Introduction
Problem Statement
John has just graduated from high school and is going to attend the University of Ontario in a few months. He currently has a cell phone plan with Sprint, but he heard from a friend who goes to UB that he should switch his cell phone plan to AT&T because Sprint does not service the UB area.
John has to decide which AT&T cell phone plan will be right for him. He goes online and finds out that AT&T is currently offering the following plans:
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Plan Name |
Cost |
Phone minutes |
Text Messages |
Additional Options |
Other details |
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Plan A |
$39.99/month
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Unlimited |
250/month** |
Users can have unlimited texts for an additional $4.99/month |
Users must sign a 12-month contract. If contract is broken, there is a fee of $99.99 |
|
Plan B |
$29.99/month |
800/month* |
200/month** |
Users can have unlimited texts for an additional $9.99/month and unlimited minutes for an additional $9.99/month |
Users must sign a 12-month contract. If contract is broken, there is a fee of $99.99 |
|
Plan C |
$49.99/month |
Unlimited |
250/month** |
Users can have unlimited texts for an additional $4.99/month |
This is a monthly plan. There is no annual contract. |
|
Plan D |
$24.99/month |
600/month* |
175/month** |
Users can have unlimited texts for an additional $9.99/month and unlimited minutes for an additional $9.99/month |
This is a monthly plan. There is no annual contract. |
*For all plans that have limited numbers of minutes, there is a fee of $0.05 for every minute used over the limit. For example, if a customer with Plan B uses 900 minutes in a month, then he or she would be charged an additional $5.00 (100 mins X $0.05) for that month.
**For all plans that have limited numbers of texts, there is a fee of $0.10 for every text over the limit. For example, a customer of Plan D that uses 200 texts in one month would be charged an extra $2.50 for that month.
John’s Usage
John has to pay for his tuition, so he doesn’t have a lot of money right now. He wants to get the least expensive plan that he can get without having to change the amount of time he spends talking on the phone and without reducing the number of texts he sends.
John estimates that he sends 6 to 10 text messages each day. He also thinks that he will be talking on the phone for about 20-30 minutes per day on weekdays and 30-40 minutes per day on weekends.
John also knows that next summer he is going to be part of a Summer Abroad program. He will be in Italy for all of June, July, and August, so he won’t be using his cell phone at all during those months.
Task
Your Tasks
Part 1: Approach………………………………………….p. 5
Part 2: Calculations………………………………………p. 6
Part 3: Conclusions and Justification…………….p. 7
Part 4: Represent Your Information Visually………p. 8
Part 5: Facts and Assumptions……………………..p. 9
Part 6: Examine Special Cases…………………….p. 10
Part 7: Critique Another Method………………..p. 11
Part 8: Polished Product…………………………p. 11
Process
Part 1: Approach/Planning a Pathway
Directions: Use the space below to write 3-5 paragraphs describing your plan to solve this problem. This portion should be completed before any calculations are done. Be specific and fully describe each step you will take to arrive at your solution. It is suggested that you make a first draft of this portion of the project on another sheet of paper first.
Optional: In addition to describing your approach in writing, you may create a flow chart or another type of visual representation of your approach on another sheet of paper and attach it to your project.
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Part 2: Calculations
Directions: Use the space below to show the calculations you made to determine which plan is the best possible choice for John. Be sure to label each part of your calculations so that anyone who reads your project can understand what each of the calculations means.
Evaluation
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0-4 |
5-7 |
8-10 |
Points awarded |
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Part 1: Approach/Planning a Pathway |
The student describes some of the steps he/she will take to arrive at a conclusion but misses many steps and/or fails to include any reasons for completing some steps |
The student describes some of the steps he/she will take to arrive at a conclusion but may miss some steps and/or fail to include reasons for completing some steps. |
Student specifically and thoroughly describes the steps he/she will take to arrive at a conclusion for this problem. The description includes reasons for completing each step. |
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Part 2: Calculations |
Student includes few of the needed calculations and/or the calculation page may not be clearly labeled or readily understood by the reader. |
Student shows some calculations used to arrive at his/her conclusion. Some parts of the calculation page may not be clearly labeled or readily understood by the reader. |
Student shows all calculations used to arrive at the phone usage amount for John AND for the cost for EACH plan. Calculation page is clearly labeled and readily understood by the reader. |
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Part 3: Conclusions and Justification |
Student may not state which plan he/she chose or gives a limited explanation of why he/she chose a particular plan. |
Student states which plan he/she chose and gives an incomplete statement of support. |
Student explicitly states which plan he/she chose and explains how his/her choice is the best of all possible options. |
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Part 4: Represent your Information Visually |
Student includes diagram, table, chart, or other visual representation that is unclear and difficult to understand, or student fails to include any visual representation of his/her information. |
Student includes diagram, table, chart, or other visual representation of the information he/she gathered, but the information is somewhat inaccurate and/or incomplete. |
Student includes a neat and accurate diagram, table, chart, or other visual representation of the information he/she calculated about each of the plans and used to make his/her decision. |
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Part 5: Facts and Assumptions |
Student fails to accurately state one assumption he/she has made and/or give an example of another assumption he/she could have made. |
Student accurately states one assumption he/she has made. Student gives an example of another assumption he/she could have made but does not fully detail its possible effects. |
Student accurately states two assumptions he/she has made. Student gives an example of another assumption he/she could have made and describes its possible effects. |
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Part 6: Examine Special Cases |
Student does not consider special cases and/or does not accurately or fully detail the possible changes to the conclusions. |
Student considers special cases but does not accurately or fully detail the possible changes to the conclusions. |
Student considers at least two special cases and describes possible changes to the conclusions. |
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Part 7: Critique Another Method |
Student completes 0-1 of the criteria in the box to the right. ---------------------------------------à |
Student completes two of the three criteria stated in the box to the right. ---------------------------------------à |
Student identifies others’ assumption, makes a supported evaluation or another’s method, and makes a connection. (q 3). |
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Part 8: Polished Product |
Final product unorganized and/or difficult to follow. |
Final product is mostly legible, organized, and easy to read. Some areas may be in need of more organization or completeness. |
Final product is legible, organized, and easy to read. There are no loose papers. Cover is decorated. |
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Turned in on Time |
Project is turned in 3 days late (10 pts). |
Project is turned in 1-2 days late (15 pts) |
Project is turned in on time (20 pts)
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Final Score:
Conclusion
Part 3: Conclusions and Justification
Directions: Answer each question below in complete sentences.
- Which cell phone plan is the best possible choice for John to buy and how much will the plan cost him?
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- How do you know that the plan you chose is the best option?
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Part 4: Represent Your Information Visually
Directions: Use the space below to represent the information you have gathered visually. This could be in the form of a table, chart, graph, or other diagram. Whatever you create should be something that another person could look at and understand why the plan you chose for John was the best option.
Part 5: Facts and Assumptions
Directions: Answer each question below in complete sentences.
- What assumptions did you make while solving this problem? Give at least two examples.
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- What is a different assumption that you could have made? How would changing this assumption have affected the choice that you made? Would you still have picked the same plan? Why or why not?
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Part 6: Examine Special Cases
Directions: Answer each question below in complete sentences.
- Describe any circumstances under which the plan you chose would NOT be the best option for John? What could change about this situation that would make one of the other plans a better choice for John?
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- If John found out that he was not going to go to Italy in the summer, would that change the plan that you chose for him? Why or why not?
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Part 7: Critique Another Method
Directions: Meet with a classmate and discuss the processes that you each used to solve this problem.
Write the name of the classmate you met with here: _______________________________________.
- What is one (or more) assumption that your classmate made that was different from an assumption that you made?
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- What is something that you think your classmate has done correctly? What is something that he/she could improve? Be specific.
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3. In order to complete this project, you were required to make calculations to compare a variety of options and make a choice about the best possible option. Where or when in your life outside of math class do you think you will need to use these skills again?
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Part 8: Polished Product
Now that you have reached the end of the project, it is time to make sure that the whole project reflects your best effort. Check for spelling errors, incomplete sentences, mathematical errors, or anything else that will take away from the quality of your project. Attach any scrap paper or rough drafts that you used to the back of the project. Then, decorate the iphone screen on the front.
Credits
Created By:
WILSON OWUOR
Teacher Page
WILSON OWUOR
Math Teacher