Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 2, Part E:
Summing Up (20 minutes)

 At the beginning of this session, we learned that finding, describing, explaining, and predicting with patterns are some of the most important skills in mathematics. We had a chance to practice these skills throughout the session as we explored several patterns. We have used many different kinds of descriptions for patterns. Two kinds of descriptions, in particular, are very important: A recursive description tells you how to get from one term to the next. In the table in Part A, for instance, some people might say, "Each output is 4 more than the previous one." That's a recursive description. In the pattern of Part D, if you said, "To get from staircase n to staircase n + 1, add n + 1 blocks," you were using a recursive description. Recursive descriptions are most useful when the instruction to get from one step to the next works no matter where you start in the pattern. But you need to know the output from one or more of the previous steps to find the next one. A closed-form description tells you how to get from any input to any output, without needing to know any previous outputs. In the table in Part A, the instruction "take the input, multiply it by 4, and add 2" or "the output for n is 4n + 2" are closed-form descriptions. In the pattern of Part D, if you said, "Staircase n has n(n + 1) / 2 blocks," you were using a closed-form description. Problem E1 Give an example from your work so far that has been a recursive description of a pattern. Did you ever describe a pattern with a closed-form description? Can you describe the use of the variable in your description?

 Problem E2 In your opinion, why is the study of patterns important, and how does it connect to algebraic thinking?

Next > Homework

 Session 2: Index | Notes | Solutions | Video