The goal of this discussion is to discuss the key information a model can give about a situation. Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to the last question about what a reasonable domain would be. In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help clarify and strengthen their partner’s ideas and writing.

If time allows, display these prompts for feedback:

• “ makes sense, but what do you mean when you say ?”
• “Can you describe that another way?”
• “How do you know ? What else do you know is true?”

Close the partner conversations, and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer. If time allows, invite students to compare their first and final drafts. Select 2–3 students to share how their drafts changed and why they made the changes they did.

After Stronger and Clearer Each Time, here are some questions for discussion:

• “Why might it be useful to know the coordinates of intercepts of a graph that models a situation?” (The intercepts tell you the value of one quantity when the other quantity is 0. In this case, that means the volume of water in the tank when it starts draining (at 0 minutes), and how many minutes it takes the tank to empty (the time when the volume is at 0 gallons).)
• “What are some important things to keep in mind when setting a graphing window?” (You want to make sure you can see any important points on the graph, which often include the intercepts, though it depends on the situation. Other responses might depend on the type of graphing technology used.)

The goal of this discussion is to connect situations, equations, and graphs. Display one or more students’ work on the last question for all to see. Point out examples in which students made sure to name the variables they used in their equations. If needed, provide others time to add that to their work. Here are some questions for discussion:

• “How are the graphs of the three situations alike? How are they different?” (They all have the same -intercept. Two of the graphs are lines, and the third is the graph of an exponential function.)
• “How are the equations you wrote alike? How are they different?” (The equations all have a 128. The two linear equations either add or subtract from 128. The exponential equation has a growth factor of , and the variable is the exponent.)
• “Which graphs have -intercepts? Which graphs have a -intercept?” (The graph of does not have an -intercept. All the graphs have the same -intercept, .)
• “What does the -intercept of each graph tell you about the situation?” (It is the initial amount.)
• “What does the -intercept (if there is one) tell you about the situation?” (For the graph of , the -intercept tells when the tank is empty. For the savings account, the -intercept is not meaningful because it would have a negative -coordinate, and negative values for time don’t make sense in this situation.)