Integers Made Easy
Dateline: 4/4/01
By Ann Zeise
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.
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
0 ______ ______ ______ +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)
0
+4
-1
0
+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
0
+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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