In the previous activity, students looked at eight different equations. In this activity, each student focuses on just one of those equations to learn about the real-world situation it represents. As they interpret the variables and values in terms of the situation, they reason abstractly and quantitatively (MP2). Extending a table they saw earlier gives students an opportunity to practice both evaluating expressions and solving equations.

This activity also asks students to create a graph of their assigned relationship on graph paper. In previous activities, students were given a grid with the axes already labeled and numbered whenever they were asked to create a graph of a relationship. Here, they must decide for themselves how to scale each axis, which is an opportunity to practice attending to precision (MP6). 

If students show they may be unsure how to set up their graph from scratch on graph paper, prompt them to think about the maximum value they want to represent on each axis and what number they could count by to get to that maximum value in the amount of space they have.

Use this time to elicit initial observations students may have made about the relationships between the dependent and independent variables in each representation. Students will continue to interpret and discuss these relationships as they create and describe visual displays in the next activity. They can also research to learn more about any unfamiliar contexts or terms. Before continuing, consider asking students to:

• Share how they rewrote their equation using words. Highlight the way students used words like “sum,” “difference,” “product,” or “quotient.”
• Share how they explained what the values from rows in their table meant in the context.
• Share what they noticed about the relationships after creating their graph.
• Share lingering questions they have about their relationships, including the meaning of words or background about any relationships. 

In this activity, students consolidate their work with equations and graphs that represent dependent and independent variables. They use multiple representations to share with each other what they have learned about their assigned relationship and the different ways each representation shows the relationship. Listen for the ways students use the vocabulary they have learned and practiced throughout the unit, in addition to how they describe relationships between variables in equations.

If time permits, conduct a Gallery Walk so students have a chance to study and discuss each other’s displays. Ask students in each group to take turns staying at their display to explain the relationship they studied or answer questions. Ask students to reflect on the following prompts at each display they visit:

• “What is the same about their relationship and your relationship? What is different?”
• “What is the independent variable in their relationship? What is the dependent variable?”
• “What could they add to the display to make their explanation of the relationship even clearer?”

Provide sticky notes that students can use to leave questions or comments for the students who created each display. Give students a moment at the end to review any questions or comments left on their displays and to make any revisions, as needed.