Unit 1, Lesson 5
The Size of the Scale Factor
Grade 7
Preparation
Lesson Narrative
In this lesson, students deepen their understanding of scale factors in two ways:
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They classify scale factors by size (less than 1, exactly 1, and greater than 1) and notice how each class of factors affects the scaled copies (MP8).
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They see that the scale factor that takes an original figure to its copy and the one that takes the copy to the original are reciprocals (MP7). This means that the scaling process is reversible, and that if Figure B is a scaled copy of Figure A, then Figure A is also a scaled copy of Figure B.
Students also continue to apply scale factors and what they learned about corresponding distances and angles to draw scaled copies without a grid.
Two of the activities are optional. In Scaling a Puzzle, students scale the 6 pieces of a puzzle individually and then assemble them to make a scaled copy of the puzzle. Students need to think strategically about which measurements to take in order to scale the pieces accurately. In Missing Figure, Factor, or Copy, students gain fluency in working with scale factor. Teachers can choose the activity that best fits the needs of their students.
- Describe (orally and in writing) how scale factors of 1, less than 1, and greater than 1 affect the size of scaled copies.
- Explain and show (orally and in writing) how to recreate the original figure given a scaled copy and its scale factor.
- Recognize (orally and in writing) the relationship between a scale factor of a scaled copy to its original figure is the “reciprocal” of the scale factor of the original figure to its scaled copy.
Let’s look at the effects of different scale factors.
Required Preparation
For the blackline master, if possible, copy each complete set on a different color of paper so that a stray slip can quickly be put back.
Print and cut puzzle pieces and blank squares from the “Scaling a Puzzle Cutouts” blackline master. Make enough copies so that each group of 6 students has 1 original puzzle and 6 blank squares.