1. To subtract integers, add the opposite of the second number instead of subtracting. 2. Adding a "zero pair" does not change the difference of a subtraction problem, but allows negatives to be subtracted by providing positive chips to remove. 3. The number line can be used to model integer subtraction by moving left for negatives and right for positives.

1. On a chip
board

2. So let’s subtract -5 - -3
Put on 5 red chips
Since we’re subtracting, we
need to take chips OFF the
board
Take off 3 red chips
(in order to subtract -
3)
So, -5 - -3 =-2

3. Now let’s subtract -3 - -5
Put on 3 red chips
How can we subtract 5 red
chips when we only have 3?
ADD TWO ZERO PAIRS!
Now you can take off
the five red chips.
-3 - -5 = 2

4. Remember, one positive
and one negative make a
ZERO PAIR

5. Say you wanted to show “+5”
on a chip board.
You could just use 5 yellow chips
or 5 yellow chips and a zero pair
or 5 yellow chips and 2 zero pairs
This is very important for subtraction!

6. Now let’s subtract 2 - 3
Put on 2 yellow chips
How can we take away 3
yellow chips when we only
have 2?
How many zero pairs do
we need?
Now you can take away
3 yellow chips.
2 - 3 = -1

7. Try subtracting -4 - -6
What should we do
first?
Do we have enough to
subtract -6?
No, so how many zero
pairs do we need to add?
Now, what do we take
away?
-4 - -6 = 2

8. Let’s try 5 - -3
What should we do
first?
Do we have enough to
subtract -3?
We need to take off 3 red
chips, and we don’t have
ANY!
So, how many zero pairs
do we need to add?
Now, what do we take
away?
5- -3 = 8

9. Let’s try one more 5 - 7
What should we do
first?
Do we have enough to
subtract 7?
No, so how many zero
pairs do we need to add?
Now, what do we take
away?
5 - 7 = -2

10. 1. Solve 5 – 3
Explain in words:
2. Solve -5 – (-3)
Explain in words:

11. 3. Solve -5 – 3
Explain in words:
1. Start with -5
2. Add 3 zero pairs
3. Remove 3 positives

12. 4. Solve 5 – (-3)
Explain in words:
5. Solve -4 – (-7)
Explain in words:

13. 6. Solve -3 – (-4)
Explain in words:
7. Write the subtraction
problem that is modeled
in the box. + + +
+ +

14. 1. What does it mean to add a “zero pair”?
2. Does adding a “zero pair” change the
difference?

15. -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
1. Model on the number line and solve. -4 – 3 =
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
2. Model on the number line and solve. 6 – 8 =

16. Rules for adding integers:
• Same signs – ADD and keep the sign.
• Different signs – SUBTRACT and
take the sign from the number that
“has more” (or is bigger in absolute
value.

17. Rules for subtracting integers:
SUBTRACTION IS ICKY! So:
1. Keep the first number the same.
2. Change the subtraction sign to addition.
3. Make the second number its opposite.
4. Use the addition rules.
Keep it! Change it! Opposite it!