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# Dilations on the Coordinate Plane, Center (0, 0)

Lesson 2 of 10

## Objective: SWBAT describe and perform dilations where the center is the origin.

#### Do Now

*5 min*

In the previous lesson, students used information from an excerpt from the book *Alice's Adventures in Wonderland* by Lewis Carroll to review and apply **scale factor**. Today's Do Now uses more examples from the book. Students are asked to find the scale factors that describe changes in Alice's height. Using examples from the book provides students with a context for the concept of scale factor, which they will later apply to performing **dilations** on the coordinate plane.

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#### Mini-Lesson

*10 min*

I will begin today's Mini-Lesson with a review of the term **dilation**. My students first learned about dilation in the eighth grade, and I reintroduced the concept briefly in a previous lesson. Today, I ask my students to explain how a quote from *Alice's Adventures in Wonderland* can be explained using the mathematical concept of dilation. We use the quote, **"One side will make you grow taller, and the other side will make you grow shorter,"** to consider how scale factors greater than one and scale factors between zero and one affect a dilation.

I then hand the students a guided practice sheet with two grids on it. They are to write the coordinates of the given points and to perform the indicated dilation (**G.SRT.1**). In these examples, students can multiply both coordinates of each point by the scale factor. I inform my students that it is only possible to use this method to dilate objects about the origin. After they have performed the dilations, I ask them to compare their results with the person next to them to ensure they are correct.

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#### Activity

*25 min*

In the Activity, students work independently to perform and describe dilations on the coordinate plane. Part A has questions than involve performing dilations about the origin using a given scale factor and Part B has questions that ask students identify the scale factor that maps a given pre-image to its image. Students are asked to write explanations in Part C. Question 10 relates back to the Mini-Lesson, while Question 11 directly addresses standard **G.SRT.1**. I pay close attention to my students work on Question 12. For this question, students must access their prior knowledge to explain why a dilation is not a **rigid motion**. We covered rigid motions in an earlier unit in my course.

As students work on the activity I circulate around the room and check that their dilations are accurate (**MP6**). The most common error students make is when multiplying. If I notice their images are not correct, I question the student about their dilation in order to help them see the mistake and correct it. I ask the students to examine the image and the pre-image to see if they are in proportion. When they reexamine their graphs considering this issue, they usually see their own mistakes.

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#### Resources

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment

- LESSON 1: Scale Factor
- LESSON 2: Dilations on the Coordinate Plane, Center (0, 0)
- LESSON 3: Dilations using Geometer's Sketchpad
- LESSON 4: Dilations on the Coordinate Plane, Center (h, k)
- LESSON 5: Properties of Dilations Extension Lesson
- LESSON 6: Similar Triangles using Geometer's Sketchpad
- LESSON 7: Finding Missing Sides of Similar Triangles
- LESSON 8: Angle-Angle Similarity Postulate
- LESSON 9: Similar Triangle Practice
- LESSON 10: Similar Triangles and the Flatiron Building