Lesson 2

Keeping the Equation Balanced

Let's figure out unknown weights on balanced hangers.

2.1: Notice and Wonder: Hanging Socks

What do you notice? What do you wonder?

Two clothing hangers with socks. 

2.2: Hanging Blocks

This picture represents a hanger that is balanced because the weight on both sides is the same.

A balanced hanger. Left side, 3 squares, 2 triangles. Right side, 1 square, 5 triangles.
  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?

     
  3. 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?



Try your own Hanger Balances!

GeoGebra Applet RQ58fzCE

2.3: More Hanging Blocks

A triangle weighs 3 grams, and a circle weighs 6 grams.

  1. Find the weight of a square.

     
  2. Find the weight of a pentagon.

     
  3. Write an equation to represent each hanger.



Try your own!

GeoGebra Applet hDfcuwNb

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 hangers. 

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. Left side, 1 square, 2 triangles. Right side, 5 triangles. Below hanger, an equation reads a plus 2 b equals 5 b.

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. Left side, 1 square. Right side, 2 triangles. Below hanger, an equation reads a equals 3 b.

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