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

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Objective

SWBAT describe and perform dilations where the center is the origin.

Big Idea

Students dilate objects on the coordinate plane and identify the scale factor of dilations that take a pre-image to an image.

Do Now

5 minutes

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.

Mini-Lesson

10 minutes

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. 

Activity

25 minutes

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.

Summary

5 minutes

At the end of the lesson, we go over Part_C from the activity sheet. I ask different students to give their answers. This allows me to assess what students understand about dilations and helps to inform my future instruction.