In this Warm-up, students are given a simple equation in three variables and are prompted to rearrange it to solve for a particular variable. In each question, only the value of one variable is given, so students need to manipulate the equation even when some quantities are unknown. The work here prepares students to rearrange other variable equations later in the lesson.

As students work, look for those who substitute the given value before rearranging and those who first isolate the variable of interest before substituting. Invite them to share their approaches during class discussion.

Some students may be unclear what it means to write an equation that "makes it easier to find the number of vertices (or faces)." Remind them of the work in an earlier activity. In the post-parade clean-up activity, for instance, they wrote the equation to quickly find the length of the road section that each volunteer would clean up, , if there were volunteers. They wrote to quickly find the number of volunteers, , if each volunteer were to clean up miles.

Select previously identified students to share their responses and strategies. Record and display for all to see the steps they take to rearrange the equations. Emphasize how each step constitutes an acceptable move and how it keeps the equation true.

Make sure students see that we can either substitute known values into the given equation before rearranging it, or we can rearrange the equation first before substituting known values. In the examples here, it doesn't matter which way it is done. Ultimately, we were solving for in the first question and for in the second question.

Explain that there will be times when one strategy might be more helpful than the other, as students will see in subsequent activities.

This activity encourages students to write an equation in two variables to represent a constraint and then to solve for each of the variables. One motivation for rearranging the equation is to find an expression that, when entered into a calculator or computer, can then be used to quickly find the value of one quantity given the value of the other.

The digital version of this activity includes instruction for using GeoGebra spreadsheets to perform calculations. As they use spreadsheet technology to create mathematical models, test them, and solve problems, students engage in aspects of mathematical modeling (MP4).

This activity gives students another opportunity to write and rearrange equations in two variables and to do so in context.

Unlike in previous activities, students no longer start by computing one quantity given numerical values of the other quantity and then generalizing the process. Instead, they are prompted to write one equation, solve for each variable, and interpret the solution. Students also articulate why one model might be more helpful than the other under a certain circumstance. Along the way, students reason quantitatively and abstractly (MP2) and engage in aspects of modeling (MP4).

Making spreadsheet technology available gives students an opportunity to choose appropriate tools strategically (MP5).