Unit 6, Lesson 14
Finding Solutions to Inequalities in Context
Grade 7
Preparation
Lesson Narrative
In this lesson, students compare equations and inequalities that represent the same situation. They interpret what each part of the equation or inequality means in the context. They solve the related equation and use the solution to the equation to reason about what values are solutions to the inequality, the values that make the inequality true.
Several of the inequalities involve negative coefficients. Students may notice that the inequality symbol in the solution is reversed from the symbol that was in the original inequality that represented the situation. The goal is for students to use context to make sense of these reversals, for example, by thinking “since represents the amount of money to spend, Diego would need to spend less than this much if he wants to have more than a certain amount left over.”
As students interpret equations, inequalities, and their solutions, they are reasoning abstractly and quantitatively (MP2).
- Interpret inequalities that represent situations with a constraint.
- Solve an equation of the form $px+q=r$ to determine the boundary point for an inequality of the form $px+q \gt r$ or $px+q \lt r$.
- Use substitution or reasoning about the context to justify (orally and in writing) whether the values that make an inequality true are greater than or less than the boundary point.
Let’s solve more complicated inequalities.
Required Preparation
Several activities suggest providing students with blank number lines to use for scratch work. One way to accomplish this is to print a line with unlabeled, evenly-spaced tick marks, and place these into sheet protectors. Students can write on these with dry-erase markers and wipe them off.