starts at mark 2 cm and ends at mark 7 cm. What is the length of the eraser?
(b) A leaf starts at mark 4 cm and ends at mark 12 cm. What is the length of the leaf? Ruler Measurement • Reading cm Scales 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Calculations:
(a) Eraser Length:
• End mark - Start mark = 7 cm - 2 cm = 5 cm.
(b) Leaf Length:
• End mark - Start mark = 12 cm - 4 cm = 8 cm.
(a) Eraser Length:
• End mark - Start mark = 7 cm - 2 cm = 5 cm.
(b) Leaf Length:
• End mark - Start mark = 12 cm - 4 cm = 8 cm.
CBSE Step-by-Step Marking Scheme
Correct calculation for eraser (7 - 2 = 5 cm)
1.5 M
Correct calculation for leaf (12 - 4 = 8 cm)
1.5 M
Q7
Convert the following measurements:
(a) 4 m into centimetres.
(b) 2 m 75 cm into centimetres.
(c) 350 cm into metres and centimetres. Unit Conversions • Metres and Centimetres 3 Marks
(a) 4 m into centimetres.
(b) 2 m 75 cm into centimetres.
(c) 350 cm into metres and centimetres. Unit Conversions • Metres and Centimetres 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions (1 m = 100 cm):
• (a) 4 m: 4 × 100 = 400 cm.
• (b) 2 m 75 cm: (2 × 100) + 75 = 200 + 75 = 275 cm.
• (c) 350 cm: 300 cm + 50 cm = 3 m 50 cm.
• (a) 4 m: 4 × 100 = 400 cm.
• (b) 2 m 75 cm: (2 × 100) + 75 = 200 + 75 = 275 cm.
• (c) 350 cm: 300 cm + 50 cm = 3 m 50 cm.
CBSE Step-by-Step Marking Scheme
Correct answer for (a): 400 cm
1.0 M
Correct answer for (b): 275 cm
1.0 M
Correct answer for (c): 3 m 50 cm
1.0 M
Q8
In Chapter 4 ('Long and Short'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Long and Short', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Inter-School Long Jump Competition
Real-World Math Context: In the primary sports day long jump final, Danish jumped 2 metres 80 centimetres. Gurjeet jumped 15 cm less than Danish, while Rehana jumped 35 cm more than Danish.
Analytical Task: How far did Gurjeet jump? How far did Rehana jump? Did Rehana cross the 3-metre mark?
1. Danish = 2 m 80 cm.
2. Gurjeet = 2 m 80 cm - 15 cm = 2 metres 65 centimetres.
3. Rehana = 2 m 80 cm + 35 cm = 2 m + 115 cm = 2 m + 1 m 15 cm = 3 metres 15 centimetres.
4. Since 3 m 15 cm > 3 m, yes, Rehana crossed the 3-metre mark.
2. Gurjeet = 2 m 80 cm - 15 cm = 2 metres 65 centimetres.
3. Rehana = 2 m 80 cm + 35 cm = 2 m + 115 cm = 2 m + 1 m 15 cm = 3 metres 15 centimetres.
4. Since 3 m 15 cm > 3 m, yes, Rehana crossed the 3-metre mark.
CBSE Assessment Rubric: 1M Gurjeet calculation + 1M Rehana calculation + 1M 3m threshold check.
5
Unit 3: Measurement & Geometry • Class 3 Mathematics (Classic CBSE)
Chapter 5: Shapes and Designs
2D Geometrical Shapes, Corners, Edges, Floor Patterns, Weaving & Tangrams
Chapter Highlights, Mathematical Ideas & Key Properties
- Comparing edges: straight edges vs curved edges.
- Corners (vertices) in 2D shapes: triangles (3), quadrilaterals (4), circles (0).
- Floor tiling patterns: tessellations that tile without gaps.
- Traditional Indian textile weaving patterns and borders.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Look at these objects: (1) A sheet of paper, (2) A wheel, (3) A blackboard, (4) An egg. State whether each object has straight edges or curved edges, and how many corners it has.
Corner & Edge Classification
2 Marks
✅ Step-by-Step Model Answer & Solution:
Classification:
• 1. Sheet of paper: Straight edges (4) → 4 corners.
• 2. Wheel: Curved edge (1 continuous circular boundary) → 0 corners.
• 3. Blackboard: Straight edges (4) → 4 corners.
• 4. Egg: Curved surface → 0 corners.
• 1. Sheet of paper: Straight edges (4) → 4 corners.
• 2. Wheel: Curved edge (1 continuous circular boundary) → 0 corners.
• 3. Blackboard: Straight edges (4) → 4 corners.
• 4. Egg: Curved surface → 0 corners.
CBSE Step-by-Step Marking Scheme
Correct straight/curved edge identification
1.0 M
Correct corner counts for all 4 items
1.0 M
Q2
In a standard 7-piece Tangram puzzle: (a) How many triangles are there? (b) Are all triangles of the same size? (c) Name the two other shapes in the puzzle.
Tangram Dissection • 7-Piece Tangram
3 Marks
✅ Step-by-Step Model Answer & Solution:
Tangram Composition:
• (a) Triangles: There are 5 triangles.
• (b) Sizes: No, they are of different sizes: 2 large triangles, 1 medium triangle, and 2 small triangles.
• (c) Other shapes: 1 Square and 1 Parallelogram.
• (a) Triangles: There are 5 triangles.
• (b) Sizes: No, they are of different sizes: 2 large triangles, 1 medium triangle, and 2 small triangles.
• (c) Other shapes: 1 Square and 1 Parallelogram.
CBSE Step-by-Step Marking Scheme
Correct count of triangles (5)
1.0 M
Distinction between large, medium, small triangles
1.0 M
Naming square and parallelogram
1.0 M
Q3
Explain what a tessellation is. Draw or describe how a combination of triangles can tile a floor completely without leaving any gaps.
Tessellation & Floor Patterns
2 Marks
✅ Step-by-Step Model Answer & Solution:
Explanation:
• A tessellation is a pattern made of repeating geometric shapes that covers a flat surface completely without any gaps or overlaps.
• Triangle Tiling: Two identical triangles can be placed together along their diagonal to form a rectangle. These rectangles can then be arranged in neat rows and columns to cover any floor seamlessly.
• A tessellation is a pattern made of repeating geometric shapes that covers a flat surface completely without any gaps or overlaps.
• Triangle Tiling: Two identical triangles can be placed together along their diagonal to form a rectangle. These rectangles can then be arranged in neat rows and columns to cover any floor seamlessly.
CBSE Step-by-Step Marking Scheme
Definition of tessellation (no gaps, no overlaps)
1.0 M
Explanation of triangle pairing to form rectangles
1.0 M
Q4
Look at a standard 6-pointed star figure made of overlapping triangles:
(a) How many small triangles can you count?
(b) How many corners (vertices) does the 6-pointed star have?
(c) Does a circle have any corners? Counting Shapes • Star and Geometrical Figures 3 Marks
(a) How many small triangles can you count?
(b) How many corners (vertices) does the 6-pointed star have?
(c) Does a circle have any corners? Counting Shapes • Star and Geometrical Figures 3 Marks
✅ Step-by-Step Model Answer & Solution:
Shape Analysis:
• (a) Small Triangles: There are 6 outer pointed triangles, plus 2 large central overlapping triangles = 8 triangles in total.
• (b) Corners: The 6 outward points form 6 corners (or 12 vertices counting inner corners).
• (c) Circle Corners: No, a circle is a continuous smooth curve with 0 corners.
• (a) Small Triangles: There are 6 outer pointed triangles, plus 2 large central overlapping triangles = 8 triangles in total.
• (b) Corners: The 6 outward points form 6 corners (or 12 vertices counting inner corners).
• (c) Circle Corners: No, a circle is a continuous smooth curve with 0 corners.
CBSE Step-by-Step Marking Scheme
Correct triangle count with explanation
1.0 M
Correct corner identification
1.0 M
Correct circle property (0 corners)
1.0 M
Q5
Identify the repeating rule (unit of pattern) in each border design:
(a) ▲ ▼ ▲ ▼ ▲ ▼ ___ ___
(b) 🔲 ⚪ 🔲 ⚪ 🔲 ⚪ ___ ___
(c) Draw the next two figures for each pattern. Weaver's Borders • Repeating Patterns 3 Marks
(a) ▲ ▼ ▲ ▼ ▲ ▼ ___ ___
(b) 🔲 ⚪ 🔲 ⚪ 🔲 ⚪ ___ ___
(c) Draw the next two figures for each pattern. Weaver's Borders • Repeating Patterns 3 Marks
✅ Step-by-Step Model Answer & Solution:
Patterns & Next Terms:
• (a) Up and Down Triangles:
- Repeating unit: [▲, ▼]
- Next two figures: ▲, ▼.
• (b) Square and Circle:
- Repeating unit: [🔲, ⚪]
- Next two figures: 🔲, ⚪.
• (a) Up and Down Triangles:
- Repeating unit: [▲, ▼]
- Next two figures: ▲, ▼.
• (b) Square and Circle:
- Repeating unit: [🔲, ⚪]
- Next two figures: 🔲, ⚪.
CBSE Step-by-Step Marking Scheme
Identification of repeating core unit for both patterns
1.5 M
Accurate continuation with next two shapes
1.5 M
Q6
In the 'Paper Clapper' activity described in the textbook:
(a) What shape of paper is used to begin with?
(b) How many times is the paper folded along its edges?
(c) What causes the loud 'pop' or clapping sound when swung down sharply? Clapper Activity • Paper Craft Geometry 3 Marks
(a) What shape of paper is used to begin with?
(b) How many times is the paper folded along its edges?
(c) What causes the loud 'pop' or clapping sound when swung down sharply? Clapper Activity • Paper Craft Geometry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Paper Clapper Mechanics:
• (a) Paper Shape: A standard rectangular sheet of paper (like newspaper or scrap notebook paper).
• (b) Folds: It is folded lengthwise in half, then folded down several times into a thick band, and finally folded in half across the middle.
• (c) The Clapping Sound: When swung sharply downward, the sudden rush of air opens the inner folded pocket violently, snapping the paper open to produce the loud clapping sound.
• (a) Paper Shape: A standard rectangular sheet of paper (like newspaper or scrap notebook paper).
• (b) Folds: It is folded lengthwise in half, then folded down several times into a thick band, and finally folded in half across the middle.
• (c) The Clapping Sound: When swung sharply downward, the sudden rush of air opens the inner folded pocket violently, snapping the paper open to produce the loud clapping sound.
CBSE Step-by-Step Marking Scheme
Correct initial paper shape (rectangular)
1.0 M
Clear description of folding sequence
1.0 M
Physical explanation of air pressure opening paper pocket
1.0 M
Q7
Classify the following 6 objects into 'Straight Edges Only' and 'Curved Edges / Both':
Postcard, Coin, Blackboard, CD/DVD, Book, Bottle cap. Straight Edges vs Curved Edges 3 Marks
Postcard, Coin, Blackboard, CD/DVD, Book, Bottle cap. Straight Edges vs Curved Edges 3 Marks
✅ Step-by-Step Model Answer & Solution:
Classification:
• Straight Edges Only:
1. Postcard
2. Blackboard
3. Book
• Curved Edges / Both:
1. Coin (Curved circular edge)
2. CD/DVD (Curved circular edge)
3. Bottle cap (Curved circular edge).
• Straight Edges Only:
1. Postcard
2. Blackboard
3. Book
• Curved Edges / Both:
1. Coin (Curved circular edge)
2. CD/DVD (Curved circular edge)
3. Bottle cap (Curved circular edge).
CBSE Step-by-Step Marking Scheme
Correct straight-edge objects classified (3 objects)
1.5 M
Correct curved-edge objects classified (3 objects)
1.5 M
Q8
In Chapter 5 ('Shapes and Designs'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Shapes and Designs', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Handloom Saree Border Design
Real-World Math Context: A master weaver from Varanasi designs a border pattern using alternating red squares and yellow triangles. Every 10 cm repeat of the pattern uses 2 squares and 4 triangles.
Analytical Task: How many squares and how many triangles will be woven along a 1-metre (100 cm) saree border?
1. Total border length = 1 metre = 100 cm.
2. Number of 10 cm pattern repeats = 100 ÷ 10 = 10 repeats.
3. Squares needed = 10 × 2 = 20 squares.
4. Triangles needed = 10 × 4 = 40 triangles.
2. Number of 10 cm pattern repeats = 100 ÷ 10 = 10 repeats.
3. Squares needed = 10 × 2 = 20 squares.
4. Triangles needed = 10 × 4 = 40 triangles.
CBSE Assessment Rubric: 1M meter to cm conversion + 1M pattern repeats + 1M shape counts.
6
Unit 4: Advanced Operations & Practical Math • Class 3 Mathematics (Classic CBSE)
Chapter 6: Fun with Give and Take
Subtraction with Borrowing, Checking by Addition, Cricket Runs & Story Problems
Chapter Highlights, Mathematical Ideas & Key Properties
- Subtraction of 3-digit numbers with regrouping across tens and hundreds.
- Verifying subtraction using inverse addition (Difference + Subtrahend = Minuend).
- Estimating differences by rounding to nearest 10 or 100.
- Solving multi-step real-world problems involving shopping and transport.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Solve: 503 - 247. Show step-by-step regrouping across zeroes. Then check your answer by addition.
Subtraction with Regrouping • Column Working
4 Marks
✅ Step-by-Step Model Answer & Solution:
Working:
H T O
5 0 3
- 2 4 7
---------
2 5 6
Regrouping Explanation:
1. Ones: 3 - 7 cannot be done. Tens place has 0, so borrow from Hundreds place.
2. Borrow 1 Hundred from 5 (leaves 4 Hundreds) → Tens becomes 10.
3. Borrow 1 Ten from 10 (leaves 9 Tens) → Ones becomes 13.
4. Ones: 13 - 7 = 6.
5. Tens: 9 - 4 = 5.
6. Hundreds: 4 - 2 = 2.
Check by Addition: 256 + 247 = 503 ✓ Verified correct.
H T O
5 0 3
- 2 4 7
---------
2 5 6
Regrouping Explanation:
1. Ones: 3 - 7 cannot be done. Tens place has 0, so borrow from Hundreds place.
2. Borrow 1 Hundred from 5 (leaves 4 Hundreds) → Tens becomes 10.
3. Borrow 1 Ten from 10 (leaves 9 Tens) → Ones becomes 13.
4. Ones: 13 - 7 = 6.
5. Tens: 9 - 4 = 5.
6. Hundreds: 4 - 2 = 2.
Check by Addition: 256 + 247 = 503 ✓ Verified correct.
CBSE Step-by-Step Marking Scheme
Correct borrowing across zero
2.0 M
Correct difference (256)
1.0 M
Correct addition check (256 + 247 = 503)
1.0 M
Q2
In a one-day cricket match, Sri Lanka made 232 runs. India has scored 123 runs so far. How many runs does India still need to win the match?
Cricket Match Scoreboard • Target Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Sri Lanka's score = 232 runs
• Runs needed to win = Sri Lanka's score + 1 = 232 + 1 = 233 runs.
• India's current score = 123 runs
• Runs still needed to win = 233 - 123 = 110 runs.
• Sri Lanka's score = 232 runs
• Runs needed to win = Sri Lanka's score + 1 = 232 + 1 = 233 runs.
• India's current score = 123 runs
• Runs still needed to win = 233 - 123 = 110 runs.
CBSE Step-by-Step Marking Scheme
Correct identification of winning target (233 runs)
1.5 M
Correct subtraction (233 - 123 = 110 runs)
1.5 M
Q3
Mohan went shopping with ₹400. He bought a shirt for ₹195 and trousers for ₹148. Without exact calculation, estimate if he has enough money. Then find his exact change.
Estimation Check • Shopping Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
1. Estimation:
• ₹195 is approx ₹200.
• ₹148 is approx ₹150.
• Total estimate = ₹200 + ₹150 = ₹350.
• Since ₹350 < ₹400, he has enough money.
2. Exact Calculation:
• Total cost = ₹195 + ₹148 = ₹343.
• Change received = ₹400 - ₹343 = ₹57.
1. Estimation:
• ₹195 is approx ₹200.
• ₹148 is approx ₹150.
• Total estimate = ₹200 + ₹150 = ₹350.
• Since ₹350 < ₹400, he has enough money.
2. Exact Calculation:
• Total cost = ₹195 + ₹148 = ₹343.
• Change received = ₹400 - ₹343 = ₹57.
CBSE Step-by-Step Marking Scheme
Clear estimation reasoning with rounded numbers
1.5 M
Exact addition (₹343) and change calculation (₹57)
1.5 M
Q4
In a one-day cricket match, Pakistan scored 232 runs. India has scored 123 runs so far.
(a) How many runs does India need to win?
(b) If Rohit scores 45 runs and Virat scores 55 runs in the next partnership, will India reach the target? Show calculations. Cricket Match Chase • Runs Needed 3 Marks
(a) How many runs does India need to win?
(b) If Rohit scores 45 runs and Virat scores 55 runs in the next partnership, will India reach the target? Show calculations. Cricket Match Chase • Runs Needed 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Runs Needed:
• Pakistan scored = 232 runs.
• Winning target = 232 + 1 = 233 runs.
• Runs scored so far = 123 runs.
• Runs needed to win = 233 - 123 = 110 runs.
(b) Partnership Runs:
• Rohit (45) + Virat (55) = 100 runs.
• New total score = 123 + 100 = 223 runs.
• Still needed to win = 233 - 223 = 10 runs.
• No, India will not reach the target yet; they will still need 10 more runs to win.
(a) Runs Needed:
• Pakistan scored = 232 runs.
• Winning target = 232 + 1 = 233 runs.
• Runs scored so far = 123 runs.
• Runs needed to win = 233 - 123 = 110 runs.
(b) Partnership Runs:
• Rohit (45) + Virat (55) = 100 runs.
• New total score = 123 + 100 = 223 runs.
• Still needed to win = 233 - 223 = 10 runs.
• No, India will not reach the target yet; they will still need 10 more runs to win.
CBSE Step-by-Step Marking Scheme
Correct winning target (233) and subtraction (110 runs)
1.5 M
Correct partnership sum (100) and conclusion (still needs 10 runs)
1.5 M
Q5
Geeta had ₹368 in her purse. She bought a book for ₹123.
(a) How much money is left in her purse?
(b) Check Geeta's remaining balance using addition. Geeta's Purse • Subtraction and Checking 3 Marks
(a) How much money is left in her purse?
(b) Check Geeta's remaining balance using addition. Geeta's Purse • Subtraction and Checking 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Money Left:
• Total in purse = ₹368.
• Book cost = ₹123.
• Subtraction: 368 - 123 = (300 - 100) + (60 - 20) + (8 - 3) = 200 + 40 + 5 = ₹245.
(b) Checking with Addition:
• Remaining money + Book cost = Total original money
• 245 + 123 = 368.
• Verified: The answer ₹245 is correct.
(a) Money Left:
• Total in purse = ₹368.
• Book cost = ₹123.
• Subtraction: 368 - 123 = (300 - 100) + (60 - 20) + (8 - 3) = 200 + 40 + 5 = ₹245.
(b) Checking with Addition:
• Remaining money + Book cost = Total original money
• 245 + 123 = 368.
• Verified: The answer ₹245 is correct.
CBSE Step-by-Step Marking Scheme
Correct subtraction (₹245)
1.5 M
Correct addition verification (245 + 123 = 368)
1.5 M
Q6
Khushboo's mother checked the electricity meter on the 1st of the month. It read 118 units. At the end of the month, the meter read 193 units.
(a) How many electricity units did the family use during the month?
(b) If each unit costs ₹5, what is the total electricity charge for the month? Electricity Meter Reading • Units Consumed 3 Marks
(a) How many electricity units did the family use during the month?
(b) If each unit costs ₹5, what is the total electricity charge for the month? Electricity Meter Reading • Units Consumed 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Units Consumed:
• Final reading = 193 units.
• Initial reading = 118 units.
• Units used = 193 - 118 = 75 units.
(b) Electricity Charge:
• 75 units × ₹5 per unit = ₹375.
(a) Units Consumed:
• Final reading = 193 units.
• Initial reading = 118 units.
• Units used = 193 - 118 = 75 units.
(b) Electricity Charge:
• 75 units × ₹5 per unit = ₹375.
CBSE Step-by-Step Marking Scheme
Correct units consumed (193 - 118 = 75 units)
1.5 M
Correct cost multiplication (75 × 5 = ₹375)
1.5 M
Q7
A train travels from New Delhi to Kanpur. The distances from New Delhi are:
• Aligarh: 130 km
• Tundla: 204 km
• Kanpur: 435 km
(a) Find the distance between Aligarh and Tundla.
(b) Find the distance between Tundla and Kanpur. Train Journey • Distance Between Stations 3 Marks
• Aligarh: 130 km
• Tundla: 204 km
• Kanpur: 435 km
(a) Find the distance between Aligarh and Tundla.
(b) Find the distance between Tundla and Kanpur. Train Journey • Distance Between Stations 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Subtraction:
(a) Aligarh to Tundla:
• 204 km - 130 km = 74 km.
(b) Tundla to Kanpur:
• 435 km - 204 km = 231 km.
(a) Aligarh to Tundla:
• 204 km - 130 km = 74 km.
(b) Tundla to Kanpur:
• 435 km - 204 km = 231 km.
CBSE Step-by-Step Marking Scheme
Correct distance for (a): 74 km
1.5 M
Correct distance for (b): 231 km
1.5 M
Q8
In Chapter 6 ('Fun with Give and Take'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Fun with Give and Take', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Village Water Tank Maintenance
Real-World Math Context: A village overhead water tank has a capacity of 850 litres. In the morning, 475 litres of water were consumed by households. Later, the pump filled 320 litres of fresh water into the tank.
Analytical Task: How much water was in the tank at the end of the day? Can the tank take another 200 litres without overflowing?
1. Water left after morning usage = 850 - 475 = 375 litres.
2. Water after fresh pumping = 375 + 320 = 695 litres.
3. Space remaining in tank = 850 - 695 = 155 litres.
4. Since 155 litres < 200 litres, no, adding 200 litres will cause the tank to overflow (by 45 litres).
2. Water after fresh pumping = 375 + 320 = 695 litres.
3. Space remaining in tank = 850 - 695 = 155 litres.
4. Since 155 litres < 200 litres, no, adding 200 litres will cause the tank to overflow (by 45 litres).
CBSE Assessment Rubric: 1M morning subtraction + 1M pumping addition + 1M capacity check.
7
Unit 4: Advanced Operations & Practical Math • Class 3 Mathematics (Classic CBSE)
Chapter 7: Time Goes on...
Seconds, Minutes, Hours, Days, Months, Years, Timeline & Age Problems
Chapter Highlights, Mathematical Ideas & Key Properties
- Categorizing events by duration: taking seconds, minutes, hours, days, months, or years.
- Reading dates and understanding different date notations (DD/MM/YYYY).
- Building a personal life timeline: chronological ordering of milestone events.
- Calculating age difference between family members.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Classify each activity into 'Seconds', 'Minutes', 'Hours', or 'Days': (a) To blink your eyes, (b) To knit a woollen sweater, (c) To boil a cup of milk, (d) For curd to set from warm milk.
Time Duration Estimation • Categorization
2 Marks
✅ Step-by-Step Model Answer & Solution:
Classifications:
• (a) Blink your eyes: Seconds (fraction of a second)
• (b) Knit a sweater: Days (usually several days or weeks)
• (c) Boil a cup of milk: Minutes (approx 3 to 5 minutes)
• (d) For curd to set: Hours (approx 6 to 8 hours).
• (a) Blink your eyes: Seconds (fraction of a second)
• (b) Knit a sweater: Days (usually several days or weeks)
• (c) Boil a cup of milk: Minutes (approx 3 to 5 minutes)
• (d) For curd to set: Hours (approx 6 to 8 hours).
CBSE Step-by-Step Marking Scheme
Correct duration category for all 4 activities
2.0 M
Q2
Look at Bincy's birth certificate: Date of birth: 02/05/2018 (2 May 2018). (a) How old was Bincy on 2 May 2026? (b) In which year did she celebrate her 5th birthday?
Birth Certificate Analysis • Date Calculations
2 Marks
✅ Step-by-Step Model Answer & Solution:
Analysis:
• (a) Age on 2 May 2026:
2026 - 2018 = 8 years old.
• (b) 5th Birthday Year:
2018 + 5 = 2023 (on 2 May 2023).
• (a) Age on 2 May 2026:
2026 - 2018 = 8 years old.
• (b) 5th Birthday Year:
2018 + 5 = 2023 (on 2 May 2023).
CBSE Step-by-Step Marking Scheme
Correct subtraction for age (8 years)
1.0 M
Correct year calculation for 5th birthday (2023)
1.0 M
Q3
Rohan's mother is 34 years old. His grandmother is 62 years old. (a) What is the age difference between Rohan's mother and grandmother? (b) If Rohan is 8 years old, by how many years is his mother older than him?
Age Difference Word Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) Mother & Grandmother:
62 - 34 = 28 years.
• (b) Mother & Rohan:
34 - 8 = 26 years.
• (a) Mother & Grandmother:
62 - 34 = 28 years.
• (b) Mother & Rohan:
34 - 8 = 26 years.
CBSE Step-by-Step Marking Scheme
Correct subtraction for grandmother & mother (28 years)
1.0 M
Correct subtraction for mother & Rohan (26 years)
1.0 M
Q4
Correct the ridiculous time words in this funny story:
'As the sun rises in the evening, Sumana wakes up. She washes her face quickly in 2 hours and runs out to the pond. She takes 10 months to reach the pond and catches a fish in 2 days.'
Rewrite the story with sensible time units (seconds, minutes, morning, hours). Ultat-Pulta Story • Absurd Time Units Correction 3 Marks
'As the sun rises in the evening, Sumana wakes up. She washes her face quickly in 2 hours and runs out to the pond. She takes 10 months to reach the pond and catches a fish in 2 days.'
Rewrite the story with sensible time units (seconds, minutes, morning, hours). Ultat-Pulta Story • Absurd Time Units Correction 3 Marks
✅ Step-by-Step Model Answer & Solution:
Corrected Sensible Story:
• 'As the sun rises in the morning (not evening), Sumana wakes up. She washes her face quickly in 2 minutes (not 2 hours) and runs out to the pond. She takes 10 minutes (not 10 months) to reach the pond and catches a fish in 2 minutes/seconds (not 2 days).'
• 'As the sun rises in the morning (not evening), Sumana wakes up. She washes her face quickly in 2 minutes (not 2 hours) and runs out to the pond. She takes 10 minutes (not 10 months) to reach the pond and catches a fish in 2 minutes/seconds (not 2 days).'
CBSE Step-by-Step Marking Scheme
Corrected morning for sunrise
1.0 M
Corrected minutes for washing face and walking
1.0 M
Sensible duration for catching fish
1.0 M
Q5
On any standard monthly calendar page, draw a 3x3 square covering 9 dates.
(a) If the date in the exact center of the 3x3 box is 14, what is the sum of all 9 dates in the box?
(b) Explain the quick trick to find this sum in 2 seconds. Calendar Magic • 3x3 Magic Square Sum 3 Marks
(a) If the date in the exact center of the 3x3 box is 14, what is the sum of all 9 dates in the box?
(b) Explain the quick trick to find this sum in 2 seconds. Calendar Magic • 3x3 Magic Square Sum 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Calendar Magic:
(a) Sum of 9 Dates:
• Quick Magic Formula: Center Number × 9.
• Center number = 14.
• Sum = 14 × 9 = 126.
(b) The Trick Explained:
• On a calendar, the numbers symmetrically surround the center number (e.g., 14-8 and 14+8, 14-7 and 14+7, 14-1 and 14+1).
• The average of all 9 numbers is exactly the center number. Therefore, simply multiplying the center date by 9 gives the exact total of all 9 dates instantly!
(a) Sum of 9 Dates:
• Quick Magic Formula: Center Number × 9.
• Center number = 14.
• Sum = 14 × 9 = 126.
(b) The Trick Explained:
• On a calendar, the numbers symmetrically surround the center number (e.g., 14-8 and 14+8, 14-7 and 14+7, 14-1 and 14+1).
• The average of all 9 numbers is exactly the center number. Therefore, simply multiplying the center date by 9 gives the exact total of all 9 dates instantly!
CBSE Step-by-Step Marking Scheme
Correct total sum (126)
1.5 M
Clear mathematical explanation of multiplying center date by 9
1.5 M
Q6
Study Bindo's birth certificate details:
• Date of Birth: 02/05/2012 (2nd May 2012)
• Registration Date: 02/06/2012
(a) In which month and year was Bindo born?
(b) How old was Bindo on 2nd May 2020?
(c) After how many days was the birth registered? Birth Certificate Analysis • Bindo's Record 3 Marks
• Date of Birth: 02/05/2012 (2nd May 2012)
• Registration Date: 02/06/2012
(a) In which month and year was Bindo born?
(b) How old was Bindo on 2nd May 2020?
(c) After how many days was the birth registered? Birth Certificate Analysis • Bindo's Record 3 Marks
✅ Step-by-Step Model Answer & Solution:
Birth Certificate Data:
• (a) Birth Month & Year: Born in May 2012 (Month 05 is May).
• (b) Age on 02/05/2020: 2020 - 2012 = 8 years old.
• (c) Registration Duration: From 2nd May to 2nd June = 1 month (or 31 days) later.
• (a) Birth Month & Year: Born in May 2012 (Month 05 is May).
• (b) Age on 02/05/2020: 2020 - 2012 = 8 years old.
• (c) Registration Duration: From 2nd May to 2nd June = 1 month (or 31 days) later.
CBSE Step-by-Step Marking Scheme
Correct month (May) and year (2012)
1.0 M
Correct age calculation (8 years)
1.0 M
Correct registration duration (1 month / 31 days)
1.0 M
Q7
Categorize the following activities into 'Takes Minutes', 'Takes Hours', and 'Takes Days/Months':
(a) Boiling an egg
(b) Knitting a woolen sweater
(c) Watching a movie
(d) Brushing your teeth
(e) Ripening of a mango on a tree How Long Does It Take? • Duration Estimates 3 Marks
(a) Boiling an egg
(b) Knitting a woolen sweater
(c) Watching a movie
(d) Brushing your teeth
(e) Ripening of a mango on a tree How Long Does It Take? • Duration Estimates 3 Marks
✅ Step-by-Step Model Answer & Solution:
Duration Categorization:
• Takes Minutes:
- Brushing your teeth (~2-3 minutes)
- Boiling an egg (~10 minutes)
• Takes Hours:
- Watching a movie (~2-3 hours)
• Takes Days or Months:
- Knitting a sweater (~several days/weeks)
- Ripening of a mango (~a few weeks/months).
• Takes Minutes:
- Brushing your teeth (~2-3 minutes)
- Boiling an egg (~10 minutes)
• Takes Hours:
- Watching a movie (~2-3 hours)
• Takes Days or Months:
- Knitting a sweater (~several days/weeks)
- Ripening of a mango (~a few weeks/months).
CBSE Step-by-Step Marking Scheme
Correct minute-duration activities
1.0 M
Correct hour-duration activities
1.0 M
Correct days/months-duration activities
1.0 M
Q8
In Chapter 7 ('Time Goes on...'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Time Goes on...', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Family Mango Tree Planting Record
Real-World Math Context: Grandfather planted a mango sapling in the family orchard in July 2016. The tree bore its first batch of mangoes in July 2021.
Analytical Task: How many years did the sapling take to bear fruit? If it is now July 2026, for how many years has the tree been bearing fruit?
1. Years to first fruit = 2021 - 2016 = 5 years.
2. Years bearing fruit up to 2026 = 2026 - 2021 = 5 years (or 6 harvest seasons including 2021).
2. Years bearing fruit up to 2026 = 2026 - 2021 = 5 years (or 6 harvest seasons including 2021).
CBSE Assessment Rubric: 1.5M years to first fruit + 1.5M active fruiting years.
8
Unit 5: Weight, Multiplication & Grouping • Class 3 Mathematics (Classic CBSE)
Chapter 8: Who Is Heavier?
Mass / Weight (kg & g), Pan Balance, Pumpkin Prize & Grocery Packing
Chapter Highlights, Mathematical Ideas & Key Properties
- Understanding mass and weight: heavier vs lighter.
- Standard units: Kilogram (kg) and Gram (g).
- 1 Kilogram = 1000 Grams (1 kg = 1000 g); 1/2 kg = 500 g.
- Balancing pans: when both pans are level, weights are equal.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
State whether you would measure the weight of the following in 'Kilograms (kg)' or 'Grams (g)': (a) A sack of wheat, (b) A gold ring, (c) A geometry compass, (d) A bag of cement.
Weight Unit Selection • Real-World Items
2 Marks
✅ Step-by-Step Model Answer & Solution:
Appropriate Units:
• (a) Sack of wheat: Kilograms (kg) (heavy staple, e.g., 25 kg)
• (b) Gold ring: Grams (g) (light jewellery, e.g., 5-8 g)
• (c) Geometry compass: Grams (g) (light tool, e.g., 50 g)
• (d) Bag of cement: Kilograms (kg) (heavy industrial bag, 50 kg).
• (a) Sack of wheat: Kilograms (kg) (heavy staple, e.g., 25 kg)
• (b) Gold ring: Grams (g) (light jewellery, e.g., 5-8 g)
• (c) Geometry compass: Grams (g) (light tool, e.g., 50 g)
• (d) Bag of cement: Kilograms (kg) (heavy industrial bag, 50 kg).
CBSE Step-by-Step Marking Scheme
Correct units for wheat and cement (kg)
1.0 M
Correct units for ring and compass (g)
1.0 M
Q2
A grocery shopkeeper has to weigh 2 kg of sugar. He has only 500 g weights. (a) How many 500 g weights must he put on the weight pan? (b) How many grams are in 2 kg?
Balance Calculations • Grams & Kilograms
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• (b) Conversion: 1 kg = 1000 g, therefore 2 kg = 2 × 1000 g = 2,000 grams.
• (a) Weights needed: 2,000 g ÷ 500 g = 4 weights of 500 g.
• (b) Conversion: 1 kg = 1000 g, therefore 2 kg = 2 × 1000 g = 2,000 grams.
• (a) Weights needed: 2,000 g ÷ 500 g = 4 weights of 500 g.
CBSE Step-by-Step Marking Scheme
Correct conversion to 2000 g
1.0 M
Correct number of 500 g weights (4)
1.0 M
Q3
Which is heavier: 1 kg of iron or 1 kg of cotton wool? Explain why many people mistakenly think iron is heavier.
Equal Weight Comparison • Volume vs Mass
3 Marks
✅ Step-by-Step Model Answer & Solution:
Explanation:
• Answer: Both are equally heavy. Both weigh exactly 1 kilogram (1 kg = 1 kg).
• Reason for Common Mistake: Iron is dense and occupies a very small volume, whereas 1 kg of cotton is fluffy and occupies a huge bag. People confuse larger size or density with weight, but on a balance scale, both balance each other perfectly.
• Answer: Both are equally heavy. Both weigh exactly 1 kilogram (1 kg = 1 kg).
• Reason for Common Mistake: Iron is dense and occupies a very small volume, whereas 1 kg of cotton is fluffy and occupies a huge bag. People confuse larger size or density with weight, but on a balance scale, both balance each other perfectly.
CBSE Step-by-Step Marking Scheme
Clear assertion that both weigh the same (1 kg)
1.5 M
Scientific explanation distinguishing volume/density from mass
1.5 M
Q4
Shabnam bought 1 kg of jaggery (gur) and 1 kg of groundnuts in the market.
(a) Which is heavier: 1 kg of jaggery or 1 kg of groundnuts?
(b) Why does the bag of groundnuts look so much bigger than the bag of jaggery? Gur and Groundnuts • Volume vs Weight 3 Marks
(a) Which is heavier: 1 kg of jaggery or 1 kg of groundnuts?
(b) Why does the bag of groundnuts look so much bigger than the bag of jaggery? Gur and Groundnuts • Volume vs Weight 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Physics & Math:
(a) Weight Comparison:
• Both weigh exactly the same (1 kg = 1 kg). Neither is heavier.
(b) Volume Difference:
• Groundnuts are light and hollow with air spaces inside their shells (low density), so 1 kg takes up a large space (volume).
• Jaggery is dense and solid (high density), so 1 kg occupies a small, compact volume.
(a) Weight Comparison:
• Both weigh exactly the same (1 kg = 1 kg). Neither is heavier.
(b) Volume Difference:
• Groundnuts are light and hollow with air spaces inside their shells (low density), so 1 kg takes up a large space (volume).
• Jaggery is dense and solid (high density), so 1 kg occupies a small, compact volume.
CBSE Step-by-Step Marking Scheme
Correct conclusion that both weigh equal (1 kg)
1.5 M
Scientific explanation of density and volume differences
1.5 M
Q5
At Kunjamma's birth, her parents distributed sweets equal to double her weight. Kunjamma weighed 3 kg at birth.
(a) How many kilograms of sweets did they distribute at her birth?
(b) On her 4th birthday, Kunjamma weighed 15 kg. How many kilograms of sweets were distributed then? Double Your Weight • Kunjamma's Parents Tradition 3 Marks
(a) How many kilograms of sweets did they distribute at her birth?
(b) On her 4th birthday, Kunjamma weighed 15 kg. How many kilograms of sweets were distributed then? Double Your Weight • Kunjamma's Parents Tradition 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Calculations:
(a) Sweets at Birth:
• Weight at birth = 3 kg.
• Double her weight = 2 × 3 kg = 6 kg of sweets.
(b) Sweets on 4th Birthday:
• Weight on 4th birthday = 15 kg.
• Double her weight = 2 × 15 kg = 30 kg of sweets.
(a) Sweets at Birth:
• Weight at birth = 3 kg.
• Double her weight = 2 × 3 kg = 6 kg of sweets.
(b) Sweets on 4th Birthday:
• Weight on 4th birthday = 15 kg.
• Double her weight = 2 × 15 kg = 30 kg of sweets.
CBSE Step-by-Step Marking Scheme
Correct calculation for birth (6 kg)
1.5 M
Correct calculation for 4th birthday (30 kg)
1.5 M
Q6
Guess which object is heavier than 1 kg and which is lighter than 1 kg:
(a) Your school bag full of books.
(b) A geometry box compass.
(c) A brick.
(d) A pair of socks. Balance Scale Estimation • Heavier or Lighter 4 Marks
(a) Your school bag full of books.
(b) A geometry box compass.
(c) A brick.
(d) A pair of socks. Balance Scale Estimation • Heavier or Lighter 4 Marks
✅ Step-by-Step Model Answer & Solution:
Weight Estimation:
• (a) School bag full of books: Heavier than 1 kg (~3 to 5 kg).
• (b) Geometry box compass: Lighter than 1 kg (~50 grams).
• (c) A brick: Heavier than 1 kg (~2.5 to 3 kg).
• (d) A pair of socks: Lighter than 1 kg (~40 grams).
• (a) School bag full of books: Heavier than 1 kg (~3 to 5 kg).
• (b) Geometry box compass: Lighter than 1 kg (~50 grams).
• (c) A brick: Heavier than 1 kg (~2.5 to 3 kg).
• (d) A pair of socks: Lighter than 1 kg (~40 grams).
CBSE Step-by-Step Marking Scheme
Correct classifications for (a) and (b)
2.0 M
Correct classifications for (c) and (d)
2.0 M
Q7
Ramesh bought from the supermarket:
• 2 kg of rice
• 500 g of dal
• 250 g of tea leaves
• 250 g of almonds
(a) Find the total weight of items bought in kilograms and grams.
(b) Is the total weight more than 3 kg or less than 3 kg? Grocery Package Weights • Finding Total Weight 3 Marks
• 2 kg of rice
• 500 g of dal
• 250 g of tea leaves
• 250 g of almonds
(a) Find the total weight of items bought in kilograms and grams.
(b) Is the total weight more than 3 kg or less than 3 kg? Grocery Package Weights • Finding Total Weight 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Addition:
• Rice = 2 kg 000 g.
• Dal = 500 g.
• Tea leaves = 250 g.
• Almonds = 250 g.
• Grams total: 500 + 250 + 250 = 1000 g = 1 kg.
• Kilograms total: 2 kg + 1 kg = 3 kg 000 g (exactly 3 kg).
(b) Comparison:
• The total weight is exactly 3 kg (neither more nor less).
• Rice = 2 kg 000 g.
• Dal = 500 g.
• Tea leaves = 250 g.
• Almonds = 250 g.
• Grams total: 500 + 250 + 250 = 1000 g = 1 kg.
• Kilograms total: 2 kg + 1 kg = 3 kg 000 g (exactly 3 kg).
(b) Comparison:
• The total weight is exactly 3 kg (neither more nor less).
CBSE Step-by-Step Marking Scheme
Correct conversion and addition (3 kg 000 g)
2.0 M
Correct equality comparison
1.0 M
Q8
In Chapter 8 ('Who Is Heavier?'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Who Is Heavier?', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
School Sports Equipment Delivery
Real-World Math Context: The sports department received a parcel containing 4 footballs (each weighing 400 g) and 2 cricket bats (each weighing 1 kg 200 g).
Analytical Task: What is the total weight of all the footballs? What is the combined total weight of all sports equipment in kilograms and grams?
1. Total footballs weight = 4 × 400 g = 1,600 g = 1 kg 600 g.
2. Total cricket bats weight = 2 × (1 kg 200 g) = 2 kg 400 g.
3. Combined weight = (1 kg 600 g) + (2 kg 400 g) = 3 kg + 1000 g = 3 kg + 1 kg = 4 kilograms (4 kg).
2. Total cricket bats weight = 2 × (1 kg 200 g) = 2 kg 400 g.
3. Combined weight = (1 kg 600 g) + (2 kg 400 g) = 3 kg + 1000 g = 3 kg + 1 kg = 4 kilograms (4 kg).
CBSE Assessment Rubric: 1M footballs multiplication + 1M bats multiplication + 1M combined weight in kg.
9
Unit 5: Weight, Multiplication & Grouping • Class 3 Mathematics (Classic CBSE)
Chapter 9: How Many Times?
Repeated Addition, Multiplication Tables, Stick Multiplication & Word Problems
Chapter Highlights, Mathematical Ideas & Key Properties
- Multiplication as 'times' or repeated addition: 4 times 3 = 3 + 3 + 3 + 3 = 12.
- Drawing stick patterns to understand multiplication intersections.
- Multiplication properties: multiplying by 0 gives 0, multiplying by 1 gives the same number.
- Solving 2-digit by 1-digit multiplication problems.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Using the stick crossing method: (a) How many sticks crossing in each direction would you draw for 4 × 5? (b) How many crossing points (dots) will you count?
Stick Crossing Multiplication • Concept
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• (a) Sticks: Draw 4 horizontal sticks and 5 vertical sticks crossing them.
• (b) Crossing Points: Each of the 4 horizontal sticks crosses all 5 vertical sticks. Total crossing points = 4 × 5 = 20 dots.
• (a) Sticks: Draw 4 horizontal sticks and 5 vertical sticks crossing them.
• (b) Crossing Points: Each of the 4 horizontal sticks crosses all 5 vertical sticks. Total crossing points = 4 × 5 = 20 dots.
CBSE Step-by-Step Marking Scheme
Correct number of horizontal and vertical sticks
1.0 M
Correct product calculation (20 dots)
1.0 M
Q2
A spider has 8 legs. How many legs do 6 spiders have altogether? Write both the repeated addition sentence and the multiplication fact.
Word Problem • Repeated Grouping
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Legs per spider = 8
• Number of spiders = 6
• Repeated Addition: 8 + 8 + 8 + 8 + 8 + 8 = 48 legs.
• Multiplication Fact: 6 × 8 = 48 legs.
• Legs per spider = 8
• Number of spiders = 6
• Repeated Addition: 8 + 8 + 8 + 8 + 8 + 8 = 48 legs.
• Multiplication Fact: 6 × 8 = 48 legs.
CBSE Step-by-Step Marking Scheme
Correct repeated addition statement
1.0 M
Correct multiplication statement (6 × 8 = 48)
1.0 M
Q3
Solve 23 × 4 using the split/box multiplication method. Show the breakdown into tens and ones.
2-Digit Multiplication • Box Method
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Box Method:
1. Split 23 into 20 + 3.
2. Multiply each part by 4:
• 20 × 4 = 80
• 3 × 4 = 12
3. Add the two partial products:
• 80 + 12 = 92.
Therefore, 23 × 4 = 92.
1. Split 23 into 20 + 3.
2. Multiply each part by 4:
• 20 × 4 = 80
• 3 × 4 = 12
3. Add the two partial products:
• 80 + 12 = 92.
Therefore, 23 × 4 = 92.
CBSE Step-by-Step Marking Scheme
Correct splitting of 23 into 20 and 3
1.0 M
Correct partial products (80 and 12)
1.0 M
Correct final sum (92)
1.0 M
Q4
There are 5 spiders in a web. Each spider has 8 legs.
(a) How many legs are there altogether? Show using repeated addition.
(b) Write the multiplication fact.
(c) If 3 octopuses join them (each with 8 arms), how many arms do the octopuses have? Leggy Animals • Multiplication as Repeated Addition 3 Marks
(a) How many legs are there altogether? Show using repeated addition.
(b) Write the multiplication fact.
(c) If 3 octopuses join them (each with 8 arms), how many arms do the octopuses have? Leggy Animals • Multiplication as Repeated Addition 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Multiplication:
(a) Repeated Addition:
• 8 + 8 + 8 + 8 + 8 = 40 legs.
(b) Multiplication Fact:
• 5 × 8 = 40 legs.
(c) Octopuses:
• 3 octopuses × 8 arms = 24 arms.
(a) Repeated Addition:
• 8 + 8 + 8 + 8 + 8 = 40 legs.
(b) Multiplication Fact:
• 5 × 8 = 40 legs.
(c) Octopuses:
• 3 octopuses × 8 arms = 24 arms.
CBSE Step-by-Step Marking Scheme
Correct repeated addition string (8+8+8+8+8 = 40)
1.0 M
Correct multiplication fact (5 × 8 = 40)
1.0 M
Correct octopus calculation (3 × 8 = 24)
1.0 M
Q5
Mithu had some matchsticks. She arranged them: 2 vertical sticks crossed by 3 horizontal sticks.
(a) How many crossing intersection points are formed?
(b) How can you find 4 × 5 using sticks?
(c) What is 4 × 5? Multiplication with Sticks • Vedic Method 3 Marks
(a) How many crossing intersection points are formed?
(b) How can you find 4 × 5 using sticks?
(c) What is 4 × 5? Multiplication with Sticks • Vedic Method 3 Marks
✅ Step-by-Step Model Answer & Solution:
Stick Multiplication Method:
(a) 2 by 3 Sticks:
• 2 vertical sticks crossed by 3 horizontal sticks create 2 × 3 = 6 intersection points.
(b) Method for 4 × 5:
• Place 4 vertical sticks parallel to each other.
• Cross them with 5 horizontal sticks.
• Count all the points where the sticks cross each other.
(c) Result:
• 4 × 5 = 20 intersection points.
(a) 2 by 3 Sticks:
• 2 vertical sticks crossed by 3 horizontal sticks create 2 × 3 = 6 intersection points.
(b) Method for 4 × 5:
• Place 4 vertical sticks parallel to each other.
• Cross them with 5 horizontal sticks.
• Count all the points where the sticks cross each other.
(c) Result:
• 4 × 5 = 20 intersection points.
CBSE Step-by-Step Marking Scheme
Correct intersection points for 2x3 (6 points)
1.0 M
Clear procedural explanation of stick arrangement
1.0 M
Correct product for 4 × 5 = 20
1.0 M
Q6
Tarva the frog jumps 3 steps at a time along a number line.
(a) Write the numbers Tarva lands on during his first 6 jumps.
(b) Which jump will land Tarva on number 27? Tarva Frog Jumps • Step Multiplication 3 Marks
(a) Write the numbers Tarva lands on during his first 6 jumps.
(b) Which jump will land Tarva on number 27? Tarva Frog Jumps • Step Multiplication 3 Marks
✅ Step-by-Step Model Answer & Solution:
Multiplication by 3:
(a) First 6 jumps:
• 1 jump: 1 × 3 = 3
• 2 jumps: 2 × 3 = 6
• 3 jumps: 3 × 3 = 9
• 4 jumps: 4 × 3 = 12
• 5 jumps: 5 × 3 = 15
• 6 jumps: 6 × 3 = 18.
(b) Jump to reach 27:
• 27 ÷ 3 = 9th jump.
(a) First 6 jumps:
• 1 jump: 1 × 3 = 3
• 2 jumps: 2 × 3 = 6
• 3 jumps: 3 × 3 = 9
• 4 jumps: 4 × 3 = 12
• 5 jumps: 5 × 3 = 15
• 6 jumps: 6 × 3 = 18.
(b) Jump to reach 27:
• 27 ÷ 3 = 9th jump.
CBSE Step-by-Step Marking Scheme
Correct first 6 multiples of 3 (3, 6, 9, 12, 15, 18)
1.5 M
Correct division to find 9th jump
1.5 M
Q7
In Class 3, there are 8 rows of desks. In each row, there are 6 desks.
(a) How many desks are in the classroom in total?
(b) If 2 children sit at every desk, how many children can sit in the classroom? Word Problem • Classroom Desks 3 Marks
(a) How many desks are in the classroom in total?
(b) If 2 children sit at every desk, how many children can sit in the classroom? Word Problem • Classroom Desks 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Multiplication:
(a) Total Desks:
• 8 rows × 6 desks per row = 48 desks.
(b) Total Seating Capacity:
• 48 desks × 2 children per desk = 96 children.
(a) Total Desks:
• 8 rows × 6 desks per row = 48 desks.
(b) Total Seating Capacity:
• 48 desks × 2 children per desk = 96 children.
CBSE Step-by-Step Marking Scheme
Correct desks multiplication (8 × 6 = 48)
1.5 M
Correct seating multiplication (48 × 2 = 96)
1.5 M
Q8
In Chapter 9 ('How Many Times?'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'How Many Times?', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Garden Flowerbed Rows
Real-World Math Context: A municipal botanical garden has 14 flowerbeds. Each flowerbed is planted with 6 marigold plants.
Analytical Task: How many marigold plants are in the garden? If 5 plants dry up, how many healthy plants remain?
1. Total marigold plants = 14 × 6 = (10 × 6) + (4 × 6) = 60 + 24 = 84 plants.
2. Healthy plants remaining = 84 - 5 = 79 healthy plants.
2. Healthy plants remaining = 84 - 5 = 79 healthy plants.
CBSE Assessment Rubric: 1.5M multiplication of 14 × 6 + 1.5M subtraction of 5 dried plants.
10
Unit 6: Patterns, Capacity & Sharing • Class 3 Mathematics (Classic CBSE)
Chapter 10: Play with Patterns
Repeating Patterns, Growing Patterns, Number Sequences & Secret Coded Messages
Chapter Highlights, Mathematical Ideas & Key Properties
- Identifying rules of repeating shape patterns (AB, AAB, ABC).
- Growing patterns in shapes and numbers (e.g., triangular numbers, square sequences).
- Even and odd number patterns: ending digits (0, 2, 4, 6, 8 vs 1, 3, 5, 7, 9).
- Secret messages: decoding messages with letter-to-number replacement rules.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Look at the pattern: 1, 3, 6, 10, ___, ___. (a) What are the next two numbers? (b) State the mathematical rule for how the pattern grows.
Growing Patterns • Number Rules
3 Marks
✅ Step-by-Step Model Answer & Solution:
Analysis:
• From 1 to 3: +2
• From 3 to 6: +3
• From 6 to 10: +4
• Next step: +5 → 10 + 5 = 15.
• Next step: +6 → 15 + 6 = 21.
• (a) Next two numbers: 15, 21 (Triangular numbers).
• (b) Rule: Each step adds 1 more than was added in the previous step (+2, +3, +4, +5, +6...).
• From 1 to 3: +2
• From 3 to 6: +3
• From 6 to 10: +4
• Next step: +5 → 10 + 5 = 15.
• Next step: +6 → 15 + 6 = 21.
• (a) Next two numbers: 15, 21 (Triangular numbers).
• (b) Rule: Each step adds 1 more than was added in the previous step (+2, +3, +4, +5, +6...).
CBSE Step-by-Step Marking Scheme
Correct calculation of 15 and 21
1.5 M
Clear rule formulation explaining growing increments
1.5 M
Q2
Classify the following as Even or Odd: 246, 381, 500, 789. What happens when you add two odd numbers together? Give an example.
Even and Odd Patterns • Properties
3 Marks
✅ Step-by-Step Model Answer & Solution:
Classification:
• 246: Ends in 6 → EVEN
• 381: Ends in 1 → ODD
• 500: Ends in 0 → EVEN
• 789: Ends in 9 → ODD.
Rule: The sum of any two odd numbers is always an EVEN number.
• Example: 3 (Odd) + 5 (Odd) = 8 (Even); 7 + 9 = 16 (Even).
• 246: Ends in 6 → EVEN
• 381: Ends in 1 → ODD
• 500: Ends in 0 → EVEN
• 789: Ends in 9 → ODD.
Rule: The sum of any two odd numbers is always an EVEN number.
• Example: 3 (Odd) + 5 (Odd) = 8 (Even); 7 + 9 = 16 (Even).
CBSE Step-by-Step Marking Scheme
Correct even/odd classification for all 4 numbers
1.5 M
Correct rule and supporting example (Odd + Odd = Even)
1.5 M
Q3
If each letter is replaced by its alphabetical position (A=1, B=2, C=3... Z=26): (a) Decode the message: '7 - 15 - 15 - 4'. (b) Encode the word 'BOOK' in numbers.
Secret Coded Message • Decoding
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) Decoding '7 - 15 - 15 - 4':
7 = G, 15 = O, 15 = O, 4 = D → GOOD.
• (b) Encoding 'BOOK':
B = 2, O = 15, O = 15, K = 11 → 2 - 15 - 15 - 11.
• (a) Decoding '7 - 15 - 15 - 4':
7 = G, 15 = O, 15 = O, 4 = D → GOOD.
• (b) Encoding 'BOOK':
B = 2, O = 15, O = 15, K = 11 → 2 - 15 - 15 - 11.
CBSE Step-by-Step Marking Scheme
Correct decoding to GOOD
1.0 M
Correct encoding for BOOK (2-15-15-11)
1.0 M
Q4
In a number tower, the number in each block is the sum of the two blocks directly below it.
The bottom row has blocks: [10], [20], [30].
(a) Find the numbers in the two blocks of the second row.
(b) Find the number in the top block of the tower. Number Towers • Pyramid Patterns 3 Marks
The bottom row has blocks: [10], [20], [30].
(a) Find the numbers in the two blocks of the second row.
(b) Find the number in the top block of the tower. Number Towers • Pyramid Patterns 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Number Tower:
• Bottom row: [10], [20], [30].
(a) Second Row:
• First block = 10 + 20 = 30.
• Second block = 20 + 30 = 50.
(b) Top Block:
• Top block = 30 + 50 = 80.
Completed Tower:
[ 80 ]
[ 30 ] [ 50 ]
[ 10 ] [ 20 ] [ 30 ]
• Bottom row: [10], [20], [30].
(a) Second Row:
• First block = 10 + 20 = 30.
• Second block = 20 + 30 = 50.
(b) Top Block:
• Top block = 30 + 50 = 80.
Completed Tower:
[ 80 ]
[ 30 ] [ 50 ]
[ 10 ] [ 20 ] [ 30 ]
CBSE Step-by-Step Marking Scheme
Correct second row blocks (30 and 50)
1.5 M
Correct top block (80)
1.5 M
Q5
Teenu and Jaggu are sending secret messages using the rule: A = 1, B = 2, C = 3 ... Z = 26.
(a) Decode the secret message: '7 - 15 - 15 - 4'
(b) Encode the word 'MATHS' into numbers. Secret Messages • Number-Alphabet Code 3 Marks
(a) Decode the secret message: '7 - 15 - 15 - 4'
(b) Encode the word 'MATHS' into numbers. Secret Messages • Number-Alphabet Code 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Cryptography:
(a) Decoding '7 - 15 - 15 - 4':
• 7 = G
• 15 = O
• 15 = O
• 4 = D
• Decoded word: GOOD.
(b) Encoding 'MATHS':
• M = 13
• A = 1
• T = 20
• H = 8
• S = 19
• Secret code: 13 - 1 - 20 - 8 - 19.
(a) Decoding '7 - 15 - 15 - 4':
• 7 = G
• 15 = O
• 15 = O
• 4 = D
• Decoded word: GOOD.
(b) Encoding 'MATHS':
• M = 13
• A = 1
• T = 20
• H = 8
• S = 19
• Secret code: 13 - 1 - 20 - 8 - 19.
CBSE Step-by-Step Marking Scheme
Correct decoding of 'GOOD'
1.5 M
Correct encoding of 'MATHS' (13-1-20-8-19)
1.5 M
Q6
Look at the growing dot patterns:
Figure 1: 1 dot
Figure 2: 3 dots (1 + 2)
Figure 3: 6 dots (1 + 2 + 3)
(a) How many dots will be in Figure 4?
(b) How many dots will be in Figure 5?
(c) What kind of numbers are these called? Growing Patterns • Geometric Series 3 Marks
Figure 1: 1 dot
Figure 2: 3 dots (1 + 2)
Figure 3: 6 dots (1 + 2 + 3)
(a) How many dots will be in Figure 4?
(b) How many dots will be in Figure 5?
(c) What kind of numbers are these called? Growing Patterns • Geometric Series 3 Marks
✅ Step-by-Step Model Answer & Solution:
Growing Pattern (Triangular Numbers):
• (a) Figure 4: 1 + 2 + 3 + 4 = 10 dots.
• (b) Figure 5: 1 + 2 + 3 + 4 + 5 = 15 dots.
• (c) Number Type: These are called Triangular Numbers because dots arranged in these quantities form equilateral triangles.
• (a) Figure 4: 1 + 2 + 3 + 4 = 10 dots.
• (b) Figure 5: 1 + 2 + 3 + 4 + 5 = 15 dots.
• (c) Number Type: These are called Triangular Numbers because dots arranged in these quantities form equilateral triangles.
CBSE Step-by-Step Marking Scheme
Correct dots in Figure 4 (10 dots)
1.0 M
Correct dots in Figure 5 (15 dots)
1.0 M
Identification of triangular numbers
1.0 M
Q7
(a) Write all even numbers between 41 and 51.
(b) What digits do all even numbers end with?
(c) Is the sum of two even numbers always even or odd? Give an example. Even and Odd Patterns • Digit Endings 3 Marks
(b) What digits do all even numbers end with?
(c) Is the sum of two even numbers always even or odd? Give an example. Even and Odd Patterns • Digit Endings 3 Marks
✅ Step-by-Step Model Answer & Solution:
Even & Odd Rules:
• (a) Even Numbers: 42, 44, 46, 48, 50.
• (b) Even Endings: All even numbers end in 0, 2, 4, 6, or 8 in the ones place.
• (c) Sum Rule: The sum of two even numbers is always Even.
- Example: 4 + 6 = 10 (Even), 12 + 14 = 26 (Even).
• (a) Even Numbers: 42, 44, 46, 48, 50.
• (b) Even Endings: All even numbers end in 0, 2, 4, 6, or 8 in the ones place.
• (c) Sum Rule: The sum of two even numbers is always Even.
- Example: 4 + 6 = 10 (Even), 12 + 14 = 26 (Even).
CBSE Step-by-Step Marking Scheme
Correct even numbers listed
1.0 M
Correct ending digits (0, 2, 4, 6, 8)
1.0 M
Correct sum rule with clear example
1.0 M
Q8
In Chapter 10 ('Play with Patterns'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Play with Patterns', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Tile Border Geometric Pattern
Real-World Math Context: A walkway is paved with a repeating 4-tile sequence: [Circle, Square, Triangle, Hexagon] that repeats continuously along a path of 50 tiles.
Analytical Task: Which shape will be on the 20th tile? Which shape will be on the 47th tile?
1. Sequence length = 4 shapes.
• 1 = Circle, 2 = Square, 3 = Triangle, 4 = Hexagon.
2. 20th tile: 20 ÷ 4 = 5 with remainder 0 (4th shape) → Hexagon.
3. 47th tile: 47 ÷ 4 = 11 with remainder 3 (3rd shape) → Triangle.
• 1 = Circle, 2 = Square, 3 = Triangle, 4 = Hexagon.
2. 20th tile: 20 ÷ 4 = 5 with remainder 0 (4th shape) → Hexagon.
3. 47th tile: 47 ÷ 4 = 11 with remainder 3 (3rd shape) → Triangle.
CBSE Assessment Rubric: 1.5M modulo calculation for 20th tile + 1.5M modulo calculation for 47th tile.
11
Unit 6: Patterns, Capacity & Sharing • Class 3 Mathematics (Classic CBSE)
Chapter 11: Jugs and Mugs
Liquid Capacity, Litres (L) & Millilitres (mL), Kheer Party & Medicine Doses
Chapter Highlights, Mathematical Ideas & Key Properties
- Estimating and measuring capacity using non-standard vs standard units.
- 1 Litre = 1000 Millilitres (1 L = 1000 mL).
- Equivalent fractions: 500 mL = 1/2 Litre; 250 mL = 1/4 Litre.
- Calculating daily water intake and beverage preparation for guests.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
How many of each container will you need to make exactly 1 Litre (1,000 mL)? (a) 200 mL glasses, (b) 100 mL medicine cups, (c) 500 mL bottles.
Capacity Combinations • Making 1 Litre
3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations for 1,000 mL:
• (a) 200 mL glasses: 1,000 ÷ 200 = 5 glasses.
• (b) 100 mL medicine cups: 1,000 ÷ 100 = 10 cups.
• (c) 500 mL bottles: 1,000 ÷ 500 = 2 bottles.
• (a) 200 mL glasses: 1,000 ÷ 200 = 5 glasses.
• (b) 100 mL medicine cups: 1,000 ÷ 100 = 10 cups.
• (c) 500 mL bottles: 1,000 ÷ 500 = 2 bottles.
CBSE Step-by-Step Marking Scheme
Correct count for 200 mL (5)
1.0 M
Correct count for 100 mL (10)
1.0 M
Correct count for 500 mL (2)
1.0 M
Q2
A doctor prescribes 5 mL of cough syrup to be taken 3 times a day for 5 days. (a) How many mL of syrup does the patient take in one day? (b) How many total mL are needed for the full 5-day course?
Medicine Dosage Calculation • Practical Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Dose per time = 5 mL
• Times per day = 3
(a) Daily consumption: 5 mL × 3 = 15 mL per day.
(b) 5-Day course total: 15 mL × 5 days = 75 mL in total.
• Dose per time = 5 mL
• Times per day = 3
(a) Daily consumption: 5 mL × 3 = 15 mL per day.
(b) 5-Day course total: 15 mL × 5 days = 75 mL in total.
CBSE Step-by-Step Marking Scheme
Correct daily dosage calculation (15 mL)
1.5 M
Correct 5-day course calculation (75 mL)
1.5 M
Q3
At the wedding party of the squirrels, 10 litres of sweet kheer was cooked. If each bowl holds 100 mL, how many guests can be served with kheer?
Kheer Party • Real-World Sharing
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Solution:
1. Total kheer = 10 litres.
2. Convert litres to millilitres: 10 × 1000 mL = 10,000 mL.
3. Capacity of 1 bowl = 100 mL.
4. Number of guests served = 10,000 ÷ 100 = 100 guests.
1. Total kheer = 10 litres.
2. Convert litres to millilitres: 10 × 1000 mL = 10,000 mL.
3. Capacity of 1 bowl = 100 mL.
4. Number of guests served = 10,000 ÷ 100 = 100 guests.
CBSE Step-by-Step Marking Scheme
Correct conversion of 10 L to 10,000 mL
1.5 M
Correct division to find 100 guests
1.5 M
Q4
At Bunny and Banno's wedding feast, delicious kheer was served:
• The donkey drank 10 glasses of 100 mL each.
• The monkey drank 5 glasses of 200 mL each.
• The elephant drank 10 litres.
(a) How many millilitres of kheer did the donkey drink? Convert to litres.
(b) How many millilitres did the monkey drink? Convert to litres.
(c) Who drank more kheer: the donkey or the monkey? Bunny and Banno's Wedding Feast • Kheer Consumption 3 Marks
• The donkey drank 10 glasses of 100 mL each.
• The monkey drank 5 glasses of 200 mL each.
• The elephant drank 10 litres.
(a) How many millilitres of kheer did the donkey drink? Convert to litres.
(b) How many millilitres did the monkey drink? Convert to litres.
(c) Who drank more kheer: the donkey or the monkey? Bunny and Banno's Wedding Feast • Kheer Consumption 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Capacity Math:
(a) Donkey's Kheer:
• 10 glasses × 100 mL = 1000 mL = 1 Litre.
(b) Monkey's Kheer:
• 5 glasses × 200 mL = 1000 mL = 1 Litre.
(c) Comparison:
• Both the donkey and the monkey drank exactly the same amount (1 Litre each).
(a) Donkey's Kheer:
• 10 glasses × 100 mL = 1000 mL = 1 Litre.
(b) Monkey's Kheer:
• 5 glasses × 200 mL = 1000 mL = 1 Litre.
(c) Comparison:
• Both the donkey and the monkey drank exactly the same amount (1 Litre each).
CBSE Step-by-Step Marking Scheme
Correct calculation for donkey (1000 mL = 1 L)
1.0 M
Correct calculation for monkey (1000 mL = 1 L)
1.0 M
Correct equality conclusion
1.0 M
Q5
A thirsty crow found a pitcher with water deep at the bottom. He dropped 10 small pebbles into the pitcher.
(a) Why did the water level rise when pebbles were dropped?
(b) If each pebble displaced 50 mL of water, by how many mL did the water level rise in total? Clever Crow Story • Water Displacement 3 Marks
(a) Why did the water level rise when pebbles were dropped?
(b) If each pebble displaced 50 mL of water, by how many mL did the water level rise in total? Clever Crow Story • Water Displacement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Water Displacement Science & Math:
(a) Why Water Rises:
• Pebbles take up space (volume) at the bottom of the pitcher. Because two objects cannot occupy the same space at the same time, the solid pebbles push the water upward.
(b) Total Water Rise:
• 10 pebbles × 50 mL = 500 mL (or half a litre).
(a) Why Water Rises:
• Pebbles take up space (volume) at the bottom of the pitcher. Because two objects cannot occupy the same space at the same time, the solid pebbles push the water upward.
(b) Total Water Rise:
• 10 pebbles × 50 mL = 500 mL (or half a litre).
CBSE Step-by-Step Marking Scheme
Clear physical explanation of volume displacement
1.5 M
Correct multiplication (10 × 50 mL = 500 mL)
1.5 M
Q6
How many of each container are required to fill a 1-litre (1000 mL) bottle completely?
(a) 500 mL bottles
(b) 250 mL glasses
(c) 200 mL cups
(d) 100 mL ladles Measuring 1 Litre • Fractional Bottle Volumes 4 Marks
(a) 500 mL bottles
(b) 250 mL glasses
(c) 200 mL cups
(d) 100 mL ladles Measuring 1 Litre • Fractional Bottle Volumes 4 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions into 1000 mL:
• (a) 500 mL: 1000 ÷ 500 = 2 bottles.
• (b) 250 mL: 1000 ÷ 250 = 4 glasses.
• (c) 200 mL: 1000 ÷ 200 = 5 cups.
• (d) 100 mL: 1000 ÷ 100 = 10 ladles.
• (a) 500 mL: 1000 ÷ 500 = 2 bottles.
• (b) 250 mL: 1000 ÷ 250 = 4 glasses.
• (c) 200 mL: 1000 ÷ 200 = 5 cups.
• (d) 100 mL: 1000 ÷ 100 = 10 ladles.
CBSE Step-by-Step Marking Scheme
Correct values for (a): 2 and (b): 4
2.0 M
Correct values for (c): 5 and (d): 10
2.0 M
Q7
An average family uses:
• Cooking & drinking: 25 Litres
• Bathing: 80 Litres
• Washing clothes & utensils: 65 Litres
(a) What is the total water used by the family in one day?
(b) If their overhead water tank holds 500 Litres, how many litres of water remain in the tank at the end of the day? Household Water Usage • Daily Estimation 3 Marks
• Cooking & drinking: 25 Litres
• Bathing: 80 Litres
• Washing clothes & utensils: 65 Litres
(a) What is the total water used by the family in one day?
(b) If their overhead water tank holds 500 Litres, how many litres of water remain in the tank at the end of the day? Household Water Usage • Daily Estimation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Usage:
(a) Total Daily Usage:
• 25 L + 80 L + 65 L = 170 Litres.
(b) Remaining Water:
• Tank capacity = 500 Litres.
• Used = 170 Litres.
• Remaining = 500 - 170 = 330 Litres.
(a) Total Daily Usage:
• 25 L + 80 L + 65 L = 170 Litres.
(b) Remaining Water:
• Tank capacity = 500 Litres.
• Used = 170 Litres.
• Remaining = 500 - 170 = 330 Litres.
CBSE Step-by-Step Marking Scheme
Correct total usage sum (170 L)
1.5 M
Correct tank remainder (330 L)
1.5 M
Q8
In Chapter 11 ('Jugs and Mugs'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Jugs and Mugs', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
School Drinking Water Conservation
Real-World Math Context: A leaking tap in the school corridor drips 100 mL of water every hour. The plumber was able to fix it after 12 hours.
Analytical Task: How much water was wasted in millilitres? How much is that in litres and millilitres?
1. Water wasted in 12 hours = 12 × 100 mL = 1,200 mL.
2. In litres and millilitres: 1,200 mL = 1,000 mL + 200 mL = 1 Litre 200 Millilitres (1 L 200 mL).
2. In litres and millilitres: 1,200 mL = 1,000 mL + 200 mL = 1 Litre 200 Millilitres (1 L 200 mL).
CBSE Assessment Rubric: 1.5M multiplication calculation + 1.5M conversion to litres and millilitres.
12
Unit 6: Patterns, Capacity & Sharing • Class 3 Mathematics (Classic CBSE)
Chapter 12: Can We Share?
Division as Equal Distribution, Equal Jumps on Number Line, Remainders & Word Problems
Chapter Highlights, Mathematical Ideas & Key Properties
- Equal sharing among individuals: understanding dividend, divisor, and quotient.
- Grouping objects into bundles of equal size.
- Division on the number line using backward jumps.
- Handling remainders: what happens when items cannot be shared equally.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
There are 28 laddoos. Mother shares them equally among 4 plates. (a) How many laddoos are on each plate? (b) Write the related multiplication fact.
Equal Sharing • Division Facts
2 Marks
✅ Step-by-Step Model Answer & Solution:
Solution:
• Total laddoos = 28
• Number of plates = 4
• (a) Division Fact: 28 ÷ 4 = 7 laddoos per plate.
• (b) Related Multiplication Fact: 4 × 7 = 28 (or 7 × 4 = 28).
• Total laddoos = 28
• Number of plates = 4
• (a) Division Fact: 28 ÷ 4 = 7 laddoos per plate.
• (b) Related Multiplication Fact: 4 × 7 = 28 (or 7 × 4 = 28).
CBSE Step-by-Step Marking Scheme
Correct division quotient (7)
1.0 M
Correct related multiplication statement
1.0 M
Q2
A teacher has 35 craft ribbons. She gives 4 ribbons to each group for an art project. (a) How many groups will receive ribbons? (b) How many ribbons will be left over?
Division with Remainder • Problem Solving
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Solution:
1. Divide 35 by 4:
• 4 × 8 = 32
• 35 - 32 = 3
2. (a) Groups receiving ribbons: 8 groups.
3. (b) Ribbons left over (remainder): 3 ribbons.
1. Divide 35 by 4:
• 4 × 8 = 32
• 35 - 32 = 3
2. (a) Groups receiving ribbons: 8 groups.
3. (b) Ribbons left over (remainder): 3 ribbons.
CBSE Step-by-Step Marking Scheme
Correct division calculation and quotient (8)
1.5 M
Correct remainder identification (3 ribbons)
1.5 M
Q3
A frog takes jumps of 3 steps at a time on a numbered track. How many jumps will it take to reach: (a) 15? (b) 27? Show the division sentences.
Frog Jump Division • Number Line
2 Marks
✅ Step-by-Step Model Answer & Solution:
Jumps:
• (a) To reach 15: 15 ÷ 3 = 5 jumps.
• (b) To reach 27: 27 ÷ 3 = 9 jumps.
• (a) To reach 15: 15 ÷ 3 = 5 jumps.
• (b) To reach 27: 27 ÷ 3 = 9 jumps.
CBSE Step-by-Step Marking Scheme
Correct jumps for 15 (5 jumps)
1.0 M
Correct jumps for 27 (9 jumps)
1.0 M
Q4
There are 21 caterpillars. They are sitting equally on 3 green leaves.
(a) How many caterpillars are on each leaf?
(b) Write the division sentence and multiplication check fact. Caterpillars on Leaves • Grouping & Division 3 Marks
(a) How many caterpillars are on each leaf?
(b) Write the division sentence and multiplication check fact. Caterpillars on Leaves • Grouping & Division 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Caterpillars per Leaf:
• Total caterpillars = 21.
• Number of leaves = 3.
• Caterpillars on each leaf = 21 ÷ 3 = 7 caterpillars.
(b) Mathematical Sentences:
• Division Sentence: 21 ÷ 3 = 7.
• Multiplication Check Fact: 3 × 7 = 21.
(a) Caterpillars per Leaf:
• Total caterpillars = 21.
• Number of leaves = 3.
• Caterpillars on each leaf = 21 ÷ 3 = 7 caterpillars.
(b) Mathematical Sentences:
• Division Sentence: 21 ÷ 3 = 7.
• Multiplication Check Fact: 3 × 7 = 21.
CBSE Step-by-Step Marking Scheme
Correct caterpillars per leaf (7)
1.0 M
Correct division sentence (21 ÷ 3 = 7)
1.0 M
Correct multiplication check fact (3 × 7 = 21)
1.0 M
Q5
Mummy bird has 12 grains of corn. She distributes them equally among her 4 baby chicks.
(a) How many grains does each chick get?
(b) If Mummy bird brings 8 more grains, how many total grains does each chick get now? Sharing Grains • Mother Bird and Chicks 3 Marks
(a) How many grains does each chick get?
(b) If Mummy bird brings 8 more grains, how many total grains does each chick get now? Sharing Grains • Mother Bird and Chicks 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
(a) Initial Sharing:
• 12 grains ÷ 4 chicks = 3 grains per chick.
(b) After Bringing 8 More Grains:
• Extra grains per chick = 8 ÷ 4 = 2 grains.
• Total grains per chick = 3 + 2 = 5 grains per chick (or 20 ÷ 4 = 5).
(a) Initial Sharing:
• 12 grains ÷ 4 chicks = 3 grains per chick.
(b) After Bringing 8 More Grains:
• Extra grains per chick = 8 ÷ 4 = 2 grains.
• Total grains per chick = 3 + 2 = 5 grains per chick (or 20 ÷ 4 = 5).
CBSE Step-by-Step Marking Scheme
Correct initial share (3 grains)
1.5 M
Correct updated share (5 grains)
1.5 M
Q6
Grandmother gave ₹60 to be divided equally among her 3 grandchildren: Anu, Bitoo, and Chintu.
(a) How many ₹10 notes will each child get?
(b) How much money does each child receive in rupees? Money Sharing • ₹10 Notes 3 Marks
(a) How many ₹10 notes will each child get?
(b) How much money does each child receive in rupees? Money Sharing • ₹10 Notes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• Total money = ₹60.
• In ₹10 notes: ₹60 = six ₹10 notes.
(a) ₹10 Notes per Child:
• 6 notes ÷ 3 children = two ₹10 notes each.
(b) Amount in Rupees:
• 2 × ₹10 = ₹20 each (or ₹60 ÷ 3 = ₹20).
• Total money = ₹60.
• In ₹10 notes: ₹60 = six ₹10 notes.
(a) ₹10 Notes per Child:
• 6 notes ÷ 3 children = two ₹10 notes each.
(b) Amount in Rupees:
• 2 × ₹10 = ₹20 each (or ₹60 ÷ 3 = ₹20).
CBSE Step-by-Step Marking Scheme
Correct number of ₹10 notes (2 notes)
1.5 M
Correct amount in rupees (₹20)
1.5 M
Q7
A frog starts at 18 on a number line and jumps 2 steps backward at a time towards 0.
(a) How many jumps does it take to reach 0?
(b) Write this as a division problem. Jumps of Frog • Division on Number Line 3 Marks
(a) How many jumps does it take to reach 0?
(b) Write this as a division problem. Jumps of Frog • Division on Number Line 3 Marks
✅ Step-by-Step Model Answer & Solution:
Division as Repeated Subtraction:
(a) Jumps:
• 18 - 2 = 16 (1 jump)
• 16 - 2 = 14 (2 jumps)
• ...
• 18 ÷ 2 = 9 jumps to reach 0.
(b) Division Problem:
• 18 ÷ 2 = 9.
(a) Jumps:
• 18 - 2 = 16 (1 jump)
• 16 - 2 = 14 (2 jumps)
• ...
• 18 ÷ 2 = 9 jumps to reach 0.
(b) Division Problem:
• 18 ÷ 2 = 9.
CBSE Step-by-Step Marking Scheme
Correct jump count (9 jumps)
1.5 M
Correct division expression (18 ÷ 2 = 9)
1.5 M
Q8
In Chapter 12 ('Can We Share?'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Can We Share?', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Library Bookshelf Organization
Real-World Math Context: The primary section library has 54 new storybooks. Each shelf can hold exactly 9 books.
Analytical Task: How many shelves will be completely filled? If 2 more books arrive, can another shelf be filled?
1. Shelves filled = 54 ÷ 9 = 6 shelves completely filled.
2. If 2 more books arrive, total books = 54 + 2 = 56.
3. To fill another (7th) shelf, they would need 9 books. Since they only have 2 extra books (7 books short), no, another shelf cannot be filled.
2. If 2 more books arrive, total books = 54 + 2 = 56.
3. To fill another (7th) shelf, they would need 9 books. Since they only have 2 extra books (7 books short), no, another shelf cannot be filled.
CBSE Assessment Rubric: 1.5M division of 54 ÷ 9 = 6 + 1.5M remainder analysis for extra books.
13
Unit 7: Data Handling & Money • Class 3 Mathematics (Classic CBSE)
Chapter 13: Smart Charts!
Tally Marks, Bar Charts, Tables, Traffic Surveys & Drawing Inferences
Chapter Highlights, Mathematical Ideas & Key Properties
- Using tally marks (bundles of 5: four vertical lines crossed by one diagonal line).
- Constructing and reading frequency tables from real-world surveys.
- Reading simple bar charts with labeled axes and scales.
- Interpreting data: finding the most popular, least popular, and total counts.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Look at the bar chart above: (a) Which is the most popular sport? (b) How many more students prefer cricket over football? (c) How many total students participated in the survey?
Bar Chart Interpretation • Sports Survey
3 Marks
✅ Step-by-Step Model Answer & Solution:
Data Reading:
• (a) Most popular sport: Cricket (18 students, highest bar).
• (b) Difference between Cricket and Football: 18 - 12 = 6 more students.
• (c) Total students: 18 + 12 + 15 + 5 = 50 students.
• (a) Most popular sport: Cricket (18 students, highest bar).
• (b) Difference between Cricket and Football: 18 - 12 = 6 more students.
• (c) Total students: 18 + 12 + 15 + 5 = 50 students.
CBSE Step-by-Step Marking Scheme
Correct most popular sport identified
1.0 M
Correct difference calculation (18 - 12 = 6)
1.0 M
Correct total students sum (50)
1.0 M
Q2
Draw tally marks for the following frequency counts: (a) 7 cars, (b) 14 bicycles, (c) 19 pedestrians.
Tally Marks Representation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Tally Mark Representations (Bundles of 5):
• (a) 7 cars:|||| || (One bundle of 5 + 2 lines)
• (b) 14 bicycles:|||| |||| |||| (Two bundles of 5 + 4 lines)
• (c) 19 pedestrians:|||| |||| |||| |||| (Three bundles of 5 + 4 lines).
• (a) 7 cars:
• (b) 14 bicycles:
• (c) 19 pedestrians:
CBSE Step-by-Step Marking Scheme
Correct tally bundle for 7
1.0 M
Correct tally bundles for 14
1.0 M
Correct tally bundles for 19
1.0 M
Q3
In a class of 30 children, 10 help in setting the dinner table, 12 help in market shopping, and 8 help in cleaning rooms. Represent this data in a clean frequency table with tally marks.
Data Table Analysis • Family Helpers
3 Marks
✅ Step-by-Step Model Answer & Solution:
Frequency Table:
| Help Activity | Tally Marks | Number of Children |
|---|---|---|
| Setting Dinner Table | 10 | |
| Market Shopping | 12 | |
| Cleaning Rooms | 8 | |
| Total | — | 30 |
CBSE Step-by-Step Marking Scheme
Correct table layout and categories
1.5 M
Correct tally grouping and frequency total (30)
1.5 M
Q4
Anu stood at a road crossing for 15 minutes and made tally marks for passing vehicles:
• Bicycles:|||| |||| || (12)
• Cars:|||| ||| (8)
• Auto-rickshaws:|||| |||| (10)
• Buses: |||| (4)
(a) How many vehicles did Anu count in total?
(b) Which vehicle was seen the most, and which the least?
(c) How many more bicycles passed than buses? Traffic on the Road • Tally Chart 3 Marks
• Bicycles:
• Cars:
• Auto-rickshaws:
• Buses: |||| (4)
(a) How many vehicles did Anu count in total?
(b) Which vehicle was seen the most, and which the least?
(c) How many more bicycles passed than buses? Traffic on the Road • Tally Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Traffic Analysis:
(a) Total Vehicles:
• 12 + 8 + 10 + 4 = 34 vehicles.
(b) Most & Least:
• Most: Bicycles (12).
• Least: Buses (4).
(c) Difference (Bicycles vs Buses):
• 12 - 4 = 8 more bicycles.
(a) Total Vehicles:
• 12 + 8 + 10 + 4 = 34 vehicles.
(b) Most & Least:
• Most: Bicycles (12).
• Least: Buses (4).
(c) Difference (Bicycles vs Buses):
• 12 - 4 = 8 more bicycles.
CBSE Step-by-Step Marking Scheme
Correct total count (34 vehicles)
1.0 M
Correct most (bicycles) and least (buses)
1.0 M
Correct difference (8)
1.0 M
Q5
A bar chart of children's favorite pets shows:
• Dogs: 10 children
• Cats: 8 children
• Parrots: 6 children
• Rabbits: 4 children
(a) Which is the most popular pet in the class?
(b) How many children like cats or parrots in total?
(c) What is the total number of children surveyed? Favourite Pets • Bar Chart Reading 3 Marks
• Dogs: 10 children
• Cats: 8 children
• Parrots: 6 children
• Rabbits: 4 children
(a) Which is the most popular pet in the class?
(b) How many children like cats or parrots in total?
(c) What is the total number of children surveyed? Favourite Pets • Bar Chart Reading 3 Marks
✅ Step-by-Step Model Answer & Solution:
Bar Chart Data:
• (a) Most Popular Pet: Dog (chosen by 10 children).
• (b) Cats or Parrots: 8 (Cats) + 6 (Parrots) = 14 children.
• (c) Total Surveyed: 10 + 8 + 6 + 4 = 28 children.
• (a) Most Popular Pet: Dog (chosen by 10 children).
• (b) Cats or Parrots: 8 (Cats) + 6 (Parrots) = 14 children.
• (c) Total Surveyed: 10 + 8 + 6 + 4 = 28 children.
CBSE Step-by-Step Marking Scheme
Correct most popular pet (Dog)
1.0 M
Correct sum for cats + parrots (14)
1.0 M
Correct total surveyed (28)
1.0 M
Q6
In a botanical garden, flowers are counted by color:
• Red roses: 25
• Yellow marigolds: 35
• Blue orchids: 15
• White lilies: 20
(a) Create a frequency table showing the colors and numbers of flowers.
(b) How many yellow marigolds and blue orchids are there combined? Flowers in the Garden • Smart Chart 3 Marks
• Red roses: 25
• Yellow marigolds: 35
• Blue orchids: 15
• White lilies: 20
(a) Create a frequency table showing the colors and numbers of flowers.
(b) How many yellow marigolds and blue orchids are there combined? Flowers in the Garden • Smart Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Frequency Table:
(b) Combined Count:
• 35 (Yellow) + 15 (Blue) = 50 flowers.
| Flower Type & Color | Number of Flowers |
|---|---|
| Red Roses | 25 |
| Yellow Marigolds | 35 |
| Blue Orchids | 15 |
| White Lilies | 20 |
| Total | 95 |
(b) Combined Count:
• 35 (Yellow) + 15 (Blue) = 50 flowers.
CBSE Step-by-Step Marking Scheme
Accurate table construction with all 4 flowers
1.5 M
Correct sum of yellow and blue flowers (50)
1.5 M
Q7
Rohan rolled a die 20 times and recorded the outcomes:
• Number 1: 3 times
• Number 2: 4 times
• Number 3: 2 times
• Number 4: 5 times
• Number 5: 3 times
• Number 6: 3 times
(a) Which face appeared the maximum number of times?
(b) Which face appeared the minimum number of times?
(c) Did any faces appear the same number of times? Dice Roll Experiment • Data Recording 3 Marks
• Number 1: 3 times
• Number 2: 4 times
• Number 3: 2 times
• Number 4: 5 times
• Number 5: 3 times
• Number 6: 3 times
(a) Which face appeared the maximum number of times?
(b) Which face appeared the minimum number of times?
(c) Did any faces appear the same number of times? Dice Roll Experiment • Data Recording 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data Analysis:
• (a) Maximum Face: Face 4 (appeared 5 times).
• (b) Minimum Face: Face 3 (appeared 2 times).
• (c) Equal Faces: Yes, Faces 1, 5, and 6 each appeared 3 times.
• (a) Maximum Face: Face 4 (appeared 5 times).
• (b) Minimum Face: Face 3 (appeared 2 times).
• (c) Equal Faces: Yes, Faces 1, 5, and 6 each appeared 3 times.
CBSE Step-by-Step Marking Scheme
Correct maximum face (4)
1.0 M
Correct minimum face (3)
1.0 M
Correct identification of tied faces (1, 5, 6)
1.0 M
Q8
In Chapter 13 ('Smart Charts!'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Smart Charts!', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
School Canteen Fruit Survey
Real-World Math Context: The canteen manager tracked fruit sales on Wednesday: Bananas (45), Apples (30), Oranges (25), and Guavas (20).
Analytical Task: Which fruit was the most demanded? What fraction of the total fruit sales did bananas represent?
1. Total fruits sold = 45 + 30 + 25 + 20 = 120 fruits.
2. Most demanded fruit: Bananas with 45 sold.
3. Fraction of bananas: 45 out of 120 = 45/120 = 15/40 = 3/8 (three-eighths).
2. Most demanded fruit: Bananas with 45 sold.
3. Fraction of bananas: 45 out of 120 = 45/120 = 15/40 = 3/8 (three-eighths).
CBSE Assessment Rubric: 1M total summation + 1M most demanded + 1M simplified fraction.
14
Unit 7: Data Handling & Money • Class 3 Mathematics (Classic CBSE)
Chapter 14: Rupees and Paise
Indian Currency, Converting Rupees to Paise, Self-Service Store Bills & Cash Receipts
Chapter Highlights, Mathematical Ideas & Key Properties
- Indian currency: coins (₹1, ₹2, ₹5, ₹10, ₹20) and notes (₹10, ₹20, ₹50, ₹100, ₹200, ₹500).
- 1 Rupee = 100 Paise (₹1 = 100 p).
- Writing amounts in rupees and paise with decimal points (e.g., ₹12.50).
- Preparing itemized shopping bills and checking total amounts and change.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (17 Solved Questions)
Q1
Convert: (a) ₹7 into paise, (b) 850 paise into rupees and paise, (c) ₹12.75 into paise.
Rupees & Paise Conversion • Arithmetic
3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions (1 Rupee = 100 Paise):
• (a) ₹7: 7 × 100 p = 700 paise.
• (b) 850 paise: 800 p + 50 p = 8 rupees and 50 paise (₹8.50).
• (c) ₹12.75: (12 × 100) + 75 = 1200 + 75 = 1,275 paise.
• (a) ₹7: 7 × 100 p = 700 paise.
• (b) 850 paise: 800 p + 50 p = 8 rupees and 50 paise (₹8.50).
• (c) ₹12.75: (12 × 100) + 75 = 1200 + 75 = 1,275 paise.
CBSE Step-by-Step Marking Scheme
Correct conversion for ₹7 (700 p)
1.0 M
Correct conversion for 850 p (₹8.50)
1.0 M
Correct conversion for ₹12.75 (1275 p)
1.0 M
Q2
Prepare a cash memo for the following purchases: 1 notebook for ₹24.50, 2 pencils at ₹6.00 each, and 1 sharpener for ₹4.50. What is the total bill amount?
Cash Memo Preparation • Bill Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo:
• Total bill = 24.50 + 12.00 + 4.50 = ₹41.00.
| Item | Rate (₹) | Qty | Amount (₹) |
|---|---|---|---|
| Notebook | 24.50 | 1 | 24.50 |
| Pencils | 6.00 | 2 | 12.00 |
| Sharpener | 4.50 | 1 | 4.50 |
| TOTAL AMOUNT: | ₹41.00 | ||
• Total bill = 24.50 + 12.00 + 4.50 = ₹41.00.
CBSE Step-by-Step Marking Scheme
Correct itemised extensions
1.5 M
Correct total addition (₹41.00)
1.5 M
Q3
A railway ticket from Station A to Station B costs ₹62.50. (a) What is the total fare for two such tickets? (b) If you hand over a ₹200 note to the ticket booking clerk, how much balance will you receive back?
Railway Ticket Booking • Money Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-step Solution:
(a) Total Ticket Fare:
2 × ₹62.50 = ₹(62.50 + 62.50) = ₹125.00.
(b) Balance Received Back:
Amount given = ₹200.00
Total fare = ₹125.00
Change = ₹200.00 - ₹125.00 = ₹75.00.
(a) Total Ticket Fare:
2 × ₹62.50 = ₹(62.50 + 62.50) = ₹125.00.
(b) Balance Received Back:
Amount given = ₹200.00
Total fare = ₹125.00
Change = ₹200.00 - ₹125.00 = ₹75.00.
CBSE Step-by-Step Marking Scheme
Correct calculation of 2 tickets fare (₹125)
1.5 M
Correct subtraction for balance change (₹75)
1.5 M
Q4
Prepare a cash memo for the following shopping trip:
• 1 toy car for ₹15.50
• 3 pencils at ₹2.50 each
• 2 toffees at ₹0.50 each
(a) Find the total amount of the bill.
(b) If you give a ₹50 note, how much change should you get back? Self-Made Cash Memo • Toy Purchases 3 Marks
• 1 toy car for ₹15.50
• 3 pencils at ₹2.50 each
• 2 toffees at ₹0.50 each
(a) Find the total amount of the bill.
(b) If you give a ₹50 note, how much change should you get back? Self-Made Cash Memo • Toy Purchases 3 Marks
✅ Step-by-Step Model Answer & Solution:
Itemized Cash Memo:
• 1 Toy Car: ₹15.50.
• 3 Pencils: 3 × ₹2.50 = ₹7.50.
• 2 Toffees: 2 × ₹0.50 = ₹1.00.
• Total Bill: ₹15.50 + ₹7.50 + ₹1.00 = ₹24.00.
Change from ₹50:
• Change = ₹50.00 - ₹24.00 = ₹26.00.
• 1 Toy Car: ₹15.50.
• 3 Pencils: 3 × ₹2.50 = ₹7.50.
• 2 Toffees: 2 × ₹0.50 = ₹1.00.
• Total Bill: ₹15.50 + ₹7.50 + ₹1.00 = ₹24.00.
Change from ₹50:
• Change = ₹50.00 - ₹24.00 = ₹26.00.
CBSE Step-by-Step Marking Scheme
Correct itemised sub-totals and sum (₹24.00)
2.0 M
Correct change subtraction (₹26.00)
1.0 M
Q5
Study the railway fare chart from New Jalpaiguri:
• To Siliguri (10 km): ₹12.50
• To Malbazar (45 km): ₹28.00
• To Alipurduar (120 km): ₹62.50
(a) What is the ticket fare for two persons traveling to Malbazar?
(b) How much more expensive is a ticket to Alipurduar than to Siliguri? Train Ticket Fare Table • Route Math 3 Marks
• To Siliguri (10 km): ₹12.50
• To Malbazar (45 km): ₹28.00
• To Alipurduar (120 km): ₹62.50
(a) What is the ticket fare for two persons traveling to Malbazar?
(b) How much more expensive is a ticket to Alipurduar than to Siliguri? Train Ticket Fare Table • Route Math 3 Marks
✅ Step-by-Step Model Answer & Solution:
Railway Fare Calculations:
(a) Two Tickets to Malbazar:
• 2 × ₹28.00 = ₹56.00.
(b) Price Difference:
• Alipurduar fare = ₹62.50.
• Siliguri fare = ₹12.50.
• Difference = ₹62.50 - ₹12.50 = ₹50.00.
(a) Two Tickets to Malbazar:
• 2 × ₹28.00 = ₹56.00.
(b) Price Difference:
• Alipurduar fare = ₹62.50.
• Siliguri fare = ₹12.50.
• Difference = ₹62.50 - ₹12.50 = ₹50.00.
CBSE Step-by-Step Marking Scheme
Correct multiplication for 2 tickets (₹56.00)
1.5 M
Correct subtraction for difference (₹50.00)
1.5 M
Q6
In the textbook activity, children place a coin under paper and rub a pencil over it:
(a) What design appears when you rub a ₹5 coin?
(b) How many 50-paise coins make ₹1?
(c) How many 25-paise coins make ₹1? Coin Rubbing & Currency Recognition 3 Marks
(a) What design appears when you rub a ₹5 coin?
(b) How many 50-paise coins make ₹1?
(c) How many 25-paise coins make ₹1? Coin Rubbing & Currency Recognition 3 Marks
✅ Step-by-Step Model Answer & Solution:
Coin Mathematics:
• (a) Coin Rubbing: The impression shows the Lion Capital of Ashoka (emblem), the numeral '5', and the rupee symbol (₹).
• (b) 50-Paise Coins in ₹1: 100 paise ÷ 50 paise = 2 coins.
• (c) 25-Paise Coins in ₹1: 100 paise ÷ 25 paise = 4 coins.
• (a) Coin Rubbing: The impression shows the Lion Capital of Ashoka (emblem), the numeral '5', and the rupee symbol (₹).
• (b) 50-Paise Coins in ₹1: 100 paise ÷ 50 paise = 2 coins.
• (c) 25-Paise Coins in ₹1: 100 paise ÷ 25 paise = 4 coins.
CBSE Step-by-Step Marking Scheme
Accurate visual impression description
1.0 M
Correct count of 50-paise coins (2)
1.0 M
Correct count of 25-paise coins (4)
1.0 M
Q7
Solve the following money additions:
(a) ₹45.50 + ₹23.75
(b) ₹120.25 + ₹85.80 Money Addition with Paise • Regrouping 3 Marks
(a) ₹45.50 + ₹23.75
(b) ₹120.25 + ₹85.80 Money Addition with Paise • Regrouping 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Money Addition:
• (a) ₹45.50 + ₹23.75:
- Paise: 50 + 75 = 125 paise = ₹1 and 25 paise.
- Rupees: 45 + 23 + 1 (carry) = 69.
- Total = ₹69.25.
• (b) ₹120.25 + ₹85.80:
- Paise: 25 + 80 = 105 paise = ₹1 and 05 paise.
- Rupees: 120 + 85 + 1 (carry) = 206.
- Total = ₹206.05.
• (a) ₹45.50 + ₹23.75:
- Paise: 50 + 75 = 125 paise = ₹1 and 25 paise.
- Rupees: 45 + 23 + 1 (carry) = 69.
- Total = ₹69.25.
• (b) ₹120.25 + ₹85.80:
- Paise: 25 + 80 = 105 paise = ₹1 and 05 paise.
- Rupees: 120 + 85 + 1 (carry) = 206.
- Total = ₹206.05.
CBSE Step-by-Step Marking Scheme
Correct addition with paise regrouping for (a): ₹69.25
1.5 M
Correct addition with paise regrouping for (b): ₹206.05
1.5 M
Q8
In Chapter 14 ('Rupees and Paise'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
Textbook Exercise • Real-Life Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In 'Rupees and Paise', how do you measure and compare quantities accurately? Explain with an example using standard units.
In-Text Activity • Hands-on Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
Practice Time • Two-Step Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ? Mental Math • Quick Calculations 2 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners. Geometry & Shapes • Edge and Corner Counting 3 Marks
✅ Step-by-Step Model Answer & Solution:
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
Pattern Time • Sequences and Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
Time & Calendar • Date Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
Equal Sharing • Division Problem
2 Marks
✅ Step-by-Step Model Answer & Solution:
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots? Data Handling • Reading a Bar Chart 3 Marks
✅ Step-by-Step Model Answer & Solution:
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
Money • Making a Change
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
School Tuck Shop Purchasing
Real-World Math Context: Kabir buys a sandwich for ₹32.50, an apple juice bottle for ₹25.00, and a fruit bun for ₹15.50 at the school canteen. He pays with a ₹100 note.
Analytical Task: What is his total canteen bill? How much change should the canteen cashier return to him?
1. Total bill = ₹32.50 + ₹25.00 + ₹15.50 = ₹(32.50 + 15.50) + ₹25.00 = ₹48.00 + ₹25.00 = ₹73.00.
2. Amount paid = ₹100.00.
3. Change to receive = ₹100.00 - ₹73.00 = ₹27.00.
2. Amount paid = ₹100.00.
3. Change to receive = ₹100.00 - ₹73.00 = ₹27.00.
CBSE Assessment Rubric: 1.5M addition of rupees and paise + 1.5M change subtraction from ₹100.