Alexander Calder liked balance. For his mobiles, he spent many hours carefully arranging metal shapes on branching wire to create a perfect balance. The result was airborne sculptures that remind us of tightrope walkers, orbiting planets, soaring birds, drifting clouds—all things delicately balanced and harmoniously moving through space.

Using Calder's Mobile

Mathematicians also like balance. They write equations to show how numbers balance. Let's look at the red shapes in Calder's mobile Black, White, and Ten Red to create some equations about the number ten.

Remember: The numbers on each side of the "=" sign must "balance" to make an equation correct.

How can you show that 5 + 5 = 10? Roll your mouse over the mobile to see one way to do it.

Can you find another way to show this equation? Roll your mouse again to find it.

Now, using the red shapes, make an equation that has more than two addends: 2 + 5 + 3 = 10 Roll your mouse over the image to see one solution showing this equation.

Can you figure out how the red shapes fit into the following equation that uses multiplication? 2 (2 + 3) = 10 This means that there are two groups, and each group has 2 + 3 in it. How can you show that with the red shapes? Roll your mouse over the image to see one solution.

Extra Credit

Which equation describes all the pieces in this mobile?

• 10 + 1 + 1 = 12
• 2 + 3 + 2 + 3 +1 + 1 = 12
• 2 (1) + 2 (2+3) = 12

They are all correct. Try it for yourself. First, print this page so that you have a picture of the mobile. Then, circle groups of shapes to show each equation.