~ 6.7 ~

Learning Targets

• I can explain how a balanced hanger and an equation represent the same situation.
• I can find an unknown weight on a hanger diagram and solve an equation that represents the diagram.
• I can write an equation that describes the weights on a balanced hanger.

In this lesson, we worked with two ways to show that two amounts are equal: a balanced hanger and an equation. We can use a balanced hanger to think about steps to finding an unknown amount in an associated equation.

The hanger shows a total weight of 7 units on one side that is balanced with 3 equal, unknown weights and a 1-unit weight on the other. An equation that represents the relationship is 7 = 3x + 1.

We can remove a weight of 1 unit from each side and the hanger will stay balanced. This is the same as subtracting 1 from each side of the equation.

An equation for the new balanced hanger is 6 = 3x

So the hanger will balance with ⅓ of the weight on each side: ⅓ • 6 = ⅓ • 3x.

The two sides of the hanger balance with these weights: 6 1-unit weights on one side and 3 weights of unknown size on the other side.

Here is a concise way to write the steps above:

7 = 3x + 1

6 = 3x after subtracting 1 from each side

2 = x after multiplying each side by ⅓

For each diagram, come up with . . .

1. One thing that must be true
2. One thing that could be true
3. One thing that cannot possibly be true

On each balanced hanger, figures with the same letter have the same weight.

1. Match each hanger to an equation. Complete the equation by writing x, y, z, or w in the empty box.
2. Find the solution to each equation. Use the hanger to explain what the solution means.

This summary video is joined with 6.8 Reasoning about Solving Equations (Part 2).