How do the shapes grow or shrink? What parts can we compare? How can we write the comparison? CPM Materials modified by Mr. Deyo
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1 Common Core Standard: 8.G.4 How do the shapes grow or shrink? What parts can we compare? How can we write the comparison? CPM Materials modified by Mr. Deyo
2 Title: IM8 Ch What Do Similar Shapes Tell Us? Date: Learning Target By the end of the period, I will apply scale factors to find unknown side lengths. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity.
3 Home Work: Sec Desc. Date Due Review & Preview 3 Problems: 6 92, 6 93, 6 97
4
5 1) Transformation Vocabulary 2) Dilation 3) Similar Figures 4) Congruent Figures
6
7 6.2.5 What Do Similar Shapes Tell Us? Graphic artists often need to make a shape larger to use for a sign. Sometimes they need to make a shape smaller to use for a bumper sticker. They have to be sure that the shapes look the same no matter what size they are. How do artists know what the side length of a similar shape should be? That is, does it need to be larger or smaller than the original? As you work with your team with shapes, ask the following questions: How can we use pairs of corresponding sides to write the scale factor? Will the scale factor between the shapes be more or less than 1? Does it matter which pair of corresponding sides we use?
8 6 86. With your team, find the scale factor between each pair of similar shapes. That is, what are the sides of each original shape multiplied by to get the new shape? a) scale factor: b) scale factor:
9 6 87. It may have been easier to recognize the scale factor between the two shapes in part (a) of problem 6 86 than it was to determine the scale factor between the two shapes in part (b). When sides are not even multiples of each other (like the sides labeled 4 in. and 5 in. in part (b), it is useful to have another strategy for finding the scale factor. Your task: Work with your team to describe a strategy for finding the scale factor between any two shapes. Refer to the questions below to begin your discussion. How can we use pairs of corresponding sides to write the scale factor? Strategy for Finding the Scale Factor Will the scale factor between the shapes be more or less than 1? Does it matter which pair of corresponding sides we use?
10 6 88. A study team was working together to find the scale factor for the two similar triangles. Study Team Claudia set up the ratio 14 to find the scale factor Issac set up the ratio to find the scale factor. Paula set up the ratio to find the scale factor. a) What did the students do differently when they found their scale factors? b) Do the triangles have more than one scale factor? If not, show how they are the same. c) Why does it make sense that the ratios are equal?
11 6 89a. Alex was working with the two triangles from problem 6 86, but he now has a few more pieces of information about the sides. He has represented the new information and his scale factor in the diagram here. a) Use the scale factor to find the length of the side labeled x. Show your work.
12 6 89b,c. Alex was working with the two triangles from problem 6 86, but he now has a few more pieces of information about the sides. He has represented the new information and his scale factor in the diagram here. b) Since Alex multiplied the side lengths of triangle G to get triangle H, he needs to undo the enlargement to find the side labeled y. What math operation would he use to undo the enlargement? Write an expression and be prepared to explain your reasoning. (If you are able, simplify the expression to find y.) c) If triangle H had been the original triangle and triangle G had been the new triangle, how would the scale factor change? What would the new scale factor be? Explain
13 6 90a. For the pairs of similar shapes, find the lengths of the missing sides. Be sure to show your calculation. You can choose which shape is new and which is original in each pair. Assume the shapes are all drawn to scale. x = y =
14 6 90b. For the pairs of similar shapes, find the lengths of the missing sides. Be sure to show your calculation. You can choose which shape is new and which is original in each pair. Assume the shapes are all drawn to scale. x = y =
15 6 90c. For the pairs of similar shapes, find the lengths of the missing sides. Be sure to show your calculation. You can choose which shape is new and which is original in each pair. Assume the shapes are all drawn to scale. x = y = z =
16 6 90d. For the pairs of similar shapes, find the lengths of the missing sides. Be sure to show your calculation. You can choose which shape is new and which is original in each pair. Assume the shapes are all drawn to scale. x = y = z =
17 6 91. Additional Challenge: On graph paper, copy the figure shown. a) Find the area of the shape. b) Enlarge the shape by a scale factor of 2, and draw the new shape. Find the area.
18 6 92. Find the scale factor and the missing side lengths. chapter/ch x = y =
19 6 93. Alex and Maria were trying to find the side labeled x in problem Their work is shown here. homework/homework/category/cc/textbook/cc3/ chapter/ch6/lesson/6.2.5/problem/6 93 Alex: "I noticed that when I multiplied by 3, the sides of the triangle got longer." Maria: "I remember that when we were dilating shapes in Lesson 6.2.2, my shape got bigger when I divided by 1." 3 a) Look at each student's work. Why do both multiplying by 3 and dividing by make the triangles larger? 3 1 b) Use Alex and Maria s strategy to write two expressions to find the value of y in problem 6 92.
20 6 94a. Consider these two equations: a) Graph both equations on the same set of axes. y = 3x 2 y = 4 + 3x chapter/ch6/le y = 3x 2 y = 4 + 3x x y x y
21 6 94b,c. Consider these two equations: b) Solve this system using the Equal Values Method. y = 3x 2 y = 4 + 3x chapter/ch6/le c) Explain how the answer to part (b) agrees with the graph you made in part (a).
22 6 95. Hollyhocks are tall, slender, flowering plants that grow in many areas of the U.S. Here are the heights (in inches) of hollyhocks that are growing in a park: 10, 39, 43, 45, 46, 47, 48, 48, 49, 50, chapter/ch a) Find the median. b) Find the quartiles. Lower Upper c) Make a box plot of the data
23 6 96. Use the graph here to add points to the table. hom chapter/ch6/lesson/6.2.5/problem x y a) Write the rule in words. b) Explain how to use the table to predict the value of y when x is 8.
24 6 97. Use these following directions to create a mystery letter. On a piece of graph paper, draw a four quadrant graph. Scale each axis from 6 to 6. Plot these points and connect them in order to create a rectangle: (2, 1), (2, 4), (3, 4), (3, 1). Be sure to connect the last point to the first point. Then follow the directions below: a) Rotate the rectangle 90 clockwise about the point (2, 1) and draw the rotated rectangle. chapter/ch6/le b) Reflect the new rectangle over the line y = 2 and draw the reflected rectangle. c) Name the letter of the alphabet that your graph resembles.
25 6 84. Kevin found the box plot below in the school newspaper. chapter/c a) Based on the plot, what percent of students watch more than 10 hours of television each week? b) Based on the plot, what percent of students watch less than 5 hours of television each week? c) Can Kevin use the box plot to find the mean (average) number of hours of television students watch each week? If so, what is it? Explain your reasoning.
26 6 85. Solve each equation. Show all work. chapter/ch6/lesson/6. a) b) 0.85x = 200 7x 6 =140
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