Scale Factor

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SWBAT calculate the scale factor of dilations.

Big Idea

Students use examples from the book Alice’s Adventures in Wonderland to explore the concept of scale factor.

Do Now

8 minutes

An ongoing strand in my course is reading excerpts from Lewis Carroll's Alice’s Adventures in Wonderland and using our reasoning skills to explore the mathematical concepts at play in the book. For today's Do Now my students will read a passage and identify the mathematical references they find in the text. Most of the references are related to measurement. Students identify “ten inches high” in the fourth paragraph, “nine feet high” in the first paragraph of the second page, and “two feet high” in the last paragraph. They may find other references, but these are the three I highlight to use later in the lesson. Although this is a long passage, it provides context for today's exploration of scale factor.

I incorporate literacy-intensive lessons in my course to help my students better comprehend word problems better. I find that it also helps them to make connections with other disciplines and increase their retention of important concepts and skills. In undertaking this effort I use literacy instruction strategies. Today I plan to use a popcorn method to read the passage aloud. One student reads out loud and then calls on another student to continue reading. I pass out highlighters and have the students identify the mathematical references as we read. At the end, I call on students to provide their examples. 


10 minutes

This lesson prepares students to use scale factor successfully to solve dilation problems (G.SRT.1). To begin today's Mini-Lesson, I highlight three examples of measurements from the passage.  I ask the students if they have any ideas with respect to analyzing and comparing these measurements. I say, "We are going to work with these measurements, are they in a useful form?" I hope that my students are alert and recognize that one measurement is in inches and the other two are in feet. This fact usually leads to some suggestions with respect to conversion into a common metric. This is a good time to check students’ familiarity with unit conversion.

We then move into a discussion about Alice’s original height.  In the story Alice is about 6 or 7 years old so we usually settle on a measurement of about 45 inches. This is another good place to check in with students’ knowledge of measurement. Many times, they lack precision or estimation skills when working with measurements, and, they demonstrate misconceptions with respect to variation. 

Next we discuss the transformations Alice underwent in the story. We calculate the scale factor for each of Alice’s changes. My students began their study of proportional reasoning in the sixth grade, but they often need a refresher. Most are able to define scale factor as the number a quantity is multiplied by in order to increase of decrease the size of the quantity. To find the scale factor, we use Alice’s new height and divide it by her original height.

Teacher's Note: After each change, Alice is a new height so her original height changes. The scale factor after the “Drink Me” potion is 2/9, after the “Eat Me” cake is 10.8, and after the fan is 2/9 again.

After students find the scale factors, I ask them to write a brief reflection about what happens to Alice when she is dilated by different scale factors. I make this move so they have time to synthesize their ideas. 


20 minutes

For today's Main Activity I give my students three questions to answer using the scale factors from the Mini-Lesson. Students will work independently to answer the questions. For Question 3, students use Alice at age 16. They have to decide on a reasonable height for Alice to be at this age. Answers will vary depending on what height they choose. After about 6 minutes, I go over the answer with students. I call on a few students to give their answers to Question 3.

Part 2 of the Activity requires students to create their own scenario and write their own questions. The questions should use the original questions as a model. The students answer their own questions to check their work. Then, they should rewrite their problem on a separate piece of paper to give to a partner as an Exit Ticket for today's lesson. 


7 minutes

For today's Exit Ticket, students must answer questions about their partner's scenarios. At the end of the lesson, each student hands in their own scenario and their partner’s. I plan to look at the papers to assess whether my students accurately found the scale factors,  and, applied them successfully.