Lesson 4

Equations and Their Solutions

Lesson Narrative

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. 

Learning Goals

Teacher Facing

  • 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.

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.

CCSS Standards

Addressing

Glossary Entries

  • constraint

    A limitation on the possible values of variables in a model, often expressed by an equation or inequality or by specifying that the value must be an integer. For example, distance above the ground \(d\), in meters, might be constrained to be non-negative, expressed by \(d \ge 0\).

  • model

    A mathematical or statistical representation of a problem from science, technology, engineering, work, or everyday life, used to solve problems and make decisions.