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Stretching and Shrinking: Scale Factors and Similar Figures

This math lesson focuses on scale factors and similar figures. Students will learn how to determine scale factors, compare areas and perimeters, and identify similar triangles. This lesson includes hands-on activities and practice problems.

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Stretching and Shrinking: Scale Factors and Similar Figures

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  1. Math CC7/8 – Be Prepared On Desk: In Your Journal: • Unit: Stretching and Shrinking • SS 2.3 Scale Factor • 10/25/2019 Do Now: Check/Signoff HomeworkGlue in CW Labsheet 2.3 Math Journal Pencil/eraser Group Bins HWTS Classwork Labsheet 2.3 HW Questions: Upcoming/Reminders: SD Test Return Monday! Partner Quiz – Tues, Oct 29 Unit Test – Wed, Nov 6 HWTS:Green Checker POD: 11HW: SS p. 43 #20-25 and #27

  2. Rectangles (mouths) J, L, and N are similar. All angles are right angles, or the same size, so you only need to check the side lengths.

  3. Draw arrows and mark the scale factor on the labsheet. Label area and perimeter on each similar figure. Scale factors (smallto large): L to J = 2 L to N = 3 J to N is = 3/2 Scale factors (large to small): J to L = ½ N to L is = 1/3 N to J is = 2/3 Reciprocals! Perimeters: J = 20 L = 10 N = 30 Area: J = 16 L = 4 N = 36

  4. The perimeterof the larger rectangle is the scale factor times the perimeter of the smaller rectangle. (All sides increasebythe same factor!) The areaof the larger rectangle is the “square of the scale factor” times the area of the smaller rectangle.

  5. Triangles (noses) O, R, and Sare similar to each other. Same shape, same angles…

  6. Mark answers on the labsheet Scale factors (large to small): R to O = ½ S to O is 1/3 S to R is 2/3 Reciprocals! Scale factors (smallto large): O to R = 2 O to S = 3 R to S = 3/2 Area: O = 1 R = 4 S = 9

  7. Yes! The areaof the larger triangle is the “square of the scale factor” times the area of the smaller triangle. The scale factor from O to S is 3and nine triangle Osfit into triangle S. (3x3 = 9 = )

  8. The first 2 triangles are similar because the scale factor for each pair of corresponding sides is constant (2) and the corresponding angles are equal. The factors from any side of the first 2 triangles to the corresponding side of the third triangle are all different, so the third triangle is NOT similarto either of the first two.

  9. Both of them are correct! Determining scale factor depends on whether you are going from the larger figure to the smaller, or from the smaller figure to the larger. The scale factor from J to L is 0.5 or ½ and fromL to J is 2

  10. Find a number that the length of the first (original) figure is multiplied by to get the corresponding length in the second figure (image). Or… Dividethe length of the second figure by the corresponding length in the first figure = Or… 4 · 2= 8

  11. NO! Using a constant scale factor to stretch or shrink sides does not change the angle size.

  12. Stretching and Shrinking Exit Ticket Last 10 min

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