1. Intro To Integers

2. Integers

3. -$1.24
-3.4 53
+$90
Integers
-21 +4
+ 1/2
-50%

5. Integers
Integers are whole numbers that describe opposite ideas in mathematics.
Integers can either be negative(-), positive(+) or zero.
The integer zero is neutral. It is neither positive nor negative, but is an integer.
Integers can be represented on a number line, which can help us understand the valve of the integer.

6. Positive Integers Are to the right of zero
Are valued greater than zero.
Express ideas of up, a gain or a profit.
The sign for a positive integer is (+), however the sign is not always needed.
Meaning +3 is the same value as 3.

7. Negative Integers Are to the left of zero Are valued less than zero.
Express ideas of down or a lose.
The sign for a negative integer is (-). This sign is always needed.

8. Zero is neither positive or negative
Positive integers
are valued more than zero, and are always to the right of zero.
Negative integers
are valued less than zero, and are always to the left of zero.

14. End of Part One

15. Representing Integers
- 1

16. - 4

17. + 3

18. - 3

19. + 2

20. + 2

21. + 2

22. + 2

23. Representing Integers
- 4 using 6 counters
+ 2 using 6 counters
0 using 6 counters
- 3 using 6 counters

24. Opposite Integers

25. The “net worth” of opposite integers is zero.

29. Opposite Integers
Opposite integers always have a “net worth” of 0. This is called the ZERO PRINCIPAL.
Opposite integer have the same “absolute value”, meaning the distance from the points on a number line to zero is the same.
This can be referred to as the integers magnitude.

30. Movement on a Number Line Magnitude and Direction
Every integer represents a magnitude and a direction.
The integer +3 describes a movement of 3 units in a positive direction.(right)
The sign (+) tells you the direction.
The number (3) indicates how far to move or the MAGNIUDE( a move- ment of 3 units)
+ 3
Direction
Magnitude

31. Which integer has a higher value?
Comparing Integers
Which integer has a higher value?
-4 or -8

35. Comparing Integers
Use your number line to help you compare each set of number.
(i.e. for the numbers 3 ,and - 2 …. 3 > < 3)
- 6, 7 b) 12, 3 c)- 5,- 8 d) 11, - 15
e) - 7, - 4 f) - 3, - 7 g) 7, - 8 h) - 13, -14

37. Putting Things Together
What is the greatest valued negative integer?

40. (3,5)
(4,-2)
(-1,-3)
(-2,1)

41. (4,5)
(-8,+3)
(-5.-1)
(-6,3)
(0,-7)

42. Comparing Integers
Use your number line to help you compare each set of numbers. Copy the question and write two sentences for each pair of numbers.
(i.e. for the numbers 3 ,and - 2 …. 3 > < 3)
- 6, 7 b) 12, 3 c)- 5,- 8 d) 11, - 15
e) - 7, - 4 f) - 3, - 7 g) 7, - 8 h) - 13, -14
i) 8, 7 j) - 8, - 7 k) 5, -1 l) 0, -2
m) 0, 3 n) - 5, 0 o) – 14, -10 p) - 9, 0
q) -7, -6 r) -1, 0 s) 4, -4 t) 0, -15

45. Comparing Integers Again
For each of the previous questions (a) to (t), write a new mathematical sentence showing how much bigger or smaller the first number is than the second.
(i.e. 3, - 2 ….. 3 is 5 more than –2)

46. Review What We Know

47. - 4

48. +1

50. -2

51. Direction
+ 3
Magnitude

52. Comparing Integers
-5 ___ -8
0 ___ -3
3 ___ +2

53. Quadrant l
(4,-5)
(-8,+3)
(-5,-1)

54. Intro To Adding Integers

55. Outcomes
A12 represent integers (including zero) concretely, pictorially, and symbolically, using a variety of models
B11 add and subtract integers concretely, pictorially, and symbolically to solve problem
B14 solve and pose problems which utilize addition of integers
B2 use mental math strategies for calculations involving integers

56. Lab Performance Evaluation
A – Student is performing beyond expected level.
B – Student is performing at upper range of expected level.
C – Student is performing at expected grade level
D – Student is performing at lower range of expected level.
E – Student is performing below expected level.

57. Areas of Evaluation Organization into activity Following directions
Presenting work neatly
Completion of work
Representing Integer sentences in words
Your ability to discover and represent Integer Rules
Making use of the Integer mat
Working quietly and cooperative

58. Net Result
Positive 9
(+5) + (+4) = +9 Or
(+4) + (+5) = +9

60. Finding The Sum of Positive Integers
When finding the sum of positive integers you add the magnitudes and keep the positive sign.

61. Net Result
Negative 10
(-3) + (-7) = -10 Or
(-7) + (-3) = -10

62. Finding The Sum of Negative Integers
When finding the sum of negative integers you add the magnitudes and keep the negative sign.

64. Net Result
Positive 2
(+7) + (-5) = +2 Or
(-5) + (+7) = +2

65. Finding The Sum of a Positive and a Negative Integer
When finding the sum of a positive and a negative integer you subtract the magnitudes and keep the sign of the integer with the largest magnitude.

67. Net Result
Zero
(+5) + (-5) = 0 Or
(-5) + (+5) = 0

68. Integer Recap You Have or Positive symbol means You’ve Earned
Negative symbol means
You Owe

69. (+3) + (-7)
(-5) + (-2)
(-3) + (-6) + (+4)
(+3) + (-2) + (+2)

70. (+50) + (-100)
(-25) + (+10)

71. Rules For Adding Integers
Positive Integers
To add two positive integers you add the magnitude and keep the positive sign.
Negative Integers
To add two negative integers you add the magnitude and keep the negative sign.
A Negative and a Positive Integer
To add a positive and a negative integer you subtract the magnitudes and keep the sign of the integer with the largest magnitude.

72. Intro To Subtracting Integers

73. (+5) – (+3) = +2
(+5) – (+3) =

74. (-6) – (-2) = -4
(-6) – (-2) =

75. (+3) – (+5) = -2
(+3) – (+5) =

76. (-2) – (-6) = +4
(-2) – (-6) =

77. (+3) – (-2) = +5
(+3) – (-2) =

78. (+1) – (+4) = -3
(+1) – (+4) =

79. (-5) – (+3) = -8
(-5) – (+3) =

80. (-2) – (-5) = +3
(-2) – (-5) =

81. Try These (-8) – (-3) = (+4) – (-5) = (-4) – (-5) = (+1) – (-6) =
(-5) – (+6) =
(-2) – (-3) =
(-20) – (-10) =
(+30) – (-3) =
(-20) – (-30) =

82. Try These (-3) – (-2) = (+6) – (-2) = (-1) – (-4) = (+3) – (-2) =
(-5) – (+2) =
(-2) – (-4) =
(-30) – (-20) =
(+50) – (-10) =
(-20) – (-30) =

83. Try These (-5) + (+2) = (+6) + (-2) = (-2) – (-6) = (+7) + (-2) =
(+8) + (-4) =
(-3) – (+6) =
(+50) – (-10) =
(-20) + (-30) =

84. Try These (-5) + (+2) = -3 (+6) + (-2) = +4 (-2) – (-6) = +4
(+7) + (-2) = +5
(+8) + (-4) = +4
(-3) – (+6) = -9
(+50) – (-10) = +60
(-20) + (-30) = -50

85. Multiplying and Dividing Integers

86. Intro To Multiplying and Dividing Integers
Site:
Go to Flashcards
Go to Non-Java Flashcards
Go to Adding, Subtracting, Multiplying and Dividing With Negative Numbers
Click on Multiplying (One by One) Use the site to help you complete the chart
Then, Go To Division (One by One)

87. (+2) x (+4) = +8
(+2) x (+4) =
This means you have two sets of four positive tiles or you have earned two groups of four dollars.

88. (+2) x (-4) = -8
(+2) x (-4) =
This means you have two sets of four negative tiles or you have two bills that you owe,each bill is for four dollars.

89. (-2) x (-4) = +8
(-2) x (-4) =
This means you don’t have two sets of four negative tiles or you don’t owe two bills, each bill is for four dollars.

90. (-2) x (+4) = -8
(-2) x (+4) =
This means you don’t have two sets of four positive tiles or you don’t have two groups of four dollars.

91. Try These (+3) x (-2) = (-2) x (-2) = (+5) x (-2) = (-3) x (+2) =

93. Try These (-91) x (-101) = (+152) x (-21) = (-19) x (+203) =

94. Try These (-91) x (-101) = (+152) x (-21) = (-19) x (+203) =

95. Multiplying Integers
FACTOR
PRODUCT + _

96. Dividing Integers
DIVIDEND
DIVISOR
QUOTIENT + _

97. Try These (-1) x (+1) x (-1) = (+1) x (+1) x (-1) =

98. Short Cuts For Multiplying Several Integer Factors
If there is an even number of negative signs, the product is positive
(-1) x (+1) x (-1) = +1
(+1) x (+1) x (-1) = -1
c. (-1) x (-1) x (+1) = +1
d. (-1) x (-1) x (-1) = -1
If there is an odd number of negative signs, the product is negative

99. Short Cuts For Multiplying Several Integer Factors
a. (-1) x (+1) x (-1) x (+1) =
b. (+1) x (+1) x (-1) x(-1) =
c. (-1) x (+1) x (-1) x (-1) x (+1) =
d. (-1) x (-1) x (-1) x (-1) x (+1) x (-1) =
e. (1) x (+1) x (-1) x (-1) x (+1) x (-1) =
(-1) x (-1) x (-1) x (-1) x (-1) x (-1) =
(-2) x (-3) x (-2) x (+1) =
(-1) x (-3) x (-2) x (-2) x (-3) =

100. Try These (-2) x (+2) x (-1)(-3)= (+1) x (+4) x (-5) =

101. (+2) x (+4) = +2
(+2) x (+4) =

102. Positive and Negative Integers
For each of the following numbers, write down an example of where it could be used and what it means in that situation. m
+3050m -$45.83

103. Order of Operations With Integers

104. Order of Operations With Integers
3 x (–7) + 4 x (-5)
15 + (+5)2 x 2
(-18) – 9 x 2

105. Practice for Problem Solving
Fiona spends $5 per week on bus fare. How much does she spend in 2 weeks?
Lucy spends 2 per week on snacks. How much does she spend in 4 weeks?
Anton earns $8 each week for baby-sitting. How much does he earn in 3 weeks?

106. Practice for Problem Solving
Lional pays $3 per day for bus transportation. How much does she pay in a school week?
Jill has $100 in the bank. She owes 3 of her friends $10 dollars each. What is her net worth?