In this activity, students interpret inequalities that represent constraints or conditions in a real-world situation. They find solutions to an inequality and reason about the context’s limitations on solutions (MP2).

The goal of this discussion is to extend the context of scored points in a basketball game by considering additional situations. Invite students to share their responses to each question. If necessary, have a student share what they know about how scoring works in basketball (free throws are worth 1 point, regular baskets are worth 2 points, baskets shot from outside a certain line are worth 3 points). Then discuss the following questions:

• “Could Noah have scored 0 points? 1 point?” (Yes, if Noah did not make any baskets. Yes, if Noah made a free throw.)
• “Could Noah have scored 2.5 points? -3 points?” (No, baskets are only worth whole numbers of points. No, a player cannot score negative points [though a student may argue that scoring for the opposing team may be the same as scoring negative points].)
• “Is it reasonable for a player to score 200 points?” (No, because there has never been an NBA game with a score that high.)

In this activity, students describe unbalanced hanger diagrams with inequalities. Students construct viable arguments and critique the reasoning of others during partner and whole-class discussions about how unknown values relate to each other (MP3).

The purpose of the discussion is for students to explain how they used inequalities to compare the weights of different shapes on the hanger diagrams. Invite groups share their responses to the questions. If time allows, ask students to describe any disagreements or difficulties they had and how they resolved them.

Remind students that a circle weighs 12 ounces and a pentagon weighs 8 ounces and display these two diagrams for all to see: 

Ask students:

• “How much would the square have to weigh for the side with the circle to be heavier? How can we represent that with an inequality?” (The square would have to weigh less than 4 ounces: or )
• “How much would the square have to weigh for the side with the pentagon and square to be heavier? How can we represent that with an inequality?” (The square would have to weigh more than 4 ounces: or \(4.)