# Grouping and Sharing

## Overview
In this chapter, students learn the fundamental concepts of **multiplication** as repeated addition and **division** as sharing or grouping equally. Through real-life contexts such as counting wheels, flowers, buttons, or food items, the chapter introduces the multiplication sign (×), formation of multiplication tables, and equal sharing methods. Activities, matching exercises, and visual representations help reinforce understanding of these concepts.

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## Key Topics Covered

### 1. Multiplication as Repeated Addition
- Multiplication is shown as adding the same number multiple times.
- Examples:
- 4 cars with 4 wheels each → 4 + 4 + 4 + 4 = 16 → 4 × 4 = 16
- 2 autorickshaws with 3 wheels each → 3 + 3 = 6 → 2 × 3 = 6
- 4 bicycles with 2 wheels each → 2 + 2 + 2 + 2 = 8 → 4 × 2 = 8

### 2. Understanding Groups
- The idea of equal groups is explained using objects like butterflies, octopuses, soldiers, and bouquets.
- Example:
- 3 butterflies, 2 wings each → 3 × 2 = 6
- 2 octopuses, 8 legs each → 2 × 8 = 16

### 3. Matching Repeated Addition with Multiplication
- Activities match repeated addition expressions to multiplication forms.
- Example:
- 5 + 5 + 5 + 5 + 5 + 5 + 5 → 7 × 5 = 35

### 4. Multiplication Tables
- Tables of 2, 3, 5, and 10 are introduced.
- Students complete the tables and connect the multiplication facts with daily examples.

### 5. Real-Life Word Problems Using Multiplication
- Gulab jamuns in groups, flower bouquets, and classroom arrangements used to apply multiplication.
- Examples:
- 6 groups of 4 → 6 × 4 = 24 flowers
- Bharti puts 4 buttons on each shirt for 7 shirts → 7 × 4 = 28 buttons

### 6. Making New Tables Using Existing Ones
- Rudra uses the table of 2 to build the table of 4.
- Using additions from other tables (e.g., 3 + 4 = 7) to form new tables like 7.

### 7. Project Work – Arrays and Multiplication Facts
- Students collect small items (buttons, caps, etc.) and arrange them in arrays.
- They then write multiplication facts for each array.
- Example:
- 3 groups of 4 → 3 × 4 = 12

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## Sharing and Division

### 8. Concept of Sharing Equally (Division)
- Introduced through real-life scenarios like sharing food or craft items.
- Sharing 8 gulab jamuns between two children → Each gets 4 (8 ÷ 2 = 4)

### 9. Division Word Problems
- Several practical sharing activities are included:
- 12 bindis on 2 ice cream cones → 6 each
- 20 beads with 5 per bracelet → 4 bracelets
- 25 roses, 5 per vase → 5 vases
- 27 candles in 3 boxes → 9 candles per box
- 24 bananas among 3 monkeys → 8 each

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## New Terms

| Term | Simple Definition |
|------------------|------------------------------------------------------------|
| Multiply | To add the same number again and again |
| Group | A set of items together |
| Sharing | Dividing something equally among others |
| Times (×) | Symbol used for multiplication |
| Array | Objects arranged in rows and columns |
| Equal | Same amount or size |
| Division | Breaking a number into equal parts |

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## Practice Sums

### Easy (3)
1. 3 baskets, each with 5 mangoes. How many mangoes in total?
**Ans**: 3 × 5 = 15
**Explanation**: Add 5 three times → 5 + 5 + 5 = 15

2. 2 plates with 4 apples each. Total apples?
**Ans**: 2 × 4 = 8

3. 4 pencils in a box. How many pencils in 3 boxes?
**Ans**: 3 × 4 = 12

### Medium (2)
4. There are 5 cars. Each has 4 wheels. How many wheels in total?
**Ans**: 5 × 4 = 20

5. 6 boys each have 2 chocolates. How many chocolates in total?
**Ans**: 6 × 2 = 12

### Difficult (3)
6. A tailor has 36 buttons. He uses 6 buttons per shirt. How many shirts?
**Ans**: 36 ÷ 6 = 6
**Explanation**: 6 buttons used per shirt, 6 shirts needed.

7. 54 flowers are used to make bracelets, 9 per bracelet. How many bracelets?
**Ans**: 54 ÷ 9 = 6

8. Rita buys 7 pencils at ₹3 each. How much money does she pay?
**Ans**: 7 × 3 = ₹21

### Very Difficult (2)
9. A car can carry 5 people. How many people can sit in 12 cars?
**Ans**: 12 × 5 = 60

10. 42 bananas are divided equally among 6 monkeys. How many each?
**Ans**: 42 ÷ 6 = 7

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