IM 8 Ch How Can I Move A Shape On A Grid (continued) November 15, 2014
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- Blaze Robbins
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1 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 by Mr. Deyo
2 Title: IM8 Ch How Can I Move A Shape On A Grid (continued)? Date: Learning Target By the end of the period, I will describe and complete transformations on a coordinate plane, and use coordinates to describe the position of objects in a plane (flat surface). 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 12, 6 14, 6 16
4
5 Vocabulary 1) Rigid Transformation 2) Translation 3) Rotation 4) Reflection
6
7 6.1.2 How Can I Move A Shape On A Grid (continued)? Have you ever had trouble giving directions? Sometimes describing where something is or how it has moved is difficult. For this reason, people often use coordinate graphs like the one shown at right. Coordinate graphs help you describe directions with words like left and down. They can also help you measure distances. Today you will work with your team to describe movement on a coordinate graph. You will also look at ways to describe where an object is on the grid before and after a transformation. As you work, use the questions below to help start math discussions with your team members. Is there a different way to get the same result? Did we give enough information? How can we describe the position?
8 6 2. While solving the key challenge in Lesson 6.1.1, Rowan made more than one move to change his key from point A to point B and from point C to point D, as shown on the graph at right. Both of these keys are shown as triangles on the Lesson Resource Page. Explore using the Challenge1 and Challenge2 puzzles (CPM). You may need to resize the window and reposition the grid by shift dragging. Your Task: With your team, describe how Rowan could have moved each key from the starting position to the ending position using slides (also called translations), turns (also called rotations), and/or flips (also called reflections). Make sure you provide enough detail to describe the moves completely. Try to find more than one way he could have moved each key. Be ready to justify your ideas with the class.
9 6 2 A to B. transformdata=mlgdqkejfaecfe Your Task: With your team, describe how Rowan could have moved each key from the starting position to the ending position using slides (also called translations), turns (also called rotations), and/or flips (also called reflections). Make sure you provide enough detail to describe the moves completely. Try to find more than one way he could have moved each key. Be ready to justify your ideas with the class.
10 6 2 C to D. transformdata=fdedpddjdiagjfaelfa Your Task: With your team, describe how Rowan could have moved each key from the starting position to the ending position using slides (also called translations), turns (also called rotations), and/or flips (also called reflections). Make sure you provide enough detail to describe the moves completely. Try to find more than one way he could have moved each key. Be ready to justify your ideas with the class.
11 6 9. WHERE DOES IT LAND? Felicia found a copy of a puzzle like the one in problem 6 1, but the lock is missing. All she has are the starting points and the moves to unlock the lock. This time her key is shaped like a triangle. The points are at A ( 5, 0), B ( 5, 3), and C ( 1, 0). Step 1: Translate 4 units to the right and 2 units up. Step 2: Reflect across the x axis. Step 3: Rotate counter clockwise 90 about point (3, 2) With your team, set up your own coordinate grid on graph paper. The questions below will help. How many quadrants (regions) should the graph have? Should it be a graph with only the first quadrant? Or a graph with four quadrants? How should the axes be scaled? How many units should you use for each side length of a grid square?
12 6 9 (continued). WHERE DOES IT LAND? The points are at A ( 5, 0), B ( 5, 3), and C ( 1, 0). Step 1: Translate 4 units to the right and 2 units up. Step 2: Reflect across the x axis. Step 3: Rotate counter clockwise 90 about point (3, 2) b) Plot triangle ABC to represent the key. c) Follow Step 1 to translate the triangle. Name the new location of each vertex, or corner, of the triangle in the form (x, y). A(, ) B(, ) C(, ) d) Complete Step 2. Sketch the triangle in its new position and label the coordinates of each vertex. A(, ) B(, ) C(, ) e) Where does Felicia s triangle end up? Complete Step 3 on the graph and label the coordinates of each vertex. A(, ) B(, ) C(, )
13 6 10. Now compare the triangle in problem 6 9 that you have after Step 3 with the original triangle. How do the lengths of the sides compare? STEP 1 How do the sizes of the angles compare? Original STEP 2 STEP 3
14 6 11. Could Felicia s team have used different steps to unlock her puzzle in problem 6 9? In other words, could she have used different moves and still have the key end up in the same final position? If it is possible, list a new set of steps that would move her key from the same starting location to the same final position. If it is not possible, explain why not. Original STEP 3
15 6 12. Draw a coordinate graph with x and y axes. Graph shapes A, B, and C as described below. a) Shape A is a triangle with vertices (1, 1), (3, 3), and (2, 4). chapter/c b) Shape B is a square with vertices (2, 1), (4, 1), (2, 3), and (4, 3). c) Shape C is a rectangle with vertices ( 3, 1), ( 3, 4), ( 1, 4), and ( 1, 1) On the same grid you used in problem 6 12, translate triangle A four units right and three units up to create triangle D. Write the coordinates of the new vertices. A(, ) B(, ) C(, ) homework chapter/ch6/lesson/6.1.2/problem/6 13
16 6 14. Graph each equation below on the same set of axes and label the point of intersection with its coordinates. y = 2x + 3 y = x + 1 x y x y chapter/ point of intersection (, )
17 6 15. Shooter Marilyn is the Spartans best free throw shooter. She normally makes three out of every four shots. In an upcoming charity event, Shooter will shoot 600 free throws. If she makes over 400 baskets, the school wins $1000. Should the Spartans expect to win the cash for the school? Show and organize your work. homework/homework/category/cc/textbook/cc3/ chapter/ch6/lesson/6.1.2/problem/6 15
18 tiledata=a2x boy XbayaAaACC3%206 16%20HW %20eTool ayaza9directions%3a%20examine%20the%20tile%20pattern %20below.%20%20Draw%20Figure%200%20and%20Figure%204.%20%20How %20many%20tiles%20will%20Figure%2010%20have %3F bmffcrbmf6cmbmfacrbmf6dibmffcmbmffdiayfmeefigure %201 bmcmhxbmcmh_bmbvhxbmcmitbmcrhxbmbvh_bmbqh_bmcrh_bmdih xbmdnhxbmbvitayireffigure %202 bmeehxbmh_crbmitcrbmeeitbmcritbmdiitbmdnitbmjpcmbmiycrbmjpdi bmitcmbmiycmbmjucmbmitdibmiydibmjudiaycsi2figure%203 ayixi1figure %204 aycteffigure%200 IM 8 Ch How Can I Move A Shape On A Grid (continued) November 15, Examine the tile pattern. Draw the 0 figure. homework/homework/category/cc/textbook/cc3/ chapter/ch6/lesson/6.1.2/problem/6 16 Draw the 4 th figure. How many tiles will Figure 10 have? Justify your answer.
19 6 17 GETTING IN SHAPE. Frank weighs 160 pounds and is on a diet to gain two pounds a week so that he can make the football team. John weighs 208 pounds and is on a diet to lose three pounds a week so that he can be on the wrestling team in a lower weight class. Frank John homework/homework/category/cc/textbook/cc3/ chapter/ch6/lesson/6.1.2/problem/6 17 If Frank and John can meet these goals with their diets, when will they weigh the same? How much will they weigh at that time? Clearly explain your method.
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
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
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
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.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
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
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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