Lesson 5: The Size of the Scale Factor
About this lesson
In this lesson, students deepen their understanding of scale factors in two ways:
 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), and
 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, Scaling a Puzzle, and Missing Figure, Factor, or Copy, 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. The individual pieces are rectangular with line segments partitioning them into regions. 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 dealing with the different aspects of scaled copies, supplying the missing information in each case.
Lesson overview
 5.1 Warmup: Number Talk: Missing Factor (10 minutes)

5.2 Activity: Card Sort: Scaled Copies (15 minutes)
 Includes "Are you Ready for More?" extension problem
 5.3 Optional Activity: Scaling A Puzzle (15 minutes)
 5.4 Optional Activity: Missing Figure, Factor, or Copy (10 minutes)
 Lesson Synthesis
 5.5 Cooldown: Scaling a Rectangle (5 minutes)
Learning goals:
 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.
Learning goals (student facing):
 Let’s look at the effects of different scale factors.
Learning targets (student facing):
 I can describe the effect on a scaled copy when I use a scale factor that is greater than 1, less than 1, or equal to 1.
 I can explain how the scale factor that takes Figure A to its copy Figure B is related to the scale factor that takes Figure B to Figure A.
Required materials:
 preprinted slips, cut from copies of the blackline master
 geometry toolkits
Required preparation:
 Print and cut sets of slips for the sorting activity from the Scaled Copies Card Sort blackline master.
 Make enough copies so that each group of 3–4 students has a set.
 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 for the Scaling a Puzzle activity from the Scaling a Puzzle blackline master.
 Make enough copies so that each group of 3 students has 1 original puzzle and 6 blank squares.
 Make sure students have access to their geometry toolkits—especially rulers and protractors.
Glossary:
 reciprocal  Dividing 1 by a number gives the reciprocal of that number. For example, the reciprocal of 12 is \(\frac{1}{12}\), and the reciprocal of \(\frac25\) is \(\frac52\).
 Access the complete Grade 7 glossary.
Standards
 This lesson builds on the standards:CCSS.5.NBT.B.6MS.5.NBT.6MO.5.NF.B.5dMO.4.NBT.A.7MO.5.NBT.A.8 CCSS.5.NF.B.4MS.5.NF.4CCSS.5.NF.B.5MS.5.NF.5CCSS.6.NS.A.1MS.6.NS.1
 This lesson builds towards the standard:CCSS.7.RP.A.2MO.7.RP.A.2aMS.7.RP.2
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses.