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**Everything about Integers**

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Interesting 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

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Definition Positive number – a number greater than zero. 1 2 3 4 5 6

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Definition Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

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Definition Opposite Numbers – numbers that are the same distance from zero in the opposite direction -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

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Definition Integers – Integers are all the whole numbers their opposites and zero. 7 opposite -7

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**Example: The opposite of 6 is -6**

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

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Interesting Integers! If there are the same number of red tiles as yellow tiles, what number is represented? zero pair It represents 0.

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**Definition The absolute value of 9 or of –9 is 9.**

Absolute Value – The size of a number with or without the negative sign. The absolute value of 9 or of –9 is 9.

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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

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Examples 7 = 7 10 = 10 -100 = 100 5 - 8 = -3= 3

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|7| – |-2| = ? -9 -5 5 9

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|-4 – (-3)| = ? -1 1 7 Purple

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**Negative Numbers Are Used to Measure Temperature**

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**Negative Numbers Are Used to Measure Under Sea Level**

30 20 10 -10 -20 -30 -40 -50

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**Negative Numbers Are Used to Show Debt**

Let’s say your parents bought a car but had 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.

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Hint If you don’t see a negative or positive sign in front of a number it is positive. 9 +

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**ADDITION AND SUBTRACTION**

Interesting Integers! ADDITION AND SUBTRACTION

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**ADDING INTEGERS We can model integer addition with tiles.**

Represent -2 with the fewest number of tiles Represent +5 with the fewest number of tiles.

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ADDING INTEGERS What number is represented by combining the 2 groups of tiles? Write the number sentence that is illustrated. = +3 +3

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**= -5 + ADDING INTEGERS Use your red and yellow tiles to find each sum.**

= ? ANSWER = -5 + = -5

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**+ - 4 = +1 = + ADDING INTEGERS -6 + +2 = ? -3 + +4 = ? -6 + +2 = -4**

ANSWER = ? + = - 4 = -4 = ? ANSWER = +1 + = +1

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**Solve the Problems -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 =**

= -8 11 7 -13 14 -18

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**Solve These Problems 3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 = 5 + -9 =**

= -2 3 -1 1 -4

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Adding Integers Number line T-Method

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**- 3 + 2 = -1 Adding Integers using the number line**

Negative three means move 3 places to the left Positive two means move 2 places to the right 1 2 -3 -2 -1 The answer is: -1

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**8 - 3 = 5 Adding Integers using the number line Positive eight means**

= 5 Positive eight means move 8 places to the right Negative three means move 3 places to the left 1 2 3 4 5 6 7 8 5 3 6 2 7 1 8 The answer is: 5

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Adding Integers T- Method T-Method

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**Use your red and yellow tiles to find each sum.**

2 + 5 = ? - + 2 + = 5 7 T-Method

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**Use your red and yellow tiles to find each sum.**

-2 + (-5) = ? - + 2 + = 5 7 T-Method

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**Use your red and yellow tiles to find each sum.**

2 + (-5) = ? + - 5 2 2 + = 3 T-Method

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**Use your red and yellow tiles to find each sum.**

= ? - + 2 2 5 + = 3 T-Method

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**Subtracting Integers and**

T- Method T-Method

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**SUBTRACTING INTEGERS +3 +3**

We often think of subtraction as a “take away” operation. Which diagram could be used to compute = ? +3 +3

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SUBTRACTING INTEGERS This diagram also represents +3, and we can take away +5. When we take 5 yellow tiles away, we have 2 red tiles left. We can’t take away 5 yellow tiles from this diagram. There is not enough tiles to take away!!

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**SUBTRACTING INTEGERS -2 - -4 = ?**

Use your red and yellow tiles to model each subtraction problem. = ? ANSWER

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**-2 - -4 = +2 SUBTRACTING INTEGERS Now you can take away 4 red tiles.**

2 yellow tiles are left, so the answer is… 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. = +2

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SUBTRACTING INTEGERS Work this problem. = ? ANSWER

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**+3 - -5 = +8 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. = +8

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SUBTRACTING INTEGERS Work this problem. = ? ANSWER

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**-3 - +2 = -5 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. = -5

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**-3 – ( -5) = 4 - 7 = (+3) - (+4) = -6 – (-7) = 5 - 9 = -9 – (-9) =**

SUBTRACTING INTEGERS -3 – ( -5) = 4 - 7 = (+3) - (+4) = -6 – (-7) = 5 - 9 = -9 – (-9) = 2 -3 -1 1 -4

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**3 – (-5) = -4 - 7 = (+3) - (-4) = -6 - 7 = 5 – (-9)= -9 - 9 =**

SUBTRACTING INTEGERS 3 – (-5) = = (+3) - (-4) = = 5 – (-9)= = 8 -11 7 13 14 -18

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**Keep in mind that subtract means add the opposite.**

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. - - 2 2 (-5) -5 = = + 5 T-Method

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**-8 – ( -2) = 5 - 4 = (+7) - (+2) = -8 – (-7) = 8 - 5 = -10 – (-2) =**

SUBTRACTING INTEGERS -8 – ( -2) = 5 - 4 = (+7) - (+2) = -8 – (-7) = 8 - 5 = -10 – (-2) = 6 1 5 -1 3 -8

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