This is the first Which Three Go Together? routine in the course. In this routine, students are presented with four items or representations and are asked “Which three go together?” and “Why do they go together?”

Students are given time to identify a set of three items, explain their rationale, and refine their explanation to be more precise or to find additional sets. The reasoning here prompts students to notice common mathematical attributes, look for structure (MP7), and attend to precision (MP6), which deepens their awareness of connections across representations.

This Warm-up prompts students to compare four linear relationships. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of a linear equation, slope, and -intercept.

Before students begin, consider establishing a small, discreet hand signal that students can display when they have an answer they can support with reasoning. Signals might include a thumbs-up or a certain number of fingers that tells the number of responses they have. Using such subtle signals is a quick way to see if students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.

Invite each group to share one reason why a set of three go together.

Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure that the reasons given are correct.

During the discussion, ask students to explain the meaning of any terminology they use, such as “rate of change,“ “slope,“ “linear equation,“ and “-intercept“ and to clarify their reasoning as needed. Consider asking:

• “How do you know ?”
• “What do you mean by ?”
• “Can you say that in another way?”

In this activity, students practice recognizing key features of graphs of linear relationships and generating equivalent equations. Allow students to use graphing technology to check their thinking. The work in this activity will be useful in the associated Algebra 1 lesson when students use situations to build connections with two-variable linear equations and graphs. As students connect the equations with the graphs and develop equivalent equations, they are making sense of problems and persevering in solving them (MP1).

The purpose of this activity is for students to practice using the key features of a graph of a linear equation to interpret key characteristics of the situation that it represents. Previously, students have made connections between linear equations, graphs, tables, and situations. The work in this activity prepares students to consider how parts of two-variable linear equations relate to features of the graphs of those equations in an associated Algebra 1 lesson. In this activity, students interpret the meaning of the key features of linear equations in the context of the given situation, allowing them to reason abstractly and quantitatively (MP2).