How Much Are You Really Being Charged Per Minute To Talk On Your Cell Phone

Algebra for All Year 2: Lesson Plan Lesson Title: Choosing and Using a Cellphone plan. Investigating Linear Functions

Authors: Tom Trusock, Doreen Paganinni, Heather Thiele Credits: Other Various Internet Sources, attributed where possible

Content Expectations:

NCTM Standards: Content Standards:  Algebra  Data Analysis and Probability Process Standards:  Problem Solving  Reasoning and Proof  Communications

CCC Standards: High School: Algebra  Create equations that describe numbers or relationships. High School Functions:  Interpret functions that arise in applications in terms of the context.  Analyze functions using different representations.  Build a function that models a relationship between two quantities.  Construct and compare linear, quadratic, and exponential models and solve problems. Interpret expressions for functions in terms of the situation they model.

Lesson Outcome: At the end of the lesson students will be able to plot real world data, perform linear regressions (or use lines of best fit) to determine their best options for making a given choice as to a telecommunications plan. Specific additional outcomes are listed in each problem.

Materials and Resources Required: Graphing calculator, pen, paper, worksheet, partner(s), graph paper, internet access for extension.

Procedures:

Suggested video introductions: http://www.youtube.com/watch?v=8N9gSS_HRcE http://www.youtube.com/watch?v=2xx8oew2OQ8 http://www.youtube.com/watch?v=ITCpJT0GVpc

Discussion starters: 1. How many folks here have a cell phone? 2. How many want one? 3. Do you pay for it or does your family? 4. Do you text? How often? 5. How do we choose a cell phone plan? 6. What options do we look for? 7. Maybe we need to make things a little simpler – just to get the point across….

Classwork: Groupwork – Time Required, 2 days. Groups of two suggested, but may be varied due to material availability. Presentation and discussion – Time Required, 1 day. Introductory Lesson (option) – Time Required, 1 day.

Additional Extensions: Choosing between different local companies. Students can obtain information over the internet. Adding in options like pre-pay or pay-as-you-go plans (IE Boostmobile, etc.)

Content Expectations:

NCTM Standards:

Content Standards:  Algebra  Data Analysis and Probability

Process Standards:  Problem Solving  Reasoning and Proof  Communications

CCC Standards:

High School: Algebra  Create equations that describe numbers or relationships.

High School Functions:  Interpret functions that arise in applications in terms of the context.  Analyze functions using different representations.  Build a function that models a relationship between two quantities.  Construct and compare linear, quadratic, and exponential models and solve problems.  Interpret expressions for functions in terms of the situation they model.

Assessment:

Students will have completed the worksheet(s) and will be required to present their answers and methodology to the class via the projector/elmo/board/etc.

Notes: Instructional methodology results. The curves given for the main project intersect at a very remote point, and thus engendered a very good discussion about picking and labeling an axis. For students not ready to leap into the piece directly, we felt that the other, simpler worksheet would be a good lead in and a good by using a more guided approach with a simpler equation. The choice remains up to the teacher to determine what to do. I found, overall that I had some very good results, and the students gained a better understanding of the importance of modeling real world events with mathematics.

Additionally, while my partner and I did not observe each other giving this particular lesson, we did observe others. I’d note that I feel this is a very instructive technique as it helps you identify areas in your own teaching that can be improved. At first I was somewhat hesitant, but ultimately, I found I spend far more time thinking about how their techniques could be best applied to my styles for the benefit of the children. Conversation between the two of us furthered that, and overall I was impressed with the outcome. Now if we can just arrange for 28 hours in a day and the certainty of a job next year (heck I’d settle for the certainty) we’d be good to go.  Choosing a cell phone plan: Investigating Linear Equations (Part 2)

In 2011, Droppedcalls.com offered the following cell phone plans:

Monthly Anytime Monthly Fee Charge for Extra Minutes Minutes 450 $39.99 $.45 per min 900 $59.99 $.40 per min 1350 $79.99 $.30 per min

1. If a customer expects to use 500 minutes per month, which plan is the best value?

2. A cell phone plan consists of a fixed cost (the monthly fee) and a variable cost (charge for extra minutes). Find a function that gives the total cost of each plan when x extra minutes are used. You will find three functions. To what family of functions do they belong? (List your tables here.)

3. Graph and label the linear functions on your calculator and graph paper. 4. Using the cost functions (or graph) from (2) above, determine the cost of using 650 total minutes and 1100 total minutes with each plan. Which plan is the best deal for each scenario?

5. The number of minutes a person uses each month often varies. Suppose that a Droppedcalls.com customer uses the total number of minutes shown below:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 303 303 450 402 501 705 605 600 300 295 375 801

Which plan would cost the consumer the least amount money over the year?

6. Using the functions you’ve predetermined and your graphing calculator, answer the following: At what number of extra minutes does the annual cost of the 900 Plan become less expensive than the 450 Plan? Similarly, where is the break even point for the 1350 and 900 plans? The 450 and 1350 plans? It may be helpful to graph all three functions on the same graph.

7. Which plan would you recommend to a consumer who expects to use between 400 and 600 minutes each month? Explain your reasoning, and justify your answer. Part A (Optional Extension)

8. Zoommobile offers a pay as you go unlimited plan for $64.99 per month with “shrinkage” – in other words, for unlimited data and text you pay a certain fee, but after every six months of on time payments (for 18 months), your rate is reduced by $5, so ultimately you will be paying $49.99 for unlimited voice, however with any of these plans you must purchase the phone. The cheapest phone you can purchase from Zoommobile is $100. Create and graph the function. (Hint, you may need to consider this piecewise.)

9. If a consumer uses around 600 minutes a month, would you recommend they go with a plan from Droppedcalls.com or the “Shrinkage” plan wi Zoommobile? Why? Linear equations and cell phone plans (Optional Preparation for Choosing a Cell Phone Lesson Plan)

This lesson has been prepared for 9th grade Algebra (Algebra 1A). The goals of the lesson are for students to plot data points on a graph, calculate the equation for the line graphed and finally to determine the y-intercept and slope of the line. Overall students will gain conceptual knowledge of a linear equation and will be exposed to a real life application of linear equations. Pass out the problem to the students. Have the students read the problem silently, then choose a student to read the problem out loud. First ask the students to state the goal of the activity. The students need to understand what they are attempting to find. Ultimately, students want to find the base rate a cell phone customer is charged every month and how much the customer is charged per minute.

Questions to initiate discussion: 1. How many minutes did you talk July? How much did that cost? 2. How many minutes did you talk August? How much did that cost? 3. How many minutes did you talk September? How much did that cost? 4. Can you organize this data into a table? Students will recognize that they have been making tables of (x,y) coordinates to graph on the coordinate plane. Some students will make the connection and graph the data points. The students should know how to calculate the slope of this line in order to find the equation of the line in the form y=mx+b. 5. What does the slope represent? 6. What does it mean when the line crosses the y-axis? The students can find the solution by making a table of data points and then graphing the points on the xy-coordinate plane. The equation of the line can then be calculated.

Source: http://www.google.com/url?sa=t&source=web&cd=1&ved=0CBYQFjAA&url=http%3A %2F%2Fwww.csun.edu%2F~mathgs%2Ffermat%2F10-06-05%2520Applications%2520of %2520linear%2520equations- Sara.doc&ei=ZfLLTcWDPISosAOpv4jdBg&usg=AFQjCNHBGPq_89np-QpBkZyJSS8fHIDJug How much are you really being charged per minute to talk on your cell phone?

You receive your phone bill for July, August and September, which comes to a grand total of $260.50. Shocked with the outrageous price, you need to find out how much you are being charged per minute. So you call the customer service line and the information you receive still does not tell you how much each minute costs.

The representative does tell you that in July you talked for 180 minutes at a total cost of $88.00. In August you used 50 minutes at a total cost of $42.50. And finally in September you talked on your cell phone for 300 minutes and you were charged $130.00.

How much are you charged per minute? And what is the base rate to use your phone per month?

Name______Student Worksheet:

1) What do you do first? Show your work. 2) Graph the points 3) Find the equation representing the liner function.

4) How much are you charged per minute? 5) What is the base rate to use your phone per month? Solution

Table of data points

Minutes (x) Cost (y) 180 $88 50 $42.50 300 $130

Equation of the line calculated from the data points:

Y = .35x + 25

How much are you charged per minute? $.35

What is the base rate to use your phone per month? $25