In middle school, students learned that a solution to an equation is a value or values that make the equation true. In this lesson, they revisit what they learned about solutions to equations in one variable and two variables. They also continue to practice modeling relationships with equations and to make sense of equations and their solutions in context (MP2, MP4).
Students verify and find solutions to given equations by checking if the values satisfy the equations and by reasoning. Some students may choose to solve equations algebraically or by performing certain sequences of steps they learned in middle school, but students are not expected to rely on algebraic methods to answer questions here. A little later in the unit, students will take a close look at the moves for rewriting and solving equations.
In the next lesson, students will revisit the idea that coordinate pairs that are on a graph of an equation in two variables are solutions to the equation.
Lesson overview
 4.1 Warmup: What is a Solution? (5 minutes)

4.2 Activity: Weekend Earnings (15 minutes)
 Includes "Are you Ready for More?" extension problem
 4.3 Activity: Calories from Protein and Fat (15 minutes)
 Lesson Synthesis
 4.4 Cooldown: Box of Tshirts (5 minutes)
Learning goals:
 Explain (orally and in writing) the meaning of solutions to equations in one variable and two variables.
 Find solutions to equations in one variable and in two variables by reasoning about the relationships in context.
 Interpret solutions to equations in one variable and in two variables.
Learning goals (student facing):
 Let’s recall what we know about solutions to equations.
Learning targets (student facing):
 I can explain what it means for a value or pair of values to be a solution to an equation.
 I can find solutions to equations by reasoning about a situation or by using algebra.
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.