Lesson objective: Understand that number lines are a visual way to represent inequalities.

Students will critique the work of another student who has drawn several inequalities on number lines.

Students bring prior knowledge of using number lines to locate solutions to equations and to compare numbers. This prior knowledge is extended from using points to using rays to show the infinite number of solutions that may be possible for an inequality. A conceptual challenge students may encounter is understanding how the representation of the ray models the context of a given situation.

The concept is developed through work with rays on number lines, which present another visual model for any inequality.

This work helps students deepen their understanding of equivalence because the ray represents a situation where the quantities are not equal and the solution can be many possible items.

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they consider each inequality and analyze the graphs made by another student to model each inequality.

**Key vocabulary:**

- inequality
- number line
- ray