## Pan Balance – Numbers

Use this tool to strengthen understanding and computation of numerical expressions and equality. In understanding equality, one of the first things students must realize is that equality is a relationship, not an operation. Many students view "=" as "find the answer." For these students, it is difficult to understand equations such as 11 = 4 + 7 or 3 × 5 = 17 – 2.

Two other tools, Pan Balance – Expressions and Pan Balance – Shapes, are natural extensions.

Begin by clicking in either the red or blue pan. Enter an expression using either the keyboard or the keypad at the bottom of the work area.

Special keypad buttons:

**Home**will move the cursor to the beginning of the expression.**End**will move the cursor to the end of the expression.**←**will move the cursor one character to the left.**→**will move the cursor one character to the right.

Notes on entering expressions:

- Using the keyboard, multiplication should be entered using *.
- Using the keyboard, division should be entered using /.
*x*^{2}and*x*^{3}are used to indicate squaring and cubing a number. They must be entered using the keypad. Each operation can be used only once.- A number in front of parentheses is recognized as multiplication. For example: 3(4 + 8) is calculated as 3×(4 + 8).
- The result of your expression will be shown above the selected pan. Invalid entries are indicated with a message.

When you are finished entering an expression in one pan, click on the other pan to enter an expression. The pans will move up and down depending on which expression is greater. When the expressions are equivalent, the pans will balance and the full equation will be entered into the **Balanced Equations** table.

At any point, you can click the **Reset Balance** button to remove the expressions from the pans. You can also click the **Reset Table** button to remove all equations from the table.

Enter 4 onto the red pan. Then, enter 9 onto the blue pan. What happens? Why?

Reset the balance. Enter 12 onto the red pan. Then, enter a sum (two numbers added together) onto the right pan that is equal to 12. What happens? Why?

Can you find another sum equal to 12? Can you find another expression using a different operation?

Can you add up three numbers that balance to 12? four numbers? What is the greatest number of numbers that you can add to balance with 12?

You have now found several expressions that equal 12. Enter one of your expressions in the red pan and another in the blue pan (don't use 12). What happens? Why?