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Published byJoel Taber Modified over 2 years ago

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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!

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Definition Positive number – a greater than zero. 0123456

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Definition Negative Negative number – a number less than zero. 0123456-2-3-4-5-6

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Definition Opposite Numbers – numbers that are the same distance from zero in the opposite direction 0123456-2-3-4-5-6

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

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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: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 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:Example: |-8| = 8 and |8| = 8 |50| = 50 and |-50| = 50

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

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|7| – |-2| = ? 1. -9 2. -5 3. 5 4. 9

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|-4 – (-3)| = ? 1. -1 2. 1 3. 7 4. 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 0 10 20 30 -10 -20 -30 -40 -50

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Negative Numbers Are Used to Show Debt Lets 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 dont see a negative or positive sign in front of a number it is positive. 9 +

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

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ADDING INTEGERS Use your red and yellow tiles to find each sum. -2 + -3 = ? ANSWER + = -5 -2 + -3 = - 5

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

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Solve the Problems -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 = -9 + -9 = -8 -18 14 -13 7 11

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These Problems Solve These Problems 3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 = 5 + -9 = -9 + 9 = -2 0 -4 1 3

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Adding Integers Number line T-Method

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-3-2 Adding Integers using the number line - 3 + 2 = Negative three means move 3 places to the left Positive two means move 2 places to the right 0 12The answer is:

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5362 Adding Integers using the number line 8 - 3 = Negative three means move 3 places to the left Positive eight means move 8 places to the right 0 12The answer is: 5 5345678 718

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

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Use your red and yellow tiles to find each sum. -2 + (-5) = ? -2 + (-5) = ? T-Method -+ 2 5 += 7

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Use your red and yellow tiles to find each sum. 2 + (-5) = ? 2 + (-5) = ? T-Method +- 2 5 += 3 2

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Use your red and yellow tiles to find each sum. -2 + 5 = ? -2 + 5 = ? T-Method -+ 25 += 3 2

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Subtracting Integers and T- Method T-Method

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SUBTRACTING INTEGERS We often think of subtraction as a take away operation. Which diagram could be used to compute + 3 - + 5 = ? +3+3 +3+3

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SUBTRACTING INTEGERS We cant 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.

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SUBTRACTING INTEGERS Use your red and yellow tiles to model each subtraction problem. - 2 - - 4 = ? - 2 - - 4 = ? ANSWER

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SUBTRACTING INTEGERS This representation of - 2 doesnt 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…

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SUBTRACTING INTEGERS Work this problem. Work this problem. + 3 - - 5 = ? ANSWER

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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

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SUBTRACTING INTEGERS Work this problem. Work this problem. - 3 - + 2 = ? ANSWER

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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

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-3 – ( -5) = 4 - 7 = (+3) - (+4) = -6 – (-7) = 5 - 9 = -9 – (-9) = SUBTRACTING INTEGERS 2 -4 -3 1 0

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3 – (-5) = -4 - 7 = (+3) - (-4) = -6 - 7 = 5 – (-9)= -9 - 9 = SUBTRACTING INTEGERS 8 7 -11 14 13 -18

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

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

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