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Geometry Session 10: Classroom Case Studies - Grades 6-8
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Session 10 Materials:

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:


What is the geometry content in this problem?


What skills do students need to work through this problem? What skills will this problem help them develop for later work?


What level of geometric thinking is expected of students in the problem? Does it ask students to bridge levels?


What other questions might extend students' thinking about the problem?


Describe a lesson that you could develop based on the content of this problem.


Problem C4


If a dart has an equal chance of landing at any point on a circular target, is it more likely to land closer to the center or closer to the edge?


Problem C5


On a geoboard, you can make different shapes.


Make at least five shapes with four boundary pegs and no pegs inside. Find the areas of each of your figures.


Make at least five shapes with four boundary pegs and one peg inside. Find the areas of each of your figures.


Continue investigating other cases using different numbers of boundary and inside pegs. Can you find a rule for the areas of the figures?


Think of a way to explain why your rule works. Hint: What happens when you add a boundary point? How much area is added? What happens when you add an interior point? How much area is added?

Note 7


Problem C6


Fernando's Frames offers a low-cost, do-it-yourself picture-framing option. To save money, you determine the shape of the frame and select and purchase the side pieces. Side pieces of various lengths are available. Corner fittings are free. Fernando helps you assemble the frame.

One day, Fernando's friend Fred came into the frame shop. He asked for six side pieces, 2, 3, 4, 5, 6, and 7 inches long. He said he could take any three of those side pieces and make a triangular frame.

"Don't be so sure of that!" said Fernando.

What is the probability that any three of these side pieces will form a triangular frame?


Problem C4 adapted from Van de Walle, John A. Geometric Thinking and Geometric Concepts. In Elementary and Middle School Mathematics: Teaching Developmentally, 4th ed. p. 338. Copyright © 2001 by Pearson Education.
Used with permission from Allyn and Bacon. All rights reserved.

Problem C6 adapted from Chapin, Suzanne; Greenes, Carole E.; Findell, Carol; and Spungin, Rika. Gold Medal Problems. p. 81. © 1999 by Glencoe/McGraw-Hill.
Used with permission. www.glencoe.com/sec/math

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