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1. 1. Do Now <ul><li>Complete the Do Now questions 1-5. </li></ul>Herzog Lesson 14a Math Procedures Monday October 5, 2009
2. 2. WELCOME TO … Ms. Herzog’s Integers Lesson!
3. 3. What is an integer??? Any whole number. It can be positive or negative. ANSWER Adding Integers! Examples: 2, -5, 245, 0, 9, -1,399
4. 4. How do we add positive and negative integers? Think in terms of number chips Example: We can think of 4 as four positive chips +4
5. 5. How do we add positive and negative integers? Think in terms of number chips Another example: We can think of -3 as three negative chips -3
6. 6. How do we add positive and negative integers? Think in terms of number chips Another example: We can think of -8 as eight negative chips -8
7. 7. How do we add positive and negative integers? Think in terms of number chips Another example: We can think of 6 as six positive chips +6
8. 8. Let’s do an example! Use number chips! 4 + 7 ANSWER 11 +4 +7
9. 9. Let’s do an example! Use number chips! -2 + 5 ANSWER 3 One negative chip and one positive chip cancel! +5 -2
10. 10. Let’s do an example! Use number chips! 3 + (-5) ANSWER -2 One negative chip and one positive chip cancel! +3 -5
11. 11. Let’s do an example! Use number chips! -8 + 5 ANSWER -3 One negative chip and one positive chip cancel! -8 +5
12. 12. Let’s do an example! Use number chips! -3 + (-5) ANSWER -8 There are no chips to cancel! -5 -3
13. 13. -3 + (-8) -11 ANSWER Number Chips! -3 -8
14. 14. 4 + (-5) -1 ANSWER Number Chips! +4 -5
15. 15. -3 + 9 6 ANSWER Number Chips! -3 +9
16. 16. Classwork 14A <ul><li>Work on problems 1-10 from the handout </li></ul>Monday October 5, 2009
17. 17. Homework: Adding Integers Handout 1-15 Homework Math Procedures Herzog Lesson 14a
18. 18. Do Now <ul><li>Complete questions 1-5. </li></ul>Herzog Lesson 14b Math Procedures Tuesday October 6, 2009
19. 19. Let’s Continue… Ms. Herzog’s Integers Lesson!
20. 20. <ul><li>So the chip method works fine for adding and subtracting smaller numbers. (e.g. -4 + 7 = 3) </li></ul><ul><li>What if we need to add larger numbers? (e.g. 65 + (-34)) </li></ul><ul><li>Writing out 99 chips would not make sense! </li></ul>
21. 21. <ul><li>One way to solve these problems: </li></ul><ul><li>If the numbers you are adding have different signs , </li></ul><ul><li>Subtract the smaller number from the larger number, then </li></ul><ul><li>Determine which number is larger </li></ul><ul><li>The sign (positive or negative) of the answer will be the sign of the larger number </li></ul>
22. 22. Do the numbers have the same sign? Yes Add the numbers together No Subtract the smaller number from the larger number Is the positive or negative number larger? Answer = What sign? + is larger Final answer is positive - is larger Final answer is negative
23. 23. If the Beginning Signs are… Then the Calculation we do is… The End Sign of our answer is… Same Add Same Different Subtract The sign of the Larger number
24. 24. 28 + 63 1. We are adding and the numbers have the same signs <ul><li>Add: </li></ul><ul><li>28 + 63 = 91 </li></ul>ANSWER: 91
25. 25. (-12) + 34 1. We are adding and the numbers have different signs <ul><li>Subtract: </li></ul><ul><li>34 – 12 = 22 </li></ul>3. 34 is larger than 12 4. Since 34 is larger, and positive , the answer will be positive ANSWER: 22
26. 26. 24 + (-42) 1. We are adding and the numbers have different signs <ul><li>Subtract: </li></ul><ul><li>42 – 24 = 18 </li></ul>3. 42 is larger than 24 4. Since 42 is larger, and negative, the answer will be negative ANSWER: -18
27. 27. -64 + 39 1. We are adding and the numbers have different signs <ul><li>Subtract: </li></ul><ul><li>64 – 39 = 25 </li></ul>3. 64 is larger than 39 4. Since 64 is larger, and negative, the answer will be negative ANSWER: -25
28. 28. 83 + (-46) 1. We are adding and the numbers have different signs <ul><li>Subtract: </li></ul><ul><li>83 – 46 = 37 </li></ul>3. 83 is larger than 46 4. Since 83 is larger, and positive, the answer will be positive ANSWER: 37
29. 29. 57 + (-74) 1. We are adding and the numbers have different signs <ul><li>Subtract: </li></ul><ul><li>74 – 57 = 17 </li></ul>3. 74 is larger than 57 4. Since 74 is larger, and negative, the answer will be negative ANSWER: -17
30. 30. -132 + 231 1. We are adding and the numbers have different signs <ul><li>Subtract: </li></ul><ul><li>231 – 132 = 99 </li></ul>3. 231 is larger than 132 4. Since 231 is larger, and positive, the answer will be positive ANSWER: 99
31. 31. Classwork 14B <ul><li>15 + (-7) </li></ul><ul><li>-7 + 15 </li></ul><ul><li>-10 + (-18) </li></ul><ul><li>-34 + 17 </li></ul><ul><li>73 + (-25) </li></ul><ul><li>-45 + (-44) </li></ul><ul><li>55 + (-75) </li></ul><ul><li>99 + (21) </li></ul><ul><li>82 + (-19) </li></ul><ul><li>(-35) + 17 </li></ul><ul><li>22 + (-111) </li></ul><ul><li>64 + (-73) </li></ul><ul><li>254 + (153) </li></ul><ul><li>(-432) + (321) </li></ul>
32. 32. Homework: Adding Integers Handout 1-15 Homework Math Procedures Herzog Lesson 14b Tuesday October 6, 2009
33. 34. Subtracting Integers Lesson!
34. 35. Subtracting Integers Let’s start with signs What is the sign on: 17 Positive
35. 36. Subtracting Integers Let’s start with signs What is the sign on: -68 Negative
36. 37. Subtracting Integers Let’s start with signs What is the sign on: 5 Positive
37. 38. Subtracting Integers Let’s start with signs What is the sign on: -22 Negative
38. 39. Subtracting Integers Now let’s work on opposites What is the opposite of: 12 -12
39. 40. Subtracting Integers Now let’s work on opposites What is the opposite of: -45 45
40. 41. Subtracting Integers Now let’s work on opposites What is the opposite of: -9 9
41. 42. Subtracting Integers To subtract integers: Add the opposite of 11 9 - 11 9 + (-11) Evaluate using integer addition 9 + (-11) = -2
42. 43. Subtracting Integers To subtract integers: Add the opposite of 8 -6 - 8 -6 + (-8) Evaluate using integer addition -6 + (-8) = -14
43. 44. Subtracting Integers To subtract integers: Add the opposite of -9 -9 – (-9) -9 + (9) Evaluate using integer addition -9 + (9) = 0
44. 45. Subtracting Integers To subtract integers: Add the opposite of -1 5 – (-1) 5 + (1) Evaluate using integer addition 5 + (1) = 6
45. 46. Subtracting Integers To subtract integers: Add the opposite of 10 -4 – (10) -4 + (-10) Evaluate using integer addition -4 + (-10) = -14
46. 47. Subtracting Integers To subtract integers: Add the opposite of -8 2 – -8 2 + 8 Evaluate using integer addition 2 + 8 = 10
47. 48. Subtracting Integers To subtract integers: Add the opposite of -5 -3 – (-5) -3 + 5 Evaluate using integer addition -3 + 5 = 2
48. 49. Subtracting Integers To subtract integers: Add the opposite of 21 12 – 21 12 + (-21) Evaluate using integer addition 12 + (-21) = -9
49. 50. Subtracting Integers To subtract integers: Add the opposite of 5 and 2 -3 – 5 – 2 -3 + (-5) + (-2) Evaluate using integer addition = 10
50. 51. Classwork <ul><li>18 – (-48) </li></ul><ul><li>0 – (-14) </li></ul><ul><li>19 – (-10) </li></ul><ul><li>-20 – 32 </li></ul><ul><li>-1 – (-31) </li></ul><ul><li>-22 – (-9) </li></ul><ul><li>39 – (-13) </li></ul><ul><li>2 – (-31) </li></ul><ul><li>0 - 14 </li></ul><ul><li>42 – 27 </li></ul><ul><li>-43 – 19 </li></ul><ul><li>3 – (-18) </li></ul><ul><li>-9 – (-39) </li></ul><ul><li>3 – (-24) </li></ul><ul><li>-47 – 48 </li></ul><ul><li>-45 – (-33) </li></ul><ul><li>2 – (-8) </li></ul><ul><li>-14 – (-50) </li></ul>