Number Play notes class 6th

DHved Learning • CLASS 6 MATHEMATICS

Chapter 3: Number Play

Explore number patterns, digit tricks, divisibility rules, factors, multiples and mathematical puzzles. Become a number detective!

Learning Goals Digits & Place Value Patterns Divisibility Factors & Multiples Puzzles Worksheet Quiz

1. Learning Goals

After completing this chapter, you should be able to:

• Understand digits, place value and digit sums.
• Recognise and continue number sequences.
• Apply divisibility rules to numbers.
• Find factors and multiples.
• Solve number puzzles using logical reasoning.

Think like a mathematician! Numbers often follow hidden rules. Observe carefully, identify the rule and use it to solve the puzzle.

2. Digits and Place Value

A digit is one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. We use digits to write numbers.

Example: Number 4,582

Digit	Place	Place Value
4	Thousands	4,000
5	Hundreds	500
8	Tens	80
2	Ones	2

Expanded form: \(4,582 = 4,000 + 500 + 80 + 2\)

Face value: The digit itself.
Place value: The value of a digit according to its position in the number.

Digit Sum

The digit sum is the sum of all digits in a number.

Example: For 472, \(4 + 7 + 2 = 13\).

Digit sums help us investigate number patterns and apply some divisibility rules.

3. Number Patterns and Sequences

A number sequence is an ordered list of numbers that follows a rule.

Pattern A: Adding the Same Number

369 1215?

Rule: Add 3 each time. The next number is \(15 + 3 = 18\).

Pattern B: Multiplying by 2

248 16?

Rule: Multiply each number by 2. The next number is \(16 \times 2 = 32\).

Pattern C: Square Numbers

149 162536

These numbers are squares: \(1^2, 2^2, 3^2, 4^2, 5^2, 6^2\).

Pattern D: Growing Differences

Sequence: 1, 3, 6, 10, 15, ...

The differences are +2, +3, +4 and +5. The next difference is +6.

Therefore, the next number is \(15 + 6 = 21\).

Pattern-solving strategy: Check whether the numbers are adding, subtracting, multiplying, dividing or following a repeating rule.

4. Divisibility Rules

A number is divisible by another number if the division leaves no remainder.

Divisor	Rule	Example
2	Last digit is 0, 2, 4, 6 or 8.	348
3	Sum of digits is divisible by 3.	123: 1 + 2 + 3 = 6
5	Last digit is 0 or 5.	725
9	Sum of digits is divisible by 9.	729: 7 + 2 + 9 = 18
10	Last digit is 0.	1,230

Worked Example

Is 4,536 divisible by 3?

Digit sum: \(4 + 5 + 3 + 6 = 18\)

Since 18 is divisible by 3, 4,536 is also divisible by 3.

Divisibility rules help you test numbers quickly without performing long division.

5. Factors and Multiples

Factors

A factor of a number divides it exactly, leaving no remainder.

The positive factors of 12 are: \(1, 2, 3, 4, 6, 12\).

Multiples

Multiples are obtained by multiplying a number by whole numbers.

Positive multiples of 4: \(4, 8, 12, 16, 20, \ldots\)

Factors	Multiples
Limited for a positive whole number.	Infinitely many positive multiples.
Factors of 10: 1, 2, 5, 10	Multiples of 10: 10, 20, 30, 40, ...

Common Factors

The factors shared by 8 and 12 are \(1, 2, 4\).

Common Multiples

A common multiple of 3 and 4 is 12 because \(12 = 3 \times 4\) and \(12 = 4 \times 3\).

Remember: Factors divide a number exactly. Multiples are produced by multiplication.

6. Number Puzzles

Puzzle 1: Find the Missing Number

\(5, 10, 15, 20, \square\)

Solution: Add 5 each time. The answer is 25.

Puzzle 2: Reverse the Digits

Take 27 and reverse its digits to get 72.

Difference: \(72 - 27 = 45\).

Try this with other two-digit numbers and observe how the difference changes.

Puzzle 3: Fill in the Blank

Which digit can replace the blank in 47□ to make the number divisible by 5?

Solution: The last digit must be 0 or 5. The numbers are 470 and 475.

Puzzle 4: Guess the Rule

\(2, 5, 11, 23, 47, \square\)

Rule: Multiply by 2 and add 1.

\(47 \times 2 + 1 = 95\)

When solving a number puzzle, write down the rule. Explaining your thinking is an important mathematical skill.

7. Practice Worksheet

Try answering these questions before revealing the answers.

1. Write 6,304 in expanded form.
2. Find the digit sum of 582.
3. Complete: 7, 14, 21, 28, ___.
4. Complete: 3, 6, 12, 24, ___.
5. Is 246 divisible by 2? Explain.
6. Is 351 divisible by 3? Show the digit sum.
7. Write all positive factors of 10.
8. Write the first five positive multiples of 6.
9. Complete: 1, 3, 6, 10, 15, ___.
10. Which digits can replace the blank in 62□ to make it divisible by 5?

Show Worksheet Answers

1. \(6,000 + 300 + 4\)
2. \(5 + 8 + 2 = 15\)
3. 35
4. 48
5. Yes, because its last digit is 6.
6. Yes. \(3 + 5 + 1 = 9\), divisible by 3.
7. 1, 2, 5, 10
8. 6, 12, 18, 24, 30
9. 21
10. 0 or 5

8. Interactive Quiz

Choose one answer for each question. Click Check Answers to see your score and explanations.

1. What is the place value of 5 in 4,582?

5 500 50

2. What comes next: 4, 8, 12, 16, ...?

18 24 20

3. Which number is divisible by 2?

136 135 131

4. Is 271 divisible by 3?

Yes No Only by 9

5. Which is a factor of 9?

2 4 3

6. Which is a multiple of 5?

35 32 43

7. Which number is divisible by 10?

125 230 234

8. Complete: 1, 3, 6, 10, 15, ...

18 20 21

9. Which number is divisible by 9?

189 182 191

10. Which last digit makes 64□ divisible by 5?

3 only 0 or 5 2 or 4

9. Quick Revision

• Place value depends on the position of a digit.
• Digit sum means adding all digits in a number.
• Number sequences follow a rule.
• Divisibility by 2: last digit is even.
• Divisibility by 3: digit sum is divisible by 3.
• Divisibility by 5: last digit is 0 or 5.
• Divisibility by 9: digit sum is divisible by 9.
• Divisibility by 10: last digit is 0.
• Factors divide a number exactly.
• Multiples are produced through multiplication.

Learning Challenge: Create your own five-term number sequence, write its rule, and ask a friend to find the next term.