We can represent integers using red and yellow counters. Red tiles will represent negative integers,...

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