The purpose of this Warm-up is to elicit what students recall about the possible number of solutions to a system of linear equations, which will be useful when students continue to solve systems of equations in their Algebra 1 class. While students may notice and wonder many things about these images, connections between the graphs and the equations are the important discussion points.

This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is the ways they can predict, with the graph of that system, the number of solutions that the system of equations has.

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 graphs. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement (such as about whether the first graph has one or two lines).

If what students notice about the equations and any connections they might make between what the graphs look like and what the equations look like do not come up during the conversation, ask students to discuss these ideas.

In this activity, students examine equations with one variable to determine the number of solutions. In the associated Algebra 1 lesson, students will find the number of solutions for a system of equations. In the discussion after this activity, students are asked to look for ways they can connect the number of solutions to the equation without solving it. As students determine the number of solutions and compare strategies with others, they are making sense of problems and persevering in solving them (MP1).

In this activity, students practice writing equations that will have 1, 0, or infinite solutions. They trade equations with a partner and challenge the partner to determine the number of solutions to the equations. Students construct viable arguments and critique the reasoning of others (MP3) when they claim the number of solutions to an equation and work to explain it to a partner.