This opening task introduces the term scaled copy. It prompts students to observe several copies of a picture, visually distinguish scaled and unscaled copies, and articulate the differences in their own words. Besides allowing students to have a mathematical conversation about properties of figures, it provides an accessible entry into the concept and gives an opportunity to hear the language and ideas that students associate with scaled figures.
Students are likely to have some intuition about the term “to scale,” either from previous work in grade 6 (e.g., scaling a recipe, or scaling a quantity up or down on a double number line) or from outside the classroom. This intuition can help them identify scaled copies. As students apply their previous experience with scaling to analyze the images, they are making sense of problems (MP1).
Expect them to use adjectives such as “stretched,” “squished,” “skewed,” “reduced,” and so on, in imprecise ways. This is fine because students’ intuitive definitions of scaled copies will be refined over the course of the lesson. As students discuss the pictures, note the range of descriptions used. Monitor for students whose descriptions are particularly supportive of the idea that lengths in a scaled copy are found by multiplying the original lengths by the same value. Invite them to share their responses later.
In the digital version of the activity, students use an applet to manipulate copies of the original image. The applet allows students to explore different transformations of the original portrait. This activity works best when each student has access to the applet because students will benefit from seeing the transformations in a dynamic way. If students don't have individual access, displaying the applet for all to see would be helpful during the launch and synthesis.
