1. Lesson 7 Percent as a Rate per 100

2. [objective]
The student will solve problems involving finding percent as a rate per 100, finding the whole given a part, and the percent.

3. [my skills]
Concepts of ratio and rate
Equivalent fractions

4. [essential questions]
How can I define percent as a ratio?
How can I find a percent when given a part and the whole?
How can I find the whole when given the part and percent of a number?

5. [Warm-Up]
Begin by completing the warm-up for this lesson on page S61

6. SOLVE Problem – Introduction
Percent as a Rate per 100

7. [lesson] SOLVE S Study the Problem
Tadarius is going to start soccer. He has to purchase a uniform, shoes, and a soccer ball. The shoes are $20, the uniform is $48, and the soccer ball is $22. If the shoes are on sale for 25% off the regular price, how much is the discount?
S Study the Problem
Underline the question.
This problem is asking me to find
the amount of the discount for the shoes.

8. Concrete - Centimeter Cubes
Percent as a Rate

9. Percent as a Rate – Centimeter Cubes
How many squares make up the whole?
100
Place 25 centimeter cubes on the grid.

10. Percent as a Rate – Centimeter Cubes
How many cubes out of 100 have been placed on the grid?
25 out of 100
Can the number of cubes be represented as a ratio in fractional form?
Yes! 𝟐𝟓 𝟏𝟎𝟎

11. Percent as a Rate – Centimeter Cubes
Add 10 more cubes to the 25 already on the grid.
Identify the ratio of cubes to 100 in word and fraction form.
35 out of 100
𝟑𝟓 𝟏𝟎𝟎

12. Percent as a Rate – Centimeter Cubes
Remove 4 of the cubes.
Identify the ratio of cubes to 100 in word and fraction form.
31 out of 100
𝟑𝟏 𝟏𝟎𝟎

13. Percent as a Rate – Centimeter Cubes
Need some more practice?
Add or remove cubes and identify the word and fraction forms.
? out of 100
? 𝟏𝟎𝟎

14. Pictorial
Percent as a Rate

15. Percent as a Rate – Pictorial
Place 10 cubes horizontally at the top of the page.
Remove each of the cubes and shade the squares using a blue colored pencil.

16. Percent as a Rate – Pictorial
Identify the ratio of blue squares to 100.
𝟏𝟎 𝟏𝟎𝟎

17. Percent as a Rate – Pictorial
How many squares per 100 are shaded on the grid? 10

18. Percent as a Rate – Pictorial
If 10 shaded squares equal the percent of squares shaded out of 100, what is the percent of 10 shaded squares?
10%

19. Percent as a Rate – Pictorial
Add 15 more cubes.
Remove each of the cubes and shade the squares using a green colored pencil.

20. Percent as a Rate – Pictorial
Identify the ratio of green squares to 100

21. Percent as a Rate – Pictorial
Determine the percent of green squares to 100.
15%

22. Percent as a Rate – Pictorial
Complete shading and identifying the ratios and percents for 20 Orange cubes and 30 Red cubes.

23. Percent as a Rate – Pictorial
Orange: 𝟐𝟎 𝟏𝟎𝟎 or 20%
Red: 𝟑𝟎 𝟏𝟎𝟎 or 30%

24. Percent as a Rate – Pictorial
How many squares are not shaded? 25
How can we write that value as a ratio?
𝟐𝟓 𝟏𝟎𝟎
How can we write that as a percent?
25%

25. Percent as a Rate – Pictorial
What does the word percent mean?
Percent means out of 100.

26. Pictorial
Percent and Ratios

27. Percent and Ratios – Pictorial
What is 40% of 100?
Write as a ratio.
What is the problem asking you to find?
40% of 100

28. Percent and Ratios – Pictorial
What is 40% of 100?
Write as a ratio.
What is the value we know?
40%

29. Percent and Ratios – Pictorial
What is 40% of 100?
Write as a ratio.
Do you know the total number of squares on the grid?
Yes, 100

30. Percent and Ratios – Pictorial
What is 40% of 100?
Write as a ratio.
So what are you really looking for?
The number of squares that equal 40%.

31. Percent and Ratios – Pictorial
What is 40% of 100?
Write as a ratio.
Identify the ratio for the shaded part of the grid.
𝟒𝟎 𝟏𝟎𝟎

32. Percent and Ratios – Pictorial
What is 40% of 100?
Write as a ratio.
How many shaded squares equal 40% of the grid? 40

33. Percent and Ratios – Pictorial
25 is what percent of 100?
Write as a ratio.

34. Percent and Ratios – Pictorial
How is Problem 3 different from Problem 1?
Problem 1 give the percent and asks for the part of the grid that is shaded. Problem 3 gives the value of shaded squares and asks for the percent.

35. Percent and Ratios – Pictorial
25 is what percent of 100?
Write as a ratio.
Identify the total number of squares on the grid?
100

36. Percent and Ratios – Pictorial
25 is what percent of 100?
Write as a ratio.
Identify the part that is shaded? 25

37. Percent and Ratios – Pictorial
25 is what percent of 100?
Write as a ratio.
Explain how we can write the value of the shaded squares as a ratio.
𝟐𝟓 𝟏𝟎𝟎

38. Percent and Ratios – Pictorial
25 is what percent of 100?
Write as a ratio.
Determine the percent of shaded squares. Justify.
𝟐𝟓% because the shaded squares equal the percent of squares shaded out of 100, or 25%

39. Percent and Ratios – Pictorial
15 is 15% of what number?
Write as a ratio.

40. Percent and Ratios – Pictorial
How is Problem 5 different from Problem 3?
Problem 3 gives the value of shaded squares and asks for the percent. Problem 5 gives the value and the percent and asks for the total value.

41. Percent and Ratios – Pictorial
15 is 15% of what number?
Write as a ratio.
Identify the total number of squares on the grid.
100

42. Percent and Ratios – Pictorial
15 is 15% of what number?
Write as a ratio.
Identify the part that is shaded. 15

43. Percent and Ratios – Pictorial
15 is 15% of what number?
Write as a ratio.
Explain how we can write the value of the shaded squares as a ratio.
𝟏𝟓 𝟏𝟎𝟎

44. Percent and Ratios – Pictorial
15 is 15% of what number?
Write as a ratio.
Determine the whole number of squares to which 15 is compared.
100

45. Percent and Ratios – Pictorial
15 is 15% of what number?
Write as a ratio.
This means that 15 is 15% of 100.

46. Abstract with Graphic Organizer
Percent as a Rate

47. Percent as a Rate – Abstract with Graphic Organizer
50 is what percent of 100?
Write as a ratio.
Determine what the problem is asking you to find.
50 is what percent of 100

48. Percent as a Rate – Abstract with Graphic Organizer
50 is what percent of 100?
Write as a ratio.
What is the value we know?
50.

49. Percent as a Rate – Abstract with Graphic Organizer
50 is what percent of 100?
Write as a ratio.
Identify the total number of squares on the grid?
100.

50. Percent as a Rate – Abstract with Graphic Organizer
50 is what percent of 100?
Write as a ratio.
Determine what you are looking for.
The percent of squares that equal 50 out of 100.

51. Percent as a Rate – Abstract with Graphic Organizer
50 is what percent of 100?
Write as a ratio.
Identify the ratio for the shaded part of the grid.
𝟓𝟎 𝟏𝟎𝟎

52. Percent as a Rate – Abstract with Graphic Organizer
50 is what percent of 100?
Write as a ratio.
50 is what percent of 100?
50%

53. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
What are you looking for in Problem 1?
Solution

54. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
What is known in the problem?
Solution
The part of 100 that is shaded, and the total number of squares on the grid, which is 100.

55. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
Identify the total number of squares on the grid.
Solution
100

56. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
What is the value of the denominator of the second fraction?
Solution
100

57. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
Why is 100 the denominator when finding a percent?
Solution
When finding a percent, a number is always compared to 100.

58. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
The numerator for this fraction is “percent.” When finding a percent, to what number is the percent compared?
Solution
100

59. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
The numerator for the first fraction is “part.” Determine what a part of the whole is using the grid.
Solution
The number of squares shaded to represent the part of the whole that is shaded.

60. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
The denominator for the first fraction is “whole.” Determine what a whole means using the grid.
Solution
The entire number of squares, including the shaded and
non-shaded squares.

61. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
We can use a proportional relationship to find missing values with percents.
Solution
part whole = % 100

62. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 50
Percent
Part
Whole =
100
Identify the part of the grid that is shaded. Record for the numerator in the “Equivalent Fraction” box.
Solution
50 squares

63. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 50
Percent
Part
Whole =
100
100
Identify the number of squares in the grid. Record for
the denominator in the
“Equivalent Fraction” box.
Solution
100 squares

64. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 50 x
Percent
Part
Whole =
100
100
Do we know the percent?
Solution
No.
Record as an “x” to represent an unknown value.

65. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 50 x
Percent
Part
Whole =
100
100
Looking at the denominators, what number can we multiply 100 by to get a product of 100?
Solution
Multiply by 1

66. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 50 x
Percent
Part
Whole =
100
100
Whatever the denominator is multiplied by, the numerator must also be multiplied by.
Solution 50 50 =
100
100
𝟓𝟎×𝟏=𝟓𝟎
50 is 50% of 100.

67. Percent as a Rate – Abstract with Graphic Organizer
2 is what percent of 4?
Compare Problem 2 to Problem 1.
There is not a grid for this problem.

68. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
100
What is the problem asking you to find?
Solution

69. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 2
Percent
Part
Whole =
100
What is the part of the whole?
Solution 2

70. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 2
Percent
Part
Whole = 4
100
What is the whole number?
Solution 4

71. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 2
Percent
Part
Whole = 4
100
What is the unknown for the equivalent fractions?
Solution
Percent.

72. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 = 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 100 2 x
Percent
Part
Whole = 4
100
How can we represent the unknown value of percent?
Solution
Represent the percent with a variable: “x.”

73. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 2 x
Percent
Part
Whole = 4
100
Find the equivalent fraction.
What is x equal to?
Solution 2 50 = 4
100
2 is 50% of 4.
x =𝟓𝟎

74. Percent as a Rate – Abstract with Graphic Organizer
What number is 75% of 4?

75. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
100
What is the problem asking you to find?
Solution

76. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole = 4
100
What is the whole for this problem?
Solution 4

77. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 75
Percent
Part
Whole = 4
100
What is the percent for this problem?
Solution
75%

78. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 x 75
Percent
Part
Whole = 4
100
How will the unknown part be represented?
Solution
With a variable: “x”

79. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 x 75
Percent
Part
Whole = 4
100
Solution
What is the final answer? 3 75 = 4
100
x = 3
3 is 75% of 4.

80. Percent as a Rate – Abstract with Graphic Organizer
1 is 25% of what number?

81. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100
Percent
Part
Whole
100
What is the problem asking you to find?
Solution

82. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 1
Percent
Part
Whole =
100
What is the part for this problem?
Solution 1

83. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 1 25
Percent
Part
Whole =
100
What is the percent for this problem?
Solution
25%

84. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 1 75
Percent
Part
Whole = x
100
How will the unknown part be represented?
Solution
With a variable: “x”

85. Percent as a Rate – Abstract with Graphic Organizer
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 1 25
Percent
Part
Whole = x
100
Solution
What is the final answer? 1 25 = 4
100
x = 4
1 is 25% of 4.

86. Abstract
Percent as a Rate

87. Percent as a Rate – Abstract
Let’s take a look at Problem 1
50 is 50% of what number?

88. Percent as a Rate – Abstract
Equivalent
Fractions
Looking for:
Unknown
part whole = percent 100 50 50
Percent
Part
Whole = x
100
Are we finding the part, the whole or the percent? Explain
Solution 50 50 =
100
100
The whole
The part and percent are given!
50 is 50% of 100

89. Percent as a Rate – Abstract
30 is 30% of what number?
Compare Problem 2 above to Problem 1.
This problem does not have a graphic organizer.

90. Percent as a Rate – Abstract
30 is 30% of what number?
What is the problem asking you to find? Explain.
The whole, because the part and the percent are given.
Explain how to set up equivalent fractions.
Use the part whole = % 100 formula and substitute in the given values.
What value do we know in the first fraction?
the part 30 =

91. Percent as a Rate – Abstract
30 is 30% of what number?
What information do we know in the second fraction?
The percent and the denominator which is always 100. 30 30 =
100

92. Percent as a Rate – Abstract
30 is 30% of what number?
How can we represent the unknown in the denominator of the first fraction?
Using a variable 30 30 = x
100

93. Percent as a Rate – Abstract
30 is 30% of what number?
Find the equivalency and record. = 30 30 30 30 = = x
100
100
100
30 is 30% of 100.

94. SOLVE Problem – Completion
Percent as a Rate per 100

95. [lesson] SOLVE S Study the Problem
Tadarius is going to start soccer. He has to purchase a uniform, shoes, and a soccer ball. The shoes are $20, the uniform is $48, and the soccer ball is $22. If the shoes are on sale for 25% off the regular price, how much is the discount?
S Study the Problem
Underline the question.
This problem is asking me to find
the amount of the discount for the shoes.

96. Eliminate the unnecessary facts. List the necessary facts.
SOLVE
Tadarius is going to start soccer. He has to purchase a uniform, shoes, and a soccer ball. The shoes are $20, the uniform is $48, and the soccer ball is $22. If the shoes are on sale for 25% off the regular price, how much is the discount?
O Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
List the necessary facts.
Shoes cost $20
25% off price

97. L Line Up a Plan Write in words what your plan of action will be
L Line Up a Plan Write in words what your plan of action will be. Determine what is not known. Set up a ratio to show the unknown, and then find the equivalent fraction with the second quantity having a denominator of 100. Choose an operation or operations. Multiplication

98. The unknown is the discount, or part, of the whole. Ratio is 𝒙 𝟐𝟎 .
V Verify Your Plan with Action Estimate your answer. Between $4.00 and $5.00 Carry out your plan.
The unknown is the discount, or part, of the whole. Ratio is 𝒙 𝟐𝟎 .
𝒙 𝟐𝟎 = 𝟐𝟓 𝟏𝟎𝟎
𝟓 𝟐𝟎 = 𝟐𝟓 𝟏𝟎𝟎
$5.00 is 25% of $20.00

99. E Examine Your Results Does your answer make sense
E Examine Your Results Does your answer make sense? (compare your answer to question.) Yes, because I am looking for the amount of the discount for the shoes. Is your answer reasonable? (compare your answer to the estimate.) Yes, it is close to my estimate of between $4.00 and $5.00.

100. Is your answer accurate?
(check your work.)
Yes.
Write your answer in a complete sentence.
The discount for the shoes is $5.00.

101. Closure
Percent as a Rate per 100

102. [essential questions]
How can I define percent as a ratio?
A percent is written as a ratio with 100 as the denominator because the percent is always compared to 100.
How can I find a percent when given a part and the whole?
Set up an equivalency with the percent represented by an “x”. For example:

103. [essential questions]
How can I find the whole when given the part and the percent?
Set up an equivalency with the whole represented by an “x”. For example:

104. Word Wall
Ratio
Percent

105. Lesson Percent as a Rate per 100