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How to teach percentages using Proportions
Math For Life SituationsVicki Angel
Manuel A. Navarro
1. Understand Ratios2. Offer instructors an
effective, easy, relevant way to teach percents using the proportion method
Objectives:
WHAT IS A RATIO?
COMPARISON BETWEEN TWO QUANTITIES OR NUMBERS.
4 puzzle parts to 3 gears
WHAT IS THE RELATIONSHIP BETWEEN THEM?
For every 4 puzzle parts, there are 3 gears.
RATIOS CAN BE WRITTEN IN 3 DIFFERENT WAYS:
· 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
• Ratios can be increased by multiplication. Example: 6 / 4 = 18 / 12 when multiplied by 3 / 3
• Order is important. Example:
4 full time to 5 part time workers it is not the same as 5 part time to 4 full time workers
What is a proportion?
In a proportion there are 2 ratios combined by the equal sign ( = ).
This makes both ratios equivalent
For example:30 to 6 = 5 to 1How do we know?By cross multiplication30 X 1 = 6 X 5 30 = 30
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?4. 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!5. 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
Basic Proportion setup
isof
%100
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
Identifying Components
8 is 20% of 40
PART
PER
CEN
T
WH
OLE
Clue Words◦ IS = Part, portion.◦ % = Percent Symbol◦ OF = Whole, original.
Identifying Components
8
is
of
%
100
is 20%
of 40
100IS
OF
%
2 & 3
Pages
DoLet’s try an exercise.
What is 20% of 40?
40
Using Proportion to find answers
?40
20%100Cross
Multiply
100
8
20
X = 800
Divide by the other number
= 8800÷
8
8 is 20% of what number?
Using Proportion to find answers
?20%100
Cross Multiply
40X = 800÷ =
8100
Divide by 3rd. Number
20
40
8
8 is what % of 40?
Using Proportion to find answers
40? %
100Cross Multiply
20X =800÷ =
8100
40
Divide by 3rd. Number
20
%
4 - 6
Pages
Do
Let’s continue our exercise.
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:
1. Q & A. Are there any questions?
2. Do you have any suggestions?
3. Do you think this is something you can use?
THANK YOU!