Scale Factors and Making Scaled Copies
This lesson develops the vocabulary for talking about scaling and scaled copies more precisely (MP6), and identifying the structures in common between two figures (MP7).
Specifically, students 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. They practice identifying scale factors.
Students then draw scaled copies of simple shapes off a grid with a focus on strengthening their understanding that the relationship between scaled copies is multiplicative, not additive. Students make careful arguments about the scaling process (MP3), have opportunities to use tools like tracing paper or index cards strategically (MP5).
As students draw scaled copies and analyze scaled relationships more closely, encourage them to continue using the terms scale factor and corresponding in their reasoning.
- 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.
- I can describe what the scale factor has to do with a figure and its scaled copy.
- I can draw a scaled copy of a figure using a given scale factor.
- I know what operation to use on the side lengths of a figure to produce a scaled copy.
To create a scaled copy, we multiply all the lengths in the original figure by the same number. This number is called the scale factor.
In this example, the scale factor is 1.5, because \(4 \boldcdot (1.5) = 6\), \(5 \boldcdot (1.5)=7.5\), and \(6 \boldcdot (1.5)=9\).
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