# Be My Multiple, I’ll Be Your Factor

## Overview

This chapter introduces the concepts of **multiples**, **factors**, **common multiples**, and **common factors** through interactive games, puzzles, and hands-on activities like coloring, number grids, and using tamarind seeds. It builds foundational number sense and deepens understanding of multiplication and division through fun storytelling and problem-solving.

## Key Topics Covered

### 1. Understanding Multiples Through Stories

* **Story of the Mouse and the Cat**:

* The mouse jumps in steps of 2 starting from the 14th step.
* The cat jumps in steps of 3 from the 3rd step.
* Students observe which steps they both land on to learn about **multiples**.
* A variation: mouse starts at step 8 and jumps 4 steps; cat starts at 5 and jumps 5 steps.

* **Objective**: To identify and compare multiples by tracking steps and analyzing patterns.

### 2. Finding Multiples Using Colour and Games

* **Colour the Grid**:

* Use red, yellow, and blue dots to mark numbers divisible by 2, 3, and 4 respectively.
* Observe numbers with all three colours (common multiples of 2, 3, and 4).
* Record letters associated with those numbers.

* **Meow Game**:

* A fun oral game replacing multiples of 3 with "Meow".
* Played again for multiples of 4 and other numbers.
* Encourages recognition of **multiples in a sequence**.

* **Objective**: To develop fluency in recognizing multiples in a visual and auditory manner.

### 3. Dice Games and Common Multiples

* **Dice Challenge**:

* Roll two dice, create 2-digit numbers.
* Place them in circles if they are multiples of given numbers (e.g., 3, 4, 5).
* Identify common multiples (e.g., 15 is a multiple of both 3 and 5).

* **Objective**: Identify **common multiples** through playful number formation and grouping.

### 4. Exploring Rectangles and Factors

* **Tamarind Seed Activity**:

* Use 12 or 15 seeds to form rectangles.
* Recognize the different **factor pairs** of numbers based on rectangular arrangements.

* **Rectangle Colouring**:

* In a grid of boxes, colour rectangles with 20 boxes in different ways.
* For example, 2 × 10, 4 × 5 — each represents a factor pair of 20.

* **Objective**: To relate factors to dimensions of rectangles and explore spatial representation of numbers.

### 5. Grouping Bangles: Listing Factors

* Example: 18 bangles can be grouped into 1, 2, 3, 6, 9, 18.
* Complete a table showing factors of different numbers.
* Connects **division** with **factor listing**.

### 6. Multiplication Grid and Factor Recognition

* Students complete a **multiplication table**.

* Identify factors of numbers using product locations in the grid.

* Examples:

* 12 has factors: 1, 2, 3, 4, 6, 12.
* 36 has factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.

* **Objective**: Strengthen multiplication understanding and help visualize **common factors**.

### 7. Factor Trees and Tiling Problems

* **Factor Trees**:

* Break down numbers like 24 into factor trees in multiple ways.
* E.g., 24 → 6 × 4 → (2×3) × (2×2).

* **Tiling Problems**:

* Determine tile sizes (2 ft, 3 ft, 5 ft) that fit evenly on paths (e.g., 90 feet).
* Smallest common multiple helps decide tile length for no cuts.

* **Objective**: Apply **LCM (Least Common Multiple)** in practical situations.


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## New Terms and Simple Definitions

| Term | Simple Definition |
| --------------------------- | --------------------------------------------------------------------------------- |
| Multiple | A number that you get when you multiply a number by 1, 2, 3, etc. (e.g., 3, 6, 9) |
| Factor | A number that divides another number exactly (e.g., 2 is a factor of 6) |
| Common Multiple | A number that is a multiple of two or more numbers (e.g., 15 is for 3 and 5) |
| Common Factor | A number that divides two or more numbers exactly (e.g., 5 for 10 and 15) |
| Rectangle | A shape with opposite sides equal and 4 right angles |
| Factor Tree | A diagram showing how a number is broken into its prime factors |
| Grid | A square arrangement of rows and columns used for puzzles or math games |
| Division | The act of splitting into equal parts |
| Multiplication | Repeated addition of the same number |
| Least Common Multiple (LCM) | The smallest number that is a multiple of two or more numbers |

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## Practice Problems

### 🟢 Easy (3)

1. **List first 5 multiples of 6.**
**Answer**: 6, 12, 18, 24, 30
**Explanation**: Multiply 6 by 1 to 5.

2. **What are the factors of 12?**
**Answer**: 1, 2, 3, 4, 6, 12
**Explanation**: All numbers that divide 12 exactly.

3. **Is 20 a multiple of 5?**
**Answer**: Yes
**Explanation**: 5 × 4 = 20

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### 🟡 Medium (2)

4. **Write the common multiples of 4 and 6 up to 50.**
**Answer**: 12, 24, 36, 48
**Explanation**: Numbers that appear in both multiples of 4 and 6.

5. **Draw all possible rectangles using 12 tamarind seeds.**
**Answer**: (1×12), (2×6), (3×4)
**Explanation**: These are all factor pairs of 12.

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### 🔴 Difficult (3)

6. **Rani, Geetha, and Naseema tiled a 90 ft path with 3 different lengths of tiles and didn’t cut any. What lengths could they be?**
**Answer**: 5 ft, 6 ft, 9 ft
**Explanation**: All these divide 90 exactly (factors of 90).

7. **Complete the multiplication chart for number 24. What are its factors?**
**Answer**: 1, 2, 3, 4, 6, 8, 12, 24
**Explanation**: All combinations like 3×8, 4×6 etc. that equal 24.

8. **Find the smallest common multiple of 4, 6, and 5.**
**Answer**: 60
**Explanation**: LCM of 4, 6, and 5 is 60.

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### 🔵 Very Difficult (2)

9. **A cat starts from step 3 and jumps 3 steps. A mouse starts from 14 and jumps 2 steps. Will they land on the same step before 28?**
**Answer**: Yes — both land on step 20.
**Explanation**: Mouse: 14, 16, 18, 20...; Cat: 3, 6, 9, 12, 15, 18, 21, 24... → Common = 18

10. **If Manoj wants to tile a 9 ft × 12 ft room without cutting tiles, which size tile should he buy: 1×1, 2×2, or 3×3?**
**Answer**: 3×3 tile
**Explanation**: 3 divides both 9 and 12 exactly. No tile will be cut.

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