# Number Play

## Overview

In this chapter, students explore the many roles numbers play in our lives—describing positions, observing patterns, solving puzzles, estimating, and playing games. The chapter builds numeric thinking, reasoning, pattern recognition, and computational thinking through engaging tasks, puzzles, and activities.

## Key Topics Covered

### 1. Understanding Numbers Through Context

* Children use numbers to describe relative height in a line.
* Numbers represent how many neighbors are taller: 0, 1, or 2.
* Challenges posed include rearranging children for specific number patterns and understanding the logic behind them.

### 2. Supercells – Comparing Neighbouring Numbers

* A cell is a **supercell** if its number is greater than all its adjacent (top, bottom, left, right) cells.
* Activities:

* Identify supercells in tables.
* Create tables with a maximum or specific number of supercells.
* Analyze whether the highest or lowest number must be a supercell.

### 3. Patterns on the Number Line

* Students position numbers like 2180, 2754, 8400, etc., on a number line.
* Identify missing or labeled numbers.
* Use of visual patterns to estimate positions.

### 4. Playing with Digits

* **Digit Sums**: Add digits in numbers like 68, 176, or 545 (all give 14).
* Explore how many digits in 2-digit, 3-digit, 4-digit, and 5-digit numbers.
* Investigate patterns in digit sums, especially of consecutive numbers.

### 5. Palindromic Numbers

* Numbers that read the same forwards and backwards (e.g., 848, 1111).
* Explore:

* All possible 3-digit palindromes using 1, 2, 3.
* Reverse-and-add method to create palindromes.
* Puzzle using digit clues to form a 5-digit palindrome.

### 6. The Magic Number – Kaprekar Constant

* Use a 4-digit number and rearrange digits to form the largest and smallest.
* Subtract and repeat the process.
* Eventually, all sequences reach **6174**, called the **Kaprekar Constant**.

### 7. Clock and Calendar Patterns

* Explore palindromic clock times (e.g., 10:01) and calendar dates (e.g., 20/12/2012).
* Determine repeating calendar years.
* Create 4-digit numbers and check properties like differences and sums.

### 8. Mental Math and Estimation

* Add numbers mentally using combinations from a set list.
* Estimate values and make sums using given number options.
* Solve puzzles like: make 1000, 14,000, 15,000, etc. using select values.

### 9. Patterned Arrangements

* Grids of repeating numbers used to calculate large sums using smart methods.
* Identify patterns and shortcuts rather than adding one-by-one.

### 10. Collatz Conjecture – A Mathematical Mystery

* Apply the Collatz rule:

* Even → divide by 2
* Odd → multiply by 3, then add 1
* Try with different numbers; see if you always reach 1.
* Explore why it is still an unsolved puzzle in mathematics.

### 11. Estimation Around Us

* Estimate number of:

* Steps to classroom or home
* Eye blinks or breaths in a day
* Students in school
* Estimate costs, distances, hours spent in school, capacity of containers, etc.

### 12. Number Games and Strategies

* **Game 1**: Say numbers up to 21 in turns. Strategy ensures a win.
* **Game 2**: Variation up to 99. Explore strategic choices.
* Create and explore your own variations.
* Additional puzzles involving digit swaps, estimations, and number sums.

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## New Terms and Simple Definitions

| Term | Simple Definition |
| ------------------ | ---------------------------------------------------------------------------------- |
| Supercell | A number in a grid that is bigger than all its nearby numbers (top, bottom, sides) |
| Palindrome | A number that reads the same forward and backward (e.g., 121, 1441) |
| Digit Sum | The total when all digits of a number are added (e.g., 1 + 7 + 6 = 14) |
| Estimation | A rough guess or approximate value |
| Kaprekar Constant | A number (6174) that is reached using a special method with 4-digit numbers |
| Collatz Conjecture | A math rule: even → divide by 2; odd → multiply by 3 and add 1, keep repeating |
| Number Line | A line where numbers are shown in order |
| Pattern | A repeated design or sequence |
| Strategy | A smart way to solve a problem or win a game |

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## Practice Questions

### Easy (3)

1. **What is the digit sum of 247?**
**Answer:** 2 + 4 + 7 = 13
**Explanation:** Add all digits.

2. **Is 121 a palindrome?**
**Answer:** Yes
**Explanation:** It reads the same forward and backward.

3. **Estimate how many students are in a school with 5 classes and 30 students in each class.**
**Answer:** 5 × 30 = 150
**Explanation:** Multiply number of classes with students per class.

### Medium (2)

4. **Find the difference between the largest and smallest number made using digits 3, 7, 0, 1.**
**Answer:** Largest = 7310; Smallest = 0137 → 137 → 7310 - 137 = 7173
**Explanation:** Arrange digits, then subtract.

5. **Mark 5030 on the number line between 5000 and 6000.**
**Answer:** 5030 is slightly ahead of 5000.
**Explanation:** Find approximate location between given values.

### Difficult (3)

6. **Create a 3-digit palindrome using digits 1, 2, 3.**
**Answer:** 121, 232, 313
**Explanation:** Use same digits front and back.

7. **Start with number 87. Reverse and add until a palindrome is formed.**

* Step 1: 87 + 78 = 165
* Step 2: 165 + 561 = 726
* Step 3: 726 + 627 = 1353
* Step 4: 1353 + 3531 = 4884
**Answer:** 4884
**Explanation:** Follow reverse-and-add steps.

8. **Apply Collatz rule on number 27 until you reach 1.**
**Answer:** 27 → 82 → 41 → 124 → ... → 1
**Explanation:** Odd: ×3+1, Even: ÷2, repeat.

### Very Difficult (2)

9. **How many 5-digit numbers have all odd digits and are between 35,000 and 75,000?**
**Answer:** You must count combinations like 35791, 73551, etc.
**Explanation:** Use only odd digits: 1, 3, 5, 7, 9; first digit must make number in range.

10. **Play the 21 game. If you are the first player, what numbers should you always say to win?**
**Answer:** Say 1 → then always jump to 5, 9, 13, 17, 21
**Explanation:** These are key numbers. If you land on them, you can force a win.

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