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Number Sequences and Patterns

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Number Sequences and Patterns

Number Sequences and Patterns

Number sequence illustration

🔢 Part 1: Identifying Patterns

1. Look at Ella's stair climbing pattern. She counts: 2, 4, 6, 8, 10...

What is the pattern rule? ________________________________

What would be the next three numbers? _____, _____, _____

2. Circle the correct pattern rule for this sequence: 5, 10, 15, 20, 25

Add 3 each time

Add 5 each time

Add 10 each time

Double each time

3. Complete these sequences by filling in the missing numbers:

a) 3, 6, 9, _____, 15, _____, 21

b) 20, 18, 16, _____, 12, _____, 8

c) 1, 3, 5, _____, 9, _____, 13

📊 Part 2: Creating Your Own Sequences

4. Create a sequence that counts in 2s starting from 4:

4, _____, _____, _____, _____, _____, _____

Describe your rule: ________________________________

5. Create a sequence that counts backwards in 5s starting from 30:

30, _____, _____, _____, _____, _____, _____

Describe your rule: ________________________________

6. Check all the sequences that show odd numbers:

1, 3, 5, 7, 9

2, 4, 6, 8, 10

11, 13, 15, 17, 19

10, 12, 14, 16, 18

🧮 Part 3: Function Notation (Simple)

7. If the rule is "add 3" and we write it as f(n) = n + 3, work out these values:

f(1) = 1 + 3 = _____

f(2) = 2 + 3 = _____

f(3) = 3 + 3 = _____

f(4) = 4 + 3 = _____

8. If f(n) = 2n (which means "multiply by 2"), work out:

f(1) = 2 × 1 = _____

f(2) = 2 × 2 = _____

f(3) = 2 × 3 = _____

f(5) = 2 × 5 = _____

9. Circle the correct function rule for the sequence: 4, 5, 6, 7, 8

f(n) = n + 3

f(n) = n + 4

f(n) = 2n

f(n) = n + 5

🕵️ Part 4: Sequence Detective Challenge

10. Be a sequence detective! Look at these mystery sequences and work out the pattern:

Mystery Sequence A: 7, 14, 21, 28, 35

Pattern rule: ________________________________

Next two numbers: _____, _____

Mystery Sequence B: 50, 45, 40, 35, 30

Pattern rule: ________________________________

Next two numbers: _____, _____

11. Create your own mystery sequence for a friend to solve:

My sequence: _____, _____, _____, _____, _____

My secret rule: ________________________________

12. Draw a picture or diagram to show how sequences work in real life (like stairs, calendar days, or counting money):

💭 Part 5: Explaining Your Thinking

13. Explain in your own words what a number sequence is:
14. Match the sequence vocabulary with their meanings:
1. Term
2. Pattern
3. Rule
4. Sequence
A. A list of numbers in order
B. Each number in a sequence
C. The instruction for making the sequence
D. The way numbers are arranged
15. Which of these sequences would you find most interesting to explore further and why?

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