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This lesson was written by me as an assignment for
C-I 304. I actually taught the "Hook" portion of the lesson to my classmates.
Compound Interest and Exponential Growth
General Info: 9th grade algebra class, 90 minute
period, Exponents and Powers unit,
second lesson of
the unit. Students have already studied compound interest.
Materials: Newspapers, magazines, financial brochures,
calculators, large sheets of graph paper, markers
Objectives: The students will know how to calculate
compound interest formulas. They will be able to construct
a graphic representation of exponential growth.
Standards: F.12.2 Use mathematical functions* (e.g.,
linear*, exponential*, quadratic*, power) in a variety of
ways, including:
-Recognizing that a variety of mathematical
and real-world phenomena can be modeled* by the
same type of function
-Translating different forms of representing
them (e.g., tables, graphs, functional notation*, formulas)
-Describing the relationships among
variable quantities in a problem
-Using appropriate technology to interpret
properties of their graphical representations (e.g.,
intercepts, slopes, rates of change, changes in rates of change, maximum*,
minimum*)
Hook: Explain the housesitting
problem to students. You are housesitting for your rich neighbor. Lay
out
both payment plans for students.
Ask students to choose a plan. Ask two or three students to explain
their choices. Call on a couple of students if no
one volunteers. Go through the calculation of the
second payment plan with the class. The students
will see the difference between exponential growth
and constant increase.
(10 minutes, approximate time for each activity will be in parentheses)
Activities: Compound interest project. Newspapers
and other sources will be laid out on a table somewhere in
the room.
-Students will number off and get into groups of three.
(2)
-One student will pick up a large sheet of graph paper
and some markers for his/her group. (3)
-The other two group members will select a couple of sources
to research interest rates from.
(occurring at same
time as above activity)
-Students will find three different interest rates for
things like mortgages, car loans, credit cards,
savings, etc. (15)
-Students will then inform the teacher of what kind of
rates they found (i.e. savings, mortgage). (5)
-The teacher will give them a dollar amount for each,
and students will calculate the growth of that
amount over a 10-year period. (10)
-Each year will be calculated, and students will plot
points and graph their results on the graph paper.
The teacher will be walking around the room, answering
questions and helping them locate the
interest rates if necessary. (10)
Assessment: The graphs made by the students will
show the students’ understanding of compound interest.
They will also reflect
the students’ knowledge of exponents. The students will also give a
brief oral
presentation about their graphs.
They will be asked to discuss their experiences with the rest of the
class. The teacher will ask questions of each group
member during the presentation. Some
possible questions
include: Where did you find your rate? Can you think of any other kinds of
rates
that could be used? What is the importance
of paying your bills right away (if a credit card)? Why
should you begin saving money early (if a savings rate)?
Is there an easier way of illustrating the
growth? Does the amount of money involved affect the shape
or growth of the graph? Other
questions will be asked by the teacher
based on the students work. Students will be assessed on the
following conditions: explanation during oral presentation,
individual participation, neatness, and
accuracy. The primary emphasis will be on the explanations
of the graphs. (30 min.)
Closure: With approximately five
minutes left in the period, the students will put away their materials and
come together as
a large group. The main ideas of compound interest will be repeated by the
teacher. The teacher will also reinforce the ideas of exponential growth
vs