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IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
CPM Materials modified by Mr. Deyo
Is there a different way to get the same result?
Did we give enough information?
How can we describe the position?
Common Core Standard: 8.G.1a, 8.G.1b, 8.G.1c, 8.G.2, 8.G.3, 8.G.4
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
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.
Learning TargetTitle: IM8 ‑ Ch. 6.1.2 How Can I Move A Shape On A Grid (continued)? Date:
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
Home Work: Sec. 6.1.2Desc. Date Due
Review & Preview
3 Problems: 6‑12, 6‑14, 6‑16
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
Vocabulary1) Rigid Transformation
2) Translation
3) Rotation
4) Reflection
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
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?
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
62. 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 6.1.2 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.
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
62 A to B.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.
http://www.cpm.org/technology/general/keylock/?transformdata=MLgdQKejfaeCFe
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
62 C to D.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.
http://www.cpm.org/technology/general/keylock/?transformdata=FDedPDdjdIAgjfaeLFa
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
69. WHERE DOES IT LAND? Felicia found a copy of a puzzle like the one in problem 61, 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 xaxis.Step 3: Rotate counterclockwise 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?
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
69 (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 xaxis.Step 3: Rotate counterclockwise 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).
d) Complete Step 2. Sketch the triangle in its new position and label the coordinates of each vertex.
e) Where does Felicia’s triangle end up? Complete Step 3 on the graph and label the coordinates of each vertex.
A( , ) B( , ) C( , )
A( , ) B( , ) C( , )
A( , ) B( , ) C( , )
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
How do the lengths of the sides compare?
How do the sizes of the angles compare?
STEP 1
Original
STEP 2
STEP 3
610. Now compare the triangle in problem 69 that you have after Step 3 with the original triangle.
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
Original
STEP 3
611. Could Felicia’s team have used different steps to “unlock” her puzzle in problem 69? 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.
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
612. Draw a coordinate graph with x‑ and y‑axes. Graph shapes A, B, and C as described below.
https://www.desmos.com/calculator/0e0sfycd7t http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch6/lesson/6.1.2/problem/612
a) Shape A is a triangle with vertices
(1, 1), (3, 3), and (2, 4).
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).
613. On the same grid you used in problem 612, translate triangle A four units right and three units up to create triangle D. Write the coordinates of the new vertices.
A( , ) B( , ) C( , )https://www.desmos.com/calculator/erukmohhhihttp://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch6/lesson/6.1.2/problem/613
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
614. Graph each equation below on the same set of axes and label the point of intersection with its coordinates.y = 2x + 3
point of intersection ( , )
https://www.desmos.com/calculator/gj24qtqsxx http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch6/lesson/6.1.2/problem/614
y = x + 1x y x y
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
615. Shooter Marilyn is the Spartans’ best freethrow 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. http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/
chapter/Ch6/lesson/6.1.2/problem/615
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
Draw the 0 figure.
616 Examine the tile pattern.
Draw the 4th figure.How many tiles will Figure 10 have? Justify your answer.
http://www.cpm.org/technology/general/tiles/?tiledata=a2x__boy__XbayaAaACC3%20616%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_bmdihxbmdNhxbmbVitayirefFigure%202__bmeehxbmh_cRbmitcRbmeeitbmcRitbmdiitbmdNitbmjpcmbmiYcRbmjpdibmitcmbmiYcmbmjUcmbmitdibmiYdibmjUdiaycsi2Figure%203__ayixi1Figure%204__ayctefFigure%200__
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch6/lesson/6.1.2/problem/616
IM 8 Ch 6.1.2 How Can I Move A Shape On A Grid (continued) November 15, 2014
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.
617 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
https://www.desmos.com/calculator/rz5hqmisd9 http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch6/lesson/6.1.2/problem/617
