Unit 2, Lesson 2
Scale Factors and Making Scaled Copies
Accelerated 7
Preparation
Lesson Narrative
This lesson develops the vocabulary for talking about scaling and scaled copies more precisely and for identifying the structures in common between two figures. Students also begin to describe the numerical relationship between the corresponding lengths in two figures using a scale factor. They see that when two figures are scaled copies of one another, the same scale factor relates their corresponding lengths. As students identify the scale factor that relates corresponding sides, they are making use of repeated reasoning (MP8).
Students strengthen their understanding that the relationship between scaled copies is multiplicative, not additive. Students make careful arguments about the scaling process (MP3) and have opportunities to use tools like tracing paper or index cards strategically (MP5).
- Comprehend the phrase “scale factor” and explain (orally) how it relates corresponding lengths of a figure and its scaled copy.
- Critique (orally and in writing) different strategies (expressed in words and through other representations) for creating scaled copies of a figure.
- Draw a scaled copy of a given figure using a given scale factor.
- Generalize (orally and in writing) that the relationship between the side lengths of a figure and its scaled copy is multiplicative, not additive.
Let's draw scaled copies.
Required Preparation
None
To create a scaled copy of a figure, all the side lengths in the original figure are multiplied by the same number. This number is called the scale factor.
In this example, the scale factor is 1.5, because , , and .