# Lesson 8

Writing and Graphing Inequalities

### Lesson Narrative

In extending their concept of numbers to all rational numbers, students began writing inequality statements that compared two numbers. In this lesson, students extend their work with inequality statements by considering comparisons with an unknown quantity. These quantities, represented by variables, often describe real-world situations, and their value is usually constrained by minimum or maximum allowable values. Students represent these situations with inequality statements and reason about possible values that make them true (MP2). As there are often many, even infinite, possibilities for the value of the variable that satisfy the constraint, students use the number line as a helpful tool to show all the possible values.

The activities in this lesson present students with two types of scenarios. When the variable represents a measurement, the possible values can usually be any number within the range satisfied by the constraint. When the variable represents a count of people or objects, the possible values are restricted to whole numbers within the range. Students also consider whether the constraint itself is included or excluded in the set of possible values, and learn how to indicate this result on the number line representation.

After writing inequality statements to represent situations, students test values to see if they make the statement true.

### Learning Goals

Teacher Facing

• Coordinate verbal, algebraic, and number line representations of inequalities.
• Critique (orally and in writing) possible values given for a situation with a constraint, including determining whether the boundary value is included and making sense of situations with discrete quantities.
• Interpret phrases that describe a quantity constrained by a maximum or minimum acceptable value, e.g. “at least,” “at most,” “up to,” “more than,” “less than”, etc., and write an inequality statement to represent the constraint.

### Student Facing

Let’s write inequalities.

### Required Preparation

Print and cut up cards from the blackline master. Prepare 1 set of 16 cards for each group of 2 students.

### Student Facing

• I can graph inequalities on a number line.
• I can write an inequality to represent a situation.