The purpose of this activity is for students to recall the connection between tables and equations. In the associated Algebra 1 lesson, students are given tables and are asked to come up with an equation to represent a possible relationship describing all the sets of two associated numbers in the table. Here, they do the reverse. Students practice using an equation to complete a table by substituting one value and determining the other. In the process, students also practice solving equations, for example, solving . Making decisions about how to approach each problem based on the variable they know and the structure of the equation gives students an opportunity to make use of structure (MP7).

Monitor for groups who use these different approaches:

• Substitute the given value into the equation and solve
• Create an equivalent equation before substituting the given value into the new equation and solve

The goal of this discussion is to make sure that students know how tables and equations connect to represent the same information and that equivalent equations can be used in the same way.

Display 2–3 approaches from previously selected students for all to see. Use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:

• “What do the approaches have in common? How are they different?”
• “Why do the different approaches lead to the same outcome?”
• “Are there any benefits or drawbacks to one representation compared to another?”

In this partner activity, students take turns applying their skills at connecting multiple representations of the same linear relationship. As students analyze different representations, they practice reasoning quantitatively and abstractly (MP2). In making connections across representations, they practice looking for and making use of structure (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?”

Be sure to collect the sets of cards for use in a future activity.

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 situation with a table and an equation. Discuss as many different sets of cards as the time allows.