The purpose of this Warm-up is for students to practice graphing inequalities on a number line, during which they recall skills used in earlier grades. In the associated Algebra 1 lesson, students will solve and graph inequalities, including those involving absolute value. Students look for and make use of structure (MP7) when using their knowledge of inequality symbols to decide the direction of the arrow and if the circle is open or closed.

The goal of this discussion is to clarify how to graph inequalities. Ask students to share their graphs of the solutions. Display the graphs of the solutions. Here are some questions for discussion:

• “How do you know if the circle should be open or closed?” (The circle represents the exact value. If the value is included, or the inequality is “or equal to,” then the circle is filled in, or closed. If the value is not included, then the circle is open.)
• “How did you decide the direction of the arrow?” (I read the statement in words and drew the arrow toward the numbers that would make the statement true. For example, “ is greater than 5” tells me that numbers greater than 5, like 6 and 7, would be solutions. Alternatively, I could have tested a point to see if that point makes the inequality true.)
• “What is a point that I could use to test for all of these inequalities?” (0 would work well because none of the inequalities are comparing to 0. It is also easy to figure out if 0 is less than or greater than a number.)

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 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).