# Lesson 6

Equality Diagrams

Let's use hanger diagrams to understand equivalent equations.

### 6.1: Notice and Wonder: Solving Equations

What do you notice? What do you wonder?

### 6.2: Hanger Diagrams

The hanger with 1 square and 2 circles is in balance.
Which of these should also be in balance? Explain your reasoning.

2. This hanger containing 2 pentagons and 6 circles is in balance. Use the hanger diagram to create two additional hangers that would be in balance.

### 6.3: Diagrams and Equations

In the previous activity, each square weighs 10 pounds and each circle weighs $$x$$ pounds.

So, this diagram could be represented by the equation. $$10 = 2x$$

1. Use each of the 6 hanger diagrams containing squares and circles from the previous activity to write an equation that represents the weights on the hanger.

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2.
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4.
5.
6.
2. Solve each equation.

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5.
6.
3. Compare the solutions to the equations with the answers from the previous activity. What do you notice?