Chapter 6 of 14
⬅️ Ch 5: Fun with Shapes Ch 7: Raksha Bandhan ➡️
NCERT Class 3 Mathematics • New NEP 2020 / NCF 2023

Chapter 6: House of Hundreds – I

Place Value (Hundreds, Tens, Ones), 3-Digit Numbers, Abacus & Expansion | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts
  • 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 (<).
House of Hundreds — Base-10 Model for 346 3 Hundreds = 300 4 Tens = 40 6 Ones = 6 346

All Textbook Exercises & In-Text Tasks (18 Questions)

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Q1 Place Value Exploration • 3-Digit Numbers
What is the place value and face value of the underlined digit in each: (a) 472, (b) 309, (c) 258?
[3 Marks]
✅ Step-by-Step Solution & Working
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.
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 Number Ordering • Ascending & Descending
Arrange the following numbers in: (a) Ascending order (smallest to largest), (b) Descending order (largest to smallest): 345, 289, 412, 198, 305.
[2 Marks]
✅ Step-by-Step Solution & Working
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.
CBSE Step-by-Step Marking Scheme
Correct ascending arrangement 1.0 M
Correct descending arrangement 1.0 M
Q3 Forming Numbers • Greatest & Smallest
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.
[3 Marks]
✅ Step-by-Step Solution & Working
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).
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 Arrow Cards Assembly • Place Value
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?
[3 Marks]
✅ Step-by-Step Solution & Working
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).
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 Abacus Representation • 3-Digit Numbers
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?
[3 Marks]
✅ Step-by-Step Solution & Working
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.
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 Number Sequences • Missing 3-Digit Numbers
Fill in the missing numbers in these sequences:
(a) 245, 246, ___, 248, ___, 250
(b) 310, 320, ___, 340, ___, 360
(c) 490, 480, ___, 460, ___, 440
[3 Marks]
✅ Step-by-Step Solution & Working
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.
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 Mental Math • Adding 10 and 100
Find the answers using mental math tricks without long column addition:
(a) 325 + 10
(b) 325 + 100
(c) 468 - 10
(d) 468 - 100
[4 Marks]
✅ Step-by-Step Solution & Working
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.
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 Textbook Exercise • Practical Problem Solving
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.
[2 Marks]
✅ Step-by-Step Solution & Working
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.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48 1 M
Multiplication 4 × 12 = 48 1 M
Q9 In-Text Activity • Concept Exploration
In 'House of Hundreds – I', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
[2 Marks]
✅ Step-by-Step Solution & Working
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.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100 1 M
Inverse check 100 - 35 = 65 1 M
Q10 Practice Time • Mental Math Drills
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ?
[2 Marks]
✅ Step-by-Step Solution & Working
Mental Calculations:
• (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 Word Problem • Real Life Application
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?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
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 Critical Thinking • Finding the Pattern
Observe the sequence related to 'House of Hundreds – I': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
[2 Marks]
✅ Step-by-Step Solution & Working
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.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72 1 M
Rule: multiples of 12 / +12 step 1 M
Q13 Estimation & Measurement • Practical Judgment
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.
[2 Marks]
✅ Step-by-Step Solution & Working
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).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items 2 M
Q14 Data Interpretation • Reading Simple Tables
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?
[3 Marks]
✅ Step-by-Step Solution & Working
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.
CBSE Step-by-Step Marking Scheme
Mango identified 1 M
Difference = 13 1 M
Total = 90 1 M
Q15 Let us Do • Shapes and Symmetry
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?
[3 Marks]
✅ Step-by-Step Solution & Working
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).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines 1 M
Triangle = 3 lines 1 M
Circle = infinite lines 1 M
Q16 Puzzle Time • Missing Number Grid
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?
[2 Marks]
✅ Step-by-Step Solution & Working
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.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning 2 M
Q17 Money & Shopping • Cash Memo Bill
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.
[3 Marks]
✅ Step-by-Step Solution & Working
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.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38 2 M
Change = ₹12 1 M
Q18 Chapter Review • Comprehensive Concept Check
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.
[3 Marks]
✅ Step-by-Step Solution & Working
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.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True 3 M
🌟 NEP 2020 Competency-Based Case Study

School Tree Plantation Drive

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?
Evaluation & Model Answer:
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.
Rubric: 1.5M addition of 3 numbers + 1.5M subtraction from 500 target.
⬅️ Ch 5: Fun with Shapes Ch 7: Raksha Bandhan ➡️