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Background For Teachers:
Ways to Gain/Maintain Attention (Primacy):
Lesson Segment 1: How can we describe the relationship between the
corresponding sides of similar figures and their areas?
As they work together in small groups, ask them to rotate roles: Builder (handles the cubes), Coach (tells builder how it should look and suggest ideas for building), Draftsman (reminds all to sketch the prisms helping each of them with the drawing), Encourager (makes sure there are no put-downs and that each person is taking a turn with the roles). Have students build and sketch, and discuss the answers to the questions as a class.
Predicting and testing the hypotheses: Remind students that in the last lesson, when finding area (or the number of squares needed to cover a similar figure), they used the scale factor squared. Ask students to predict what might happen with the scale factor when finding volumes of similar figures. Have them look for a pattern that relates the scale factor to the number of cube units in each prism. Make sure student focus on the relationship between the scale factor and the new volume. They should begin to see that the units of volume in the larger figure are always the original volume multiplied by the cube of the scale factor. When they write the ratio for each make this explicit: The volume of the larger figure is the cube of the scale factor multiplied by the volume of the smaller figure. Help them make the connection between volume being measured in cubed units and the scale factor being cubed when finding the volume of the larger prism.
Lesson Segment 2: How can the relationship between volumes of similar
figures help us find missing areas?
Play Lie Detector again for completing the worksheet, Volume of Similar Figures.
Students should make the foldable and fill in the blanks to show each step.
Application review of the affect of scale factor on length, area, and volume.
Have student play Jenga as described on the attached worksheet.
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