The purpose of this Warm-up is to elicit the idea that looking at the graph of two lines simultaneously can yield information about solutions that satisfy both constraints in a situation, which will be useful when students solve systems of equations graphically in their Algebra 1 class. While students may notice and wonder many things about these images, intersection points and solutions are the important discussion points.

When students articulate what they notice and wonder about the point of intersection and what it means in the situation, 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 ask for clarification, point out contradicting information, or voice any disagreement.

If the meaning of the point of intersection does not come up during the conversation, ask students to discuss this idea.

The purpose of this activity is to give students contexts to help connect graphical representations to descriptions of situations. Students make use of the structure to connect the situations to the graphs (MP7).

This will be useful when students study solving systems of linear equations in their Algebra 1 class.

The purpose of this activity is for students to practice graphing and making sense of the graphs of systems of equations. Students construct equations from descriptions of situations, graph those equations, and then consider points on the graph in context. This will be useful in their Algebra 1 class when students write their own system of equations to represent situations. As students interpret the parts of the equations and make sense of the points, they are making sense of problems and persevering in solving them (MP1).

If students are proficient at graphing lines, provide access to graphing technology to focus student work on the creation of the equations and interpretation of the results.