How to Teach Percentages Using Proportions Math For Life Situations By Reda Berry.
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Transcript of How to Teach Percentages Using Proportions Math For Life Situations By Reda Berry.
How to Teach Percentages Using Proportions
Math For Life Situations
By
Reda Berry
Objectives• Understand ratios
• Offer instructors an effective, easy, and relevant way to teach percents using the proportion method
What is a Ratio? • A ratio is a comparison of two numbers
4 puzzle parts to 3 gears
How do you write a ratio?
• 4 puzzle parts to 3 gears– 4 to 3– 4 : 3– 4/3
More about Ratios• Ratios can be reduced by division
Example: 6/4 = 3/2 (when divided by 2/2)
6 to 4 = 3 to 2
6:4 = 3:2
• Ratios can be increased by multiplication Example: 6/4 = 18/22 (when multiplied by 3/3)
6 to 4 = 18 to 22
6:4 = 18:22
Find the Ratio mistake• A ratio is a comparison of two numbers
– 34 customers to 7 sales = 34 to 7
– 20 adults to 100 Children = 100: 20
– 25 female employees to 90 total employees = 5/18
Find the Ratio mistake• A ratio is a comparison of two numbers
– 34 customers to 7 sales = 34 to 7 correct– 20 adults to 100 Children = 100: 20 should be
20:100– 25 female employees to 90 total employees =
5/18 correct 25/90 divided by 5 = 5/18
Proportions• When two pairs of numbers have the same ratio, like the
numbers 2, 7 and 10, 35 we say they are proportional.
The equation 2/7 = 10/35 is a proportion• In any proportion, the cross products are equal notice
that 2 x 35 = 7 x 10
70 = 70
Notice: We can use this fact to solve a proportion if one of the 4 numbers is unknown
Word Problem #1• If it takes 2 gallons of
paint to paint a room which has 480 ft² to be painted, how many gallons will it take to paint a room which has 1200 ft² to be painted?
Word Problem #1 solved• If it takes 2 gallons of
paint to paint a room which has 480 ft² to be painted, how many gallons will it take to paint a room which has 1200 ft² to be painted?
• 2 gallons paint
• 480 ft² to be painted
• How much paint?
• 1200 ft² to be painted
2/480 = x/1200
2 x 1200 = 480x
2400 = 480x
2400/480 = x
5 gallons of paint = x
Word Problem #2• An 8 lb turkey breast
contains 36 servings of meat. How many pounds of turkey breast would be needed for 54 servings?
Word Problem #2 solution• An 8 lb turkey breast
contains 36 servings of meat. How many pounds of turkey breast would be needed for 54 servings?
8 lb/36 = x lb/54
8 x 54 = 36x
432 = 36x
432/36 = 36/36x
12 = x
Check:
8 x 54 = 36 x 12
432 = 432
How do you introduce percents?
1. What is 20% of 40?
2. 45 is 45% of what number?
3. 35 is what percent of 70?
Students get confused on how to solve these problems.
?????
1. When do I multiply?
2. When do I divide?
3. How do you multiply or divide with percents?
4. Please, give me an easy way to do it!
The answer is a PROPORTION!
• All percent problems are composed of three parts– Percent– Part– Whole
• The answer lies in identifying which one is missing.
Basics of Percents
The percent proportion part percent number whole 100
100
*part is to whole as part is to whole*
isof
%
The percent proportion using key words
Identifying Components
8 is 20% of 40• Clue Words– IS = Part, portion– % = Percent Symbol– OF = Whole, original
Identifying Components8
isof
%100
is 20% of 40
100IS
OF%
Identifying Components
isof
%100
is 20% of 40
1008
OF%
Identifying Components
isof
%100
is 20% of
1008
40%
Identifying Components
isof
%100
is % of
1008
4020
Using proportions to find answers
What is 20% of 40?
isof
%100100
?40
20
Using proportions to find answers
What is 20% of 40?
isof
%100100
Using proportions to find answers
What is 20% of 40?
isof
%100100
?40
20
Using proportions to find answers
8 is 20% of what number?
isof
%100100
Using proportions to find answers
8 is 20% of what number?
isof
%100100
8?
20
Using proportions to find answers
8 is what % of 40?
isof
%100100
Using proportions to find answers
8 is what % of 40?
isof
%100100
840
?
Start with teaching students how to identify the three components using CLUE WORDS◦ Is – defines the part, or portion
◦ Of – defines the whole or original amount
◦ % symbol – defines percent
Basics of Percents
Percent Word Problem #1• On average, about 40% of the
body weight of an adult male is muscle. If a certain man weights 225 lbs, how many pounds should be muscle?
A. 325 lbs
B. 25 lbs
C. 90 lbs
D. 112.5 lbs
Percent Word Problem #1 Solved
• On average, about 40% of the body weight of an adult male is muscle. If a certain man weights 225 lbs, how many pounds should be muscle?
x/225 = 40/100
100x = 225 x 40
100x = 9000
x = 9000/100
x = 90
Check:
100 x 90 = 225 x 40
9000 = 9000
Percent Word Problem #2• Mrs. Jackson makes
$450 a week. She pays $90 a week for food. Money spent for food is what percent of Mrs. Jackson’s income?
Contemporary GED Math, 2002
Percent Word Problem #2 solved• Mrs. Jackson makes
$450 a week. She pays $90 a week for food. Money spent for food is what percent of Mrs. Jackson’s income?
90/450 = x/100
90 x 100 = 450x
9000 = 450x
9000/450 = x
20% = x
Check
90 x 100 = 450 x 20
9000 = 9000
Contemporary GED Math, 2002
Percent Word Problem #3• Eighteen people
attended David’s evening math class. This represents 75% of the number registered for the class. How many people are registered for his class?
Contemporary GED Math, 2002
Percent Word Problem #3 solution• Eighteen people attended
David’s evening math class. This represents 75% of the number registered for the class. How many people are registered for his class?
18/x = 75/100
18 x 100 = 75x
1800 = 75x
1800/75 = x
24 = x
Check:
18 x 100 = 75 x 24
1800 = 1800
Contemporary GED Math, 2002
1. Multiplication? Division?2. Eliminates the need to convert
percent into decimals.3. Introduces students to variables.4. Fractions, Unit conversions and
Geometry applications.
Advantages: