Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 10, Part C:
Problems That Illustrate Geometric Reasoning

In This Part: Geometric Reasoning Problems, Part 1 | Geometric Reasoning Problems, Part 2

As you look at the next set of problems, answer these questions:

 a. What is the geometry content in this problem? b. What skills do students need to work through this problem? What skills will this problem help them develop for later work? c. What level of geometric thinking is expected of students in the problem? Does it ask students to bridge levels? d. What other questions might extend students' thinking about the problem? e. Describe a lesson that you could develop based on the content of this problem.

Problem C4

Use any materials that allow you to construct the following shapes. Some may not be possible. If you think one of the constructions is impossible, say what makes you think so.

 a. Make a four-sided shape with two opposite sides the same length but not parallel. b. Make several six-sided shapes, some with one pair of sides parallel, some with two pairs of sides parallel, some with three pairs of sides parallel, and some with no pairs of sides parallel. c. Make some shapes with all 90° angles. Make shapes with this property and three, four, five, six, and seven sides.

 Problem C5 List all the properties of a rectangle that you can think of. From your list, choose sets of two or three statements that you think would make a good definition for a rectangle. Is there more than one possible definition? Note 8

 Problem C6 Begin with a convex polygon with a given number of sides. Connect two points on the figure to form two new polygons. What is the total number of sides in the two resulting polygons?

 Problems C4-C6 adapted from Van de Walle, John A. Geometric Thinking and Geometric Concepts. In Elementary and Middle School Mathematics: Teaching Developmentally, 4th ed. pp. 329-344. Copyright © 2001 by Pearson Education. Used with permission from Allyn & Bacon. All rights reserved.

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 Session 10, Grades 3-5: Index | Notes | Solutions | Video