LESSON TSW Perform a sequence of transformations using two or more of the following: translations reflections rotations dilations CC Standards 8.G.3Describe the effect of dilations, translations, rotations, and reflections on two- dimensional figures using coordinates. 8.G.4Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Mathematical Practices #1 Make sense of problems and persevere in solving them. #6Attend to precision. #7 Look for and make use of structure. #8Look for and express regularity in repeated reasoning.

Bell work

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?

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 bellow. 6-8.

Both of these keys are shown as triangles on the Lesson Resource Page (See next two slides) 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 6-8 Continued If technology is available, explore using the Challenge1Challenge1 and Challenge2 puzzles on theChallenge2 CPM Website. Note: Activity is in Lesson

Resource Sheet Part A

Resource Sheet Part B

MOVING ON TO OUR NEXT PROBLEM!

Help Felicia find out where the lock is by following her steps. The following questions are designed to help you. a.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? 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 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.

Let’s check your answers:

LAST PROBLEM IN OUR LESSON!

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? How do the sizes of the angles compare? 6-10

Practice #1 Plot the pre-image, Quadrilateral A(2, -4), B(6,-4), C(5, -7), D(1, -7) Reflect the quadrilateral over the y-axis creating image A’B’C’D’ Translate figure A’B’C’D’ left 3 and up 6 to form A’’B’’C’’D’’ Write the coordinates of A’’B’’C’’D’’ Coordinates A’’B’’C’’D’’ Classwork

Practice #2 Rotate triangle XYZ 90° counter-clockwise about the origin to form image X’Y’Z’ Reflect X’Y’Z’ over the x-axis creating image X’’Y’’Z’’ Write the coordinates of X’’Y’’Z’’ Coordinates X’’Y’’Z’’ Classwork

Practice #3 Coordinates A’’’B’’’C’’’D’’’ Dilate ABCD using a scale factor of 2 to form image A’B’C’D’ Translate your new dilated image left 2 and up 8 to form image A’’B’’C’’D’’ Reflect A’’B’’C’’D’’ over the y-axis creating image A’’’B’’’C’’’D’’’ Write the coordinates of A’’’B’’’C’’’D’’’ Classwork

Practice #4 Plot the pre-image, Triangle A(-8,2), B(-8, -6), C(-4, -6) Rotate the triangle 180° counter-clockwise about the origin forming image A’B’C’ Dilate A’B’C’ using a scale factor of ½ creating image A’’B’’C’’ Write the coordinates of A’’B’’C’’ Coordinates A’’B’’C’’’ Classwork