1. _____________________________________________
Operations With Integers
-4
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Middle Grades
Mathematics Methods
-8

2. Minus…What does it mean?
In algebra, the minus sign can mean three things.
 In front of a number, the minus sign means
“negative”.
 In front of any expression, the minus sign means
“the opposite of”.
 Between two expressions, the minus sign means
“subtract” or “take away”.

3. Adding Integers
Teaching the Idea:
Integers are positive and negative whole
numbers and zero.
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When you add opposites, such as 3 and -3, the
result is 0.

4. Adding Integers
Teaching the Idea:
Integers are positive and negative whole
numbers and zero.
_________________________________________
When you add opposites, such as 3 and -3, the
result is 0.
Three zero pairs.
No counters are left, so the result is 0.

5. Example Problems:
To model addition of integers, put on the first number,
put on the second number, cancel what you can, and then
count.
1. -10 + (-3) =
1. -8 + 9 =
1. 4 + (-7) =
1. -12 + (-6) =
1. 4 + 3 =
1. -5 + 2 =
What patterns do you notice?

6. Subtracting Integers
To model subtraction, put on the first number,
take off the second number, and count.
-2 - 5
(Sometimes there are not enough blocks to take off,
so “zero” may be added until there are enough
counters to remove.)
Negative 2 put on, not enough to take five,
so add five zero pairs, and then take five,
count what is left.

7. Subtracting Integers
To model subtraction, put on the first number,
take off the second number, and count.
-2 - 5
(Sometimes there are not enough blocks to take off,
so “zero” may be added until there are enough
counters to remove.)
Negative seven left

8. Subtraction Examples:
Put on, add zero as needed, take off, count.
1. -10 - 3 =
1. 6 - 9 =
1. 4 - (-7) =
1. -12 – (-6) =
1. 7 - 3 =
1. -5 - 2 =
What patterns do you notice?

9. Multiplication of Integers
Consider the four cases:
3(2) 3(-2)
3 sets of two is 6 3 sets of negative two is -6
-3(2) -3(-2)
Opposite of 3 sets of two is -6 Opposite of 3 sets of negative two is 6

10. Minus…What does it mean?
In algebra, the minus sign can mean three things.
 In front of a number, the minus sign means
“negative”.
 In front of any expression, the minus sign means
“the opposite of”.
 Between two expressions, the minus sign means
“subtract” or “take away”.

11. Division of Integers
Recall there are four ways to write a division expression.
Relate division of integers to multiplication:
For example:
12/3 What times 3
equals 12?