This is the first of three activities in which students make connections between different functions represented in different ways. In this activity, students are given a graph and a table of temperatures from two different cities and are asked to make sense of the representations in order to answer questions about the context (MP2).

Display the graph and table for all to see. Select groups to share how they used the two different representations to get their answers for each question. To further student thinking about the advantages and disadvantages of each representation, ask:

• “Which representation do you think is better for identifying the highest recorded temperature in a city?” (The graph, since I just have to find the highest part. In the table I have to read all the values in order to find the highest temperature.)
• “Which representation do you think is quicker for figuring out the change in temperature between 1:00 p.m. and 5:00 p.m.?” (The table is quicker since the numbers are given, and I only have to subtract. In the graph, I have to figure out the temperature values for both times before I can subtract.)

This is the second of three activities in which students make connections between different functions represented in different ways. In this activity, students are given an equation and a graph of the volumes of two different objects. Students then compare inputs and outputs of both functions and what those values mean in the context of the shapes (MP2).

In the digital version of the activity, students use an applet to compare the two functions. The applet allows students to have an interactive version of the graph to identify coordinates. Use the digital version if it would benefit students identifying points more precisely.

The purpose of this discussion is for students to think about how they used the information from the different representations to answer questions about the context.

Display the equation and graph for all to see. Direct students’ attention to the reference created using Collect and Display. Ask students to share how they used the representations to answer the questions. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases. Consider asking the following questions to prompt students to expand on their answers:

• “How did you use the given representations to find an answer? How did you use the equation? The graph?”
• “For which problems was it nicer to use the equation? The graph? Explain your reasoning.”

In this activity, students continue their work comparing properties of functions represented in different ways. Students are given a verbal description and a table to compare and decide whose family traveled farther over the same time intervals. The purpose of this activity is for students to continue building their skill interpreting and comparing functions.

If students do not notice that Elena’s family’s speed has different units than Andre's family, ask

• “What do you notice so far about the information you have for the two families?”
• “What needs to be true to compare two rates?”

The purpose of this discussion is for students to think about how they use a verbal description and table to answer questions related to the context. Ask students to share their solutions and how they used the equation and graph. Consider asking some of the following questions:

• “How did you use the table to get information? How did you use the verbal description?”
• “What did you prefer about using the description to solve the problem? What did you prefer about using the table to solve the problem?”