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Advanced Growing Patterns Stations

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Advanced Growing Patterns Stations

Work through each station. Show calculations where asked and explain your reasoning in complete sentences.

Station 1: Analyse and Describe Patterns

1.The first three arrangements contain 3, 7 and 13 squares. Which rule describes how the number of squares changes from one arrangement to the next?

Add 4 squares every time.
Add consecutive even numbers, starting with 4.
Double the previous total and add 1.
Add twice the arrangement number each time.

2.For the pattern whose first three arrangements contain 3, 7 and 13 squares, with the increases continuing by consecutive even numbers starting at 4, write an algebraic rule for the number of squares, T, in arrangement n.

3.Use the rule T = n² + n + 1 to find the number of squares in arrangement 15. Show your calculation.

4.A different pattern has T = n² + 2n dots in arrangement n. Find the number of dots in arrangements 1, 4 and 8.

Arrangement n

Number of dots

________

Station 2: Multi-Step Pattern Growth

5.A fence design uses 8 posts for design 1, 15 posts for design 2, and 22 posts for design 3. The number of posts increases by the same amount each time. If each post costs $12, how much will the posts for design 10 cost?

6.Pattern A begins 5, 9, 13, 17, … and Pattern B begins 2, 6, 18, 54, …. Find the first term number at which Pattern B is greater than 200, then find Pattern A’s value at that same term number.

7.Write a linear rule for a pattern whose 6th term is 50 and whose terms increase by 7 each time. Check that your rule gives 50 when n = 6.

Station 3: Reasoning and Justification

8.A linear pattern has term 3 equal to 14 and term 7 equal to 30. Is there enough information to determine every term in the pattern? Explain how you know and give its rule.

9.A sequence has rule T = 3n² − 2n + 5. Explain why its terms do not have a constant first difference, so the sequence is not linear.

10.Assume a linear pattern has term 5 equal to 31 and term 8 equal to 58. Find its common increase and the value of term 20. Show your working.

11.Which kind of pattern is generally the best starting model for a city population that grows by a roughly constant percentage each year?

Linear growth, because the same number is added each year.
Quadratic growth, because the increases follow a squared rule.
Exponential growth, because the population is multiplied by a similar factor each year.