Lesson: Mathematics & Fundraising
Time: 73 minutes
Goals / Objectives:
1. Students will review the following concepts: rate, proportion, and percentage.
2. Students will apply these concepts to this unit on fundraising.
3. Students will perform the appropriate calculations, using multiplication and division.
Standards:
1. Make sense of problems and persevere in solving them.
2. Reason quantitatively and use units to solve problems.
3. Create equations that describe numbers or relationships.
Purpose:
1. To prepare students to perform the mathematical calculations necessary to be
successful in this unit.
2. To encourage the comprehension of math strategies.
“ Comprehension tasks can include complex math problems in which the students must
decide upon a particular strategy or algorithm before applying it. Rather than simply
applying a formula or algorithm, the student must know why the formula or algorithm is
appropriate” (Anderman & Anderman, 2010, p. 11).
Differentiation:
Students will have the option of using calculators at any time. The assessment will be
guided for students with an Individualized Education Plans (IEPs). Students will have the
option of completing the assessment by verbally explaining the steps, if they have
documented difficulties with writing. Students may use a laptop to type in a document or
they may complete the work on a separate sheet of paper (if the space provided in not
sufficient).
Materials:
- Pencils, calculators, laptops (if needed),graphic organizers, assessment.
Organization: (2-3 minutes)
Students will work in their project groups (of up to 4 students).
Students will complete the formative assessment individually.
Introduction:
Teacher: "In his 1859 autobiography, Abraham Lincoln wrote about his
childhood in Indiana. “There were some schools, so called; but no
qualification was ever required of a teacher beyond ‘readin, writin,
and cipherin’ to the Rule of Three. . . . Of course when I came of age
I did not know much. Still somehow, I could read, write, and cipher
to the Rule of Three; but that was all.” After his short stint at school,
Lincoln went on to teach himself algebra and geometry from books.
The “Rule of Three” refers to a method of solving a proportion, a
sentence such as “4 is to 6 as 3 is to ? .” It is equivalent to solving
4/6 = 3/x. In a simple proportion such as this, whenever you know three
out of the four numbers, you can determine the fourth. The Rule of
Three is a method that dates from ancient times and is not usually
taught today. Today we use algebra, and so are able to solve this and
more complicated proportions" (Brown, Breulin, Degner, Eddins, Edwards,
Jakucyn, et al., 2008, p. 301).
Warm-up Activity: (20 mins.)
Teacher: “Today, we are going to review and integrate the following concepts:
percentage, proportion, and rate. If there were eight of you that had cereal this
morning and there were 20 students in the class, what percentage of the class had
cereal for breakfast? What math operation could we use to find the answer? Yes,
division!”
8 / 20 = .4
“ Does .4 mean that 4% of the students had cereal for breakfast? Let’s check that number.
Remember the percent means “per 100”. If our fraction is 8 / 20, how many is that per
100. To solve this we can use a proportion.”
8 / 20 = x / 100
Now use the Mean-Extremes Property (cross-multiplication).
8 * 100 = x * 20
Simplify.
800 = 20x
Divide both sides by 20.
x = 40
.4 is the same as 40 %
How many of you had cereal for breakfast this morning? Please raise your hand. Let’s
calculate that percentage.” Students will calculate the percentage (calculators, optional).
(# of students that had cereal for breakfast / # of students in the class) =
___ / ___ = ______ = __?__ %
___ / ___ = x / 100
___ * 100 = x * ___
x = _______, which represents _______%
Shortcut: ( ___ / ___ ) * 100 = _______ %
Teacher can model on the board, if necessary. Teacher will check group answers and
discuss using the shortcut above.
“To review rate, let’s consider how long it might take you to get to school? If you live 10
miles from school, the time it takes to get here depends on your rate or average speed in
miles per hour. If it took you 30 minutes to get to school on the bus, what was the rate in
miles per hour? To find the rate in miles per hour, we are going to need to convert
minutes to hours first, using another proportion. There are 60 minutes in one hour.
30 / 60 = x / 1
Now use the Mean-Extremes Property (cross-multiplication).
30 * 1 = 60 * x
Simplify.
30 = 60x
Divide both sides by 60.
x=½
30 minutes is ½ of an hour.
To find the rate in miles per hour, you can now set up the following proportion.
10 miles / ½ hour = x miles / 1 hour
Cross-multiply.
10 * 1 = ½ * x
Divide both sides by ½ . (hint: use your calculator)
x = 20
Your average speed would be 20 miles per hour.
Remember that the bus makes a lot of stops, so the average speed (rate) is slower than the
speed limit along the way.”
Activity: Math and Fundraising (25 minutes)
Teacher: As you pass out the graphic organizer, explain the following:
“Fundraising for a charity usually involves more than just asking people to donate
money for your charity. Often there is an associated product or service that you provide
in order to receive donations. We are going to look at an example to determine the
amount of money that you might be able to raise for your charity.
Graphic Organizer: FrayerModel_Percentage_Proportion_Rate.doc
Teacher: Project the Graphic Organizer (using an overhead/LCD projector).
Model the example for/with the students, if needed. Each student in the group
must complete the graphic organizer and show their work/calculations. Observe
and assist groups, as needed, to make sure that all students complete the work.
When a group is done, they can take the individual assessment.
Proportion & Rate:
If you purchase 50 bracelets for
$30.00 to sell for your fundraiser,
how much did you pay for each
bracelet?
(total cost / # of bracelets = cost /
bracelet)
Rate & Earnings:
If you sell all 50 bracelets at the new
cost per bracelet, how much money
will you earn in total?
(new cost * # of bracelets)
Percentage & Rate:
If you want to earn 25% more than
you spent on each bracelet for the
charity, how much would you need to
sell each bracelet for?
(new cost = initial cost + 25% of the
initial cost)
Summary questions:
How much money did you
spend on each bracelet?
How much money did you sell
each bracelet for?
How much money did you
earn by selling all of the
bracelets?
Formative
Assessment: (15 minutes)
Graphic Organizer: FrayerModel_Expenses_Revenue_Profit.doc
Teacher: Read the Vocabulary (Expenses, Revenue and Profit). “Use the results
from the first graphic organizer to complete the “Bracelet Example” and the “Tshirt” Example. Pass in both Graphic Organizers with your name on them when
you are done.”
Students: Uses the results from the first graphic organizer to complete the
“Bracelet Example” and then “T-shirt Example”, showing their work/calculations.
Grading Rubric: MathLesson1_AssessmentRubric.doc
Closure: (approx. 10 minutes)
Teacher: “Your homework with your group is to decide on some products and
services and the costs of some of those products or services. Your next few
lessons will include tips on advertising and ways to help you minimize your
costs. As a group, please complete this worksheet bring it to your next lesson.”
Handout: ProductServicePlanningWorksheet.xls