Lesson 26

Testing Points to Solve Inequalities

These materials, when encountered before Algebra 1, Unit 2, Lesson 26 support success in that lesson.

Lesson Narrative

The mathematical purpose of this lesson is to give students a chance to name and analyze common incomplete strategies and concepts when working with inequalities. Students engage in error analysis on the topic of testing points around a given boundary to determine which half of the real number line contains solutions to an inequality, and on the the topic of solving equations.

Error analysis around solving equations helps students continue to hone the foundational skill of solving equations, which is useful for finding the boundary point of the solutions of a linear inequality. Exploring the reasoning behind testing points helps students make strategic choices as they solve inequalities.

In the supported Algebra 1 lesson, students are using their understanding of systems of inequalities with two variables to create a mathematical model for designing trail mix.

Students have the opportunity to construct viable arguments and critique the reasoning of others (MP3) as they engage in error analysis.

Learning Goals

Teacher Facing

  • Analyze common errors when solving linear equations.
  • Understand the purpose, when solving inequalities, of testing points on either side of the solution to the related equation.

Student Facing

  • Let’s critique some peoples’ reasoning.

CCSS Standards


Building Towards