# New Tech Network Exemplary Project

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```					                       New Tech Network Exemplary Project

Project Title: Can You Hear Me Now?

Subject: Math

Course: Algebra

Project Summary: Students will analyze cell phone plans in order to make a recommendation to customers on which
plan is best for their needs. Students will also research phone plans online, and find the plan that is right for their own
daily usage.

Teacher Materials and Resources                                                                                           3-6

Project Documents and Instructions                                                                                       7-15

Project Related Resources and Links                                                                                    16-21

Assignments and Homework                                                                                               22-27

Assessment and Evaluation                                                                                              28-31

Please note: The following page (2) is a screen capture taken from the NTN Echo New Tech Project Library. The
remaining pages (3-31) are the individual Project Resources that exist within this project’s Project Briefcase. They have
been compiled into this document to facilitate their access and viewing.
Subject: Math

Course: Algebra

Project Title: Can You Hear Me Now?

Project Summary: Students will analyze cell phone plans in order to make a recommendation to customers on which
plan is best for their needs. Students will also research phone plans online, and find the plan that is right for their own
daily usage.

PROJECT BRIEFCASE

Teacher Materials and Resources

Project Library Submission Form

   Facts and Stats

o     Subject Areas: Algebra I

o     Length (Weeks): 3

o     Quarter Used: 1st

   Project Summary: Students will analyze cell phone plans in order to make a recommendation to customers on
which plan is best for their needs. Students will also research phone plans online, and find the plan that is right
for their own daily usage.

   Project Overview: In this project students will be investigating 4 different cell phone plans and making a
recommendation to customers about which plan best fits their needs. Each plan will be presented to the
students in a different format: written text, graphically, function form, and table form. Students must identify
key information, create a table and graph, and write a function for each plan. Following their analysis, they will
make recommendations to 3 customers with different cell phone needs. They must support their
recommendations with the data they have collected.

The main objectives of this project are to introduce the students to function notation, develop their skills of
writing and graphing functions, and to be able to identify the domain and range of a function.

o     17.0 Students determine the domain of independent variables and the range of dependent variables
defined by a graph, a set of ordered pairs, or a symbolic expression.

o     18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic
expression is a function and justify the conclusion.
o     Written Communication: Students created a written report which described their findings
o     Oral Communications: Students presented their findings to a customer
o     Technology Literacy: Students used excel to graph and creating a power point presentation
o     Collaboration: Students worked in a group on daily assignments and to complete the project
o   Critical Thinking: Students looked at calculations, graphs, and data in order to make a recommendation
to a customer
o   Math Content: Students learned how to identify variables, write equations, make tables and graphs, and
analyze information
   Driving Question or Problem Statement: How can we analyze data for key information and represent it in
different formats?
   Scaffolding Activities and Assignments
o   Determine what information should be included in a cost analysis of a cell phone plan
o   Analyze each plan: write a function, create a table, create a graph, find the cost per minute, etc.
o   Make a recommendation for each customer based on their needs
   Final Product(s) and Assessment Methods
o   Scaffolding Activities
   Cost Analysis
   Presentation to Customer
o   How is it assessed? (peer, panel, presentation)
   Project Resources (books, movies, web links, materials and supplies): Online Math Help (http://www.math.com)
   Teacher Notes and Comments (suggestions, next steps, etc.): Each plan is presented in a different format so that
students get used to analyzing data in a variety of ways. It also gives them an example of what a function, graph,
or table looks like. They can work off of these examples to create their own functions, graphs, etc. This project
was a great way to introduce function notation. The students could see the value of using appropriate variables
in their equations. It also made the idea of domain and range easy to understand because it was tied to a real
world example.

I started each class with a warm-up that connected the project with the concepts being taught. This allowed for
time to clarify any confusion or to discuss any new ideas. Another key piece of the project was that I had the
students come up with the criteria for the cost analysis. This gave the students more ownership over the project.
Finally, I had parents act as the customers. They were given surveys to fill out which assessed the student's
presentation and knowledge. This made the project seem more realistic to the students.

Teacher Guidelines and Instructions

   Summary: In this project students will be investigating 4 different cell phone plans and making a
recommendation to customers about which plan best fits their needs. Each plan will be presented to the
students in a different format, including in written text, graphs, and function form. Students must identify key
information, create a graph, and write a function for each plan. Following their analysis, they will make
recommendations to 3 customers with different cell phone needs. They must support their recommendations
with the data they have collected.

   Driving Question: How can we analyze data for key information and represent it in different formats?
Project Calendar

   Day 1: Project Launch

o   group contracts

o   brainstorm key information

   Day 2: Report Outline

o Decide on key information for report
o Determine monthly charges and cost per minute of each plan
o Lesson on functions - function notation / domain and range
o HW 1
   Day 3: Creating a Table and Graph
o Complete a table for minutes and monthly fees of each plan
o Lesson on Piece-wise functions
o HW: Graph each plan using your tables
   Day 4: Writing Functions
o Graph plans on the computer
o Lesson - writing and evaluating functions
o Write each plan as a function
o Begin working on key information
o HW 2
   Day 5: Draft of Report
o Customer Questions Journal
o Work on a rough draft of your report
o Review functions - evaluating, domain and range, graphing
o HW 3
   Day 6: Work on Project
o Work on reports - complete all key information, begin working on a recommendation for each customer
o Review
o HW: Review Problems
   Day 7: Quiz
o Work on reports - finalize recommendations
o Prepare for presentations - complete presentation plan
o QUIZ
   Day 8: Project Due/Meet the Customers
o Turn in final draft of report
o Present reports to customers (have customers fill out a survey for each group)

Journal Prompts Used

   Please review the customer profiles and key information below. If there is any information you feel your group
needs in order to complete your analysis, please submit those questions in a response.

o   Customer Profiles
o   Key Information
Warm-ups

    Warm-up #1

The following graph shows the monthly fee for Cellular Plus. Use the graph to answer the following questions:
1. What is the monthly fee?
2. How many minutes are included in the monthly fee?
3. If a customer goes over the minutes included in the fee, how much will they be charged per minute?
4. What would the customer pay if they used 700 minutes?
 Warm-up #2

Cellular Now charges \$35.00 per month for 250 minutes. All additional minutes are \$.20.

1. Find the monthly fee for each of the minutes listed below:

Total Minutes       Monthly Fee
100
200
300
400
500

2. Does this plan represent a function? Why or why not?
3. If the plan is a function, list the domain and range.
4. Write an equation for the plan in function notation.
5. Graph the plan below

    Warm-up #3

Cell Star is offering a cell phone plan for \$60 per month for 600 minutes. Any additional minutes are \$.60 per
minutes.

1. Write a function for the plan
2. Use the functions to find the fee for using 1000 minutes
3. If the domain of the function is {200, 300, 400} find the range of the function

    Warm-up #4

1. If f(x) = -3x ? 2, evaluate when x = 4
2. If c(t) = 2t ? 5 and the domain is {1, 4, 10}, find the range
3. If f(x) = 5x3 + 2x2 ? x + 1, evaluate when x = t

Functions Quiz

Recognitions: This project was adapted from curriculum produced by Ready to Teach: http://rtt.pbs.org/rtt/index/cfm
Project Documents and Instructions

Group Contracts

Please complete a group contract. You may use the template below or create your own.

Group Contract

   I. Members:

o     Please list all group member names

   II. Absence Policy

o     What is your policy for a group member being absent the day of a presentation or when an assignment
is due?

   III. Work Policy

o     What is the policy on contributing to the group, meeting deadlines, and sharing the workload?

o     What if one of your group members commits plagiarism?

o     What is the role of the group leader?

   V. Member Dismissal

o     What circumstances will lead to a member being dismissed?

o     Will your group vote to dismiss a member?

o     Can a group member leave under their own will?

o     Who will maintain possession of the work completed prior to a member leaving the group?
Project Calendar

Monday                Tuesday           Wednesday          Thursday          Friday

Read entry doc                       Decide on key
information for report
Group Contracts
Determine monthly
Read customer profiles               charges and cost per
minute of each plan
Brainstorm key
information                          Lesson on functions

HW 1
Lesson on writing and
Complete a table for evaluating functions                  Submit questions to
minutes and monthly                                            customers
fees of each plan  Write each plan as a
function                             Work on a rough draft
Lesson on Piece-wise                                         of your report
functions      Begin working on key
information                             Review functions
HW: Graph each plan
HW 3
Work on reports          Prepare for                         Project Due
presentations
Review                                                 Presentations
Quiz

HW: Review
Customer Profiles

Celia, Jim, and Linda have consulted Cell Zone for assistance in choosing a wireless plan that is right for each of them.
They have supplied Cell Zone with the following information about the cell phone usage:

Customer Name                                              Profile
Celia is an attorney who spends most of her time in court, so she has to
conduct her daily business between sessions. She spends over two hours
Celia          on her cell phone each day, checking with her assistant and returning calls
to clients. She also travels among four courthouses, and needs to call
ahead if she is going to arrive late.
Jim is a retired pediatrician who lives alone and spends the winter months
in Florida. He is writing a book about asthma with a colleague, and confers
Jim           with him by phone for about an hour each week. Jim also likes to check in
with his children and their families on weekends. On weekdays during the
day, he occasionally calls friends up north to socialize, or calls his
grandchildren after they're home from school to hear about their day.
Linda is a high school math teacher who has a one-year-old daughter and
an ailing mother at home. She has an aide, Fiora, who stays with them
Linda          while Linda is at work. Linda calls home several times a day, and has also
instructed Fiora to call her if there is any kind of emergency. But the school
phone is often tied up. Linda wants to purchase a cell phone so that she
can check in with Fiora during her free periods, call her husband, or take
care of errands by phone when she can grab a few minutes.
Phone Plans
Analyzing a Cell Phone Plan: Your three customers are anticipating a report from you with key information about
available plans. Your manager would like to know what information you are going to be presenting. As a group,

Be sure to consider how needs of customers differ, as well as how different plans have very different fees and
limitations.

Key Information for Report
 Your group will meet with each of the 3 customers. During your meeting, please provide a report on the
following information for each plan:

1. Monthly fee

2. Number of peak minutes included in monthly fee

3. Cost per minute (beyond peak minutes)

4. Fee for night and weekend minutes

5. Long distance and/or roaming charges

6. Monthly cost for 100 - 1000 minutes (in the form of a table)

7. A graph for each plan (done on the computer)

8. A function (equation) for each plan

9. Pros and Cons of each plan

   When you have completed all of the above tasks for each plan, your group will need to review the information
and make a recommendation for each customer, as outlined below:

10. Customer recommendation - which plan should they choose and why?

   Be sure to use specific information about the customer and each plan

   You will need to submit a typed copy of your report

Analyzing Monthly Fees (part 1)

   When you meet with each of your 3 customers, you need to be able to tell them which plan is the cheapest for
different monthly minutes.

   In order to do this you will need to find the monthly fee of each plan, for the minutes listed below.

   Begin by filling in the following tables:

o   Verizon Cingular

o   T-Mobile AT & T
Analyzing Monthly Fees (part 2)

   Complete the tables below and graph the information for each plan on a separate graph.

o   Verizon AT & T

o   Cingular T-Mobile

Finding a Plan That’s Right for You

Research cell phone plans online. Decide which plan is best for your own usage and do an analysis of that plan. Explain
why you selected that plan, what your monthly fee would be for at least 3 different monthly minutes, provide a graph,
and write a function.
Customer Satisfaction Survey

Customer Satisfaction Survey

ensure that Cell Zone representatives are providing customers with useful, accurate, and complete information.

Did the Cell Zone Representatives…       (1 = did not meet expectations, 5 = exceeded expectations)

1       2       3       4       5

2. Provide a recommendation that will best meet your needs?

1       2       3       4       5

3. Provide sufficient information about each available plan?

1       2       3       4       5

4. Provide clear and informative graphics, such as tables or charts?

1       2       3       4       5

5. Appear to be professional and knowledgeable?

1       2       3       4       5

Thank you for your time and feedback!

Notes on Functions

I. Key terms:

Function: A set of points or equation where every input has exactly one output. In other words, for every x, there is only
one y.

Ex) {(1, 3), (9, 0), (4, 5), (2, 3)}

This is a function because x is not repeated.

Domain: The set of all x-coordinates in a function.

Ex) The domain of the function above is {1, 9, 4, 2}

Range: The set of all y-coordinates in a function.

Ex) The range of the function above is {3, 0, 5}

II. Function Notation

a. What is function notation?

Function notation replaces the y in an equation with f(x), pronounced "f or x".

Ex) Given y = 3x + 2 is a function, write the equation in function notation.

y = 3x + 2

f(x) = 3x + 2

b. Why do we use function notation?

Function notation helps to specify what an equation is talking about. By using variables that represent the quantities in
the problem, we are making our work more clear and precise.

c. How do we decide what variables to use?

Choose variables that can easily be associated with a quantity. For example, if you were working with area and
circumference, you would likely use the variables A and C.

Ex) A car travels 50 mph. Find the distance traveled over time.

Since we are talking about distance and time, it makes sense to use the variables d and t. Thus an equation might be...

d(t) = 50t

III. Evaluating a Function

a. Remember that parenthesis in function notation do not indicate multiplication. "f(x)" means "plug in a value for x".

b. You evaluate a function just as you would evaluate any equation.
Substitute or plug in the value of x.

Ex) Given f(x) = 3x2 + 5x ? 6, evaluate at x = 2.

f(2) = 3(2)2 + 5(2) ? 6

f(2) = 3(4) + 5(2) ? 6

f(2) = 12 + 10 ? 6

f(2) = 22 ? 6

f(2) = 16

This means (2, 6) is a point in the function.

IV. Piecewise Functions

a. A piecewise function is any function that is in, well, pieces!

b. Piecewise functions usually indicate intervals for each part of the function.

Ex) f(x) =

If we evaluate f(0) we would use the part of the function for the interval x < 2.

f(x) = 2x + 1

f(0) = 2(0) + 1 = 1

If we evaluate f(5) we would use the part of the function for the interval x > 2.

f(x) = x + 4

f(5) = 5 + 4 = 9

c. Graphs of a piecewise function always have several distinct parts (as shown below).

Each part of the graph represents a part of the function "equation".

V. Evaluating a function at a variable

a. You can evaluate a function at a variable rather than a number.

Ex) Given f(x) = 6x + 8, evaluate at x = t (plug in t for x).

f(t) = 6t + 8

VI. Finding the Range

a. You can use a function and its given domain to find its range.

Evaluate the function at each given value of the domain.

Ex) Given f(x) = 3x ? 5 and the domain is {0, 2, -1} find the range.
f(0) = 3(0) ? 5 = -5

f(2) = 3(2) ? 5 = 1

f(-1) = 3(-1) ? 5 = -8

Therefore the range is {-5, 1, -8}.

VII. Graphing a Function

a. If you know the equation for a function, you can graph it by creating a table.

In other words, find the domain and range of the function.

Ex) Given f(x) = x + 1, graph the function in the interval 0 < x < 5.

xy

01

12

23

34

45

56
Functions Review

I. Key terms:

Function: A set of points or equation where every input has exactly one output.

In other words, for every x, there is only one y.

Ex) {(1, 3), (9, 0), (4, 5), (2, 3)}

This is a function because x is not repeated.

Domain: The set of all x-coordinates in a function.

Ex) The domain of the function above is {1, 9, 4, 2}.

Range: The set of all y-coordinates in a function.

Ex) The range of the function above is {3, 0, 5}.

II. Function Notation

What is function notation?

Function notation replaces the y in an equation with f(x), pronounced “f or x”.

Ex) Given y = 3x + 2 is a function, write the equation in function notation.

y = 3x + 2

f(x) = 3x + 2

Why do we use function notation?

Function notation helps to specify what an equation is talking about. By using variables that represent the quantities in
the problem, we are making our work more clear and precise.

How do we decide what variables to use?

Choose variables that can easily be associated with a quantity. For example, if you were working with area and
circumference, you would likely use the variables A and C.

Ex) A car travels 50 mph. Find the distance traveled over time.

Since we are talking about distance and time, it makes sense to use the variables d and t. Thus an equation might be…

d(t) = 50t

III. Evaluating a Function

Remember that parenthesis in function notation do not indicate multiplication. “f(x)” means “plug in a value for x”.

You evaluate a function just as you would evaluate any equation.

Substitute or plug in the value of x.
Ex) Given f(x) = 3x2 + 5x – 6, evaluate at x = 2.

f(2) = 3(2)2 + 5(2) – 6

f(2) = 3(4) + 5(2) – 6

f(2) = 12 + 10 – 6

f(2) = 22 – 6

f(2) = 16

This means (2, 6) is a point in the function.

IV. Piecewise Functions

A piecewise function is any function that is in, well, pieces!

Piecewise functions usually indicate intervals for each part of the function.

2 x  1       x2

Ex) f(x) = 
x4          x2

If we evaluate f(0) we would use the part of the function for the interval x < 2.

f(x) = 2x + 1

f(0) = 2(0) + 1 = 1

If we evaluate f(5) we would use the part of the function for the interval x > 2.

f(x) = x + 4

f(5) = 5 + 4 = 9

c. Graphs of a piecewise function always have several distinct parts (as shown below).

Each part of the graph represents a part of the function “equation”.
V. Evaluating a function at a variable

a. You can evaluate a function at a variable rather than a number.

Ex) Given f(x) = 6x + 8, evaluate at x = t   (plug in t for x)

f(t) = 6t + 8

VI. Finding the Range

You can use a function and its given domain to find its range.

Evaluate the function at each given value of the domain.

Ex) Given f(x) = 3x – 5 and the domain is {0, 2, -1} find the range.

f(0) = 3(0) – 5 = -5

f(2) = 3(2) – 5 = 1

f(-1) = 3(-1) – 5 = -8

Therefore the range is {-5, 1, -8}.

VII. Graphing a Function

If you know the equation for a function, you can graph it by creating a table.

In other words, find the domain and range of the function.

Ex) Given f(x) = x + 1, graph the function in the interval 0 < x < 5.

Web sites that may be useful for this project: Online Math Help (http://www.math.com/)
Assignments and Homework

Functions HW 1

State the domain and range for each. Is the relation a function?

1. {(6, -8), (-1, -3), (7, -3), (-7, -3), (1, 9)}           2. {(-3, 9), (7, -6), (2, 1), (4, -7), (4, -1), (1, -7)}

3. {(-3, -1), (-5, -9), (0, 3), (-5, 6)}                    4. {(0, 4), (4, 4), (-8, -5)}

5. {(63, 152), (124, 152), (-13, 147), (-19, 152)}          6. {(-41, -78), (-35, 81), (-16, -119)}

7. {(21.44, -177.42), (48.36, -168.55), (48.36, -182.44)} 8. {(-11, -33), (19, -79), (51, -27)}

9. {(99, -166), (75, -154), (-34, 124)}                     10. {(164, -118), (-19, -115), (-40, -118)}
Solve:

11. n ÷ 28 = 2     12. 59 = a – 16               13. 66.4 = 16.6a

14. x - 32 = 12    15. x + 37 = 57 + 34   16. 14 + 57 = 49 + y

b                   y   23214                                2
17.       7.3     18.                                 19. x        11
11                 53    318                                11

1    2576
20.      b        21. 2744 = 49a                       22. 570 = 57a
14     56
Functions HW 2
Functions HW 3
Functions HW Review
Assessments and Evaluation

Content Rubric
Oral Presentation Rubric
Written Communication Rubric

Content Standards Covered by this Unit

   17.0 Students determine the domain of independent variables and the range of dependent variables defined by
a graph, a set of ordered pairs, or a symbolic expression.

   18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression
is a function and justify the conclusion.

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