In this lesson, students apply their knowledge of the relationships between original and scaled figures. Students decide what information is necessary to move backwards and forwards between lengths, surface areas, and volumes of an original solid and its dilation. They communicate with each other to obtain the data they need to solve a problem. Then, in an optional activity, they create a mathematical model of a realworld situation.
As students persist in asking their peers for information, they are making sense of a problem (MP1).
Lesson overview
 8.1 Warmup: Going Backwards (5 minutes)
 8.2 Activity: Info Gap: Originals and Dilations (20 minutes)

8.3 Optional Activity: Jumbo Can (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 8.4 Cooldown: Dog Food Bags (5 minutes)
Learning goals:
 Coordinate scale factors for lengths, surface areas, and volumes.
Learning goals (student facing):
 Let’s practice moving back and forth between scale factors for lengths, surface areas, and volumes.
Learning targets (student facing):
 I can calculate scale factors for lengths, surface areas, and volumes if I’m given any 1 of the 3 factors.
Required materials:
 Preprinted slips, cut from copies of the blackline master
 Scientific calculators
Required preparation:
 Optionally, obtain several cylindrical beverage cans of different shapes and sizes.
Standards:
 This lesson builds towards the standard(s): CCSS.HSGGMD.A.1MS.GGMD.1MO.G.GMD.A.1
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and 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.