In this lesson, students analyze the graphs of cube root and square root equations in geometric contexts. This work builds on earlier lessons in the unit that analyzed square root and cube root graphs. Students also use concepts of rearranging formulas to highlight a quantity of interest and understanding the nature of the intersection points of the graphs of two equations.
As students relate the accuracy of volume calculations to a situation, they’re modeling with mathematics (MP4).
One of the activities in this lesson works best when each student has access to devices that can run the Desmos applet, because students will benefit from seeing the relationship in a dynamic way.
Lesson overview
 18.1 Warmup: Parade Balloon: Part 1 (5 minutes)
 18.2 Activity: Parade Balloon: Part 2 (20 minutes)

18.3 Activity: Beach Ball Balloon (10 minutes)
 Digital applet in this activity
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 18.4 Cooldown: Circular Logo (5 minutes)
Learning goals:
 Use square root and cube root graphs to solve geometry problems arising from situations.
Learning goals (student facing):
 Let’s use volume and graphing to solve problems.
Learning targets (student facing):
 I can use cube root and square root graphs to solve geometric problems.
Required materials:
 Graphing technology
 Scientific calculators
Required Preparation
 Acquire devices that can run Desmos (recommended) or other graphing technology.
 It is ideal if each student has their own device. (Desmos is available under Math Tools.)
 Devices are required for the digital version of the activity Beach Ball Balloon.
 The digital version is recommended for all classes over the paper and pencil version.
Standards:
 This lesson builds on the standards: CCSS.HSACED.A.4MS.ACED.4CCSS.HSAREI.D.11MS.AREI.11CCSS.HSFIF.C.7.bMS.FIF.7bCCSS.HSGGMD.A.3MS.GGMD.3MO.A1.CED.A.4MO.A2.REI.B.3MO.A1.IF.C.7MO.G.GMD.A.2
 This lesson builds towards the standards: CCSS.HSFIF.C.7.bMS.FIF.7bMO.A1.IF.C.7
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