In this activity, students are formally introduced to the phrase “solution to an inequality” as a number that can be used in place of the variable to make the inequality true. Students use given height restrictions for a variety of amusement park rides to explore these ideas. They represent the height restrictions as inequality statements and graph those inequalities on the number line. Students reason abstractly when determining whether a value is a solution to one or more of the inequalities and what that means in context (MP2).

The purpose of this discussion is for students to communicate their understanding of what it means to be a solution to an inequality. Display the question for all to see, and give students 2–3 minutes to draft a response:

“What does it mean to be a solution to an inequality?”

Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response. In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help their partner clarify and strengthen their ideas and writing.

If time allows, display these prompts for feedback: 

• “ makes sense, but what do you mean when you say . . . ?”
• “Can you describe that another way?”
• “How do you know . . . ? What else do you know is true?”

Close the partner conversations, and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer. Here is an example of a second draft:

“When a number is a solution to an inequality, that number could be used in place of the variable and the statement would be true.” 

If time allows, invite students to compare their first and final drafts. Select 2–3 students to share how their drafts changed and why they made the changes they did.

This activity provides an additional opportunity for students to play a game to practice reasoning about whether given values make an inequality true. The goal of the game is for one student to guess a mystery number using as few inequalities as possible.

The purpose of this discussion is for students to share their most successful strategies for guessing the mystery number. Here are some possible questions for discussion: 

• “When giving clues, how did you decide which inequalities would be the most helpful?”
• “When receiving clues, were some inequalities more helpful than others as you tried to guess the mystery number? Why?”
• “How can you check that a value is or is not a solution to an inequality statement?” (I can replace the variable in the statement with the number and see if the statement is true.)
• “How can you use a number line to check that a value is or is not a solution to an inequality represented?” (I can plot the value on the number line and see if it falls within a shaded region.)