Staying in Balance
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.”
- 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 $px=q$.
Let's use balanced hangers to help us solve equations.
- 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.
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