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.
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1 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
2 Title: IM8 Ch What Can I Create? Date: Learning Target By the end of the period, I will create expressions to represent shape movement on the coordinate graph and determine whether a shape has been translated, rotated, or reflected. 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 36, 6 37, 6 38
4
5 Vocabulary 1) Rigid Transformation 2) Translation 3) Rotation 4) Reflection
6
7 6.1.4 What Can I Create? In the last several lessons, you have described translations using coordinates. You have also developed strategies for determining where an object started when you know how it was translated and its final position. In this lesson, you will continue to practice transforming objects on a coordinate graph by translating (sliding), rotating (turning), and reflecting (flipping). As you work, visualize what each object will look like after the transformation. Use the graph to check your prediction. Is there a different way to get the same result? Did we give enough information? How can we describe the position?
8 6 33. BECOMING AN ARTIST Have you ever seen directions for drawing a cartoon figure such as a face? Usually these directions start by helping you to put some basic shapes together to form an outline. Then they give you ideas for how to finish the drawing. An example showing how you could draw a dinosaur is at right. Your task: Obtain Lesson 6.1.4A Resource Page from your teacher. On it, shapes A, B, and C are provided for you. Follow the directions below to create a design. Whenever one of the shapes is mentioned below, start with the original shape on the left side of the paper. The final result of each step is part of the outline of the design. Draw a rectangle with vertices (5, 0), (9, 0), (9, 8), and (5, 8). Translate circle A so that its center is at (7, 6). Describe how the shape moved. Rotate (turn) triangle C 180 clockwise about the point ( 6, 3). Record the coordinates of the new vertices. Then add 15 to each x coordinate and graph the final result. What transformation does "adding 15" represent? Reflect (flip) triangle B across the y axis. Record the new coordinates of the vertices. Describe how the coordinates have changed from the original shape. A new shape, triangle D, has vertices at ( 7, 13), ( 8, 11) and ( 6, 11). Translate triangle D so that its top vertex is at (7, 4). Describe this translation with words. Translate triangle C to the right 11 units. Then reflect the result across the horizontal ( ) line that goes through y = 3. Record the new coordinates for triangle C. Translate circle A so that the x coordinates increase by 13 units and the y coordinates increase by 11 units. Record the coordinates of the center of circle A in its new position.
9 Draw a rectangle with vertices (5, 0), (9, 0), (9, 8), and (5, 8). Translate circle A so that its center is at (7, 6). Describe how the shape moved. Rotate (turn) triangle C 180 clockwise about the point ( 6, 3). Record the coordinates of the new vertices. Then add 15 to each x coordinate and graph the final result. What transformation does "adding 15" represent? Reflect (flip) triangle B across the y axis. Record the new coordinates of the vertices. Describe how the coordinates have changed from the original shape. A new shape, triangle D, has vertices at ( 7, 13), ( 8, 11) and ( 6, 11). Translate triangle D so that its top vertex is at (7, 4). Describe this translation with words. Translate triangle C to the right 11 units. Then reflect the result across the horizontal ( ) line that goes through y = 3. Record the new coordinates for triangle C. Translate circle A so that the x coordinates increase by 13 units and the y coordinates increase by 11 units. Record the coordinates of the center of circle A in its new position.
10 %20RP.pdf CREATE A DESIGN Now create your own design using basic shapes A through F on the Lesson 6.1.4C Resource Page. Write complete directions on the next page (such as those in problem 6 33) for creating your design. Make sure you provide all of the necessary information.
11 %20RP.pdf CREATE A DESIGN Write complete directions here (such as those in problem 6 33) for creating your design. Make sure you provide all of the necessary information.
12 6 35. Additional Challenge: Visualize a pattern of squares covering a coordinate graph as show at right. What transformations could you make to move the whole pattern so that the squares and lines in the pattern line up exactly over other squares and lines?
13 6 27a,b. Erin started with one corner of a figure located at P( 4, 5) and translated it to end at P'(6, 8). To find out how far the shape moved horizontally, she decided to find the difference between the two x coordinates. She wrote: 6 ( 4). a) When Erin simplified 6 ( 4) she got 2 as her answer. Is this correct? If not, what is the correct simplification? chapter/c b) Write another expression to find out how far the shape moved vertically ( ). Simplify both expressions and describe the translation. P (, ) P (x: + =,y: + = ) P' (, )
14 6 27c. Describe each of the translations below. chapter/ch (3, 2) (5, 9) ( 1, 4) (6, 2) (0, 0) ( 4 7) ( 2, 9) (2, 9)
15 homework/homework/category/cc/textbook/cc3/ chapter/ch6/lesson/6.1.4/problem/6 36 a) Write directions to translate the original triangle to make the new triangle. b) What are the coordinates of the vertices (corners) of the new shape? N 1 (, ) N 2 (, ) N 3 (, ) c) On your graph, reflect the original triangle across the y axis. What are the coordinates of the new triangle? N' 1 (, ) N' 2 (, ) N' 3 (, )
16 6 37 Make a table and graph for the rule y = 3x chapter/ch What is the rule? y = ( )x + ( ) x y
17 6 38. Solve the system of equations below using the Equal Values Method. chapter/ch6/l a = 12b + 3 a = 2b 4
18 6 39. Ms. Cai's class is studying a tile pattern. The rule for the tile pattern is y = 10x + 8. Kalil thinks that Figure 12 of this pattern will have 108 tiles. Is he correct? Show your work and justify your answer. chapter/ch6/le
19 6 40. Angela is picking mountain blueberries for a delicious pie. She can pick cup of blueberries in 2 minutes. If she needs 2.5 cups of blueberries for the pie, how long will it take her to pick the berries? Show your work homework/homework/category/cc/textbook/cc3/ chapter/ch6/lesson/6.1.4/problem/6 40 Angela will need minutes to pick two and a half cups of blueberries.
20 6 41 Juan thinks that the graph of 6y + 12x = 4 is a line. homework chapter/ch6/lesson/6.1.4/problem/6 41 a) Solve Juan's equation for y. 6y + 12x = 4 b) Is this equation linear? That is, is its graph a line? Explain how you know. c) What are the pattern of growth and y intercept of this graph? y = ( )x + ( )
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.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 Title: IM8 Ch.
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
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
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.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
The activities here offer you a chance to reflect about what you have learned during this chapter.
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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
Name: Date: Per: WARM UP
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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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