In this activity, students are presented with an equation that represents a relationship. They then create a table and a graph of the relationship. Finally, they consider which representation is the most helpful to answer questions about the relationship.

This activity prepares students to compare two verbal descriptions of contexts and create a table of values to use to answer questions about the contexts in the associated Algebra 1 lesson. This activity is also useful for when students analyze or create the graph of a relationship from a table in upcoming lessons.

When students explain correspondences between equations, verbal descriptions, tables, and graphs, they are reasoning abstractly and quantitatively (MP2).

The purpose of this discussion is to highlight how different representations can be used for the same situation. In an earlier activity, students translated a verbal description of a problem into a table and discussed the advantages of a table. Focus this discussion on how the table provided data points for the graph and what the advantages of a graphical representation might be.

Direct students’ attention to the reference created using Collect and Display. Ask students to share the representations they selected for each question. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

Here are some questions for discussion:

• “What is the purpose of a graph?” (It allows us to see the overall shape of data and the trend of data.)
• “What are some advantages of using a graph?” (Graphs show patterns and the ups and downs of data, in visual ways, and they also allow us to visually compare patterns. Graphs often communicate more information than tables.)
• “What is a disadvantage of using a graph?” (Exact values can be difficult to read.)

In this partner activity, students take turns matching different representations of the same situations. If desired, they can also identify and create any missing representations (this would require removing some cards from the sets distributed). The practice will be helpful when students make connections between verbal and tabular representations in the associated Algebra 1 lesson. A sorting task gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7).

Once all groups have completed the Card Sort, discuss:

• “Which matches were tricky? Explain why.”
• “Did you need to make adjustments in your matches? What might have caused an error? What adjustments were made?”

The purpose of this discussion is to make connections between representations. Select 2–3 groups to share one of their sets of cards and how they matched a verbal description with a table and a graph. Discuss as many different sets of cards as the time allows.

If students created their own representations, look for different groups that created unique representations for the missing ones.