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Numerical Patterns Exploration

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Numerical Patterns Exploration

Numerical Patterns Exploration

Mathematical patterns and sequences illustration

📊 Part 1: Pattern Recognition

1. Look at each sequence below. Circle whether the pattern is increasing or decreasing:

a) 3, 6, 9, 12, 15, ...

Increasing

Decreasing

b) 20, 17, 14, 11, 8, ...

Increasing

Decreasing

c) 5, 10, 15, 20, 25, ...

Increasing

Decreasing

2. What is the constant difference in each pattern above?

a) Constant difference: _______

b) Constant difference: _______

c) Constant difference: _______

📋 Part 2: Completing Pattern Tables

3. Complete the table for the pattern: 4, 7, 10, 13, 16, ...
Term Position (n) 1 2 3 4 5 6
Term Value 4 7 10 13 ____ ____
4. What would be the 10th term in this pattern?
5. Describe the pattern rule in words:

🔢 Part 3: Algebraic Notation

6. For the pattern 2, 5, 8, 11, 14, ..., which algebraic rule is correct?

n + 3

3n - 1

3n + 2

2n + 3

7. Write the algebraic rule for each pattern:

a) 6, 12, 18, 24, 30, ...

Rule: nth term = ______________

b) 1, 4, 7, 10, 13, ...

Rule: nth term = ______________

c) 25, 22, 19, 16, 13, ...

Rule: nth term = ______________

8. Show your working to find the rule for pattern: 3, 8, 13, 18, 23, ...

🔍 Part 4: Pattern Detective Challenge

9. Fill in the missing terms in these patterns:

a) 7, _____, 13, 16, _____, 22

b) 50, 45, _____, 35, _____, 25

c) _____, 9, 15, _____, 27, 33

10. Check all the characteristics that apply to increasing patterns:

Each term gets larger

The constant difference is positive

Each term gets smaller

The pattern goes up by the same amount each time

The constant difference is negative

11. Match each pattern with its correct description:
1. 4, 8, 12, 16, ...
2. 30, 25, 20, 15, ...
3. 1, 5, 9, 13, ...
A. Decreasing by 5
B. Increasing by 4
C. Increasing by 4

✏️ Part 5: Create Your Own Pattern

12. Create your own increasing pattern with a constant difference of 6:

_____, _____, _____, _____, _____, _____

13. Write the algebraic rule for your pattern:
14. Explain in words how your pattern works:
15. Real-world connection: Describe a situation where you might see an increasing numerical pattern in everyday life:

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