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Linear Patterns and Equations

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Linear Patterns and Equations worksheet preview

Linear Patterns and Equations

Pattern and algebra illustration

📊 Part 1: Recognising Linear Patterns

1. Complete the pattern table below:

Position: 1, 2, 3, 4, 5

Value: 5, 8, 11, _____, _____

2. What is the rule for this pattern?

Add 3 each time

Add 5 each time

Multiply by 2 each time

Add 2 each time

3. Look at this growing pattern: 4, 7, 10, 13, 16...

a) What would be the 7th number in this pattern? _____

b) Write the rule in words: Start at _____ and ________________

4. Which of these patterns are linear (growing by the same amount each time)? Tick all that apply:

2, 4, 8, 16, 32...

1, 6, 11, 16, 21...

10, 7, 4, 1, -2...

3, 6, 12, 18, 36...

🔢 Part 2: Number Sentences and Equations

5. Solve these open number sentences:

a) 5 × _____ = 35

b) _____ ÷ 4 = 9

c) 7 × _____ = 42

d) 48 ÷ _____ = 8

6. Are these number sentences true or false? Circle your answer:

a) 6 × 8 = 48 TRUE / FALSE

b) 72 ÷ 9 = 7 TRUE / FALSE

c) 5 × 9 = 54 TRUE / FALSE

d) 63 ÷ 7 = 9 TRUE / FALSE

7. Write a number sentence for this word problem:

Sarah has some stickers. She gives 6 stickers to each of her 4 friends. She uses 24 stickers in total. Write an equation to show this:

📝 Part 3: Algebraic Thinking

8. Use the variable 'n' to represent the position number. Write an algebraic rule for this pattern:

Position (n): 1, 2, 3, 4, 5

Value: 3, 6, 9, 12, 15

Rule: _____ × n = value

9. If the rule is "2n + 1", what would be the value when n = 6?
10. Match each algebraic expression to its meaning:
3n
n + 5
2n - 1
Add 5 to the position number
Multiply the position number by 3
Double the position number then subtract 1
11. Create your own linear pattern and write its rule:

My pattern: _____, _____, _____, _____, _____

Rule in words: _________________________________

Rule using algebra: _____________________________

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