Unit 1, Lesson 6
Scaling and Area (Optional)
Grade 7
Preparation
Lesson Narrative
This lesson is optional. In this lesson, students are introduced to how the area of a scaled copy relates to the area of the original shape. Students build on their grade 6 work with exponents to recognize that the area changes by the square of the scale factor by which the sides changed. Students will continue to work with the area of scaled shapes later in this unit and in later units in this course. Although the lesson is optional, it will be particularly helpful for students to have already had this introduction when they study the area of circles in a later unit.
In two of the activities in this lesson, students build scaled copies using pattern blocks as units of area. This work with manipulatives helps accustom students to a pattern that many find counterintuitive at first (MP8). (It is a common but false assumption that the area of scaled copies increases by the same scale factor as the sides.) After that, students calculate the area of scaled copies of parallelograms and triangles to apply the patterns that they discovered in the hands-on activities (MP7).
- Calculate and compare (orally and in writing) the areas of multiple scaled copies of the same shape.
- Generalize (orally) that the area of a scaled copy is the product of the area of the original figure and the “square” of the scale factor.
- Recognize that a two-dimensional attribute, like area, scales at a different rate than do one-dimensional attributes, like length and distance.
Let's build scaled shapes and investigate their areas.
Required Preparation
Prepare to distribute the pattern blocks, at least 18 blue rhombuses, 18 green triangles, and 10 red trapezoids per group of 3–4 students. For the Are You Ready for More? prepare to distribute 7 yellow hexagons per group.
If there are not enough pattern blocks for each group to have a full set, consider rotating the blocks of each color through the groups. Using real pattern blocks is preferred, but the Digital Activity can be used if physical manipulatives are unavailable.
For the digital version of the activity, acquire devices that can run the applet.
Redistribute the pattern blocks so that students can make scaled copies of their assigned figure. Each group needs only one type of block, either 20 blue rhombuses, 15 red trapezoids, or 24 green triangles.
Using real pattern blocks is preferred, but the Digital Activity can be used if physical manipulatives are unavailable.
For the digital version of the activity, acquire devices that can run the applet.