Equal Groups – Class 4 Maths Chapter 9 Notes & NCERT PDF

Class 4MathematicsChapter 9NCERT book: Maths Mela - Class 4

Notes and a simple summary of Chapter 9 of the NCERT Class 4 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 9: Equal Groups

Introduction

"Equal Groups" is the multiplication and division chapter of Maths Mela Class 4. It starts with animals jumping on a number line, moves to flowers in Gulabo's garden, cupcakes in Radha's bakery, wheels, legs and boats, and ends with "always, sometimes or never true" statements. The focus (as the Note for Teachers says) is on multiplying 1-, 2- and 3-digit numbers by 1-digit numbers, breaking the number of groups into tens to make it easy.

What's in this Chapter

Animal Jumps (multiples) – The frog jumps 3 steps at a time and touches 0, 3, 6, 9, 12 … – the multiples of 3. It never touches 67. The squirrel jumps 4 steps (needs 15 jumps to reach 60), the rabbit 6 steps (its smallest 3-digit landing number is 102, after 17 jumps) and the kangaroo 8 steps. To reach 48 the rabbit jumps 8 times and the kangaroo 6 times.

Common multiples – Numbers touched by both frog and squirrel (12, 24, 36 …) are common multiples of 3 and 4. For rabbit and kangaroo: 24, 48, 72 …

Cat and rat – The cat is on 6 and jumps 3; the rat is on 12 and jumps 2. After 6 jumps each, both are on 24, so the cat catches the rat at 24.

Gulabo's Garden – 12 lilies with 3 petals each: 10 × 3 = 30 and 2 × 3 = 6, so 12 × 3 = 36. Here 12 is the number of groups (multiplier), 3 is the group size (multiplicand) and 36 is the product. 80 hibiscus petals with 5 petals per flower means 80 ÷ 5 = 16 flowers.

Arrays – Saplings in rows, strawberry boxes in columns and cupcakes in trays show multiplication as rows × columns. Radha bakes 18 cupcakes per tray; 2 trays make 36; 108 cupcakes need 6 trays; a square tray of 36 is 6 × 6.

The Doubling Magic – Magician Anvi doubles 23 flowers into 46. Doubling always gives an even number, so 3, 5, 7 or 9 can never be the ones digit of a double.

Multiplication chart – Children fill a 10 × 10 chart and look for patterns: row 7 equals column 7, row 8's ones digits repeat 8, 6, 4, 2, 0.

Multiples of 10 and 100 – 10 × 3 = 30, 20 × 3 = 60; 100 bikes × 2 people = 200.

Multiplying using 10s – 18 × 4 = 10 × 4 + 8 × 4 = 40 + 32 = 72. 23 carts × 8 rods = 160 + 24 = 184. 125 autos × 8 passengers = 800 + 160 + 40 = 1000.

Division by taking away groups – 58 wheels for 3-wheeled tempos: take away 30 (10 tempos), 15 (5), 9 (3), 3 (1) → 19 tempos with 1 wheel left. 108 people in 9 boats: 12 people in each boat.

Key Ideas

Multiplication means equal groups: number of groups × group size = product.

Multiples of a number are what you land on when you skip count by it.

Split big multipliers into tens and ones (18 = 10 + 8) to multiply easily.

Division undoes multiplication; take away easy groups (10s, 5s) and add up the parts.

Some division leaves a remainder (58 ÷ 3 = 19, remainder 1).

Activities from the Book

Find hidden multiplication and division sentences in a number grid.

Arrange 36, 8, 12 and 24 cupcakes in different rows and columns.

Make stories for 34 × 3, 75 × 5, 46 × 6 and 50 × 9.

Decide whether statements are always, sometimes or never true.

Words to Learn

Multiple – a number reached by skip counting (गुणज)

Common multiple – a multiple of two numbers (सार्व गुणज)

Product – the answer of multiplication (गुणनफल)

Multiplier – number of groups (गुणक)

Array – objects in rows and columns (पंक्ति-स्तंभ व्यवस्था)

Double – two times a number (दुगुना)

Divide – share into equal groups (भाग देना)

Remainder – what is left over (शेषफल)

Tips for Parents & Teachers

Hop on a chalk number line in steps of 3, 4, 6 and 8.

Use buttons or tokens to make arrays and swap rows and columns.

Practise doubling with coins: double ₹17, double ₹45.

Let children invent their own stories for multiplication sums.

Common Mistakes

Adding instead of multiplying (12 × 3 is not 15).

Forgetting the leftover in division (58 ÷ 3 has 1 wheel left).

Thinking 67 is a multiple of 3 because it is "near" 66.

💡 Key Learning Points

✓Multiples are the numbers reached by skip counting; common multiples belong to two numbers.
✓Multiplication = number of groups × group size; arrays show it as rows × columns.
✓Split the multiplier into tens and ones (18 × 4 = 40 + 32) to multiply bigger numbers.
✓Division can be done by taking away easy groups; sometimes a remainder is left.
✓Doubling always gives an even number.

👨‍🏫 Teaching Tips

→Use a floor number line for animal jumps and let children physically jump.
→Give counters to build arrays for 12, 24 and 36 in different ways.
→Encourage breaking numbers into tens (10 + 8) before using any algorithm.
→Mix 'share' and 'measure' division stories, as the chapter suggests.
→Let children create multiplication stories from their own lives.
→Use the 10 × 10 chart to hunt for patterns in rows and columns.
→Discuss 'always / sometimes / never true' statements with examples and counter-examples.

📋 Assessment Questions

Can the child list multiples of 3, 4, 6 and 8 and find common ones?
Can the child multiply a 2- or 3-digit number by a 1-digit number by splitting into tens?
Can the child solve a division word problem and state any remainder?
Can the child explain why doubles are always even?

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