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.1a, 8.G.1b, 8.G.1c, 8.G.2, 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 Are They Similar? Date: Learning Target By the end of the period, I will apply scale factors to various shapes and evaluate if those shapes are congruent, similar, or neither. 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 70, 6 71, 6 72
4
5 1) Dilation Vocabulary 2) Scale Factor 3) Similar Figures 4) Congruent Figures
6
7 6.2.3 Are They Similar? Have you ever noticed how many different kinds of cell phones there are? Sometimes you might have a cell phone that is similar to one of your friends cell phones because it is the same brand, but it might be a different model or color. Occasionally, two people will have the exact same cell phone, including brand, model, and color. Sorting objects into groups based on what is the same about them is also done in math. As you work with your team to sort shapes, ask the following questions: How do the shapes grow or shrink? What parts can we compare? How can we write the comparison?
8 6 52. UNDOING DILATION In Lesson 6.2.1, you looked at dilations and multiplied each of the coordinates of a shape to change its size. Now you will explore how to undo dilations. Charlie multiplied each coordinate of the vertices of a shape by 4 to create the dilated shape. %20RP.pdf a) If Charlie multiplied to find this shape, what operation would undo his dilation? Why? b) Undo the dilation (multiply by 1 / 4) on the graph at right. Label the vertices of Charlie s original shape. How does the shape compare to the dilated shape?
9 6 64a. WHICH SHAPES ARE SIMILAR? If two shapes appear to have the same general relationship between sides, how can you decide for sure if the shapes are similar? Work with your team to: %206.2 Carefully cut out the original shape and shapes A through G from one copy of the Lesson Resource Page. Decide how each shape is related to the original shape. Compare the angles and the sides of shapes A through G to the original shape. a) Which shapes are similar to the original shape? Give specific reasons to justify your conclusions. Which shapes are NOT similar?
10 6 64b. WHICH SHAPES ARE SIMILAR? If two shapes appear to have the same general relationship between sides, how can you decide for sure if the shapes are similar? Work with your team to: b) Now look only at the shapes that are similar to the original shape. What do these shapes have in common? %206.2 What is different about them? Be specific.
11 6 64c,d. WHICH SHAPES ARE SIMILAR? If two shapes appear to have the same general relationship between sides, how can you decide for sure if the shapes are similar? Work with your team to: c) When two shapes are similar, the scale factor is the number you multiply the length of the side of one shape by to get the length of the corresponding side of the new shape. What is the scale factor between the original shape and shape E? Is each side of the shape enlarged the same number of times? Use a ruler to help you decide, if needed. %206.2 d) What is the scale factor between the original shape and shape C? Why is it less than 1?
12 6 65. Shapes that are similar but do not grow or shrink are called congruent shapes. a) Which shape from problem 6 64 is exactly equal to the original shape in every way? b) Record the pairs of shapes above that appear to be congruent to each other. c) Get a piece of tracing paper from your teacher and use it to check that the shapes you identified as congruent have exactly the same size and shape. Were you correct? If not, why not?
13 6 66. Quan enlarged shape Q to make shape P, below. Are his shapes similar? If they are similar, identify the scale factor (multiplier). If they are not, demonstrate that at least one pair of sides does not share the scale factor. If they are similar, identify the scale factor (multiplier). If they are not, demonstrate that at least one pair of sides does not share the scale factor.
14 6 67. Draw each of the shapes in problem 6 66 on graph paper. Color code the corresponding sides on each shape using the colors you see fit. a) Compare the same colored sides of each shape. What do you notice about those sides? b) Compare each of the other five sides of shape P with their corresponding sides on shape Q. What do you notice about those pairs of sides? c) Imagine enlarging shape P to make a new shape R that has a base 25 units long. If shape R is similar to shape P, predict the length of the shorter vertical side of shape R without drawing the shape. What is the scale factor in this situation?
15 6 68 Using the triangle shown at right as the original figure, predict which of the scale factors below would enlarge (make bigger) or reduce (make smaller) the shape. (Do not actually make a new shape.) Your task: After you write down your prediction, decide which scale factor each member of your team will use. Then copy the original figure on graph paper and draw a similar triangle using your scale factor. a) Show your new triangle to your teammates and check your predictions. Which scale factors made the triangle larger? Which made the triangle smaller? Is there a pattern?
16 6 68b,c,d,e) b) Which parts of the new triangles remained the same as the original triangle? Which parts changed? How do you know? c) Each of the new triangles is similar to the original triangle used to create it. Compare the corresponding (matching) sides and angles to each other. Describe the relationship or explain why you think there is no relationship. d) What scale factor could you use to create a triangle that is congruent to the original? Explain. e) Additional Challenge: Find a scale factor that will make a similar shape that is larger than the original but has a scale factor less than 2.
17 6 69. LEARNING LOG "Finding Similar Shapes" Date: In your Learning Log, explain how to determine when shapes are similar. To decide if two shapes are similar, what do you need to know about the side lengths? The angles?
18 6 70. Which of the shapes here appear to be similar? Explain how you know. Shape Shape chapter/ch6/ Shape is similar to Shape because Shape is similar to Shape because Shape is similar to Shape because
19 6 71. A local deli sells 6 inch sub sandwiches for $2.95. Now the deli has decided to sell a family sub that is 50 inches long. If they want to make the larger sub price comparable to the price of the smaller sub, how much chapter/ch6/lesson/6.2.3/problem/6 71 should it charge? Show all work. homework/homework/category/cc/textbook/cc3/
20 6 72. Represent the tile pattern below with a table, a rule, and a graph. homework/homework/category/cc/textbook/cc3/ chapter/ch6/lesson/6.2.3/problem/6 72 x y y = ( )x + ( )
21 6 73a,b. How many solutions does each equation below have? How can you tell? a) 4x = 4x + 3 b) 6T 3 = 3T chapter/c How many solutions? How many solutions? How can you tell? How can you tell?
22 6 73c,d. How many solutions does each equation below have? How can you tell? chapter/c c) d) 6(2m 3) 3m = 2m 18 + m y 2 = 4y y + 8 How many solutions? How many solutions? How can you tell? How can you tell?
23 6 74 Simplify each expression. a) b) ( ) chapter/ch6/lesson
24 6 74 Simplify each expression. c) d) ( 7 ) 9 chapter/ch6/les
25 6 75. Look carefully at the key at right. chapter/ch Which of the keys (a,b,c,d) could you create by spinning (rotating) the original key? How? Which keys could you create by flipping (reflecting) the original key? How?
Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr.
Common Core Standard: 8.G.3, 8.G.4 Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 6.2.2
How do the shapes grow or shrink? What parts can we compare? How can we write the comparison? CPM Materials modified by Mr. Deyo
Common Core Standard: 8.G.2, 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 Title: IM8 Ch. 6.2.4 What Sequence Makes
Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr.
Common Core Standard: 8.G.3 Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 6.1.4 What
Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr.
Common Core Standard: 8.G.3 Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 6.2.1 What
How do the shapes grow or shrink? What parts can we compare? How can we write the comparison? CPM Materials modified by Mr. Deyo
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 Title: IM8 Ch. 6.2.6 How Do I Find A Missing
IM 8 Ch How Can I Move A Shape On A Grid (continued) November 15, 2014
Common Core Standard: 8.G.1a, 8.G.1b, 8.G.1c, 8.G.2, 8.G.3, 8.G.4 Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified
How can you simplify? How can you get x alone? Is there more than one way to simplify? Is there always a solution? CPM Materials modified by Mr.
Common Core Standard 8.EE.7a, 8.EE.7b How can you simplify? How can you get x alone? Is there more than one way to simplify? Is there always a solution? CPM Materials modified by Mr. Deyo Title: IM8 Ch.
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What is a solution to both equations? What does it look like? What is the growth pattern? What is the y intercept? CPM Materials modified by Mr.
Common Core Standard: 8.EE.8a What is a solution to both equations? What does it look like? What is the growth pattern? What is the y intercept? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 5.2.1
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Focus Questions How does the new shape compare to the old shape? How do the coordinates of the new shape compare to the coordinates of the old shape?
Learning Target: Extend their techniques for using integer expressions to record movement on a number line to using expressions to represent movement on the coordinate graph. Practice identifying whether
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Represent and solve problems involving multiplication and division. 3.OA.1.Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example,
= = The number system. Module. Glossary Math Tools... 33
- > + > < - %. < + a = - = = b in. F - - Module The number sstem Lesson Rational and Irrational Numbers........ 8.NS. Lesson ompare and Order Numbers......... 8 8.NS., 8.NS. Lesson Estimate the Value of
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Lesson 4. Objective: Compare and classify quadrilaterals. Lesson Suggested Lesson Structure. Multiply by 4 (8 minutes)
Lesson 4 3 7 Lesson 4 Objective: Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (12 minutes) (7 minutes) (31 minutes) (10 minutes) (60 minutes)
Unit 3: Congruence & Similarity
Approximate Time Frame: 6 weeks Connections to Previous Learning: In previous grades, students made scale drawings of geometric figures and solved problems involving angle measure, surface area, and volume.
Name: Period: Unit 1. Modeling with Geometry: Transformations
Name: Period: Unit 1 Modeling with Geometry: Transformations 1 2017/2018 2 2017/2018 Unit Skills I know that... Transformations in general: A transformation is a change in the position, size, or shape
, 6.7,, Order the numbers from least to greatest. 1. 1, 0, 2, 5, 4. Simplify the expression. 10.
Getting Ready for Pre-Algebra or Algebra Summer Math Practice The following are practice questions to evaluate the students understanding of concepts and skills taught in seventh grade as a readiness for
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CTB/McGraw-Hill. Math Grade 8 Fall Benchmark Assessment Test ID: 87738
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