Advanced Growing Patterns Stations

Name:

Date:

🔍 Station 1: Complex Pattern Analysis

1. A pattern starts with 3 squares in Shape 1, then 7 squares in Shape 2, then 13 squares in Shape 3. What is the pattern rule?

Add 4 each time

Add consecutive even numbers (4, 6, 8...)

Multiply by 2 then add 1

Add the position number × 2

2. Using the pattern from Question 1, write an algebraic expression for the number of squares in Shape n:

Number of squares = ________________

3. How many squares would be in Shape 15 using this pattern? Show your working:

4. A growing pattern follows the rule: Shape n has (n² + 2n) dots. Complete the table:

Shape 1: _____ dots Shape 4: _____ dots Shape 8: _____ dots

📐 Station 2: Multi-Step Pattern Growth

5. A fence pattern grows as follows: Shape 1 uses 8 posts, Shape 2 uses 15 posts, Shape 3 uses 22 posts. If posts cost $12 each, how much would Shape 10 cost to build?

6. Two patterns are growing simultaneously:

Pattern A: 5, 9, 13, 17... Pattern B: 2, 6, 18, 54...

At which term number will Pattern B first exceed 200? _______

What will be the value of Pattern A at that same term? _______

7. Create your own growing pattern where Shape n has exactly 50 elements. Write the algebraic rule and verify it works:

🧠 Station 3: Advanced Reasoning & Justification

8. Maya claims that in any linear growing pattern, if you know Term 3 and Term 7, you can find any other term. Is she correct? Explain your reasoning with an example:

9. A pattern follows the rule: Term n = 3n² - 2n + 5. Without calculating, explain how you know this pattern is NOT linear:

10. Challenge: Design a pattern where Term 5 = 31 and Term 8 = 58. What would Term 20 be? Show all working and explain your method:

11. Reflection: Which type of growing pattern (linear, quadratic, or exponential) would be most suitable for modelling population growth in a city? Justify your choice: