CA-226 Chapter 9 - Algebra SECTION 9.5 CLASS ACTIVITY 9-N X Reasoning about Repeating Patterns CCSS CCSS SMP3, 5.0A.3 Assume that the following pattern of a square followed by 3 circles and 2 triangles continues to repeat: HOOOAAGOODAAHOOOAALO .. 1. What will be the 100th shape in the pattern? Explain how you can tell. 2. How many circles will there be among the first 100 entries of the sequence? Explain your reasoning. 3. Here are three ways that students answered part 2: Amanda: There are 6 circles among the first 10 shapes. Because 100 is 10 sets of 10, there will be 10 sets of 6 circles. So there are 10 X 6 = 60 circles among the first 100 shapes. Robert: My idea was like Amanda's but I got a different answer. I said there were 10 circles among the first 20 shapes. Because 100 is 5 sets of 20, there will be 5 sets of 10 circles. So there are 5 X 10 = 50 circles among the first 100 shapes. Kayla: I got the same answer as Robert, but I thought about it in a different way. The pattern repeats in sets of 6 and 3 of those 6 are circles. So half of the shapes are circles and z of 100 is 50, so there are 50 circles. Discuss these students' ways of reasoning. Are any of their methods valid? Why or why not