Unit 1, Lesson 8
Transformations
Integrated Math 2
8.1
Warm-up
Tile Transformations
Instructional Routines
Notice and Wonder
Materials
None
Activity Narrative
This activity is designed to remind students how to describe transformations. They may begin with informal language, such as “flip” instead of “reflection” or “shift” instead of “translation.” Since students will have opportunities to review formal language later in the lesson, there is no need to spend extra time on it during this activity.
Launch
Tell students to close their books or devices (or to keep them closed). Display the image in the Task Statement for all to see. Give students 1 minute of quiet think time, and ask them to be prepared to share at least one thing they notice and one thing they wonder. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the image.
If rigid transformations do not come up during the conversation, ask students to discuss this idea. Record any language students use to describe transformations, including informal descriptions. Students will formalize their language in the Activity Synthesis and the next activity.
Tell students to open their books or devices. Give students 2 minutes of quiet work time to complete the task.
Activity
None- Describe how you can get from Figure A to Figure A'.
- Describe how you can get from Figure B to Figure B'.
Student Response
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Activity Synthesis
The purpose of this discussion is to determine what students remember about transformations. Tell students that the proofs in upcoming lessons require some transformations, so it’s important that we review this topic now.
Ask students, “What do you know about the labels A and A'?” (Figure A' is the image after Figure A is transformed. Figure A is called the “preimage.”)
Then ask students, “What information do we need to clearly describe the following rigid transformations?”
- Translation (distance and direction)
- Reflection (line of reflection)
- Rotation (center and angle)
Lesson Synthesis
The purpose of this discussion is to review how to describe and perform transformations. Students will perform a translation and a rotation in the next lesson, so focus on these two transformations during this discussion.
Display the image shown here. Give students a minute to think about how to describe the sequence. Ask students to share their description with a partner and then refine their answer using the language from the reference chart.
After students have shared precise descriptions, ask students, “How would you perform one of these transformations? How do you know you have created an accurate image?” As students share their answers, demonstrate their methods.
Student Lesson Summary
A translation slides a figure a given distance in a given direction. The distance and direction are given by a directed line segment. Here is a translation of 3 points. Notice the directed line segments
We define a reflection across a line
A rotation is a transformation with a center, angle, and direction (clockwise or counterclockwise). Let’s rotate a point
- The rotation takes point
to a point . -
rotates counterclockwise around the circle to end at . - The angle
degrees.
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