Chapter 4 of 14
Chapter 4: Thousands Around Us
Place Value, Face Value, Expanded Form, Number Names & Abacus | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Extending 3-digit place value to 4-digit numbers: Thousands (Th), Hundreds (H), Tens (T), Ones (O).
- Smallest 4-digit number is 1,000; largest 4-digit number is 9,999.
- Place Value vs. Face Value of digits in a 4-digit number.
- Writing numbers in expanded form and standard form.
- Ordering 4-digit numbers on a number line and comparing using >, <, and =.
All Textbook Exercises & In-Text Tasks (15 Questions)
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Q1
Place Value vs. Face Value
In the numeral 6,835: (a) What is the place value and face value of 8? (b) What is the place value and face value of 6? (c) Write 6,835 in expanded notation and word form.
[3 Marks]
✅ Step-by-Step Solution & Working
(a) For digit 8:
• Face Value = 8 (the digit itself).
• Place Value = 8 × 100 = 800 (Eight Hundred).
(b) For digit 6:
• Face Value = 6.
• Place Value = 6 × 1,000 = 6,000 (Six Thousand).
(c) Expanded Notation & Word Form:
• Expanded Form: 6,000 + 800 + 30 + 5
• Number Name: Six thousand eight hundred thirty-five.
• Face Value = 8 (the digit itself).
• Place Value = 8 × 100 = 800 (Eight Hundred).
(b) For digit 6:
• Face Value = 6.
• Place Value = 6 × 1,000 = 6,000 (Six Thousand).
(c) Expanded Notation & Word Form:
• Expanded Form: 6,000 + 800 + 30 + 5
• Number Name: Six thousand eight hundred thirty-five.
CBSE Step-by-Step Marking Scheme
Correct place and face value for 8 & 6
1.5 M
Correct expanded form and word name
1.5 M
Q2
Number Formation & Comparison
Using the digits 3, 0, 7, and 9 only once: (a) Form the largest possible 4-digit number. (b) Form the smallest possible 4-digit number. (c) Find the difference between them.
[3 Marks]
✅ Step-by-Step Solution & Working
(a) Largest 4-digit number:
To make the largest number, arrange digits in descending order: 9,730.
(b) Smallest 4-digit number:
We cannot put 0 at the thousands place (or it becomes a 3-digit number). So choose the smallest non-zero digit first (3), followed by 0, then remaining digits in ascending order: 3,079.
(c) Difference:
9,730
- 3,079
--------
6,651
Check: 3,079 + 6,651 = 9,730. Correct!
To make the largest number, arrange digits in descending order: 9,730.
(b) Smallest 4-digit number:
We cannot put 0 at the thousands place (or it becomes a 3-digit number). So choose the smallest non-zero digit first (3), followed by 0, then remaining digits in ascending order: 3,079.
(c) Difference:
9,730
- 3,079
--------
6,651
Check: 3,079 + 6,651 = 9,730. Correct!
CBSE Step-by-Step Marking Scheme
Correct largest number 9,730
1.0 M
Correct smallest number 3,079 (justifying 0 placement)
1.0 M
Accurate subtraction working 6,651
1.0 M
Q3
Place Value & Expanded Form • 4-Digit Numbers
In the number 7,408: (a) Write its expanded form, (b) Find the difference between the place value and face value of the digit 4.
[3 Marks]
✅ Step-by-Step Solution & Working
1. Expanded Form:
7,408 = 7,000 + 400 + 0 + 8 (or 7 Thousands + 4 Hundreds + 0 Tens + 8 Ones).
2. Place Value vs. Face Value of 4:
• Place Value of 4: Since 4 is in the hundreds place = 4 × 100 = 400.
• Face Value of 4: The digit itself = 4.
• Difference: 400 - 4 = 396.
7,408 = 7,000 + 400 + 0 + 8 (or 7 Thousands + 4 Hundreds + 0 Tens + 8 Ones).
2. Place Value vs. Face Value of 4:
• Place Value of 4: Since 4 is in the hundreds place = 4 × 100 = 400.
• Face Value of 4: The digit itself = 4.
• Difference: 400 - 4 = 396.
CBSE Step-by-Step Marking Scheme
Correct expanded form
1.5 M
Place value (400), face value (4), difference (396)
1.5 M
Q4
Estimation • Rounding Numbers
A cricket stadium sold 6,874 tickets on Saturday. Round this attendance to: (a) the nearest 10, (b) the nearest 100, (c) the nearest 1,000.
[3 Marks]
✅ Step-by-Step Solution & Working
Rounding 6,874:
• (a) Nearest 10: The ones digit is 4 (< 5), so round down to 6,870.
• (b) Nearest 100: The tens digit is 7 (≥ 5), so round up to 6,900.
• (c) Nearest 1,000: The hundreds digit is 8 (≥ 5), so round up to 7,000.
• (a) Nearest 10: The ones digit is 4 (< 5), so round down to 6,870.
• (b) Nearest 100: The tens digit is 7 (≥ 5), so round up to 6,900.
• (c) Nearest 1,000: The hundreds digit is 8 (≥ 5), so round up to 7,000.
CBSE Step-by-Step Marking Scheme
Nearest 10: 6,870
1.0 M
Nearest 100: 6,900
1.0 M
Nearest 1,000: 7,000
1.0 M
Q5
Textbook Exercise • Real-World Context
In Chapter 4 ('Thousands Around Us'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Practice Time • Measurement & Conversions
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
[3 Marks]
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
✅ Step-by-Step Solution & Working
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Try These • Geometry and Shapes
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
[3 Marks]
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
✅ Step-by-Step Solution & Working
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
Money & Accounts • Rate List Calculation
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
[3 Marks]
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
✅ Step-by-Step Solution & Working
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
Fractions Exploration • Parts of a Whole
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
[3 Marks]
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
✅ Step-by-Step Solution & Working
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
Time & Clocks • Elapsed Time
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
[3 Marks]
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
✅ Step-by-Step Solution & Working
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
Perimeter & Area • Fencing a Field
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing.
[3 Marks]
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing.
✅ Step-by-Step Solution & Working
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Mental Math • Division and Multiplication
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
[2 Marks]
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
✅ Step-by-Step Solution & Working
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Patterns & Symmetries • Rotational Turns
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)?
[2 Marks]
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)?
✅ Step-by-Step Solution & Working
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
Smart Charts • Data Interpretation
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
[3 Marks]
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
✅ Step-by-Step Solution & Working
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
Chapter Review • True or False
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth).
[3 Marks]
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth).
✅ Step-by-Step Solution & Working
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study
Bank Token Display Counter
At a rural bank branch, token numbers run from 1,001 to 2,000. Customer Aman holds token 1,489. Customer Priya holds token 1,512.
Analytical Task: How many tokens are there strictly between Aman's token and Priya's token? Who will be served first?
Evaluation & Model Answer:
Aman will be served first because 1,489 < 1,512.
Tokens between them:
1,512 - 1,489 - 1 = 22 tokens strictly between them (from 1,490 to 1,511).
Tokens between them:
1,512 - 1,489 - 1 = 22 tokens strictly between them (from 1,490 to 1,511).
Rubric: 1 Mark for identifying Aman served first; 1 Mark for calculating 22 tokens.