2 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 integerPositive integer
3 DefinitionPositive number – a number greater than zero.123456
4 DefinitionNegative number – a number less than zero.-6-5-4-3-2-1123456
5 DefinitionOpposite Numbers – numbers that are the same distance from zero in the opposite direction-6-5-4-3-2-1123456
6 DefinitionIntegers – Integers are all the whole numbers their opposites and zero.7opposite-7
7 Example: The opposite of 6 is -6 What are Opposites?Two integers the same distance from the origin, but on different sides of zeroEvery positive integer has a negative integer an equal distance from the originExample: The opposite of 6 is -6The opposite of -2 is 2
8 Interesting Integers!If there are the same number of red tiles as yellow tiles, what number is represented?zero pairIt represents 0.
9 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 of9 or of –9 is 9.
10 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 valueOpposites have the same absolute values since they are the same distance from zeroExample: |-8| = 8 and |8| = 8|50| = 50 and |-50| = 50
14 Negative Numbers Are Used to Measure Temperature
15 Negative Numbers Are Used to Measure Under Sea Level 302010-10-20-30-40-50
16 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 addin -$5.000 to show they still owe the bank.
17 HintIf you don’t see a negative or positive sign in front of a number it is positive.9+
18 ADDITION AND SUBTRACTION Interesting Integers!ADDITION AND SUBTRACTION
19 ADDING INTEGERS We can model integer addition with tiles. Represent -2 with the fewest number of tilesRepresent +5 with the fewest number of tiles.
20 ADDING INTEGERSWhat number is represented by combining the 2 groups of tiles?Write the number sentence that is illustrated.= +3+3
21 = -5 + ADDING INTEGERS Use your red and yellow tiles to find each sum. = ?ANSWER= -5+= -5
34 SUBTRACTING INTEGERS +3 +3 We often think of subtraction as a “take away” operation.Which diagram could be used to compute= ?+3+3
35 SUBTRACTING INTEGERSThis 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!!
36 SUBTRACTING INTEGERS -2 - -4 = ? Use your red and yellow tiles to model each subtraction problem.= ?ANSWER
37 -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
38 SUBTRACTING INTEGERSWork this problem.= ?ANSWER
39 +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
40 SUBTRACTING INTEGERSWork this problem.= ?ANSWER
41 -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
44 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.--22(-5)-5==+5T-Method