Lenape Regional High School District – BOE Approved 2/15/12
Algebra I
[Implement start year (2012-2013)]
Revision Committee Members, email, extension
Jeanie Isopi
[email protected]
Paula C. Marques
[email protected]
Sandy O’Neal
[email protected]
Robert Schwartz
[email protected]
ext. 2244
ext. 8981
ext. 8720
ext. 8108
Unit # 6 Exponential Functions
Stage 1 – Desired Results
st
Established Goals
21 Century Themes
2009 NJCCC Standard(s), Strand(s)/CPI #
(http://www.nj.gov/education/cccs/2009/final.htm)
Common Core Curriculum Standards for Math and English
(http://www.corestandards.org/)
( www.21stcenturyskills.org )
Seeing Structure in Expressions A-SSE: 1
Interpret the structure of expressions
Creating Equations A-CED: 1, 2
Create equations that describe numbers or relationships
Interpreting Functions F-IF: 1, 2, 8b
Understand the concept of a function and use function notation.
Analyze functions using different representations.
_x_Global Awareness
_x_Financial, Economic, Business and Entrepreneurial Literacy
___Civic Literacy
_x_Health Literacy
_x_Environmental Literacy
st
21 Century Skills
Learning and Innovation Skills:
_x_Creativity and Innovation
_x_Critical Thinking and Problem Solving
_x_Communication and Collaboration
Information, Media and Technology Skills:
_x_Information Literacy
_x_Media Literacy
_x_ICT (Information, Communications and
Technology) Literacy
Life and Career Skills:
_x_Flexibility and Adaptability
_x_Initiative and Self-Direction
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
___Social and Cross-Cultural Skills
_x_Productivity and Accountability
_x_Leadership and Responsibility
Enduring Understandings:
Students will understand that . . .
Essential Questions:
EU1
EU1
non-linear change can be represented by graphs, mathematical
models, and equations.
How can mathematical language be used to describe non-linear
change?
an exponential function can model growth or decay of an initial
amount.
How can we model situations using exponents?
EU2 critical vocabulary is necessary to communicate and understand
mathematics in the real world.
EU2 How can critical vocabulary terms be used to better enhance the
understanding of mathematics?.
Knowledge:
Students will know that . . .
Skills:
Students will be able to . . .
EU1
EU1
an exponential function can model growth or decay in real life
when describing situations such as population growth,
compound interest, and car depreciation.
distinguish between linear and non-linear functions.
recognize when an exponential model is appropriate
(growth or decay).
x
the graph of an exponential function of the form y ab will
never equal zero and will have exactly one y -intercept.
in the exponential function
amount and
y
determine if an exponential function is increasing or
decreasing.
ab x , a represents the initial
b represents the growth/decay factor.
compound interest can be found using the formula
graph exponential functions.
model exponential growth and decay.
calculate compound interest.
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
A
r
P1
n
nt
, where A represents the balance, P
represents the principal (initial deposit), r represents the
annual interest rate (expressed as a decimal), n represents
the number of times interest is compounded yearly, and t
represents the time in years.
EU2 demonstrate the correct usage and application of critical vocabulary.
EU2 critical vocabulary is necessary to communicate and understand
mathematics in the real world.
Stage 2 – Assessment Evidence
Recommended Performance Task: (Suggestion: May assign only one part or all)
You are a recent college graduate. You must use your knowledge of exponential growth and decay functions to make some important financial
decisions. For example, you will have to decide where you will bank and invest your money. You will also decide whether or not to invest large amounts
of money into a home or automobile are wise financial decisions.
Part I
You just received $10,000 from a long lost uncle as a graduation gift. You must decide which financial institution and what type of account you will put
it in. Your goal is to obtain as much interest as possible, because you have big plans for the future.
Steps:
(1) Visit the websites of several financial institutions to determine which bank/account offers the best interest rates. Be aware of extra fees and
required minimum balances.
(2) Use the worksheet provided to record your findings for the top three saving accounts. It must be turned in with your final project.
(3) Use the highest yielding interest rate to determine what your account will be worth in 10, 25, and 40 years.
RESOURCES
Bank of America
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Chase Bank
US Bank
ING Direct HSB Direct
MSN
Wells Fargo
California Bank and Trust
City National Bank
Part II
Now that you are commuting to work every day, you are considering buying a new car. However, you are undecided if you should invest in a new car
or just keep the one you have. You have heard that cars depreciate a lot, and you don't want to waste your hard earned money.
Let's do a little investigating to see if cars really do depreciate and if so, by how much.
Decide on a used automobile that you would like to purchase. Find the auto in an advertisement in the newspaper, car magazine, or internet. You
must attach a copy of the advertisement to your work. The vehicle must be at least 3 years old. For it, you must:
Determine the current price.
Determine the original price when the car was sold new.
What is the rate of depreciation? Write an equation that represents the model of the car’s depreciation.
Using that model, what will the car be worth in 5 years?
Graph the information above. You may sketch your graph on graph paper or use an online graphing program.
When will the car be worth zero?
Is a car an investment? Why or why not?
Use the second worksheet provided to record your findings.
RESOURCES:
Cars for Sale
Auto Trader
Kelley Blue Book
Graphmatica
Graph Func Online
Web Graphing
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Part III
Decide on a house that is being advertised for sale. Include a copy of the advertisement in your work.
What is the current value of the house?
How old is the house?
What was the original price of the home or the price of the home when purchased years ago?
What is the rate of appreciation? Write an equation to represent the home’s appreciation.
Using that model, what will be the price of the home in 10 years?
Show a graph of the information above. You may sketch your graph on graph paper or use an online graphing program.
When will the home triple in value? (From current value)
Is a house an investment? Why or why not?
Again, use the worksheet provided to record your results.
RESOURCES: http://www.prudentialcal.com/
Prudential
Tarbell
Century 21
Zillow
Hint: it may be easier to decide on a house in which you know the current owners. You can ask them what they paid when they purchased
the home. Don't forget to find out what year they purchased it. Then use a site such as Zillow to determine the current price of the house.
Evaluation
Completeness
Use of
Beginning
Developing
Accomplished
Exemplary
1
2
3
4
The assignment is
missing one or more of
the three main parts.
Not all questions
completed and/or
missing equations
All parts are
completed, but may
include incomplete
responses,
thoughts, or ideas.
All responses give a
thorough
explanation.
Answers &
responses are
thoughtful and
complete.
No correct equations and
/or no correct results.
Wrong equation used in
at least one of the
problems and/or several
Although incorrect,
the appropriate type
of equations are
Correct equations
are used for each
problem. All work is
Score
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Exponential/Decay
Models
Use of Graphs
Presentation
computational mistakes.
Graphs are completely
incorrect, no indicators,
impossible to read.
Presentation lacks two or
more parts and/or not
presented in the form
required. Lacking any
form of order/neatness.
used for each
problem and/or
minor computational
mistakes.
done correctly.
Graphs are
Graphs are incorrect, but
generally correct,
are the right form (i.e.
but contain a couple
exponential when they
of errors and/or are
should be) and/or
missing some of the
missing indicators and/or needed indicators.
hard to read.
Graphs are easy to
read.
All graphs are
correct, include
necessary
information, and are
easy to read.
Presentation
includes all
necessary
information, but is
unorganized or
lacking neatness or
color.
Presentation is neat
and includes all
required material. All
material is organized
in a way that is
interesting and easy
to understand. Use
of color.
Presentation is missing a
part or is hard to
read/understand. Little
attention to neatness.
Conclusion
Please take time to contemplate your findings. Are they relevant? If not, why? Please be prepared to discuss your findings and your thoughts with the
class.
(Adapted from WebQuest by Bobbie Smith and Mark Fitzpatrick at Vista Murrieta High School.
http://questgarden.com/75/84/4/090121190659/index.htm
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Worksheets
Worksheet #1
Name of
Bank/
Institution
Type of
Account
Exponential Equation Model:__________________________
(write the formula that you will be using)
Annual
Interest
Rate
Equation
representing
total amount
after 10 yrs.
Equation
representing
total amount
after 25 yrs.
Equation
representing
total amount
after 40 yrs.
Use the best results to answer the following questions.
1. How much money will be in your account after 10
years?_____________________
2. By what percent will your savings increase after 10 years? _____________________
Show your work here.
3. How much money will be in your account after 40 years? _____________________
4. By what percent will your savings increase after 40 years? _____________________
Show your work here.
Worksheet #2
Vehicle Information:
Make_________________ Model_________________ Year_________________
Current price:
Original price when the car was sold new:
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Write an equation that represents the model of the car’s depreciation:
What is the rate of depreciation? (show work)
Using that model, what will the car be worth in 5 years? (show work)
Graph the information above. Attach graph to this form.
When will the car be worth zero? (show work)
Is a car an investment? Why or why not?
Worksheet #3
What city and state is the house located? _______________________
What is the current value of the house? _______________________
How old is the house? _______________________
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
What was the original price of the home? _______________________
Write an equation to represent the home’s appreciation. (show work)
What is the rate of appreciation? (show work)
Using that model, what will be the price of the home in 10 years? (show work)
Show a graph of the information above. Attach graph to this form.
When will the current price of the home triple in value? (show work)
Is a house an investment? Why or why not?
Other Recommended Evidence:
Tests on graphing exponential growth and decay functions, modeling exponential growth and decay, finding compound and simple interest.
Quizzes on identifying exponential growth and decay functions by inspection of function and/or its graph, discriminating between exponential
functions, linear, and quadratic functions.
Assessed Elements from Recommended Performance Tasks
Other teacher-graded evaluations
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Presentations of student research
Cumulative Benchmark Assessment at end of marking period.
Stage 3 – Learning Plan
Suggested Learning Activities:
(A) – acquisition (M) – meaning (T) – transfer
Activities:
Activity #1: Population growth modeled concretely as students see the increase in number of fish in water and graphically as well.
http://www.otherwise.com/population/exponent.html (A)
Activity #2: Through a TI-Nspire activity, students will identify the characteristics of exponential functions. The activity can be found at
http://education.ti.com/calculators/timathnspired/US/Activities/Detail?sa=5022&t=5025&id=11976. (A)
Activity #3: Growth and Decay Experiment (attached). Students will use M&M’s to develop growth and decay models for which they will find
equations.(M/T)

Additional DI Activities can be found on the LRHSD Differentiated Instruction Wiki http://wiki.lrhsd.org/groups/lrhsdmathwiki/
Critical Vocabulary:
The following terms should be utilized:
-exponential function
-growth factor
-exponential growth
-decay factor
-exponential decay
-principal
-compound interest
-interest rate
The following is the suggested sequence of learning activities and number of days for the Algebra 1 L2 class. Adjustments should be made
accordingly for other levels.
Introduction of Performance Task –day 1
Introduction of exponential functions: growth/decay (Activity #1) -days 1, 2, 3
Introduction of exponential functions: graphs (Activity #2 and #3) -days 4, 5, 6 (include quiz)
Compound interest: equations and applications –days 7, 8
Recommended Performance Task -days 9, 10
Assessment -days 11, 12 (includes review)
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Activity #2: Lab…Growth & Decay
Experiment #1: Growth
1. Start this experiment with 4 M&M’s in a cup. Shake the cup and pour the M&M’s onto
a napkin. Count the number of M&M’s that have the M showing. Add a new M&M for
each one with an M showing. Record the total number of M&M’s in the table below.
Using the new total of M&M’s each time, repeat the procedure five more times.
Trial #
0
Number
of M&M”S
4
1
2
3
4
5
6
2. Create a scatterplot. Label the x -axis “Trial” and the y -axis “Number of M&M’s.”
3. Using your graphing calculator, find an exponential model which fits your data.
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Write the equation: ________________________
Graph the exponential function on the graph above.
4. Predict the number of M&M’s on trial #9: __________
5. Predict the number of trials needed to have 300 M&M’s: _____________
6. The equation in (3) is of the form y ab x , where x is the trial number.
a) What does a represent in your data?
b) What does b have to do with the way your M&M’s are growing?
Experiment #2: Decay
1. Start this experiment with a cupful of M&M’s. Shake the cup and pour the M&M’s onto
a napkin. Count the number of M&M’s. Write this as the number for Trial #0. Remove all
M&M’s that have the M showing. Record the total number left in the table below. Using
the new total of M&M’s each time, repeat the procedure five more times. Note: If the
number of M&M’s reaches zero at any point, the experiment is over at that time and you
should not use the zero result as a part of your data.
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
Trial #
0
Number
of M&M”S
1
2
3
4
5
6
2. Create a scatterplot. Label the x -axis “Trial” and the y -axis “Number of M&M’s.”
3. Using your graphing calculator, find an exponential model which fits your data.
Write the equation: ________________________
Graph the exponential function on the graph above.
4. Why did I tell you not to use the 0 value as part of your data?
LRHSD (2011) Adapted from ASCD © 2004
Lenape Regional High School District – BOE Approved 2/15/12
5. Interpret the coefficients a and b in your equation from part (3).
LRHSD (2011) Adapted from ASCD © 2004