Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 10, Grades 6-8, Part E:
Critiquing Student Lessons (20 minutes)

In the Grades 6-8 curriculum, students are frequently asked to think about patterns, but often their "pattern sniffing" skills end with simply finding the next object.

For each of the problems below, answer the following questions:
Note 8

 a. What algebraic ideas are in this problem? b. How are patterns used in this problem? c. What mathematics do you think students would learn from this problem? d. How would you modify the problem, or what additional questions might you ask, to incorporate the framework for analyzing patterns?

Problem E1

How many tiles will be in the eighth figure of this pattern? How do you know?

Problem E2

 a. Make a drawing of the next V-patterns. b. Is it possible for a V-pattern to have 84 dots? Why or why not? c. How many pairs are there in each V-pattern? d. How many dots will be in the sixth V-pattern? e. Make a V-pattern with 19 dots. f. Fill in the missing values in the table below. V-number means the number of pairs. Describe any patterns you see.
 V-Number Number of Dots 1 3 2 5 3 7 4 ? 5 ? 6 ?

 Problem E1 taken from Gateways to Algebra and Geometry, An Integrated Approach by John Benson, Sara Dodge, Walter Dodge, Charles Hamberg, George Milauskas, And Richard Rukin. Copyright 1997 by McDougal Little Inc. All rights reserved. Used by permission of McDougal Littlel Inc.. "Problem E2 taken from Ups and Downs, Student Book p.6. Reprinted from Mathematics in Context, copyright 1998, with permission from Encyclopaedia Britannica Inc.

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