Balanced Moves

Fill in the table with values for x or y that make this equation true: 3x + y = 15.


Match Hangers to Equations.

Figures A, B, C, and D shows a system of hangers. The total weight on each side of the hangers is balanced by the total weight on the other side.

Here are some equations. Each equation represents one of the hanger diagrams.

(1). The letters below represent the figures above. Choose the one that matches the given equation.

Each variable (x, y, and z) in the equations represents the weight of each shape in the hangers.

(2). Which shape goes with ??

(3). Which shape goes with ??

(4). Which shape goes with ?

(5). Explain what was done to each equation to create the next equation. If you get stuck, think about how the hangers changed.

(i). What was done to go from A to B?

(ii). What was done to go from B to C?

(iii). What was done to go from C to D?


Identify a Solution Step.

Match each set of equations with the move that turned the first equation into the second.


Match a Card with a Solution Step.

Each of the cards 1 through 5 show two equations. Each of the cards A through F describe a move that turns one equation into another. Match each number card with a letter card.

One of the letter cards will not have a match. For this card, write two equations showing the described move.


In this hanger, the weight of the triangle is and the weight of the square is .



Andre and Diego were each trying to solve 2+ 6 = 3– 8. Describe the first step they each make to the equation.

(1). The result of Andre’s first step was –+ 6 = -8.

(2). The result of Diego’s first step was 6 = – 8.


Do you agree with either of them? Why?