Figures B, C, and D show the result of simplifying the hanger in Figure A by removing equal weights from each side.

Let be the weight of the blue square, be the weight of a green triangle, and be the weight of a red circle.

1. Draw an arrow from each hanger to the next and describe the move that keeps the hanger in balance near each arrow.

2. Here are some equations. Each equation represents one of the hanger diagrams. Write the matching equation on the line below each hanger diagram.
3. Describe the move that keeps the equation for diagram A equivalent to the equation for diagram B.

1. Your teacher will give you a set of cards. Take turns with your partner to match a pair of equations with a description of the valid move that is used to rewrite the first equation as the second.
   1. For each match that you find, explain to your partner how you know it’s a match.
   2. For each match that your partner finds, listen carefully to your partner's explanation. If you disagree, discuss your thinking and work to reach an agreement.
2. One of the letter cards does not have a match. For this card, write two equations showing the described move.

1. Noah and Lin both solve the equation .

   Do you agree with either of them? Explain your reasoning.

   Noah's solution:

   Lin's solution:

2. Elena is asked to solve . What do you recommend she does to each side first?
3. Diego is asked to solve . What do you recommend he does to each side first?