LESSON PLAN (Linda Bolin) - Granite School District

LESSON PLAN (Linda Bolin)
Lesson Title: Solving Percent Problems With Proportions
Course: Math 7 Date: Jan Lesson 7
Utah State Core Content and Process Standards:
2.1c Solve problems involving proportions
2.1b Solve percent problems using ratio and proportion including problems involving
discounts, interest, taxes, tips, and percent increase or decrease
a) 1.4b Recognize percents as ratios based on 100
b) 1.3b Predict the effect of operating with percents as an increase or decrease of
the original value
Lesson Objective(s): Students will use proportion equations to solve percent problems.
Enduring Understanding (Big
Ideas):
Proportions can be used to solve a
variety of problems.
Skill Focus:
Set up and solve proportion
equations for percent problems
Essential Questions:
• Why is a percent ratio based on 100?
• How can a proportion be used to solve a problem
involving percent?
Vocabulary Focus:
Ratio, proportion, percent
Materials:
• Foldables: Percent Estimator
• Calculators
• Percent Estimator manipulative (made from card stock) for each pair, Percent Estimator
Template for Smart Pal, Smart Pals, markers and cleaning cloths
• Several Sales Ads
• Book “If The World Were A Village” (David Smith)
• Percent Concentration Game on Transparency
• Worksheets: Percent Estimator, If The World Were A Village, The Bargain Store, Just Put It
On My Credit Card, Payday Loans
Assessment (Traditional/Authentic): observation, performance task, journal
Ways to Gain/Maintain Attention (Primacy): stories, graphic organizer, shopping
simulation
Written Assignment:
Percent Estimator Practice “If The World Were A Village worksheet”, Journal: foldable for each
student (attached), text practice as needed.
Content Chunks
Starter:
1. Order these from least to greatest: 45%, 4.5%, 450%, 4/5
2. Amee takes her resting heart rate and counts 8 beats in 6 seconds. Use a
proportion to find the number of beats in one minute. Then write this as a rate
beats/minute.

Lesson Segment 1: Why is a percent ratio based on 100? How can a
proportion be used to solve a problem involving percent?
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)?
Do “Vizualizing Percents In Our World” with the students, shading in the appropriate percent as
they visualize the fraction of the whole given in each problem.
To help students visualize the percent of a number, give student pairs a Percent Estimator
Foldable and Smart Pal with Percent Estimator Practice worksheet. The Percent Estimators come
four to a page. Copy them on card stock and slit the 0% line on each bar to allow a slider strip to
be moved up and down the fraction and the percent bars. Cut 1 ½ “ strips from a different color
card stock to use as slider bars. They should be inserted in the slit on each bar, so there are 2
sliders per Estimator.
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 and Practice worksheet for
both % and part to total. Using the bar, they should try to determine about what number out of
the total number given represents the percent given. 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.
a) 25% of 20 b) 40% of 30 c) 10% of 50 d) 75% of 10
Ask students to describe what 150% of a number would look like, 200%, etc.
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, worksheet, and Smart Pals. This time have
them estimate 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 %?
Lesson Segment 2: How can proportions be used to solve percent problems?
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 3: 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 4: How can proportions be used to solve percent increase
and decrease problems?
Your text will also have plenty of practice problems for increase and decrease that can
be used. Again it is useful for students to consider whether the question wants them
to find more than 100% of the original (increase) or less than 100% of the original
(decrease). Helping students determine
Q. What is the increase or decrease?
Q. Will the result be more or less than 100% of the original?
The attached “The Bargain Store” worksheet can be used as a role model. Students
often mistakenly think taking 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)

Visualizing Percents in Our World
Name__________________
For each of the following, shade the approximate given percent in the box
and shade or circle the percent on the sketch. Label the percent on the
sketch.
1. I got 25 % off the cost of a shirt. 2. My sister is about 70% my height.
100%
90%
80%
70%
60%
50%
40%
30%
20 %
10 %
$1 $1
$1
$1 $1
100%
90%
80%
70%
60%
50%
40%
30%
20 %
10 %
3. I got 80% of the problems on 4. I ate 10% of the cookies.
my last test correct.
100%
90%
80%
70%
60%
50%
40%
30%
20 %
10 %
%Test
Name
1. xxx 2. xxx
3. xxx 4. xxx
5. xxx 6. xxx
7. xxx 8. xxx
9. xxx 10. xxx
11. xxx 12. xxx
13. xxx 14. xxx
15. xxx 16. xxx
17. xxx 18. xxx
19. xxx 20. xxx
100%
90%
80%
70%
60%
50%
40%
30%
20 %
10 %

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 Practice
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.
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?
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?
6. If we were in proportion to the World Village,
how many chickens would there be?
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 Your 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.
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?
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
Percent
30 means per
or out of 75%
100
13 14 15 16
Define
“Percent” 160 $5.20
9.9 out of
13.2 is what
%?
60 % of
What
number is
18?
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,