# Lesson 12

Balanced Moves

### Lesson Narrative

In this lesson students move from using hangers to using equations in order to represent a problem. In the warm-up they match a series of hangers with the corresponding series of equations. They see how moves that maintain the balance of a hanger correspond to moves that maintain the equality of an equation, such as halving the value of each side or subtracting the same unknown value from each side. In the next activity students match pairs of equations with the corresponding equation move—performing the same operation on each side—that produces the second from the first. In the activity after that, they compare different choices of moves that lead to the same solution. In this activity the solution is negative, which would not have been representable with hangers. Students can check that it is a solution by substituting into the equation, reinforcing the idea that a solution is a number that makes the equality in an equation true, and that different moves maintain the equality. As students reason about why the steps in solving an equation maintain the equality and compare different solution methods, they engage in MP3.

Teacher Notes for IM 6–8 Math Accelerated
This lesson is the first in a sequence of 6 lessons where students learn to work with equations that have variables on each side. Look for opportunities to connect the work from the previous unit solving equations that had a single variable on one side and the work from the previous section rewriting expressions with the work of this section. In particular, students will build directly on this work in a later unit when they begin working directly with systems of equations.

### Learning Goals

Teacher Facing

• Compare and contrast (orally and in writing) solution paths to solve an equation in one variable by performing the same operation on each side.
• Correlate (orally and in writing) changes on hanger diagrams with moves that create equivalent equations.

### Student Facing

Let's rewrite equations while keeping the same solutions.

### Required Preparation

Print and cut up the Matching Equation Moves blackline master for the matching activity. Prepare one set of cards for every 2 students.

### Student Facing

• I can add, subtract, multiply, or divide each side of an equation by the same expression to get a new equation with the same solution.