Lesson 2Keeping the Equation Balanced

Learning Goal

Let’s figure out unknown weights on balanced hangers.

Learning Targets

  • I can add or remove blocks from a hanger and keep the hanger balanced.

  • I can represent balanced hangers with equations.

Warm Up: Notice and Wonder: Hanging Socks

Problem 1

What do you notice? What do you wonder?

Two hangers, one balanced with two red socks and one unbalanced with two blue socks.

Activity 1: Hanging Blocks

Problem 1

This picture represents a hanger that is balanced because the weight on each side is the same.

A balanced hanger diagram with 3 squares and 2 triangles on the left and 1 square and 5 triangles on the right.

    1. Elena takes two triangles off of the left side and three triangles off of the right side. Will the hanger still be in balance, or will it tip to one side? Which side? Explain how you know.

    2. Use the applet to see if your answer to question [1] was correct. Can you find another way to make the hanger balance?

    open applet in presentation mode

  2. If a triangle weighs 1 gram, how much does a square weigh? After you make a prediction, use the applet to see if you were right. Can you find another pair of values that makes the hanger balance?

    open applet in presentation mode
Print Version

This picture represents a hanger that is balanced because the weight on each side is the same.

A balanced hanger diagram with 3 squares and 2 triangles on the left and 1 square and 5 triangles on the right.

  1. Elena takes two triangles off of the left side and three triangles off of the right side. Will the hanger still be in balance, or will it tip to one side? Which side? Explain how you know.

  2. If a triangle weighs 1 gram, how much does a square weigh?

Are you ready for more?

Problem 1

Try your own Hanger Balances!

open applet in presentation mode
Print Version

Activity 2: More Hanging Blocks

Problem 1

  1. Find the weight of a square.

    open applet in presentation mode

    Find the weight of a pentagon.

    open applet in presentation mode

  2. Write an equation to represent each hanger.

Print Version

  1. Find the weight of a square in Hanger A and the weight of a pentagon in Hanger B.

  2. Write an equation to represent each hanger.

Are you ready for more?

Problem 1

Are you ready for more?

Try your own!

open applet in presentation mode
Print Version

What is the weight of a square on this hanger if a triangle weighs 3 grams?

A balanced hanger diagram with 3 triangles and 2 blue squares on the left and 1 square and 2 triangles on the right.

Lesson Summary

If we have equal weights on the ends of a hanger, then the hanger will be in balance. If there is more weight on one side than the other, the hanger will tilt to the heavier side.

Three hanger diagrams. The first and third have uneven amounts of triangles on each side and is unbalanced. The middle one is balanced with 3 triangles on each side.

We can think of a balanced hanger as a metaphor for an equation. An equation says that the expressions on each side have equal value, just like a balanced hanger has equal weights on each side.

A balanced hanger diagram with 1 square and 2 triangles on the left side and 5 triangles on the right side illustrating the equation a + 2b = 5b

If we have a balanced hanger and add or remove the same amount of weight from each side, the result will still be in balance.

A balanced hanger diagram with a square on the left and 3 triangles on the right illustrating a = 3b.

We can do these moves with equations as well: adding or subtracting the same amount from each side of an equation maintains the equality.