Illustrative Mathematics Grade 8, Unit 1, Lesson 4: Making the Moves

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Illustrative Math
Grade 7

Lesson 4: Making the Moves

Let’s draw and describe translations, rotations, and reflections.

Illustrative Math Unit 8.1, Lesson 4 (printable worksheets)

Lesson 4 Summary

The following diagram shows how to draw and describe translations, rotations, and reflections.

Lesson 4.1 Reflection Quick Image

Here is an incomplete image. Your teacher will flash the completed image twice. Your job is to complete the image on your copy.
Open Applet

• See Video for Whole Lesson

Lesson 4.2 Make That Move

Your partner will describe the image of this triangle after a certain transformation. Sketch it here.
Open Applet

Lesson 4.3 A to B to C

Here are some figures on an isometric grid. Explore the transformation tools in the tool bar. (Directions are below the applet if you need them.)

1. Name a transformation that takes Figure A to Figure B. Name a transformation that takes Figure B to Figure C.
2. What is one sequence of transformations that takes Figure A to Figure C? Explain how you know.
   Open Applet
   Translate
3. Select the Vector tool.
4. Click on the original point and then the new point; you should see a vector.
5. Select the Translate by Vector tool.
6. Click on the figure to translate, and then click on the vector.
   Rotate
   
7. Select the Rotate around Point tool.
8. Click on the figure to rotate, and then click on the center point.
9. A dialog box will open; type the angle by which to rotate and select the direction of rotation.
   Reflect
   
10. Select the Reflect about Line tool.
11. Click on the figure to reflect, and then click on the line of reflection.

Are you ready for more?

Experiment with some other ways to take Figure A to Figure C. For example, can you do it with. . .

• No rotations?
• No reflections?
• No translations?

Lesson 4 Practice Problems

1. For each pair of polygons, describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q.
2. Here is quadrilateral ABCD and line l. Draw the image of quadrilateral ABCD after reflecting it across line l.
3. Here is quadrilateral ABCD.
   Draw the image of quadrilateral ABCD after each rotation using B as center.
   a. 90 degrees clockwise
   b. 120 degrees clockwise
   c. 30 degrees counterclockwise

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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