U3L3 Measuring Dilations

This lesson gives students more opportunities to practice drawing dilations precisely by reasoning about the definition of a dilation (MP6). Students construct and compare several examples of dilations, and then measure corresponding lengths and distances in the dilated and original figure. Through experimentation, students conjecture that all distances and lengths in the scaled figure are increased or decreased according to the same ratio given by the scale factor. In this lesson they justify that the distances to the center of the dilation from the scaled figure and from the original figure have the same ratio as the scale factor because of how dilations are defined. They also notice that the ratios of corresponding lengths within the original and scaled figure are the same as the scale factor, but that this fact doesn’t come directly from the definition. In this course, we don’t prove this relationship, instead we leave it as an assertion, justified only by experimentation. This activity includes lesson summary videos and practice problems 

By JOEL NELSON