This Week in Math…

1. This Week in Math… • Monday: Are we really ready for a test in two days?? Pretest WAKE UP call!! Go over/ Correct! and glue in notebook as a study guide for test! HW- Integer Puzzle Sheet, Test Tuesday! • Tuesday: Review +,- integers using number line and counters. Multiply Integers on a Number Line, Jeopardy Test Review Game, HW- Test Tomorrow! Review Interactive Notebook Complete HW Review Sheet. • Wednesday: Review Huddle, Test on Integers, Complete Scholastic Math Magazine Activities. Weekly Review 1 sheet only! • Thursday: Go over the test and correct, Complete I Can… Statements, Introduce/Review Exponents and Play Expo Calculator Races or Exponent Bingo? HW-Worksheet • Friday: More Exponents including exponents with negative bases, like -3 squared, -(3)squared, (-3)squared, -(3 squared), No homework. • Next week: Order of Operations!

2. Inventing a New Model Yesterday, you used the number line to help you think about adding integers. In this problem, you will explore another way to model the addition of integers. Amber’s mother is an accountant. One day, Amber heard her mother talking to a client on the phone. During the conversation, her mother used the phrases “in the red” and “in the black”.

3. That evening at dinner, Amber asked her mother what these terms meant. Her mother said: “When people in business talk about income and expenses, they often use colors to often describe the numbers they are dealing with. Black refers to profits (or income); A company that is making money, or has money, is “in the black”; Red refers to losses (or expenses). A company that is losing money or owes money, is “in the red.”

4. Amber was studying Integers in her math class and thought she could use these ideas of “in theblack” and “in the red” to model the addition of positive and negative integers. Chip Board = +1 = -1 Her model uses a chip board and black and red chips. Each black chip represents +1 and each red chip represents -1. For example, this chip board shows a value of +5:

5. = +1 = -1 Chip Board This chip board shows a value of -5

6. Chip Board To represent -4 + -3 =, Amber started with an empty chip board. She represented -4 by putting four red chips on the board. To represent the addition of -3, she put three more red chips on the board. Since there were 7 red chips on the board, Amber concluded that the sum (answer) of -4 and -3 is -7. -4 + -3 = -7

7. = +1 = -1 Chip Board Amber showed her idea to Adil. Adil liked Amber’s model, but he wasn’t sure how to use it to add a negative number and a positive integer. Amber modeled the next problem using the chip board: -4 + +5 Amber started with an empty chip board. She put 4 red chips on the board to represent -4. To add +5, Amber added five black chips to the board.

8. Amber said that next she had to simplify the board so that the answer would be easier to read. She reminded Adil that +1 and -1 are opposites, they add to 0. So a pair of one black chip (+1) and one red chip (-1) represents 0. Amber circled as many black-red pairs as she could. Chip Board -4 + +5 = +1 Since each pair represents 0, the pairs are removed from the chip board and not counted. Only one black chip remains, that represents the answer or sum. +1

9. Chip Board Now, let’s try one more addition problem together. +8 + -6 = +2 First you put 8 black chips to represent +8. The answer to the sum is +2 because only 2 black chips are left on the chip board. Remove all the black-red pairs because they represent 0.

10. = +1 = -1 Try These on Your Dry Erase Board Using Two Different Colors Counters! Make a key to indicate which color will be negative and which will be positive. • -8 + (-10)= • 9 + (-12)= • -3 + 11=

11. = +1 = -1 Subtracting Integers with Counters • Add the Opposite!! • Same, Change, Change!!!!!!

12. CHIP BOARD CHIP BOARD -6 – (-2)= Set up problem on board with 6 negative chips, then add back the opposite: SCC – (-2)= + (+2) Red and Black pairs cancel out which is why they are called zero pairs! How many chips are left? Negatives or Positives?

13. CHIP BOARD Try it yourself now, draw a chip board for the number sentence below. –8 – (– 7)= The answer is –1!!!

14. CHIP BOARD -1 = +1 = • Try These using your Counters: • 6 – (-12)= • 5 – 11 = • -3 – (-13)=

15. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Adding And Subtracting On a Number Line!

16. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Whole numbers are numbers like 0, 1,2,3,4,5,6 If we go to the left of 0, then we find a list of numbers on the number line called integers. These are negative integers These are positive integers 0 is neither negative or positive

17. Adding Integers -10 -10 -9 -9 -8 -8 -7 -7 -6 -6 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 3 + 2 = Both the 3 and the 2 are positive numbers. That means that you begin at 0 and go right to 3. Then from 3, you go 2 more spaces to the right because 2 is positive also. Now, when you have negative numbers you follow the same idea, but you move to the left of the number line. Like this: -3 + -2= -5

18. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Adding negative integers with positive integers When you add a negative integer with a positive integer, you need to follow these steps: -3 + +2 = ? Start at 0, move three units to the left because it is the negative direction that represents -3. To show you added +2, you move 2 units to the right because it is the positive direction that represents +2. Where do you end up?

19. -10 -10 -9 -9 -8 -8 -7 -7 -6 -6 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 Addition Sentences using Number lines How would you write a number sentence for the following? Could it be this? -3 + -4 = -7 What is your answer? Now, try this one; -3+ +5 =+2

20. Now, try these on separate number lines. 1. -5 + +8 = 2. -4 + +9 = 3. -2 + -3 + +10 =

21. Example 2: (-2) + 5 • Our car starts from 0 facing right. • It then backs up 2 units (to the left) because it sees the - sign.

22. Example 2: (-2)+ 5 • Our car starts from 0 facing right. • It then backs up 2 units (to the left) because it sees the - sign. • Next it will move forward by 5 units.(click to see animation)

23. Example 2: (-2)+ 5 • Our car starts from 0 facing right. • It then backs up 2 units (to the left) because it sees the - sign. • Next it will move forward by 5 units.

24. Example 2: (-2)+ 5 • Our car starts from 0 facing right. • It then backs up 2 units (to the left) because it sees the - sign. • Next it will move forward by 5 units.

25. Example 2: (-2)+ 5 • Our car starts from 0 facing right. • It then backs up 2 units (to the left) because it sees the - sign. • Next it will move forward by 5 units.Now it stops at +3, therefore the answer to (-2) + 5 is 3. Please go to the next tutorial for subtractions.

26. Subtraction • There is a big difference between addition and subtraction. • In addition, our car is always facing right, because that is the positive direction, • but in subtraction, the car has to turn around (180 deg) first. Click when you are ready.

27. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units.(Click to start animation)

28. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units.

29. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units.

30. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units.

31. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units. • Next it will turn around because it sees the subtraction symbol – . • Click to see animation.

32. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units. • Next it will turn around because it sees the subtraction symbol – .

33. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units. • Next it will turn around because it sees the subtraction symbol – .

34. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units. • Next it will turn around because it sees the subtraction symbol – . • Our car still starts at 0 facing right. • It then moves forward 5 units. • Next it will turn around because it sees the subtraction symbol – . • Finally it will move forward (to the left) by 3 units. • click to see animation.

35. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units. • Next it will turn around because it sees the subtraction symbol – . • Finally it will move forward (to the left) by 3 units.

36. Example 3: 5 – 3 • Our car still starts at 0 facing right. • It then moves forward 5 units. • Next it will turn around because it sees the subtraction symbol – . • Finally it will move forward (to the left) by 3 units. Since the car stops at 2, the answer to 5 – 3 must be 2. Click to see the next example.

37. Example 4: (-4) – 2 • Our car still starts at 0 facing right. • It then backs up 4 units because it sees the negative symbol - in front of 4.(Click to see animation.)

38. Example 4: (-4) – 2 • Our car still starts at 0 facing right. • It then backs up 4 units because it sees the negative symbol - in front of 4.

39. Example 4: (-4) – 2 • Our car still starts at 0 facing right. • It then backs up 4 units because it sees the negative symbol - in front of 4.

40. Example 4: (-4) – 2 • Our car still starts at 0 facing right. • It then backs up 4 units because it sees the negative symbol - in front of 4.

41. Example 4: (-4) – 2 • Our car still starts at 0 facing right. • It then backs up 4 units because it sees the negative symbol - in front of 4. • Now it has turn around because of the subtraction symbol –. (click to go on)

42. Example 4: (-4) – 2 • Our car still starts at 0 facing right. • It then backs up 4 units because it sees the negative symbol - in front of 4. • Now it has turn around because of the subtraction symbol –.

43. Example 4: (-4) – 2 • Our car still starts at 0 facing right. • It then backs up 4 units because it sees the negative symbol - in front of 4. • Now it has turn around because of the subtraction symbol –.

44. Example 4: (-4) –2 • Finally it moves forward by 2 units. (click to go on)

45. Example 4: (-4) –2 • Finally it moves forward by 2 units.

46. Example 4: (-4) –2 • Finally it moves forward by 2 units.

47. Example 4: (-4) –2 • Finally it moves forward by 2 units.

48. Example 4: (-4) –2 • Finally it moves forward by 2 units.

49. Example 4: (-4) – 2 • Finally it moves forward by 2 units. The car now stops at -6, therefore the answer to (-4) – 2 is -6. Click to see the next example.

50. Example 5: 2 – (-3) • Our car starts from 0 facing right. • It then moves 2 units to the right. • (Click to see animation)