# Lesson 3

Staying in Balance

### Lesson Narrative

The goal of this lesson is for students to understand that we can generally approach $$p+x=q$$ by subtracting the same thing from each side and that we can generally approach $$px=q$$ by dividing each side by the same thing. This is accomplished by considering what can be done to a hanger to keep it balanced.

Students are solving equations in this lesson in a different way than they did in the previous lessons. They are reasoning about things one could “do” to hangers while keeping them balanced alongside an equation that represents a hanger, so they are thinking about “doing” things to each side of an equation, rather than simply thinking “what value would make this equation true.”

### Learning Goals

Teacher Facing

• Interpret hanger diagrams (orally and in writing) and write equations that represent relationships between the weights on a balanced hanger diagram.
• Use balanced hangers to explain (orally and in writing) how to find solutions to equations of the form $x+p=q$ or $px=q$.

### Student Facing

Let's use balanced hangers to help us solve equations.

### Student Facing

• I can compare doing the same thing to the weights on each side of a balanced hanger to solving equations by subtracting the same amount from each side or dividing each side by the same number.
• I can explain what a balanced hanger and a true equation have in common.
• I can write equations that could represent the weights on a balanced hanger.

Building Towards

### Glossary Entries

• coefficient

A coefficient is a number that is multiplied by a variable.

For example, in the expression $$3x+5$$, the coefficient of $$x$$ is 3. In the expression $$y+5$$, the coefficient of $$y$$ is 1, because $$y=1 \boldcdot y$$.

• solution to an equation

A solution to an equation is a number that can be used in place of the variable to make the equation true.

For example, 7 is the solution to the equation $$m+1=8$$, because it is true that $$7+1=8$$. The solution to $$m+1=8$$ is not 9, because $$9+1 \ne 8$$

• variable

A variable is a letter that represents a number. You can choose different numbers for the value of the variable.

For example, in the expression $$10-x$$, the variable is $$x$$. If the value of $$x$$ is 3, then $$10-x=7$$, because $$10-3=7$$. If the value of $$x$$ is 6, then $$10-x=4$$, because $$10-6=4$$.

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