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Integers Made Easy

Learning to use Positive and Negative Numbers

Learning to use integers starts with a review of basic arithmetic, adding a definite “ground zero” and left-right, negative-positive concepts. It helps to have a carpet similar to this one, and one small, toy car, about the same length or smaller then the lines on the road.

Integers can be learned using a town carpet and a toy car.
39″ x 36″
by Melissa & Doug
Using a village carpet and a small car, you can get across the concepts of adding and subtracting positive and negative integers.

Start with your small car in the middle of the intersection at the top center of the carpet, facing right. The car will drive one dotted line per count. Tell you child that the middle of the intersection is zero (0).

First Problem: 3 + 2

0  3  2 = 5

Ask your child how many dotted lines have been traveled in all. He should say, “5.” This should be easy for the older child, and he’ll think you are a bit nuts for going over this with him, but it gets harder.

Now show him how the car will work with subtraction.

Second problem: 5 – 2

The car is already at line 5.

0  5

Throw the gears into reverse making suitable gear grinding noises. Go in reverse back two lines.

0 3 ______ ______ 5

Ask your child at what line the car is now on. He should say, “3.”

Here comes the new concept. Explain to your child that the “facing right” direction from now on will be thought of as “positive” and that the car will face right whenever the numbers used have a “+” in front of them.

Write out the first and second problems as (+3) + (+2) and (+5) – (+2) and drive the little car in the same fashion. Have your child make up some of his own integer problems like these and drive the little car forward to the right and in reverse.

0  +5

Now tell him that cars would be in big trouble if they could only go right or in reverse. Sometimes they need to go left.

In the world of integers, when we go left, we use the negative sign on numbers or “-“.

Count the lines going to the left of the intersection as being -1 (negative 1), -2, -3, -4, -5, and so on.

Explain to him that when his car is facing left, the numbers will always have a “negative” value symbol.

Practice making u-turns in the middle of the intersection, making suitable tire squeals, during a game something like “Simon Says.” You fire off numbers like “Plus 3” or “Minus 5” and he has to turn the car right or left, or keep it going the same way if the sign is the same as the previous call.

Tell your child to drive the car first -2 and then -3 lines to the left. Ask him where he is now. He should say something like, “5 to the left” or better, “negative 5.”

-5  -2  0

Tell him he has successfully done the integer problem (-2) + (-3) (Negative 2 plus negative 3). Do this several times with different problems your child makes up, within the range of the lines on the carpet.

Leave the car where it is, throw it in reverse, making suitable grinding gear noises of course, and tell him to drive it backwards 3 lines. Ask him where he is now. (-2) (He has done the problem (-5) – (-3) = (-2)

-5 ______ ______ ______ -2 0

Do a quick test to see if he has these rules for the game down correctly:

  • A positive symbol right next to the number means “Turn the car to the right.”
  • A negative symbol right next to the number means “Turn the car to the left.”
  • Addition (+) means “Drive the car forward, no matter which way it is facing.”
  • Subtraction (-) means “Throw the car in reverse, no matter which way it is facing.”

Time to learn to turn around mid-block!

Tell your child to drive “positive 4” and then “negative 1” He should drive to the right 4, turn around and drive forward 1. Where are you? (This is an example of (+4) + (-1). Ask him how else he could get to the same line. He might say that it is the same as driving “positive 4” then reversing or subtracting “positive 1.”

0  +4

______ ______ ______ +3  +4


Try several more problems like this. See if your child asks, “But what happens if we go through the intersection???” Go ahead and try it! do make a brief stop on “0” just as you do the numbered lines.

Here’s (+4) + (-5)
   +4

-1     +4


Here’s another one to try: (-3) – (-5) How would you think this through? Drive to the left to the -3 line. The 5 is negative, so I stay facing left. I’m doing subtraction, so I shift gears, and go in reverse. Where do I wind up?

-3    +2

Allow your child to use his map and car to do his integer math work for as long as he needs to.


Variations to the game might be a small horse passing next to fence posts, or a plane flying east and west from Nebraska on a large map of the country. This can also be adapted for “up” and “down,” for example, using marks on the side of a tub, and using a toy that flies into the air and then dives into the water.

Track temperature changes outdoors. Have your child explain the reading differences in terms of integers.

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