Lesson objective: Understand that inequalities show a relationship between expressions.

Students bring prior knowledge of writing and solving equations to model equivalent relationships. This prior knowledge is extended to modeling relationships with inequalities as students use the inequality symbols to write mathematical representations of unequal situations and identify possible solutions to each inequality. A conceptual challenge students may encounter is that the solutions to an inequality are often any real number, not just whole numbers. Some students also have difficulty understanding that a solution can be extremely close to a number without equaling that number.

The concept is developed through work with balance scales, which model that one quantity is larger or smaller than another quantity. Since balance scales are used to model solving equations, they provide a good visual for students to understand unequal relationships.

This work helps students deepen their understanding of equivalence because they now work with representing relationships that are not equalivalent.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they analyze a problem to determine the nature of the inequality and the values that will make the solution true.

**Key vocabulary:**

- greater than
- inequality
- less than

**Special materials needed:**

- optional: balance scales for students to create their own inequalities