LESSON PLAN
Name: Mark Nixon
Title of lesson: Exponential functions and Interest rates
Date of lesson: Friday 2nd week
Length of lesson: 1 hour 15 minutes
Description of the class: 8th grade pre
algebra
Name of course: Project based Pre algebra
Grade level: 8th
Honors or regular: regular
Source of the lesson:
Connected Math curriculum
TEKS addressed:
¤111.24.
Mathematics, Grade 8.
(a) Introduction.
(3) Problem solving, language and communication,
connections within and outside mathematics, and formal and informal
reasoning underlie all content areas in mathematics. Throughout mathematics
in Grades 6-8, students use these processes together with technology
(at least four-function calculators for whole numbers, decimals, and
fractions) and other mathematical tools such as manipulative materials
to develop conceptual understanding and solve problems as they do
mathematics.
(b) Knowledge
and skills.
(1) Number,
operation, and quantitative reasoning. The student understands that
different forms of numbers are appropriate for different situations.
The student is expected to:
(A) compare
and order rational numbers in various forms including integers, percents,
and positive and negative fractions and decimals;
I.
I. Overview
The lesson will show students
how to calculate interest and graph exponential functions. Citizens need to be able to make rational
choices about money, interest and debt; this lesson will give the
students tools to begin to understand these issues.
II. Performance or learner
outcomes
Students will be able to compute the total cost of a car loan. Students will be able to describe and identify different kinds
of graphs.
Resources, materials and supplies needed
A class set of TI-83 (or similar graphing calculators)
IV. Supplementary materials, handouts. ŌGrowing,
GrowingĶ Connected Mathematics 8th Grade Curriculum, Investigation One
pp. 5-10. and
a post test.
Five-E Organization
Teacher
Does
Probing Questions
Student
Does
| Engage: 10 min What allowance would you prefer? $1000 dollars a day for a month or a
penny today, two pennies tomorrow and four pennies the third
day or what I might call the daily double? Ask this question
several times leaving the daily double untouched and decreasing
the $100 by a factor of 10. |
As votes
change ask students why they are switching.
Is there a point where we can all agree on one allowance
over the other? How
much will you have at the end of the month if I pay ($1000,
$10) the fixed amount daily? |
A few students
will hold out until you are offering only $10 a day. Students will respond with the appropriate 30 times x. |
| Explore:
10 min Okay now please
get out your calculators and letÕs see if we guessed this right.
15 min PART TWO Okay IÕd like
you to get into your learning groups and read about exponential
growth. (p.5-6 Connect Mathematics) How
is our daily double related to exponential growth? Now using the y= button at the top left corner of your calculator
read about the King of Montarek. (p.7-10 C. M.) And evaluate
and graph the three different plans for the peasantÕs reward. Please copy your graph free hand and be prepared to present
to your peers. |
I think you
understand how to figure out the amount at the end of the month
with the same daily allowance, does anyone want to explain how
to find out whatÕs going on in the Daily Double?
Tell me what you see.
PART TWO How is our
daily double related to exponential growth?
(this is a rhetorical question better answered at the
end of the MontarekÕs Reward exercise than the beginning. Priming
the pump) 1. What does
your y equal? (what value
does your x, y represent) 2. What does
your x equal? 3. How is this similar to what we just
did with the daily double? |
Student by
this time have had some experience with calculators and will
present different strategies, most likely theyÕll use the repeating
button strategy press equals many times.
Students will respond that they are getting huge numbers
fast. (when you donÕt have to do it longhand it goes fast)
PART TWO Students work
efficiently in groups. 1. The amount
of money rewarded. 2. The number
of squares on the chess board. 3. TheyÕve
replaced days with squares on a chess board. |
| Explain: 10 min Before we have
been looking at functions that were linear, 5 apples for a dollar,
16 miles to the gallon.
We could represent this function as a line on a graph,
but cars donÕt ride on square wheels and much of life isnÕt
explained by a straight line. Many things grow exponentially.
Under the right conditions every amoeba splits into four
every hour. Bacteria grow exponentially. |
(what
is a function?)
1. What is
interest? 2. What do
we pay interest on? 3. What is
the difference between simple and compounded interest? 4. What is
appreciation? 5. What is
depreciation? |
1. Interest
is the percentage charged to use someone elseÕs money. 2. Pawn shop
tickets, mortgages, car loans , college loans , pay day loans. 3. Simple interest
is calculated once at the end of the term of the loan. 4. Compound interest is added every day, month, quarter or
other period. 5. Appreciation
is how things become more valuable over time. 6. Depreciation
is a calculation of how things become less valuable over time. |
| Extend
/ Elaborate: 15 min Another common
form of non-linear equation is compounded interest. LetÕs think about a car loan. If I pay $16,599
for a new car and the bank loans me that money for three years
at 5% simple interest, IÕll end up paying back how much? [p*(1+i)]
If weÕre talking about compound interest the formula is different.
Final amount=Principle * (1+i/t)^#t or the final amount paid
on a loan equals the principle times the sum of 1 (100%) and
the interest rate divided by the period (t=time) raised to the
power of the number of periods.
So once again we have an exponential function.
|
1. What is
interest? 2. What do
we pay interest on? 3. What is
the difference between simple and compounded interest? 4. What is
appreciation? 5. What is
depreciation? 6.F=P*(1+i/t)^#t Is this a linear
function? 7. Can you
guess what it might look like? 8. Using your
calculator can you tell me what IÕll have paid for my $16,599
at the end of a three year loan at 8% compounded monthly? |
1. Interest
is the percentage charged to use someone elseÕs money. 2. Pawn shop
tickets, mortgages, car loans , college loans , pay day loans. 3. Simple interest
is calculated once at the end of the term of the loan. Compound interest
is added every day, month, quarter or other period. 4. Appreciation
is how things become more valuable over time. 5. Depreciation
is a calculation of how things become less valuable over time. 6. No. 7. Maybe a
curve like the earlier ones. 8. 16599*(1+.08/12)^36= 21084 |
| Evaluate: 15 min Students will
be given a short post test.
The test will ask for mathematical understanding and
ask the students to provide a visual interpretation as well. |
|
|
Percent effort each team member contributed to this
lesson plan:
___%___ ____Name of group member_____________________
___%___ ____Name of group member_____________________