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Adding and Subtracting

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Presentation on theme: "Adding and Subtracting"— Presentation transcript:

1 Adding and Subtracting
Rational Numbers

2 Whole Numbers - ex. "0, 1, 2, 3, 4, ... Integers -
Positive numbers that represent a "whole." ex. "0, 1, 2, 3, 4, ... Zero is a special case. Integers - Positive and negative numbers that represent a "whole." ex. "... -4, -3, -2, -1, 0, 1, 2, 3, 4, ..."

3 Are ALL numbers included in the integers group?
So all Whole Numbers are included in the Integers group. Are ALL numbers included in the integers group?

4 Rational Numbers - Any positive or negative whole numbers that can be written as a fraction. ex. "-1" "0.5" "-0.5"

5 Integers Rational Numbers Whole Numbers

6 *Opposite numbers always add up to 0.
Numbers that are the same distance from 0 on a number line, but have different signs. *Opposite numbers always add up to 0. *Opposite numbers have the same Absolute Value.

7 Find the Opposite 1) 10 = 2) -5 = 3) 0.3 =

8 Absolute Value - The distance from 0 that a number is on a number line. (In either direction) ex. 5 5 -5 5

9 What are Whole Numbers? What are Integers? What are Rational Numbers? *Give an example of each. What are opposites? *Give an example. What is absolute value? Review: Homework: Wksht 4-1 Rational Numbers, Opposites and Absolute Value # 1-10

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11 Adding Positive and Negative Numbers using a Number Line
-3 + (-7) = * Always start at 0. * Negatives move LEFT. Positives move RIGHT. ? -3

12 * Always start at 0. * Negatives move LEFT. Positives move RIGHT. 5 + (-3) =

13 * Always start at 0. * Negatives move LEFT. Positives move RIGHT. 4 + (-8) =

14 * Always start at 0. * Negatives move LEFT. Positives move RIGHT. =

15 More?

16 My Friends Pete Neil

17 Anytime I hang out with Neil, I have a real negative time
Anytime I hang out with Neil, I have a real negative time. He really brings me down. My mood = -1

18 The only thing worse than hanging out with Neil, is hanging out with TWO Neils!
My mood = ?

19 Pete, however, is pretty cool. He always knows how to cheer me up.
What does Pete do to my mood? My mood = ?

20 How do you think I feel when my mom makes me play with Pete AND Neil at the same time?

21 So obviously, Pete and Neil are OPPOSITES. They cancel out.
When they are balanced, they make my mood 0. Meh. 1 + (-1) = 0 But when they are unbalanced, my mood can change. 1 + (-3) =

22 Adding/Subtracting Integers
BrainPop Adding/Subtracting Integers

23 5 + (-6) = =

24 5 + (-2) = -4 + (-4) + 5 =

25 Additive Inverses - Two opposites added together to make 0 are called Additive Inverses ex = 0 4 + (-4) = 0

26 Review: HW: Wksht 4-2 Adding Integers #1-9 Number Lines: Positives go?
Negatives go? -10 + (-3) = Using Pete and Neil. = 5 + (-3) = 150 + (-15) = HW: Wksht 4-2 Adding Integers #1-9

27 Extra Review

28 Subtracting Integers If I am hanging out with 6 Petes, and 5 Neils show up, what will happen to my mood?
 Write this number sentence: If I am hanging out with 6 Petes, and 5 Petes go home, what will happen to my mood? What do we see? Adding negatives is the same as subtracting positives. They both affect our answer the same.

29 The Chef’s Hot and Cold Cubes
(Interactive Mathematics Program) In a far-off place, there was once a team of amazing chefs who cooked up the most marvelous food ever imagined. They prepared their meals over a huge cauldron, and their work was very delicate and complex. During the cooking process, they frequently had to change the temperature of the cauldron in order to bring out the flavors and cook the food to perfection. They adjusted the temperature of the cooking either by adding special hot cubes or cold cubes to the cauldron or by removing some of the hot or cold cubes that were already in the cauldron.

30 + = Additive Inverses + =
The cold cubes were similar to ice cubes except that they didn’t melt, and the hot cubes were similar to charcoal briquettes, except they didn’t lose their heat. If the number of cold cubes in the cauldron was the same as the number of hot cubes, the temperature of the cauldron was 0 degrees on their temperature scale. + = Additive Inverses + =

31 = = Think about how the hot and cold cubes affect the temperature.
For each hot cube that was put in the cauldron, the temperature went up one degree; for each hot cube removed, the temperature went down one degree. Similarly, each cold cube put in lowered the temperature one degree and each cold cube removed raised it one degree. The chefs used positive and negative numbers to keep track of their changes they were making to the temperature. Think about how the hot and cold cubes affect the temperature. Which cubes should represent positive numbers and which cubes should represent negative numbers? = =

32 to represent these actions and their overall result.
For example, suppose 4 hot cubes and 10 cold cubes were dumped into the cauldron. Then the temperature would be lowered by 6 degrees altogether, since 4 of the 10 cold cubes would balance out the 4 hot cubes, leaving 6 cold cubes to lower the temperature 6 degrees. They would write 4 + (-10) = -6 to represent these actions and their overall result.

33 How can we take away 2 cold cubes?
Adding Zero Pairs Similarly, if they added 3 hot cubes and then removed 2 cold cubes, the combined result would be to raise the temperature 5 degrees. In that case, they would write 3 - (-2) = 5 How can we take away 2 cold cubes?

34 Show the expression using Zero Pairs.
And if they wrote = -11, it would mean that first 5 cold cubes were added and then 6 hot cubes were removed, and that the combined result was to lower the temperature 11 degrees. Show the expression using Zero Pairs.

35 Sometimes the chefs wanted to change the temperature of the soup without adding any cubes in. To do this they simply used their large ladle and scooped out hot or cold cubes. If they wanted to warm the soup up, they scooped out a ___________ cube. If they wanted to cool the soup down they scooped out a _____________ cube.

36 -5 - 2 = -7 Write the number sentence and solve.
Suppose one of the chefs accidentally tossed in 5 cold cubes and then removed 2 hot cubes to adjust the temperature. How would these actions have changed the temperature of the soup? Write the number sentence and solve. = -7

37 Cooking with Integers In pairs, use your manipulatives to model each problem. Then, write and solve a number sentence for each. Finally, write what the "Overall Temperature Change" would be for each problem. When finished, come up with a rule to describe how to subtract integers. We will discuss possible answers as a class.

38 Subtracting Integers Rule:
Keep Change Change or simply turn the two -'s into a + Give Example

39 Review: ALSO HW: Subtracting Integers Worksheet #1-20 3 + (-5) =
Adding Negatives is the same as Subtracting Positives. 3 + (-5) = Review: = ALSO Adding Positives is the same as Subtracting Negatives. 3 + 5 = 3 - (-5) = HW: Subtracting Integers Worksheet #1-20

40 If the signs are the same: Add/The sign stays.
Easy Rules: Addition: If the signs are the same: Add/The sign stays. If the signs are different: Subtract/ Use highest Absolute Value to find sign. Subtraction: Double Negatives: Change to positive. Regular: Add the opposite of 2nd number.

41 Adding and Subtracting Rational Numbers
- 1 __ 2 + 2 = 6 - 8 = __ 5 22 - ) ( __ 11 22 + = 3 - (-4) = 1.2 + (-0.5) = =

42 5 __ 6 __ 2 3 __ 3 4 - ( ) + 1

43 __ __ __ 3 1 4 - ( ) + 1 8 5 10

44 A football team gains 4 yards on each of 3 consecutive plays
A football team gains 4 yards on each of 3 consecutive plays. Find the total change in yards from where the team started. 50 40 30 20 10 End Zone

45 A football team gains 12 yards on their first play
A football team gains 12 yards on their first play. Loses 2 yards on their second play. And loses 15 yards on their third play. Find the total change in yards from where the team started. 50 40 30 20 10 End Zone

46 A football team loses 7 yards on each of 3 consecutive plays
A football team loses 7 yards on each of 3 consecutive plays. Find the total change in yards from where the team started. 50 40 30 20 10 End Zone

47 Review: Comparing, Adding, and Subtracting Integers worksheet HW:

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