Previously, students have repeatedly solved an equation for one of the variables after the values of the other variables are specified. They then generalized that process and learned that it is possible, and sometimes preferable, to first solve for the variable, before substituting known values or performing calculations.
In this lesson, they practice solving for the variable first and obtaining an expression that defines it in terms of the others. They see that doing so allows them to solve problems more efficiently.
Spreadsheets and other computer programs can help illustrate the benefits of isolating a variable. Students see that once a variable of interest is isolated and expressed in terms of all the other variables, a computer program can use that expression (even if it seems complicated) and speedily calculate its value when the other variables take on different values. The interactive model is a powerful way to test different assumptions in a situation (MP4).
Lesson overview
 9.1 Warmup: Faces, Vertices, and Edges (5 minutes)

9.2 Activity: Cargo Shipping (20 minutes)
 Digital applet in this activity
 Includes "Are you Ready for More?" extension problem
 9.3 Activity: Streets and Staffing (10 minutes)
 Lesson Synthesis
 9.4 Cooldown: Carnival Tickets (5 minutes)
Learning goals:
 Practice writing equations in two or more variables and solving for a particular variable.
 Solve for a variable by performing acceptable operations, including when the values of other quantities in a multivariable equation are not known.
Learning goals (student facing):
 Let’s solve an equation for one of the variables.
Learning targets (student facing):
 I can write an equation to describe a situation that involves multiple quantities whose values are not known, and then solve the equation for a particular variable.
 I know how solving for a variable can be used to quickly calculate the values of that variable.
Required materials:
 Fourfunction calculators
 Spreadsheet technology
Required preparation:
 Acquire devices that can run GeoGebra (recommended) or other spreadsheet technology.
 It is ideal if each student has their own device. (A GeoGebra Spreadsheet is available under Math Tools.)
 Devices are required for the digital version of the activity "Cargo Shipping."
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