# Lesson 17

Number of Solutions in One-Variable Equations

These materials, when encountered before Algebra 1, Unit 2, Lesson 17 support success in that lesson.

### Lesson Narrative

In this lesson, students examine one-variable equations to determine the number of solutions it has. Students then have the chance to practice their skills by writing their own equations with different numbers of solutions. In the associated Algebra lesson, students examine the number of solutions for a system of equations.

Students make use of structure (MP7) when they notice things about the graph of a system of equations. They make use of repeated reasoning (MP8) when they recognize patterns in equations that will result in a certain number of solutions. Students also construct viable arguments critique the reasoning of others (MP3) when they create equations and explain their reasoning for the number of solutions.

### Learning Goals

Teacher Facing

- Recognize when one-variable equations will have one, zero, or infinite solutions.
- Write one-variable equations that have one, zero, or infinite solutions.

### Student Facing

- Let's look at the number of solutions an equation may have.