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.
Learning Targets
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.
CCSS Standards
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 \(10x\), the variable is \(x\). If the value of \(x\) is 3, then \(10x=7\), because \(103=7\). If the value of \(x\) is 6, then \(10x=4\), because \(106=4\).