The purpose of this activity is to give students practice writing and graphing equations from situations. In the next activity and in the supported Algebra 1 lesson, students will write and graph inequalities. Students then assess the meaning of points off of the line in the situation provided and interpret whether those points might be valid in the situation. As students interpret their answers in context they reason abstractly and quantitatively (MP2).

The purpose of the discussion is to examine points on and off the lines to and determine what they might mean in the situations.

Here are some questions for discussion:

• "What are the coordinates for a point on the line that represents the orchard situation? What do the coordinates mean in that situation?" (The point is on the line. This means that Jada could pick 5 pounds of apricots and 15 pounds of plums.)
• "What are the coordinates for a point above the line that represents the orchard situation? What do the coordinates mean in that situation? Is it realistic?" (The point is above the line. This means Jada would pick 2 pounds of apricots and 30 pounds of plums. While it is possible for a person to pick that much, she wanted only 20 total pounds of fruit.)
• "The point is above the line that represents the maximum run speed for the videogame character. Describe a situation where this might be possible." (If the character has an item that ignores the carry weight or something that boosts its run speed, then maybe this is possible.)

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

Monitor for groups who use:

• Whether the inequality is less than or greater than and whether the shading is to the upper left or lower right.
• Whether the equation is strictly less than or greater than, or less than or equal to, or greater than or equal to, and whether the graphed line is dashed or solid.
• Testing solutions in the situation, equation, and graph.
• The boundary equation to determine the correct graphed line.

Monitor for groups that struggle to make sense of the graphs involving a vertical or horizontal line.

The goal of this discussion is to make connections between the representations of situations involving inequalities. Display 2–3 approaches from previously selected students for all to see. Ask the students to share their approach. Use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:

• “How is focusing on whether the inequality is strictly less than or greater than the same as focusing on how the graph is shaded? How are they different?”
• “How does the inequality symbol show up in each representation?”