Chapter 9 of 14
Chapter 9: House of Hundreds – II
3-Digit Numbers from 500 to 999, Comparison, Estimation & 1000 | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- 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.
All Textbook Exercises & In-Text Tasks (18 Questions)
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Q1
Number Sequence & Transition • Milestones
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?
[3 Marks]
✅ Step-by-Step Solution & Working
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
Place Value Table • Hundreds, Tens, Ones
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.
[3 Marks]
✅ Step-by-Step Solution & Working
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
Comparison Rules • 3-Digit Numbers
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.
[3 Marks]
✅ Step-by-Step Solution & Working
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
3-Digit Number Comparison • Greater Than / Less Than
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
[4 Marks]
(a) 648 ___ 684
(b) 705 ___ 507
(c) 830 ___ 800 + 30
(d) 999 ___ 1000
✅ Step-by-Step Solution & Working
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
Forming Greatest and Smallest Numbers
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.
[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.
✅ Step-by-Step Solution & Working
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
Ordering Numbers • Ascending & Descending
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).
[3 Marks]
(a) Arrange them in Ascending Order (smallest to largest).
(b) Arrange them in Descending Order (largest to smallest).
✅ Step-by-Step Solution & Working
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
Skip Counting Beyond 500 • Number Track
Write the next 3 numbers in each sequence:
(a) 550, 600, 650, ___, ___, ___
(b) 720, 740, 760, ___, ___, ___
(c) 980, 985, 990, ___, ___, ___
[3 Marks]
(a) 550, 600, 650, ___, ___, ___
(b) 720, 740, 760, ___, ___, ___
(c) 980, 985, 990, ___, ___, ___
✅ Step-by-Step Solution & Working
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
Textbook Exercise • Practical Problem Solving
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.
[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.
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 – II', 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.
• 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]
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ?
✅ Step-by-Step Solution & Working
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
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.
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 – II': 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.
• 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]
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard.
✅ 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).
• (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]
(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?
✅ 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.
• (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]
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have?
✅ 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).
• (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.
• 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.
• 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]
(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.
✅ 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.
• (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
Marathon Bib Number Allocation
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?
Evaluation & Model Answer:
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.
Rubric: 1.5M inclusive count calculation + 1.5M runners between calculation.