Positively Negative

"I know how to do it on this...It makes it easy to do it. You can see it all...This is cool!"

This is a virtual manipulative for learning about positive and negative integers using a number line.

By clicking on the up and down arrows, you can choose two operands (numbers to operate on) and an operation on the left side. Underneath the operands you will see the result of that operation as a number. To the right of the numbers you will see the number lines that represent those numbers and the operation.

If you can see this, you may not have Java installed or may not have a recent enough version. This program needs Java (1.5 or later). (Apple users should get it from Apple)

A few things you may want to try. For each one, what do you observe?

  1. Try adding two small positive numbers, like 2 + 3. How does the 2 appear as a number line? How does the 3 appear? Where is the zero of the number line that represents 3? Describe how you can see the sum on the number lines.
  2. Try adding zero to a number, or adding a number to zero. What do you get?

  3. Try adding a number to its negative, for example 3 + −3 or −5 + 5. What do you get? How can you see that on the number line?

  4. Try adding two positive numbers, like 2 + 4. Then add the corresponding negative numbers, like −2 + −4. What is similar? Different? (Look at the result and the number lines).

  5. Try adding a positive to a negative. Is the sum positive or negative? Is it alwys positive or always negative? Play with the operands to experiment.
  6. Now do similar things with subtraction. Notice that subtraction looks just like addition on the number line except that instead of adding the second operand directly, we add its blue opposite, technically called its additive inverse.
  7. I'm not thrilled with how I did multiplication; see what you think.

Do you have any questions or any suggestions? Please contact me!

Jon Dreyer • Math tutorComputer Science tutorwww.mathtutorlexington.com
781-696-2614 • 81 Baker Ave, Lexington MA 02421-6228 • email

I have no special talent. I am only passionately curious. —Albert Einstein