# Equal Groups

## Summary

### 1. Understanding Equal Jumps and Multiples

Animals are used to explore the concept of skip counting and multiples:

* **Frog** jumps 3 steps at a time (multiples of 3)
* **Squirrel** jumps 4 steps at a time (multiples of 4)
* **Rabbit** jumps 6 steps at a time
* **Kangaroo** jumps 8 steps at a time

Students learn:

* How many steps it takes for each animal to reach a number
* Common multiples between animals (e.g., multiples of 3 and 4 for frog and squirrel)
* Observing patterns in reaching numbers like 48 or 60 using different jumps

### 2. Multiplication through Grouping

Multiplication is introduced through everyday scenarios:

* Gulabo counts petals in flowers (e.g., 12 flowers with 3 petals each = 36 petals)
* Counting saplings in rows and columns
* Boxes of strawberries and trays of cupcakes in multiplication arrays

Students practice:

* Writing multiplication statements
* Understanding "number of groups × number in each group"

### 3. Arrays and Patterns

Learners explore multiplication using visual arrays:

* Arranging objects like cupcakes in trays
* Using doubling to simplify calculations
* Observing doubling patterns (e.g., double of 14 = 28)

Patterns in the ones digit of products (e.g., 8, 6, 4, 2, 0, ...) are explored for understanding repetition and even-odd number behavior.

### 4. Multiplication Tables and Patterns

A multiplication grid (1 to 10) is analyzed to identify:

* Rows and columns with all even/odd numbers
* Repeated patterns in ones digit
* Rows with all digits from 0 to 9 in the ones place

Students are encouraged to recognize symmetry in multiplication tables and discover common multiples using coloring techniques.

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Here is **Part 2** of the chapter summary continued from above:

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### 5. Multiplication Using 10s and 100s

Children explore multiplication where the number of groups is a multiple of 10 or 100:

* Example: 10 tricycles with 3 wheels each → 10 × 3 = 30 wheels
* Using blocks of 10 and 100 to simplify large multiplications:

* 40 × 6 = 240
* 60 × 8 = 480
* 300 × 4 = 1200

### 6. Word Problems and Application

Real-world scenarios help solidify multiplication:

* Radha bakes cupcakes and arranges them in trays
* Potters make and pack kulhads (earthen cups)
* Calculating contributions in school mela, students multiplying quantities with money and items

### 7. Division through Grouping and Sharing

Introduction to division using partial quotients:

* 58 wheels for 3-wheeled tempos → 58 ÷ 3
* Breaking the dividend into easier chunks (e.g., taking away 30, 15, 9, 3, etc.)
* 88 legs = how many cows (88 ÷ 4)

Patterns and relationships between multiplication and division are explored.

### 8. Division Patterns

Observing patterns while dividing multiples:

* 30 ÷ 3 = 10, 300 ÷ 3 = 100
* 500 ÷ 5 = 100
* 800 ÷ 4 = 200

### 9. Mixed Practice and Reasoning

Combining multiplication and division:

* Problem-solving with school trips, toy train distances, rafting
* Savings and distribution of money
* Estimating number of trips, passengers, materials

Logical reasoning:

* Classifying statements as Always, Sometimes, or Never true
* Evaluating mathematical truths and patterns

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## New Words and Simple Meanings

| Term | Meaning in Simple English |
| ---------------- | --------------------------------------------------------------------------------- |
| Multiple | A number that comes when we multiply another number (e.g., 12 is a multiple of 3) |
| Grouping | Putting items together in equal sets |
| Array | A pattern of objects in rows and columns |
| Skip Counting | Counting by jumping numbers like 3, 6, 9, 12... |
| Multiply | To add the same number many times |
| Divide | To split into equal parts |
| Quotient | The answer we get after dividing |
| Pattern | A repeated or regular way things are arranged |
| Ones Digit | The last number on the right in a number |
| Partial Quotient | Dividing a number step by step using easy parts |

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## Practice Problems

### Easy (3)

1. A frog jumps 3 steps each time. How many steps will it take to reach 18?
**Answer**: 6 jumps (3 × 6 = 18)

2. What is the product of 8 and 5?
**Answer**: 40

3. Radha bakes 9 cupcakes in 1 tray. How many cupcakes in 2 trays?
**Answer**: 18 (9 × 2)

### Medium (2)

4. A car has 4 wheels. How many wheels do 12 cars have?
**Answer**: 48 (12 × 4)

5. There are 84 legs of cows. How many cows are there? (Each cow has 4 legs)
**Answer**: 21 (84 ÷ 4)

### Difficult (3)

6. A school has 465 students. Each student gets 2 pencils. How many pencils are needed?
**Answer**: 930 (465 × 2)

7. A bakery makes 108 cupcakes. Each tray holds 18 cupcakes. How many trays were used?
**Answer**: 6 (108 ÷ 18)

8. 23 bullock carts need 8 bamboo rods each. How many rods in total?
**Answer**: 184 (23 × 8)

### Very Difficult (2)

9. A toy train travels 88 km daily. How far does it travel in 7 days?
**Answer**: 616 km (88 × 7)

10. 259 people went for rafting. Each raft carries 7 people. How many rafts were used?
**Answer**: 37 (259 ÷ 7; remainder 0, so 37 rafts)

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