The purpose of this activity is to write inequalities that represent their given graphs. Students will see graphs of inequalities and will need to interpret each open or closed circle and direction of the arrow to describe the inequality algebraically. In the associated Algebra 1 lesson, students will work with inequalities and their graphs. When students interpret the graphs of inequalities and express them algebraically, they reason abstractly and quantitatively (MP2).

The purpose of this discussion is to clarify how to algebraically write inequalities of a graph, including those that are expressed with more than one part.

Direct students’ attention to the reference created using Collect and Display. Ask students to share their inequalities. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

Here are some questions for discussion:

• “Describe the meaning of in words.” ( is between -1 and 2, including -1 and not including 2.)
• “What was the most challenging part of writing the inequalities?”
• “Is 0 a good point to test for all of these inequalities? Explain your reasoning.” (No, 0 is not a good point to test for the last inequality because 0 is an endpoint.)

The purpose of this activity is for students to solve inequalities and connect them with graphs. In the associated Algebra 1 lesson, students will solve inequalities involving absolute value.

In this partner activity, students take turns solving inequalities. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

The goal of this discussion is to review how to solve and graph inequalities. Much of the discussion takes place between partners. Invite students to share how they matched each inequality with a graph.

• “Which matches were tricky? Explain why.” (Deciding between Graphs D and F was hard because the only difference was the direction of the arrow.)
• “Did you need to make adjustments in your matches? What might have caused an error? What adjustments were made?”