##
* *Reflection: Intrinsic Motivation
Transformations Review - Section 4: Unit Review Problem Set

In the last question on the review, students create compositions of transformations that will produce the given image. I have included an additional challenge where students look for compositions of **only** reflections to produce the image. This extension was suggested to me by a college professor who stated that there is a minimum of three reflections required. In class, one young man found a solution involving four reflections, and several students were able to do it with five. As the students left my classroom, I heard them declaring that they would continue to work on it over the weekend - pretty awesome!

Postscript:

I have worked on this myself now. In order to find the three line reflections, one needs to construct three perpendicular bisectors, using the corresponding vertices of the triangles. I have done this using a compass and straightedge and it does do the trick, mapping one triangle onto the other, but finding the equations of these lines is not an easy task by any means, and is beyond anything I would ask my students to do at this point in time.

*Intrinsic Motivation: An Extension on Problem 10*

# Transformations Review

Lesson 5 of 6

## Objective: SWBAT apply their knowledge of the concepts covered in this unit to a unit review problem set.

*90 minutes*

#### Lesson Opener

*5 min*

I begin this assessment day lesson with a quick Do Now to get students thinking about the equations of lines and their use in transformations in the plane.

#### Resources

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#### Going Over the Homework

*10 min*

The homework assignment (Practice with Transformations) was a collection of multiple-choice questions from previous Statewide assessments. For review, I call on students to give their answer to each question. If everyone agrees, we move onto the next question; if anyone disagrees, we take the time to discuss that question.

The most difficult question on the assignment is typically Number 25. The answer choices include a reflection across y=-x **and** a rotation of -90 degrees. We have come across negative angles occasionally in this unit, especially when the students were making up their own compositions, but this is another chance to discuss this concept.

#### Resources

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This is a simple matching activity to review and build confidence before the assessment. Students, working in pairs, match the preimage to the image, given a composition of transformations. I make both plain paper and graph paper available to the students for this activity, so they have choices with regard to how they find their solutions.

I run the Composition, Matching Cards materials off using different colored paper. I cut them out ahead of time, rather than using class time, and I mix the colors, so that every student-pair's cards contain the preimage and composition in one color and the image in a different color. (See the Photo of Composition Cards.) I also hand out an answer sheet, on which the students record their answers.

When all the pairs finish discussion (**MP3**), the matching of cards, and the recording of their answers, we go over the answers as a group.

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#### Lesson Closing

*5 min*

I spend the last five minutes of this class tying up any loose ends. I let the students know when I am available for any extra help, and ask for suggestions from the students as to how they might go about preparing for the test.

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