Chapter 8 of 14
⬅️ Ch 7: Raksha Bandhan Ch 9: House of Hundreds – II ➡️
NCERT Class 3 Mathematics • New NEP 2020 / NCF 2023

Chapter 8: Fair Share

Concept of Equal Sharing, Grouping, Introduction to Division & Fractions | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts
  • 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.
Fair Share — Sharing 12 Laddoos Equally Among 3 Children Rohan (4) Priya (4) Ali (4) 12 ÷ 3 = 4 Laddoos per Child

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

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Q1 Equal Sharing • Division Basics
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.
[3 Marks]
✅ Step-by-Step Solution & Working
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.
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 Equal Grouping • Practical Word Problem
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?
[2 Marks]
✅ Step-by-Step Solution & Working
Solution:
• 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 Fractions of a Collection • Halves & Quarters
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.
[3 Marks]
✅ Step-by-Step Solution & Working
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).
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 Fraction of a Collection • Word Problem
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.
[3 Marks]
✅ Step-by-Step Solution & Working
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.
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 Equal Sharing with Remainder • Pencils Problem
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.
[3 Marks]
✅ Step-by-Step Solution & Working
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.
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 Visual Fractions • Shading Geometric Figures
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?
[3 Marks]
✅ Step-by-Step Solution & Working
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.
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 Team Formation • Equal Division
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?
[3 Marks]
✅ Step-by-Step Solution & Working
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.
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 Textbook Exercise • Practical Problem Solving
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.
[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 'Fair Share', 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 'Fair Share': 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

Picnic Fruit Distribution

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?
Evaluation & Model Answer:
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.
Rubric: 1M bananas division + 1M oranges division + 1M total per basket.
⬅️ Ch 7: Raksha Bandhan Ch 9: House of Hundreds – II ➡️