NCERT Class 2 Maths (Joyful Mathematics) · Chapter 8
Grouping and Sharing
Equal groups, repeated addition, the × sign, tables of 2, 3, 5, and 10, making new tables, and sharing equally.
📌 What you’ll learn in this chapter
- Counting equal groups by adding again and again
- Writing “times” as ×
- 3 × 4 and 4 × 3 give the same answer
- Tables of 2, 3, 5, and 10, and making bigger tables
- Sharing equally and making groups
🍪 Let’s Begin: Biscuit Packets
Mummy brings 3 packets of biscuits. Each packet has 5 biscuits. Chintu counts: 5 + 5 + 5 = 15.
Mummy smiles: “That’s 3 times 5, which is 15! We write it as 3 × 5 = 15.” 🍪
✖️ Part 1: Equal Groups and Times
| Groups | Adding | Times | Answer |
|---|---|---|---|
| 2 hands with 5 fingers each | 5 + 5 | 2 × 5 | 10 |
| 3 tricycles with 3 wheels each | 3 + 3 + 3 | 3 × 3 | 9 |
| 4 stools with 4 legs each | 4 + 4 + 4 + 4 | 4 × 4 | 16 |
💡 Turn-around trick
2 rows of 6 chairs = 12, and 6 rows of 2 chairs = 12. So 2 × 6 = 6 × 2. Swapping the numbers gives the same answer!
⚠️ Common mistake
Writing 4 × 3 = 7 (adding instead of multiplying). ❌ 4 × 3 means 3 + 3 + 3 + 3 = 12.
📋 Part 2: Making Tables
Add two tables to make a new one! Table of 2 + table of 2 = table of 4:
| Table of 2 | 2 | 4 | 6 | 8 | 10 |
| Table of 2 | 2 | 4 | 6 | 8 | 10 |
| Table of 4 | 4 | 8 | 12 | 16 | 20 |
🍬 Part 3: Sharing Equally
Riya has 10 toffees for herself and her friend. She gives one to each, again and again, until they are all gone. Each gets 5.
Making groups: 12 flowers, 4 in each vase, so 4 + 4 + 4 = 12 and we need 3 vases.
✏️ Practice Time
Try these on your own first, then check your answer below each question.
Q1. 5 + 5 + 5 + 5 = ? Write it using ×.
✅ Answer4 × 5 = 20
Q2. 6 cows. Each has 4 legs. How many legs in all?
✅ Answer6 × 4 = 24 legs
Q3. Share 15 mangoes equally among 3 children.
✅ AnswerEach child gets 5 mangoes (5 + 5 + 5 = 15).
Q4. 20 pencils, 10 in each box. How many boxes?
✅ Answer2 boxes
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Pages 83–84 · WheelsBicycles, autos, and cars
✅ AnswerRamya added 4 seven times: 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28, so 7 times 4 is 28.
Cars: number of cars = 7 · wheels in each car = 4 · total = 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28 · 7 times 4 is 28 · 7 groups of 4 is 28 · 7 × 4 = 28 · You are adding 7 fours.
Page 85 · Wings, legs, and soldiersCars: number of cars = 7 · wheels in each car = 4 · total = 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28 · 7 times 4 is 28 · 7 groups of 4 is 28 · 7 × 4 = 28 · You are adding 7 fours.
Fill in
✅ AnswerButterflies: 3 butterflies, 2 wings each · 2 + 2 + 2 = 6 · 3 groups of 2 is 6 · 3 times 2 is 6 · 3 twos are 6 · 3 × 2 = 6
Octopuses: 2 octopuses, 8 legs each · 8 + 8 = 16 · 2 groups of 8 is 16 · 2 times 8 is 16 · 2 eights are 16 · 2 × 8 = 16
Soldiers: 4 lines, 10 in each · 10 + 10 + 10 + 10 = 40 · 4 times 10 is 40 · 4 tens are 40 · 4 × 10 = 40
Page 86 · Complete the table and matchOctopuses: 2 octopuses, 8 legs each · 8 + 8 = 16 · 2 groups of 8 is 16 · 2 times 8 is 16 · 2 eights are 16 · 2 × 8 = 16
Soldiers: 4 lines, 10 in each · 10 + 10 + 10 + 10 = 40 · 4 times 10 is 40 · 4 tens are 40 · 4 × 10 = 40
Table
✅ AnswerFingers: 5 + 5 + 5 · 3 times 5 · 3 × 5 = 15
Bananas: 3 + 3 + 3 + 3 + 3 + 3 · 6 times 3 · 6 × 3 = 18
Oranges: 4 + 4 + 4 + 4 · 4 times 4 · 4 × 4 = 16
Pencils: 5 + 5 · 2 times 5 · 2 × 5 = 10
Balls: 5 + 5 + 5 · 3 times 5 · 3 × 5 = 15
Bananas: 3 + 3 + 3 + 3 + 3 + 3 · 6 times 3 · 6 × 3 = 18
Oranges: 4 + 4 + 4 + 4 · 4 times 4 · 4 × 4 = 16
Pencils: 5 + 5 · 2 times 5 · 2 × 5 = 10
Balls: 5 + 5 + 5 · 3 times 5 · 3 × 5 = 15
Match the following
✅ Answer9 + 9 + 9 → 3 × 9 → 27
5 + 5 + 5 + 5 + 5 + 5 + 5 → 7 fives are → 35
3 + 3 + 3 + 3 + 3 → 5 times 3 → 15 (shown in the book)
10 + 10 + 10 + 10 → 4 groups of 10 → 40
8 + 8 + 8 → 3 × 8 → 24
7 + 7 → 2 sevens are → 14
Pages 87–88 · Tables of 2, 3, 5, and 105 + 5 + 5 + 5 + 5 + 5 + 5 → 7 fives are → 35
3 + 3 + 3 + 3 + 3 → 5 times 3 → 15 (shown in the book)
10 + 10 + 10 + 10 → 4 groups of 10 → 40
8 + 8 + 8 → 3 × 8 → 24
7 + 7 → 2 sevens are → 14
Complete the tables
✅ AnswerTable of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Table of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Table of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Table of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Write each as “2 fours are 8 → 2 × 4 = 8” and so on.
Pages 89–91 · How many?Table of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Table of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Table of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Write each as “2 fours are 8 → 2 × 4 = 8” and so on.
Groups and word problems
✅ AnswerRam and Gopal both used 12 flowers: 4 × 3 = 3 × 4. Swapping the numbers doesn’t change the answer.
4 groups of 5: 4 times 5 is 20 · 4 × 5 = 20 gulab jamuns · 5 groups of 4: 5 times 4 is 20 · 5 × 4 = 20
6 groups of 4: 6 × 4 = 24 flowers · 4 groups of 6: 4 × 6 = 24 flowers
A. Bindis: 8 packets, 5 each · 8 groups of 5 · 8 × 5 = 40 bindis
B. Buttons: 7 shirts, 4 each · 7 groups of 4 · 7 × 4 = 28 buttons
C. Pencils: 6 pencils at ₹4 · 6 × 4 = 24 · Rita gives ₹24
D. Cars: 5 people each · 8 × 5 = 40 people
Pages 91–92 · Making tables4 groups of 5: 4 times 5 is 20 · 4 × 5 = 20 gulab jamuns · 5 groups of 4: 5 times 4 is 20 · 5 × 4 = 20
6 groups of 4: 6 × 4 = 24 flowers · 4 groups of 6: 4 × 6 = 24 flowers
A. Bindis: 8 packets, 5 each · 8 groups of 5 · 8 × 5 = 40 bindis
B. Buttons: 7 shirts, 4 each · 7 groups of 4 · 7 × 4 = 28 buttons
C. Pencils: 6 pencils at ₹4 · 6 × 4 = 24 · Rita gives ₹24
D. Cars: 5 people each · 8 × 5 = 40 people
Tables of 6 and 8
✅ AnswerTable of 6 (3 + 3): 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Table of 6 row: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Table of 8 (2 + 6): 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Project (24 objects): 1 × 24, 2 × 12, 3 × 8, 4 × 6, 6 × 4, 8 × 3, 12 × 2, 24 × 1
Pages 93–94 · Sharing gulab jamuns and laddoosTable of 6 row: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Table of 8 (2 + 6): 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Project (24 objects): 1 × 24, 2 × 12, 3 × 8, 4 × 6, 6 × 4, 8 × 3, 12 × 2, 24 × 1
Share equally
✅ AnswerA. There were 8 gulab jamuns · B. Yes · C. Each got 4
Ritu’s cones: 12 bindis on 2 cones = 6 on each.
Pooja’s laddoos: 7 + 5 = 12 laddoos. 12 shared in 3 plates = 4 in each plate.
Pages 95–97 · How many groups?Ritu’s cones: 12 bindis on 2 cones = 6 on each.
Pooja’s laddoos: 7 + 5 = 12 laddoos. 12 shared in 3 plates = 4 in each plate.
Bracelets, vases, and boxes
✅ AnswerGarima: 20 beads, 5 in each bracelet, gives 4 bracelets.
A. 21 beads, 7 on each string → 3 strings · B. 54 flowers, 9 in each → 6 bracelets · C. 25 roses, 5 in each → 5 vases
D. 27 candles in 3 boxes → 9 in each box · E. 30 buttons, 6 on each → 5 shirts · F. 24 bananas for 3 monkeys → 8 each
A. 21 beads, 7 on each string → 3 strings · B. 54 flowers, 9 in each → 6 bracelets · C. 25 roses, 5 in each → 5 vases
D. 27 candles in 3 boxes → 9 in each box · E. 30 buttons, 6 on each → 5 shirts · F. 24 bananas for 3 monkeys → 8 each
👨👩👧 Tips for Parents
- Count shoes in pairs: “5 pairs = 5 × 2 = 10 shoes.”
- Let your child share snacks equally among family members.
- Say the table of 2, 5, or 10 while climbing stairs.