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Everything about Integers
We can represent integers using red and yellow counters.
Red tiles will represent negative integers, and yellow tiles will represent positive integers.
Negative integer Positive integer
Interesting Integers!
DefinitionPositive number – a number greater than zero.
0 1 2 3 4 5 6
DefinitionNegative number – a number less than zero.
0 1 2 3 4 5 6-1-2-3-4-5-6
Definition
Opposite Numbers – numbers that are the same distance from zero in the opposite direction
0 1 2 3 4 5 6-1-2-3-4-5-6
DefinitionIntegers – Integers are all the whole numbers their opposites and zero.
7 opposite -7
What are Opposites?• Two integers the same distance from the
origin, but on different sides of zero• Every positive integer has a negative integer an equal distance from the origin
• Example: The opposite of 6 is -6
The opposite of -2 is 2
Interesting Integers!If there are the same number of red tiles
as yellow tiles, what number is represented?
zero pair
It represents 0.
DefinitionAbsolute Value – The size of a number with or without the negative sign.
The absolute value of 9 or of –9 is 9.
What is Absolute Value?
• Distance a number is from zero on a number line (always a positive number)
• Indicated by two vertical lines | |• Every number has an absolute value
• Opposites have the same absolute values since they are the same distance from
zero
• Example: |-8| = 8 and |8| = 8
|50| = 50 and |-50| = 50
Examples
7 = 7
10
100
10 =
-100 =
5 - 8 = -3= 3
|7| – |-2| = ?1. -92. -53. 54. 9
|-4 – (-3)| = ?1. -12. 13. 74. Purple
Negative Numbers Are Used to Measure Temperature
Negative Numbers Are Used to Measure Under Sea Level
0102030
-10-20-30-40-50
Negative Numbers Are Used to Show Debt
Let’s say your parents bought a car buthad to get a loan from the bank for $5,000.When counting all their money they add in -$5.000 to show they still owe the bank.
Hint
If you don’t see a negative or positive sign in front of a number it is positive.
9+
ADDITION AND SUBTRACTION
Interesting Integers!
ADDING INTEGERSWe can model integer addition with tiles.Represent -2 with the fewest number of tiles
Represent +5 with the fewest number of tiles.
ADDING INTEGERSWhat number is represented by combining the
2 groups of tiles?
Write the number sentence that is illustrated.
-2 + +5 = +3
+3
ADDING INTEGERSUse your red and yellow tiles to find each
sum.
-2 + -3 = ?ANSWER
+ = -5
-2 + -3 = -5
ADDING INTEGERS -6 + +2 = ?
+ = - 4
+ = +1
-3 + +4 = ?
ANSWER
ANSWER
-6 + +2 = -4
-3 + +4 = +1
Solve the Problems
-3 + -5 =4 + 7 =(+3) + (+4) =-6 + -7 = 5 + 9 =-9 + -9 =
-8
-18
14-13
7
11
Solve These Problems
3 + -5 =-4 + 7 =(+3) + (-4) =
-6 + 7 = 5 + -9 =-9 + 9 =
-2
0 -4
1
-1
3
Adding IntegersNumber line
T-Method
-3 -2
Adding Integersusing the number line
- 3 + 2 =
Negative three means move 3 places to the left
Positive two means move 2 places to the right
0-1
1 2
The answer is: -1
-1
5
3
6
2
Adding Integersusing the number line
8 - 3 =
Negative three means move 3 places to the left
Positive eight means move 8 places to the right
0
1 2
The answer is: 5
5
3 4 5 6 7 8
7
1
8
Adding IntegersT- Method
T-Method
Use your red and yellow tiles to find each sum.
2 + 5 = ?
T-Method
- +
25
+ =
7
Use your red and yellow tiles to find each sum.
-2 + (-5) = ?
T-Method
- +
25
+ =
7
Use your red and yellow tiles to find each sum.
2 + (-5) = ?
T-Method
+ -
2 5+ =
3
2
Use your red and yellow tiles to find each sum.
-2 + 5 = ?
T-Method
- +
2 5+ =
3
2
Subtracting Integers andT- Method
T-Method
SUBTRACTING INTEGERSWe often think of subtraction as a “take
away” operation.Which diagram could be used to compute +3 - +5 = ?
+3 +3
SUBTRACTING INTEGERS
We can’t take away 5
yellow tiles from this
diagram. There is not
enough tiles to take
away!!
This diagram also
represents +3, and we can
take away +5.
• When we take 5 yellow
tiles away, we have 2 red
tiles left.
SUBTRACTING INTEGERSUse your red and yellow tiles to model
each subtraction problem.
-2 - -4 = ?
ANSWER
SUBTRACTING INTEGERS
This representation
of -2 doesn’t
have enough
tiles to take
away -4.
Now if you add 2 more
reds tiles and 2 more
yellow tiles (adding zero)
you would have a total of
4 red tiles and the tiles
still represent -2.
Now you can take away 4 red tiles.
-2 - -4 = +2
2 yellow tiles are left, so the answer is…
SUBTRACTING INTEGERS
Work this problem.
+3 - -5 = ?ANSWER
SUBTRACTING INTEGERS• Add enough red and
yellow pairs so you can take away 5 red tiles.
• Take away 5 red tiles, you have 8 yellow tiles left.
+3 - -5 = +8
SUBTRACTING INTEGERS
Work this problem.
-3 - +2 = ?ANSWER
SUBTRACTING INTEGERS• Add two pairs of red and
yellow tiles so you can take away 2 yellow tiles.
• Take away 2 yellow tiles, you have 5 red tiles left.
-3 - +2 = -5
-3 – ( -5) =4 - 7 =(+3) - (+4) =-6 – (-7) = 5 - 9 =-9 – (-9) =
SUBTRACTING INTEGERS
2
-4
-3
1
-1
0
3 – (-5) =-4 - 7 =(+3) - (-4) =
-6 - 7 = 5 – (-9)=-9 - 9 =
SUBTRACTING INTEGERS
8
7
-11
14
13
-18
In order to subtract two integers, you would need to re-write the problem as an addition problem.
Keep in mind that subtract means add the opposite.
T-Method
2 - (-5) =2 -
+
-5
5
=
-8 – ( -2) =5 - 4 =(+7) - (+2) =-8 – (-7) = 8 - 5 =-10 – (-2) =
SUBTRACTING INTEGERS
6
3
1
-1
5
-8
