The purpose of this Warm-up is to elicit the idea that points on the graph of the equation are solutions to the equation, which will be useful when students explore graphs of linear equations in their Algebra 1 class. While students may notice and wonder many things about these images, the marked points above, below, and on the graph of the equation are the important discussion points.

When students articulate what they notice and wonder about the graph, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the points on, above, and below the line do not come up during the conversation, ask students to discuss this idea. Ask students to describe those points in terms of the graph (for example, above, on, or below the line, or to the left of, right of, or on the line) as well as in terms of the context (more or fewer balloons for the same length of streamers).

In this partner activity, students take turns describing graphs and use that reasoning to match graphs with equations. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3). As students work, encourage them to refine their descriptions of graphs by using more precise language and mathematical terms (MP6).

Monitor for students who match only one equation with each graph and for disagreements about which equation goes with which graph.

The purpose of this activity is for students to practice identifying the parts of a linear equation that affect specific features of its graph, specifically the slope and -intercept. This will be useful when, in an associated Algebra 1 lesson, students make connections between two-variable linear equations and their graphs and situations that they represent. As students identify the key features, they are looking for and making use of structure (MP7).