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Main Curriculum Tie:
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?
Give each team of students 16 of each pattern block: orange squares, green triangles, blue rhombi. They will be building growing patterns, or growing generations of similar figures. Geometry Standard in the 7th Grade Utah Mathematics Core uses the terms "scale drawings" rather than generations. Make clear to students that each generation is a scale drawing of the original figure. Work with them in completing the Growing Generations of Similar Figures investigation worksheet , discussing the answers to the questions on page 2 of the worksheet through # 2 on the second page. Ask them to be looking for a pattern that relates the scale factor to the number of area units in each generation.
To help students visualize the figures in the table for # 3 on the second page of Growing Generations of Similar Figures, give each a Centimeter Paper. Students can sketch each of the generations listed in the table for the “5 cm²” shape (as shown in red on the attached key for the Centimeter Paper) as well as the 2nd and 3rd generation listed in the table for the “4 yd²” shape as shown in green. As they sketch the figures, compare the areas, and complete these first six rows of the table on the worksheet, have them focus on the relationship between the scale factor and the original area. They should begin to see that the units of area in the larger figure are always the original area multiplied by the square of the scale factor. Help them make the connection between area being measured in square units and the scale factor being squared when finding the area of the larger generation. Students should then be able to complete the last four rows of the table by using the pattern described rather than needing to sketch.
Lesson Segment 2: How can the relationship between areas of similar figures
help us find missing areas?
Play Lie Detector for completing the worksheet, Area of Similar Figures.
Journal: Have students take the roll of expert explaining a student who had just come into the class. Students should write a complete explanation for how to answer the following question using words, drawings and math symbols. An evaluation for math writings has been attached. Students should do the writing on the back of the evaluation.
Question: You have a great photo that is 3” by 5”. You want to enlarge the area of the picture using a scale factor of 3. What is the area of the larger picture? Will it fit on your 9 x 12 scrapbook page?
Assign text practice as needed.
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