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Math 902 Transition to Algebra and Problem Solving Words  Pictures.

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Presentation on theme: "Math 902 Transition to Algebra and Problem Solving Words  Pictures."— Presentation transcript:

1 Math 902 Transition to Algebra and Problem Solving Words  Pictures

2 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is thirteen units larger than x. (sum) Problem #1 Words  Pictures

3 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is thirteen units larger than x. (sum) Problem #1 Words  Pictures

4 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is five units less than x. (difference) Problem #2 Words  Pictures

5 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is five units less than x. (difference) Problem #2 Words  Pictures

6 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is four times larger than x. (product) Problem #3 Words  Pictures

7 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is four times larger than x. (product) Problem #3 Words  Pictures

8 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is one-third of x. (fractional part) Problem #4 Words  Pictures

9 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is one-third of x. (fractional part) Problem #4 Words  Pictures

10 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is one less than twice the value of x. Problem #5 Words  Pictures

11 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is one less than twice the value of x. Problem #5 Words  Pictures

12 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is eight more than half the value of x. Problem #6 Words  Pictures

13 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is eight more than half the value of x. Problem #6 Words  Pictures

14 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is six more than one-fifth the value of x. Problem #7 Words  Pictures

15 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is six more than one-fifth the value of x. Problem #7 Words  Pictures

16 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is one-sixth of three more than the value of x. Problem #8 Words  Pictures

17 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is one-sixth of three more than the value of x. Problem #8 Words  Pictures

18 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is three times the difference of the value of x and five. Problem #9 Words  Pictures

19 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Problem #9 Words  Pictures Illustrate a rectangle that is three times the difference of the value of x and five.

20 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustrate a rectangle that is one-quarter of the sum of three times the value of x and two. Problem #10 Words  Pictures

21 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Problem #10 Words  Pictures Illustrate a rectangle that is one-quarter of the sum of three times the value of x and two.

22 Math 902 Transition to Algebra and Problem Solving Order of Operations  Pictures

23 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. EXAMPLE #1 Order of Operations  Pictures Single Operation 1 Op 1 SUM

24 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. EXAMPLE #2 Order of Operations  Pictures 2 Operations Op 1 DIVISION Op 2 SUBTRACTION 1 2

25 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. EXAMPLE #3 Order of Operations  Pictures 3 Operations Op 1 DIVISION Op 2 SUM Op 3 TIMES

26 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. EXAMPLE #4 Order of Operations  Pictures 4 Operations Op 1 TIMES Op 2 DIFFERENCE Op 3 DIVISION Op 4 SUM

27 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. EXAMPLE #5 Order of Operations  Pictures 5 Operations Op 1 DIVIDE Op 2 SUM Op 3 TIMES Op 4 SUM Op 5 DIVIDE

28 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #1 Order of Operations  Pictures

29 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #1 Order of Operations  Pictures

30 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #2 Order of Operations  Pictures

31 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #2 Order of Operations  Pictures

32 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #3 Order of Operations  Pictures

33 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #3 Order of Operations  Pictures

34 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #4 Order of Operations  Pictures

35 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #4 Order of Operations  Pictures

36 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #5 Order of Operations  Pictures

37 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #5 Order of Operations  Pictures

38 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #6 Order of Operations  Pictures

39 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #6 Order of Operations  Pictures

40 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #7 Order of Operations  Pictures

41 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #7 Order of Operations  Pictures

42 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #8 Order of Operations  Pictures

43 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #8 Order of Operations  Pictures

44 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #9 Order of Operations  Pictures

45 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #9 Order of Operations  Pictures

46 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #10 Order of Operations  Pictures

47 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right by first determining the order of operations and then constructing the illustration determined by the order in which the expression is evaluated. Problem #10 Order of Operations  Pictures

48 Math 902 Transition to Algebra and Problem Solving Symbols  Pictures “FREE RESPONSE with your mind! THINK it out without the Order of Operations.”

49 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #1 Symbols  Pictures

50 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #1 Symbols  Pictures

51 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #2 Symbols  Pictures

52 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #2 Symbols  Pictures

53 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #3 Symbols  Pictures

54 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #3 Symbols  Pictures

55 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #4 Symbols  Pictures

56 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #4 Symbols  Pictures

57 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #5 Symbols  Pictures

58 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #5 Symbols  Pictures

59 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #6 Symbols  Pictures

60 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #6 Symbols  Pictures

61 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #7 Symbols  Pictures

62 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #7 Symbols  Pictures

63 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #8 Symbols  Pictures

64 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #8 Symbols  Pictures

65 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #9 Symbols  Pictures

66 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #9 Symbols  Pictures

67 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #10 Symbols  Pictures

68 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #10 Symbols  Pictures

69 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #11 Symbols  Pictures

70 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #11 Symbols  Pictures

71 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #12 Symbols  Pictures

72 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #12 Symbols  Pictures

73 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #13 Symbols  Pictures

74 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #13 Symbols  Pictures

75 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #14 Symbols  Pictures

76 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #14 Symbols  Pictures

77 Math 902 THIS IS A TOUGH ONE! Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #15 Symbols  Pictures

78 Math 902 THIS IS A TOUGH ONE! Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #15 Symbols  Pictures

79 Math 902 Transition to Algebra and Problem Solving At the end of this section, let me know if these tasks are more difficult than the two earlier sets of tasks. you think Pictures  Symbols

80 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #1 Pictures  Symbols What is the Algebraic Expression?

81 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #1 Pictures  Symbols What is the Algebraic Expression?

82 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #2 Pictures  Symbols What is the Algebraic Expression?

83 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #2 Pictures  Symbols What is the Algebraic Expression?

84 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #3 Pictures  Symbols What is the Algebraic Expression?

85 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #3 Pictures  Symbols What is the Algebraic Expression?

86 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #4 Pictures  Symbols What is the Algebraic Expression?

87 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #4 Pictures  Symbols What is the Algebraic Expression?

88 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #5 Pictures  Symbols What is the Algebraic Expression?

89 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #5 Pictures  Symbols What is the Algebraic Expression?

90 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #6 Pictures  Symbols What is the Algebraic Expression?

91 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #6 Pictures  Symbols What is the Algebraic Expression?

92 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #7 Pictures  Symbols What is the Algebraic Expression?

93 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #7 Pictures  Symbols What is the Algebraic Expression?

94 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #8 Pictures  Symbols What is the Algebraic Expression?

95 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #8 Pictures  Symbols What is the Algebraic Expression?

96 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #9 Pictures  Symbols What is the Algebraic Expression?

97 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #9 Pictures  Symbols What is the Algebraic Expression?

98 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #10 Pictures  Symbols What is the Algebraic Expression?

99 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #10 Pictures  Symbols What is the Algebraic Expression?

100 Math 902 You’ve been here before Transition to Algebra and Problem Solving Pictures  Solution We’re going to solve equations made from the expressions in the last two sections for the unknown values of x. Let’s demonstrate your logic and math.

101 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #1 Pictures  Solution The expression has a value of 52; so what is the value of x? 52

102 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 45 Problem #1 Pictures  Solution The expression has a value of 52; so what is the value of x? 52

103 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #2 Pictures  Solution The expression has a value of 50; so what is the value of x?

104 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #2 Pictures  Symbols The expression has a value of 50; so what is the value of x? x = 38

105 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #3 Pictures  Symbols The expression has a value of 45; so what is the value of x? 45

106 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #3 Pictures  Symbols The expression has a value of 45; so what is the value of x? 45 x = 53

107 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #4 Pictures  Solution The expression has a value of 55; so what is the value of x? 55

108 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 64 Problem #4 Pictures  Solution The expression has a value of 55; so what is the value of x? 55

109 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #5 Pictures  Solution The expression has a value of 75; so what is the value of x? 75

110 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 15 Problem #5 Pictures  Solution The expression has a value of 75; so what is the value of x? 75

111 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #6 Pictures  Solution The expression has a value of 12; so what is the value of x? 12

112 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 36 Problem #6 Pictures  Solution The expression has a value of 12; so what is the value of x? 12

113 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #7 Pictures  Solution The expression has a value of 15; so what is the value of x? 15

114 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 40 Problem #7 Pictures  Solution The expression has a value of 15; so what is the value of x? 15

115 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #8 Pictures  Solution The expression has a value of 90; so what is the value of x? 90

116 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 54 Problem #8 Pictures  Solution The expression has a value of 90; so what is the value of x? 90

117 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #9 Pictures  Solution The expression has a value of 52; so what is the value of x? 52

118 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 16 Problem #9 Pictures  Solution The expression has a value of 52; so what is the value of x? 52

119 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #10 Pictures  Solution The expression has a value of 73; so what is the value of x? 73

120 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 20 Problem #10 Pictures  Solution The expression has a value of 73; so what is the value of x? 73

121 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #11 Pictures  Symbols The expression has a value of 14; so what is the value of x? 14

122 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #11 Pictures  Symbols The expression has a value of 14; so what is the value of x? x = 22 14

123 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #12 Pictures  Symbols The expression has a value of 35; so what is the value of x? 35

124 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #12 Pictures  Symbols The expression has a value of 35; so what is the value of x? 35 x = 11

125 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #13 Pictures  Solution The expression has a value of 25; so what is the value of x? 25

126 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 28 Problem #13 Pictures  Solution The expression has a value of 25; so what is the value of x? 25

127 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #14 Pictures  Solution The expression has a value of 13; so what is the value of x? 13

128 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 24 Problem #14 Pictures  Solution The expression has a value of 13; so what is the value of x? 13

129 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #15 Pictures  Solution The expression has a value of 30; so what is the value of x? 30

130 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 6 Problem #15 Pictures  Solution The expression has a value of 30; so what is the value of x? 30

131 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #16 Pictures  Solution The expression has a value of 5; so what is the value of x? 5

132 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 21 Problem #16 Pictures  Solution The expression has a value of 5; so what is the value of x? 5

133 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #17 Pictures  Symbols 20 The expression has a value of 20; so what is the value of x?

134 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #17 Pictures  Symbols x = The expression has a value of 20; so what is the value of x?

135 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #18 Pictures  Symbols The expression has a value of 22; so what is the value of x? 22

136 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #18 Pictures  Symbols The expression has a value of 22; so what is the value of x? 22 x = 3

137 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #19 Pictures  Symbols The expression has a value of 26; so what is the value of x? 26

138 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #19 Pictures  Symbols The expression has a value of 26; so what is the value of x? 26 x = 7

139 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #20 Pictures  Symbols The expression has a value of 10; so what is the value of x? 10

140 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #20 Pictures  Symbols The expression has a value of 10; so what is the value of x? 10 x = 52

141 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #21 Pictures  Symbols The expression has a value of 9; so what is the value of x? 9

142 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #9 Pictures  Symbols Problem #21 Pictures  Symbols The expression has a value of 9; so what is the value of x? 9 x = 7

143 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: Problem #22 Pictures  Symbols 4 The expression has a value of 8; so what is the value of x?

144 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the quantity requested. Illustration: x = 27 Problem #22 Pictures  Symbols 4 The expression has a value of 8; so what is the value of x?

145 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #23 Pictures  Solution The expression has a value of 80; so what is the value of x? 80

146 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 55 Problem #23 Pictures  Solution The expression has a value of 80; so what is the value of x? 80

147 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #24 Pictures  Solution The expression has a value of 15; so what is the value of x? 15

148 Math 902 Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 6 Problem #24 Pictures  Solution The expression has a value of 15; so what is the value of x? 15

149 Math 902 THIS IS A TOUGH ONE! Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. Problem #25 Pictures  Solution The expression has a value of 0.75; so what is the value of x? 0.75

150 Math 902 THIS IS A TOUGH ONE! Transition to Algebra and Problem Solving Using the rectangle below representing an unknown value, x, illustrate the expression at the right. x = 15 Problem #25 Pictures  Solution The expression has a value of 0.75; so what is the value of x? 0.75

151 Math 902 Recalling the Order of Operations Transition to Algebra and Problem Solving Symbols  Solution

152 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving As demonstrated in our examples in class, to solve an equation involving: ADDITION, we do the opposite and SUBTRACT, SUBTRACTION, we do the opposite and ADD, MULTIPLICATION, We do the opposite and DIVIDE, DIVISION, we do the opposite and MULTIPLY. Examples #1 Symbols  Solution

153 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra If an equation involves more than one operation, before you solve for x: Suppose a value was assigned for x, number the order in which the expression is evaluated and solve in “reverse” order. Examples #2 Symbols  Solution

154 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving If an equation involves more than one operation, before you solve for x: Suppose a value was assigned for x, number the order in which the expression is evaluated and solve in “reverse” order. Examples #3 Symbols  Solution

155 Problem #1 Symbols  Solution x = Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Solve for x:

156 Problem #1 Symbols  Solution x = Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Solve for x: 19

157 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Solve for x: Problem #2 Symbols  Solution x =

158 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Solve for x: Problem #2 Symbols  Solution x = 68

159 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Solve for x: Problem #3 Symbols  Solution x =

160 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Solve for x: Problem #3 Symbols  Solution x = 13

161 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Solve for x: Problem #4 Symbols  Solution x =

162 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Solve for x: Problem #4 Symbols  Solution x = 45

163 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #5 Symbols  Solution x = Solve for x: (First number the order in which the expression is computed and work backwards.)

164 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #5 Symbols  Solution x = Solve for x: (First number the order in which the expression is computed and work backwards.)

165 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #6 Symbols  Solution x = Solve for x: (First number the order in which the expression is computed and work backwards.)

166 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #6 Symbols  Solution x = Solve for x: (First number the order in which the expression is computed and work backwards.)

167 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #7 Symbols  Solution x = Solve for x: (First number the order in which the expression is computed and work backwards.)

168 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #7 Symbols  Solution x = 23 Solve for x: (First number the order in which the expression is computed and work backwards.) 2 1

169 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #8 Symbols  Solution x = Solve for x: (First number the order in which the expression is computed and work backwards.)

170 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #8 Symbols  Solution x = 5 Solve for x: (First number the order in which the expression is computed and work backwards.)

171 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #9 Symbols  Solution x = Solve for x: (First number the order in which the expression is computed and work backwards.)

172 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #9 Symbols  Solution x = 7 Solve for x: (First number the order in which the expression is computed and work backwards.) 2 1 3

173 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #10 Symbols  Solution x = Solve for x: (First number the order in which the expression is computed and work backwards.)

174 Math 902 To draw or not to draw, it’s your choice. Transition to Algebra and Problem Solving Problem #10 Symbols  Solution x = 20 Solve for x: (First number the order in which the expression is computed and work backwards.)

175 Math 902 THIS IS WHAT IT IS ALL ABOUT! Transition to Algebra and Problem Solving Words  Solution Applications (some from your text)

176 TV Watching. On average, people age 12 or older spent 1704 hours watching TV in This is 202 more than in Determine the number of hours people in this age group spent watching TV in Math 902 Transition to Algebra and Problem Solving Problem #1 Words  Solution FROM YOUR TEXT on page 65 problem # 9 PROBLEM FROM TEXTBOOK

177 Longest Rivers. The longest river in the world is the Amazon in South America at about 4225 miles. The longest river in the United States is the Missouri-Mississippi at about 3860 miles. How much longer is the Amazon? Math 902 Transition to Algebra and Problem Solving Problem #2 Words  Solution FROM YOUR TEXT on page 65 problem # 12 PROBLEM FROM TEXTBOOK

178 Motorcycle Sales. Motorcycle sales totaled 521,000 in the United States in Sales in 2006 exceeded this total by 669,000. How many motorcycles were sold in 2006? Math 902 Transition to Algebra and Problem Solving Problem #3 Words  Solution FROM YOUR TEXT on page 67 problem # 27 PROBLEM FROM TEXTBOOK

179 Yard-Sale Profit. Ruth made $312 at her yard sale and divided the money equally among her four grandchildren. How much did each child receive? Math 902 Transition to Algebra and Problem Solving Problem #4 Words  Solution FROM YOUR TEXT on page 67 problem # 29 PROBLEM FROM TEXTBOOK

180 Refrigerator Purchase. Gourmet Deli has a chain of 24 restaurants. It buys commercial refrigerator for each store at a cost of $1019 each. Determine the total cost of the purchase. Math 902 Transition to Algebra and Problem Solving Problem #5 Words  Solution FROM YOUR TEXT on page 67 problem # 33 PROBLEM FROM TEXTBOOK

181 Elena buys 5 video games at $64 each and pays them with $10 bills. How many $10 bills does it take? Math 902 Transition to Algebra and Problem Solving Problem #6 Words  Solution FROM YOUR TEXT on page 69 problem # 49 PROBLEM FROM TEXTBOOK

182 The balance in Dylan’s bank account is $749. He uses his debit card for purchases of $34 and $65. Then me makes a deposit of $123 from his paycheck. What is his new balance? Math 902 Transition to Algebra and Problem Solving Problem #7 Words  Solution FROM YOUR TEXT on page 69 problem # 52 PROBLEM FROM TEXTBOOK

183 A mining company estimates that a crew must tunnel 2000 feet into a mountain to reach a deposit of copper ore. Each day, the crew tunnels about 500 feet. Each night, about 200 feet of lose rocks rolls back into the tunnel. How many days will it take the mining company to reach the copper deposit? Math 902 Transition to Algebra and Problem Solving Problem #8 Words  Solution FROM YOUR TEXT on page 84 problem # 67 PROBLEM FROM TEXTBOOK

184 Laura has a charge of $477 on her credit card, but she then returns a sweater that costs $129. How much does she now owe on her credit card? Math 902 Transition to Algebra and Problem Solving Problem #9 Words  Solution FROM YOUR TEXT on page 103 problem # 72 PROBLEM FROM TEXTBOOK

185 Surface Temperature on Mercury. Surface temperatures on Mercury vary from 840°F on the equator when the planet is closest to the sun to -290°F at night. Find the difference between these temperatures. Math 902 Transition to Algebra and Problem Solving Problem #10 Words  Solution FROM YOUR TEXT on page 104 problem # 104 PROBLEM FROM TEXTBOOK

186 Peter had $4.00 while Mary had $7.oo. How much did they have altogether? Math 902 Transition to Algebra and Problem Solving Problem #1 Words  Solution

187 Peter had $4.00 while Mary had $7.oo. How much did they have altogether? Math 902 Transition to Algebra and Problem Solving Problem #1 Words  Solution

188 Jim took $23.00 with him to go shopping. His sister, Loretta took $13.00 more than he did. How much did Loretta take shopping? Math 902 Transition to Algebra and Problem Solving Problem #2 Words  Solution

189 Jim took $23.00 with him to go shopping. His sister, Loretta took $13.00 more than he did. How much did Loretta take shopping? Math 902 Transition to Algebra and Problem Solving Problem #2 Words  Solution

190 Barbara fills a container with 9 cartons of maple syrup. Each carton contains 2 quarts of maple syrup. What is the capacity of the container (in quarts)? Math 902 Transition to Algebra and Problem Solving Problem #3 Words  Solution

191 Bonnie spent a total of $140 on her car. Jim spent 5 times the amount that Bonnie spent. What was the total spent by Bonnie and Jim? Math 902 Transition to Algebra and Problem Solving Problem #4 Words  Solution

192 Bonnie spent a total of $140 on her car. Jim spent 5 times the amount that Bonnie spent. What was the total spent by Bonnie and Jim? Math 902 Transition to Algebra and Problem Solving Problem #4 Words  Solution

193 Jerry weighed himself. His weight was 175 lbs. He was 5 times heavier than his brother, Sam. What was the difference in their weight? Math 902 Transition to Algebra and Problem Solving Problem #5 Words  Solution

194 Jerry weighed himself. His weight was 175 lbs. He was 5 times heavier than his brother, Sam. What was the difference in their weight? Math 902 Transition to Algebra and Problem Solving Problem #5 Words  Solution

195 Mary had a box of mangos. After giving 3 mangos each to 7 children, she had 20 left. How many mangos were there in the box at first? Math 902 Transition to Algebra and Problem Solving Problem #6 Words  Solution

196 Mary had a box of mangos. After giving 3 mangos each to 7 children, she had 20 left. How many mangos were there in the box at first? Math 902 Transition to Algebra and Problem Solving Problem #6 Words  Solution

197 Dylan bought 4 boxes of cookies. There were 12 chocolate and 8 sugar cookies in each box. He put together a platter of 40 chocolate and 25 sugar cookies for church. How many of each kind of cookies did he have left? Math 902 Transition to Algebra and Problem Solving Problem #7 Words  Solution

198 Dylan bought 4 boxes of cookies. There were 12 chocolate and 8 sugar cookies in each box. He put together a platter of 40 chocolate and 25 sugar cookies for church. How many of each kind of cookies did he have left? Math 902 Transition to Algebra and Problem Solving Problem #7 Words  Solution

199 Mary had 1240 picture cards. She kept 80 cards for herself and gave the rest to a group of children. Each child received 8 cards. How many children were in the group? Math 902 Transition to Algebra and Problem Solving Problem #8 Words  Solution

200 Mary had 1240 picture cards. She kept 80 cards for herself and gave the rest to a group of children. Each child received 8 cards. How many children were in the group? Math 902 Transition to Algebra and Problem Solving Problem #8 Words  Solution

201 Each pen cost 85 cents while a package of 3 pencils costs 65 cents. Kyle purchased 8 pens and 12 pencils. How much did Kyle spend on his purchase? Math 902 Transition to Algebra and Problem Solving Problem #9 Words  Solution

202 Each pen cost 85 cents while a package of 3 pencils costs 65 cents. Kyle purchased 8 pens and 12 pencils. How much did Kyle spend on his purchase? Math 902 Transition to Algebra and Problem Solving Problem #9 Words  Solution

203 For the past 4 months, Grace’s salary was $1895 per month. She saved $3032 during the 4 months and spent the rest. How much did she spend? Math 902 Transition to Algebra and Problem Solving Problem #10 Words  Solution

204 For the past 4 months, Grace’s salary was $1895 per month. She saved $3032 during the 4 months and spent the rest. How much did she spend? Math 902 Transition to Algebra and Problem Solving Problem #10 Words  Solution

205 Bob had a total of $825 to spend on Christmas shopping. He spent 2/3 of it on his wife’s present. How much did he spend on his wife’s present? Math 902 Transition to Algebra and Problem Solving Problem #11 Words  Solution

206 Simi withdrew $1224 from his savings. He spent half of it on fixing his car. One-third of what he had remaining was used for school. How much did he have left? Math 902 Transition to Algebra and Problem Solving Problem #12 Words  Solution

207 Simi withdrew $1224 from his savings. He spent half of it on fixing his car. One-third of what he had remaining was used for school. How much did he have left? Math 902 Transition to Algebra and Problem Solving Problem #12 Words  Solution

208 Sally took three-eight of a cake to her office to share with her office mates, and her sister ate one-fifth of the remaining portion. What fraction of the cake was left? Math 902 Transition to Algebra and Problem Solving Problem #13 Words  Solution

209 Sally took three-eight of a cake to her office to share with her office mates, and her sister ate one-fifth of the remaining portion. What fraction of the cake was left? Math 902 Transition to Algebra and Problem Solving Problem #13 Words  Solution

210 Judy bought some eggs. She used 2/5 of the eggs to bake cakes. She had 18 eggs left. How many eggs did she did she buy? Math 902 Transition to Algebra and Problem Solving Problem #14 Words  Solution

211 Judy bought some eggs. She used 2/5 of the eggs to bake cakes. She had 18 eggs left. How many eggs did she did she buy? Math 902 Transition to Algebra and Problem Solving Problem #14 Words  Solution

212 Fred could not divide the amount of money in his pocket equally among his 4 kids. His wife gave him an additional $3 after which each of his 4 kids received $8. How much money did Fred have at the beginning? Math 902 Transition to Algebra and Problem Solving Problem #15 Words  Solution

213 Fred could not divide the amount of money in his pocket equally among his 4 kids. His wife gave him an additional $3 after which each of his 4 kids received $8. How much money did Fred have at the beginning? Math 902 Transition to Algebra and Problem Solving Problem #15 Words  Solution

214 Cindy received 2/5 of her grandfather’s estate which totaled $220,000. How much did she receive? Math 902 Transition to Algebra and Problem Solving Problem #16 Words  Solution

215 Cindy received 2/5 of her grandfather’s estate which totaled $220,000. How much did she receive? Math 902 Transition to Algebra and Problem Solving Problem #16 Words  Solution

216 Marian’s portion of lottery ticket winnings was $1,575,000 which was 3/8 of the total. How much was the total winnings? Math 902 Transition to Algebra and Problem Solving Problem #17 Words  Solution

217 Marian’s portion of lottery ticket winnings was $1,575,000 which was 3/8 of the total. How much was the total winnings? Math 902 Transition to Algebra and Problem Solving Problem #17 Words  Solution

218 Jimmy shops at the farmer’s market each weekend and buys twice as many bananas compared to the total amount of all the other fruits he purchases. he purchased 7 apples, 4 pears, and 3 oranges. How many bananas did he buy? Math 902 Transition to Algebra and Problem Solving Problem #18 Words  Solution

219 Jimmy shops at the farmer’s market each weekend and buys twice as many bananas compared to the total amount of all the other fruits he purchases. he purchased 7 apples, 4 pears, and 3 oranges. How many bananas did he buy? Math 902 Transition to Algebra and Problem Solving Problem #18 Words  Solution

220 Tristan divided a certain amount of money into 3 equal shares. He gave the first share to Betty, the second share to Veronica, and then divide the remainder into 3 equal shares and gave one share to Archie. He kept the rest totaling $24. How much money did Tristan have at the beginning? Math 902 Transition to Algebra and Problem Solving Problem #19 Words  Solution

221 Tristan divided a certain amount of money into 3 equal shares. He gave the first share to Betty, the second share to Veronica, and then divide the remainder into 3 equal shares and gave one share to Archie. He kept the rest totaling $24. How much money did Tristan have at the beginning? Math 902 Transition to Algebra and Problem Solving Problem #19 Words  Solution

222 Tom spent three-quarters of his money on a dictionary. He spent one-half of the remainder on a calculator. The dictionary cost $30 more than the calculator. How much does the dictionary cost? Math 902 Transition to Algebra and Problem Solving Problem #20 Words  Solution

223 Tom spent three-quarters of his money on a dictionary. He spent one-half of the remainder on a calculator. The dictionary cost $30 more than the calculator. How much does the dictionary cost? Math 902 Transition to Algebra and Problem Solving Problem #20 Words  Solution


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