LESSON PLAN (Linda Bolin) - Granite School District

LESSON PLAN (Linda Bolin)
Lesson Title: Percent Problems Using Proportions
Course: Pre-algebra Date December Lesson 3
Utah State Core Content and Process Standards:
2.2b, 1.2b Solve problems involving percents including problems involving discounts,
interest, taxes, tips, and percent increase or decrease
1.2b Predict the effect of operating with percents as an increase or decrease of the original
value
Lesson Objective(s): Solve Percent Problems Using Proportions
Enduring Understanding
(Big Ideas):
Proportional reasoning is
essential in problem solving
Essential Questions:
• How can proportions be used to solve percent problems?
Skill Focus:
Apply proportions to percent
problems
Vocabulary Focus:
Ratio, numerator, proportion, denominator, percent
Materials:
• Calculators, once deck of cards (without faces gives you # 1-10)
• Several Sales Ads
• Percent Concentration Game on Transparency
• Percent Estimator manipulative (made from card stock) for each pair, Percent Estimator
Template for Smart Pal, Smart Pals, markers and cleaning cloths
• Book “If The World Were A Village” (David Smith)
• Worksheets: Percent Estimator, If The World Were A Village, The Bargain Store, Just Put It
On My Credit Card, Payday Loans
Assessment (Traditional/Authentic): Performance tasks
Ways to Gain/Maintain Attention (Primacy):
manipulative, calculators, literature, real world connections, games
Written Assignment:
• Percent Estimator
• If The World Were A Village
• The Bargain Store
• Just Put It On My Credit Card
• Payday Loans
• Game: Ups and Downs Of Life (Percent increased or decreased)
Post vocabulary on the board
Content Chunks
Starter:
1. Solve these proportions
a) 2.5/7 = 7.5/x b) x/4 = 15/20
2. Write the decimal for each
a) 30% b) 5/100 c) 6.5%

Lesson Segment 1: How can proportions be used to solve percent problems?
Do Stand-Up If, where the students stand for a statement if they believe it is true. Ask a few
students to justify their choice to stand or not.
1. Percent means a part out of 100.
2. If we say 50% of our class prefers chocolate ice cream, this means 50 of us prefer chocolate ice
cream.
3. 50% of our class would be about 18 people.
Q. So if 50% means 50 out of every 100, how can we know how many that is out of 36 (or
whatever number of students is in the class)?
To help students visualize the percent of a number, give student pairs a Percent Estimator and
Smart Pal with Percent Estimator graphic to shade. Students work together to slide a covered card
stock bar on the % side and on the part to total number side to see the ratios. They should also
shade the Smart Pal for both % and part to total. Using the bar, they should try to determine about
what fraction of the whole represents the percent given. Use:
a) 25% of 20 b) 40% of 30 c) 10% of 50 d) 75% of 10
After estimating using the Percent Estimator, have the students set up a proportion using
part/total = %/100 as the ratios, and have them find the exact number.
Q. What if we knew the part to total ratio, but didn’t know what percent that would be. How could
we find a percent?
Repeat the visualization with the Percent Estimator and Smart Pals. This time have them estimate
about what the part to total ratio bar would look like and slide the bar up the % side to estimate
the percent. Use:
a) 30/40 is what %? b) 12/48 is what %? c) 10/25 is what % d) 1/12 is what %?
Read parts of the book, “If The World Were A Village” by David Smith. Use the attached worksheet
to find out how many people that would be in the classroom if the class were typical of the world.
Lesson Segment 2: How can proportions be used to solve tax and interest
problems?
Use appropriate text problems involving tax and interest to practice setting up
proportions to solve. Students will need to determine what the part represents, and
what the total represents in the first ratio if you use:
__Part__ = _%_
Total 100
If you are finding the total cost after tax is being paid, it is helpful for students to
consider the part as original price plus tax, the total as original price, and the percent

as 100% plus the tax percent. To help with this have students model purchasing
something and ask questions such as:
Q. What is the tax?
Q. Is tax added or subtracted for the item price?
Q. Will the total cost including tax be more or less than 100% of the original price?
The attached Shopping Spree Worksheet helps students connect to their world. Give
groups several sales ads to look through to spend their “$1000” limit.
Lesson Segment 3: How can proportions be used to solve percent increase
and decrease problems?
Game: Ups and Downs of Life
Tell students you want to play a game “with their lives”. This means you will
work on problems they can relate to in their lives. Discuss ideas for things that may be
increasing or decreasing in their lives such as height, allowance, GPA, cost of items
they buy, number of hours they can watch TV or play electronic games, family size,
etc. Ask for someone to give tell you something that has increased or decreased in
their life. Help them set up a couple of problems focusing on:
Q. What was the original?
Q. How much did it change?
Q. How will I set up a proportion?
To identify the position of the numbers in the ratios, you might use a mnemonic such
as, “Down with 100, Up with percent. Down with the old, UP with the difference.”
The Difference = Percent
The old 100
To play the game, divide the class in half creating teams A and B. Shuffle a deck
of cards without the faces to get numbers 1—10. Black cards are positive numbers.
Red are negative. Ask students to give you an idea for something that has changed in
their lives. Nearly every change can be described using numbers. Have students set
up the problem and find the percent increase or decrease. You may want to give them
time to work with their small group before calling on a student.
Both teams start with a score of 0. Have a student from The A team explain the
problem to the class. If they do well, they choose a card from the deck. Positive
numbers are added to their teams score. Negative numbers are subtracted from the
other team’s score. Continue asking for situations and having students set up
proportions to find the percent increase or decrease, alternating teams to answer. The
team with the most points at the end of the allotted time, wins.
The attached “The Bargain Store” worksheet is a good investigation. Students often
mistakenly think taking an additional percent off can eventually result in paying
nothing. This worksheet investigates the idea of accumulated percent decrease.
Lesson Segment 4: Practice Game- Play Percent Concentration (attached)

Total % Total #
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0% 0
Total % Total #
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0% 0
Total % Total #
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0% 0
Total % Total #
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0% 0

Percent Estimator
Name_______________
1. 4. 7.
100% Total ___
100% Total ___ 100% Total ___
100%
100%
100%
90%
80%
90%
80%
90%
80%
70%
60%
50%
40%
30%
20%
10%
70%
60%
50%
40%
30%
20%
10%
70%
60%
50%
40%
30%
20%
10%
2.
100% Total ___
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
5.
100% Total ___
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
8.
100% Total ___
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
3.
100% Total ___
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
6.
100% Total ___
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
9.
100% Total ___
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%

Name_________________
Since the “World Village” described in the book has exactly 100 people in it, we can
use percent proportions to find some interesting data for our class. See the attached
facts sheet to help you set up your proportions.
1. What is the total number of people
in our classroom? Explain how you
could find the number of us that makes
up 10% of this class.
7. If we were in proportion to the
World Village, how many of us would
always be hungry?
2. If we were in proportion to the
World Village, how many of us would
come from North America?
3. If we were in proportion to the
World Village, how many of us would
speak English?
4. If we were in proportion to the
World Village, how many of us would be
between 10 and 19 years old?
5. If we were in proportion to the World
Village, how many of us would be
Muslim? Christian?
6. If we were in proportion to the
World Village, how many chickens
would there be?
8. If we were in proportion to the
World Village, how many of us would
spend a large part of the day trying to
find safe water to drink?
9. If we were in proportion to the
World Village, how many of us would
not be able to read?
10. If we were in proportion to the
World Village, how many of us would
make less than $1.00 per day?
11. If we were in proportion to the
World Village, how many of us would
not have electricity or Television?
12. If we were in proportion to the
World Village, how many people will be
in our class in 5 years?

World Village Facts 2002
If the world were shrunk to a village of 100 people where all conditions were
proportional, these are the facts about the village:
5 would be from North America
9 would speak English
19 are between the ages of 10 and 19
19 are Muslims. 32 are Christians
189 chickens are in our Village
60 are always hungry
25 spend a large part of the day looking for safe water
17 of the 88 people old enough to read, can’t read at all
20 make less than $1.00 per day
24 have no electricity and no water
The size of our class would double every five years

The Bargain Store
Name______________
You go into a clothing store with $100. The banner on the window says 50% off
everything in the store. As you walk into the store, you see a special room where
everything is marked an additional 25% off. In that room is a long table with a sign
that says, “Take another 20% off these items”.
Shade the box on the right to show the score for the next five questions.
1. Predict what an item on the table that was originally $40
would cost you.
% Ratio
Score Score
100
5/5
Computing:
2. What would the $40 item cost if it was marked 50% off?
Show work.
3. What would that item cost if an additional 25% were
taken off? Show work.
80
60
40
4/5
3/5
2/5
4. Now, what would the item cost if another 20% were
taken off? Show your work.
20
1/5
5. How did your prediction compare to the actual cost?
0
0/5
6. Estimate how much you would spend on an item from the long table that originally
cost $50. If tax were 6%, what the approximate cost be? Explain your reasoning.
7. How much would you expect to pay for an item from the long table with an original
price of $80? If tax were 7.5%, what would the cost be? Show your reasoning below.
8. Could you buy an item from the long table that was originally $500? Explain.

Name________________________
Date _______
Just Put it on my Credit Card?
Which Credit Card Company uses which advertising slogan?
1) Roses: $50. Candy: $35. The smile on her face: PRICELESS!
2) It pays to ....
3) It’s everywhere you want to be...
4) What’s in you’re wallet?
a) MasterCard b) Discover c) Visa d) Capital One
Which credit card company do you prefer? How does their slogan appeal to you? How does
their slogan encourage you to buy items using their card?
$1000 Shopping Spree
Your credit card company has given you a $1000 limit. You are going on a shopping spree.
Choose from the sales ads to reach your card limit. You must purchase more than one item.
Item
# of these you will
buy
Price each
Total for this
item
Total spent: ________________

The Bill
Your company is very nice. They do not expect you to pay this back all at once. You may
make minimum payments each month of $30. Your Credit Card Company will charge you
1.5% interest on the unpaid balance each month. The formula for finding the amount of
interest you will pay each month is prt = I, where p is the principle or balance, r is the
percent rate of interest (written as a decimal), t is the time, and I is the $ amount of interest.
Use the table below to organize and calculate the balance each month for 6 months.
Month #
1
Beginning
Balance $
(p)
Rate
(%)
(r)
Time
(t)
Amount of
Interest
(I)
Ending
Balance
Payment $
2
3
4
5
6
How long do you predict it would take you to pay off your principle or balance if you
continue to pay the minimum of $30 each month?
How much do you think you would need to pay each month to pay this debt off in a year?

Payday Loans?
Name ______________
Date ______
C. You haven’t been saving your money. You desperately need
$100. You decide to go to Payday Loans. Here’s how Payday
Loans works. You write a check for $116, and they give you
$100 cash. In two weeks, they cash your check. You are
charged 16% to use the $100 for two weeks. If you don’t have
that money in the bank in two weeks, they will hold the check
another two weeks for an additional 16%. Every two weeks
that you don’t have the money for them to cash your check,
they charge you an additional 16% simple interest.
1. Write a prediction as to whether this is reasonable? Explain your hypothesis.
2. A typical car loan rate is 5% for one year. What would you expect to pay for a
$100 loan at the end of the year?
3. A typical credit card loan rate is 20% per year. What would you expect to pay for
a $100 loan at the end of the year?
4. The Payday loan company’s rate is 16% every two weeks. There are 26 two-week
periods in a year. What total percent would this be in a year?
5. What would you expect to pay the Payday Loan Company for your $100 loan at the
end of a year using simple interest?
6. What if you couldn’t pay the Payday Loan Company for five years. What would you
end up paying back for the $100 loan?

What would
you pay if
you got
20% off
$50?
Percent Concentration
1 2 3 4
If the tax
rate is
$12.72 6.5%, what
is the tax on
$80
If you paid
$16.05 for a
$15 item,
what was
the tax rate?
5 6 7 8
40 is 25% of
what this
number $40 7%
What would
you pay for
a $12 item
with 6%
tax?
9 10 11 12
9.9 out of
13.2 is what
%?
30
Percent
means per
or out of
100
75%
13 14 15 16
60 % of
What
number is
18?
Define
“Percent” 160 $5.20
Put the game on a transparency. Put small post-its over the squares. Have students
select the number of a square. Lift the flap post-it. Have the student select a number
for a square they think may be a match. Lift that. When students find a match, the
post-its are removed from the two squares and a point is given to that team.
Answers: 1-6, 2-8, 3-16, 4-7, 5-15, 9-12, 11-14, 13-10,