In this activity, students interpret graphs representing the number of customers at different businesses as a function of time. Students are given scenarios and select the best business for each scenario. In the associated Algebra 1 lesson, students describe graphs on their own. This activity supports students by giving them some options for interpreting the graphs. As students explain their reasoning they have the opportunity to attend to precision in their language (MP6).

The purpose of the discussion is to interpret the graphs in the situations.

Use Critique, Correct, Clarify to give students an opportunity to improve a sample written response to the last question by correcting errors, clarifying meaning, and adding details.

• Display this first draft:
  On a 30-minute or 1-hour break I would visit business A because it seems popular.
  Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft.
• Select 1–2 students or groups to slowly read aloud their draft. Record for all to see as each draft is shared. Then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.

Here are some additional questions for discussion:

• “What type of business do you think is represented by the line with decreasing slope?” (A place that is busier in the morning, like a coffee shop or the post office.)
• “The shape of business A’s graph is very different from the other graphs. What kind of business could that be?” (It is busiest during times that aren’t meal times, so it might be a business that closes for lunch. Possibly a dentist’s office or a small business with limited staffing.)

In this activity, students practice drawing graphs that could represent situations described. Student solutions do not need to be exact, but attention should be paid to the descriptions. 

The purpose of the discussion is to recognize considerations students have when drawing their graphs. Select students to share their work. If possible, display selected graphs for all to see while the students describe how they drew the graph. Here are some questions for discussion:

• “How did you use the given rate for Diego’s walk?” (I used it as the slope. I knew that after 1 hour he would be 3 miles from home, so I connected the points and with a line. Since he was walking at a steady rate, I continued the line across the graph.)
• “How did you decide how long it would probably take to run down the phone battery to 0? How long until it was charged to full?” (I thought about how long my phone usually lasts and I think it can go almost a full day. Then it doesn’t take very long to charge, so I drew the graph so that it took 1 hour to charge.)