The purpose of the lesson is for students to strengthen their understanding of geometric measurement and dimension by analyzing relationships between surface area and volume in application problems.
The lesson starts with a process familiar from previous grades: solving a problem involving area. This is used as an entry point for students to explore properties of shapes that maximize surface area for a given volume. Then they study surface area to volume ratios of animals with different shapes and sizes.
As students draw conclusions about surface area and volume relationships, they are making sense of a problem and persevering to solve it (MP1).
Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
Lesson overview
 16.1 Warmup: Maximize Area (5 minutes)

16.2 Activity: Maximize in Three Dimensions (15 minutes)
 Includes "Are you Ready for More?" extension problem
 16.3 Activity: Assume a Spherical Elephant (10 minutes)
 16.4 Optional Activity: Measuring Strength (10 minutes)
 Lesson Synthesis
 16.5 Cooldown: Minimize Area (5 minutes)
Learning goals:
 Use surface area and volume relationships and ratios to solve problems.
Learning goals (student facing):
 Let’s use volume and surface area to solve problems.
Learning targets (student facing):
 I can use surface area and volume relationships to solve problems.
Required materials:
 Scientific calculators
Required preparation:
 For the activity Maximize in Three Dimensions, prepare a class 5column chart on which students can record their data.
Standards:
 This lesson builds on the standards: CCSS.7.G.B.6MS.7.G.6CCSS.8.G.C.9MS.8.G.9MO.7.GM.B.6bMO.8.GM.C.9b
 This lesson builds towards the standard: CCSS.HSGMG.A.3MS.GMG.3MO.G.MG.A.3
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