Lesson 22

Situations with Constraints

These materials, when encountered before Algebra 1, Unit 2, Lesson 22 support success in that lesson.

Lesson Narrative

The mathematical purpose of this lesson is for students to familiarize themselves with situations that involve constraints. In previous lessons, students have written equations to represent situations and examined points on or off lines out of context. This lesson builds on that understanding by asking students to consider whether points off the line are reasonable in the context given. This will support students to make sense of the situations they will encounter in their Algebra 1 class that involve inequalities, and the mathematical structures underlying situations with constraints.

Students have an opportunity to reason abstractly and quantitatively (MP2) as they make sense of constraints in situations as well as constraints represented by graphs and inequalities.

Learning Goals

Teacher Facing

  • Interpret points on and off of a line in a given context and recognize their feasibility in the same context.
  • Represent situations involving constraints verbally, symbolically, and graphically.

Student Facing

  • Let’s study situations that have constraints.

Required Preparation

For the Matching Graphs and Inequalities activity, print and cut up slips from the blackline master. Prepare 1 copy for every 2 students.

CCSS Standards

Building On


Building Towards