Chapter 9 — Equal Groups

Chapter 9 of the Class 4 Mathematics NCERT textbook (Maths Mela), "Equal Groups", introduces multiplication and division through engaging activities like animal jumps, Gulabo's garden, doubling magic, and real-life word problems involving vehicles, cupcakes, and pottery. Students explore multiples, common multiples, multiplication tables up to 10×10, multiplying by tens and hundreds, and the partial-quotient method for division. Download the PDF and read the summary and Q&A below to master these concepts.

• Multiples and Common Multiples via Animal Jumps — The chapter opens with animals jumping fixed steps on a number line — a frog jumping 3, a squirrel 4, a rabbit 6, and a kangaroo 8. Numbers each animal lands on are its multiples. When two animals land on the same number (e.g., both the rabbit and kangaroo land on 24), those are common multiples of their jump sizes.
• Multiplication Using Equal Groups and Arrays — Through Gulabo's garden and Radha's bakery, the chapter builds multiplication as counting equal groups. Students find petals (12 lily flowers × 3 petals = 36) and arrange cupcakes in rows and columns. Breaking the multiplier into 10s and remaining units — for example, 18 × 4 = (10 × 4) + (8 × 4) = 72 — is the key strategy taught.
• Multiplying by Multiples of 10 and 100 — A dedicated section counts wheels on tricycles and cars to show that 20 × 3 = (10 × 3) + (10 × 3) = 60 and that 100 × 4 = 400. The pattern extends to 3-digit multipliers: 125 × 8 is split into (100 × 8) + (20 × 8) + (5 × 8) = 800 + 160 + 40 = 1000. Students also complete pattern tables like 1 × 3, 10 × 3, 100 × 3 to generalise the rule.
• Division by Partial Quotients — Division is introduced through sharing problems — ferrying 108 people across 9 boats, or fixing 58 wheels onto 3-wheeled tempos. The partial-quotient method lets children subtract easy groups (10s, 5s, then smaller) repeatedly until nothing remains. For 58 ÷ 3, students take away 30 (10 tempos), then 15 (5 tempos), then 9 (3 tempos), then 3 (1 tempo) to get 19 with 1 left over.

1. 01Multiples of 3, 4, 6, and 8 are explored using frog, squirrel, rabbit, and kangaroo jumps on a number line.
2. 02Common multiples are numbers that two different animals (jump sizes) both land on — e.g., common multiples of 6 and 8 include 24.
3. 03Multiplication is broken into equal groups: multiplier (number of groups) × multiplicand (group size) = product.
4. 04A 10 × 10 multiplication table is built by filling row × column products, and students look for even/odd patterns and repeating ones digits.
5. 05Doubling is used as a multiplication strategy; magician Anvi's trick demonstrates doubling numbers like 23 → 46.
6. 06Multiplying by multiples of 10 or 100 follows a pattern: 6 × 8 = 48, so 60 × 8 = 480 and 600 × 8 = 4800.
7. 073-digit numbers are multiplied by a single digit by splitting into hundreds, tens, and ones — e.g., 125 × 8 = 800 + 160 + 40 = 1000.
8. 08Division uses the partial-quotient method: subtract groups of 10s and smaller multiples until the remainder is less than the divisor.