In the two diagrams, all the triangles weigh the same and all the squares weigh the same.

For each diagram, what is one thing that *must *be true.

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For each diagram, what is one thing that *could *be true.

For each diagram, what is one thing that *cannot possibly *be true.

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

Which hanger matches with the following equation:

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What letter belongs in the empty box of this equation: ?

Which hanger matches with the following equation:

What letter belongs in the empty box of this equation: ?

Which hanger matches with the following equation:

What letter belongs in the empty box of this equation: ?

Which hanger matches with the following equation:

What letter belongs in the empty box of this equation ?

Solve for w in this equation .

w = ______

Use the hanger to explain what the solution means.

Solve for z in this equation .

z = ______

Use the hanger to explain what the solution means.

Solve for x in this equation .

x = ______

Use the hanger to explain what the solution means.

Solve for y in this equation .

y = ______

Use the hanger to explain what the solution means.

Here are some balanced hangers where each piece is labeled with its weight.

Write an equation for Hanger A.

7 = ____________

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Write an equation for Hanger B.

____________ = 31

Write an equation for Hanger C.

6.8 = ____________

Write an equation for Hanger D.

____________ = 17/2

Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.

Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.