# Expressions and Equations / Equations and Operations

Activity 5 of 18
In this lesson students investigate the relationship between the solution to an equation and the solution to a new equation formed by adding, subtracting, multiplying, or dividing one or both sides of the original equation by a numerical value.

## Planning and Resources

Objectives
Students should be able to identify solution-preserving mathematical moves related to equations and moves that do not preserve solutions.  They can describe a strategy for finding a solution for an equation.

Vocabulary
expression
equation
variable
solution

Standard:

## Lesson Snapshot

#### Understanding

Students develop an understanding of “solution-preserving moves” by thinking carefully about the structure of relationships expressed by an equation and how to exploit that structure to find a solution.

### What to look for

Be sure students explicitly state what x represents in in the previous two questions. One example of confusion might be in the question above where x could represent the number of brownies Steve got or the total number of brownies his team made.

### Sample Assessment

What number makes the following equation true?

$\frac{1}{\mathrm{12}}$ + x = $\frac{3}{4}$

Answer: $\frac{2}{3}$

#### The Big Idea

You can add or subtract a number from both sides of a given equation and the new equation will have the same solution as the original equation.

### What are the students doing?

Students might note that you can add or subtract a number from both sides of a given equation and the new equation will have the same solution as the original equation.

### What is the teacher doing?

The focus in this lesson is not on developing a formal procedure for finding solutions but rather on thinking carefully about the structure of the relationships expressed by an equation and how to exploit that structure to find a solution.