Unit 5: Seeing Structure and Generalizing (MP7 and MP8)

5.2 Making Sense of a Growing Pattern

Take a few minutes to complete an activity titled, Square Tiles. Upon completion of this task, you will have an opportunity to view a student making sense of the same problem.

Solve the problem before viewing the videos:

Square Tiles

Tiles are arranged to form pictures like the ones below:

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After completing the activity, view the videos of a 6th grade student solving the same problem. In the pre-interview, the student had only to find the 10th and 100th term in the pattern. In the post-interview, she solved all parts of the problem. The pre-interview was in September and the post-interview was in May of her 6th grade year.

Consider the following questions as you view the videos:

• What strategies for finding a generalization does Tamara use in the pre-interview? In the post-interview?
• What is the role of visualization in her work? Of structure of the pattern?
• How is repeated reasoning used to get a generalization?
• What is Tamara’s facility in using symbolic representations for the square tiles pattern?
• How does Tamara structure her arithmetic computations to keep track of her work?

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