Number Patterns and Sequences

P6 Mathematics - Term I, Topic 4

Lesson 4 of 4

Learning Objectives:

• Identify and describe number patterns
• Find the rule in a sequence
• Continue patterns using +, -, ×, ÷

Mental Warm-Up!

Continue these patterns:

1. 2, 4, 6, ___, ___, ___
2. 5, 10, 15, ___, ___, ___
3. 1, 2, 4, ___, ___, ___

Warm-Up Answers

1. 2, 4, 6, 8, 10, 12 (add 2)
2. 5, 10, 15, 20, 25, 30 (add 5)
3. 1, 2, 4, 8, 16, 32 (multiply by 2)

What is a Pattern?

A pattern is a set of numbers following a specific RULE

A sequence is an ordered list of numbers following a pattern.

Each number in a sequence is called a TERM

Finding the Rule

The Secret: Look at what happens between terms!

For addition/subtraction patterns:
→ Subtract consecutive terms

For multiplication/division patterns:
→ Divide consecutive terms

Type 1: Addition Patterns (+)

Rule: Add the same number each time

Example: 3, 6, 9, 12, 15, ...

Finding the rule:

• 6 - 3 = 3
• 9 - 6 = 3
• 12 - 9 = 3

Rule: Add 3 (+3)

More Addition Examples

Example 2: 7, 14, 21, 28, 35, ...

• Rule: +7 (these are multiples of 7!)

Example 3: 4, 9, 14, 19, 24, ...

• Rule: +5

Example 4: 11, 22, 33, 44, 55, ...

• Rule: +11 (multiples of 11!)

Type 2: Subtraction Patterns (-)

Rule: Subtract the same number each time

Example: 50, 45, 40, 35, 30, ...

Finding the rule:

• 50 - 45 = 5 (going down by 5)

Rule: Subtract 5 (-5)

More Subtraction Examples

Example 2: 100, 88, 76, 64, 52, ...

• Rule: -12

Example 3: 1000, 900, 800, 700, ...

• Rule: -100

The numbers get SMALLER!

Type 3: Multiplication Patterns (×)

Rule: Multiply by the same number each time

Example: 2, 4, 8, 16, 32, ...

Finding the rule:

• 4 ÷ 2 = 2
• 8 ÷ 4 = 2
• 16 ÷ 8 = 2

Rule: Multiply by 2 (×2)

More Multiplication Examples

Example 2: 3, 9, 27, 81, ...

• Rule: ×3

Example 3: 5, 25, 125, 625, ...

• Rule: ×5

The numbers grow FAST!

Special Sequences to Know

Even Numbers

2, 4, 6, 8, 10, 12, ... (Rule: +2)

Odd Numbers

1, 3, 5, 7, 9, 11, ... (Rule: +2)

Square Numbers

1, 4, 9, 16, 25, 36, ... (Rule: 1², 2², 3², 4², ...)

Finding Missing Numbers

Example 1: 5, 10, ___, 20, 25

Step 1: Find the rule

• 10 - 5 = 5, so rule is +5

Step 2: Apply the rule

• 10 + 5 = 15

Answer: 5, 10, 15, 20, 25

Finding Missing Numbers

Example 2: 3, 6, 12, ___, 48

Step 1: Find the rule

• 6 ÷ 3 = 2
• 12 ÷ 6 = 2
• Rule is ×2

Step 2: Apply the rule

• 12 × 2 = 24

Answer: 3, 6, 12, 24, 48

Finding Missing Numbers

Example 3: 81, 72, ___, 54, 45

Step 1: Find the rule

• 81 - 72 = 9
• Rule is -9

Step 2: Apply the rule

• 72 - 9 = 63

Answer: 81, 72, 63, 54, 45

Practice: Find the Rule

1. 4, 8, 12, 16, 20, ... (Rule: ___)
2. 100, 90, 80, 70, ... (Rule: ___)
3. 1, 3, 9, 27, 81, ... (Rule: ___)

Practice: Answers

1. 4, 8, 12, 16, 20, ... (Rule: +4)
2. 100, 90, 80, 70, ... (Rule: -10)
3. 1, 3, 9, 27, 81, ... (Rule: ×3)

Practice: Continue the Pattern

1. 6, 12, 18, ___, ___, ___
2. 64, 56, 48, ___, ___, ___
3. 2, 6, 18, ___, ___

Practice: Answers

1. 6, 12, 18, 24, 30, 36 (+6)
2. 64, 56, 48, 40, 32, 24 (-8)
3. 2, 6, 18, 54, 162 (×3)

Practice: Missing Numbers

1. 5, 10, ___, 20, 25
2. 3, ___, 12, 15, 18
3. 2, 4, ___, 16, 32

Practice: Answers

1. 5, 10, 15, 20, 25 (+5)
2. 3, 6 (or 9), 12, 15, 18 (+3)
3. 2, 4, 8, 16, 32 (×2)

Create Your Own Pattern!

Using the rule "+7" starting from 3:

3, 10, 17, 24, 31, ...

Your turn: Create a pattern using "×2" starting from 5!

Quick Assessment ✓

1. What is the rule for: 5, 15, 25, 35, ...?

2. Continue: 1, 4, 9, 16, ___

3. Find the missing number: 2, 6, ___, 54, 162

Quick Assessment: Answers

1. Rule: +10

2. 1, 4, 9, 16, 25 (square numbers: 1², 2², 3², 4², 5²)

3. 2, 6, 18, 54, 162 (×3)

Topic 4 Summary!

What We Learned

Term 1 Complete!

You've now completed ALL 4 Topics of Term 1:

• Topic 1: Sets
• Topic 2: Whole Numbers
• Topic 3: Operations on Whole Numbers
• Topic 4: Patterns and Sequences

18 lessons completed!

Pattern Types to Remember

Homework

1. Continue for 3 more terms:

   • 7, 14, 21, ___, ___, ___
   • 96, 84, 72, ___, ___, ___
   • 4, 12, 36, ___, ___, ___

2. Find missing numbers:

   • 8, ___, 24, 32, 40
   • 100, 81, ___, 49, 36

3. Create your own pattern with 5 numbers and write the rule.

Remember!

Finding the Rule:

1. Look at consecutive terms
2. Calculate the difference OR quotient
3. Check if the rule works for ALL terms
4. Apply the rule to continue or find missing numbers

Congratulations!

You've completed Topic 4 and Term 1!

Great work on Patterns and Sequences!

Next Term: Fractions, Data Handling, Money, Distance-Time-Speed