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

Continue these patterns:

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

Warm-Up: Checking the Answers Together

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 in Mathematics?

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

The Secret to Finding Any 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 Examples of Addition Patterns

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 Examples of Subtraction Patterns

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 Examples of Multiplication Patterns

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

• Rule: ×3

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

• Rule: ×5

The numbers grow FAST!

Special Sequences Worth Knowing Well

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 a Missing Number: Addition

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 a Missing Number: Multiplication

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 a Missing Number: Subtraction

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 Each Time

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

Practice Answers: Finding the Rule

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 Each Pattern Given

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

Practice Answers: The Continued Patterns

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

Practice: Find the Missing Numbers

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

Practice Answers: The Missing Numbers

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

Now Create Your Own Number 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: Check Your Understanding

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: The Correct 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: All Four Lessons

What We Learned

Term 1 Complete: All Four Topics

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!

The Three Pattern Types to Remember

Homework: More Practice with Patterns

1. Continue 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.

Remember These Four Steps Always

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 on Finishing Term 1

You've completed Topic 4 and Term 1!

Great work on Patterns and Sequences!

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