Sample solutions to Data Deals
Graph of Data Deals
Data Deals
Submitted By:
In this lesson, students compare data plans from different cell phone plans to determine which is a better deal for different amounts of data usage. The plans that are chosen can be represented as linear functions, the cost of the monthly charge and per gigabyte for extra data. Graphing the functions illustrates the rate of change and the "break even points" to help determine when each plan is a better deal.
You may want to update the given data plans to reflect the most current offers from current cell phone providers.
Tell students that you are helping a friend shop for a new cell phone plan. You have researched a couple of different options but its kind of confusing. Here are some options your friend is considering:
- Metro by T Mobile: $70/month for unlimited talk, text, and data
- Republic Wireless: $15/month for unlimited talk and text; $5 per GB of data
- Verizon: $45/month for unlimited talk and text and 8 GB data; $15 for each extra GB of data.
Ask students to share their knowledge and understanding of cell phone plans and how they work. Some examples of questions you could ask include:
- Does anyone have a cell phone plan with data? How does it work?
- What does GB mean?
- What kinds of things do you do on a phone that would use data?
- Some companies have a pay as you go plan and some have monthly plans. Do you know what the difference is?
NOTE: You may want to replace this with information that is more current, but keep the plans relatively simple: one with a constant monthly charge, and two with different rates (monthly charges). To make this task more accessible, you can start with just the T-Mobile and Republic options at first and then add in the Verizon option.
After reading the task, ask students to paraphrase the plans in their own words. Make sure they understand how cell phone plans work with a monthly change, the difference between talk, text, and data, and what a GB of data means. Make sure that students understand the idea of a monthly charge: that you pay at the end of each month based on how much data you have used.
Ask students to make a prediction. Which do they think is a better deal and why? What are some of the factors they should consider? Students should mention that it will depend upong the amount of data use each month or other factors-- cellular coverage and knowledge of the companies, for example.
Let's say she only uses 1GB or less of data a month. Can we figure out how much each phone will cost her for one month?
| GB of data | Metro | Verizon | Republic |
| 1 | |||
Have students work in small groups to continue to explore which phone is a better deal. If students are struggling to get started or stuck you can ask
- Start with Republic and figure out the cost for 1, 2, and 5 GBs. Is the cost going up or down? What makes the cost increase?
- Start with one GB amount: How does the cost compare across the plans? Will that always be true?
Students can solve this problem by creating tables, or writing and solving equations (see student work examples at the bottom)
You may want to have students use a graphing program, like excel, or a graphing calculator to focus more on the meaning of the meaning of the graphs than on graph construction.
Select a range of student solutions for the discussion. Look for students who have created a table, equations, or graphs, and show them in that order to help them make connections. If students don't create a graph you can do that together as a class by working from a table or organized list.
As you project each solution, ask students to discuss:
- Where do you see the monthly charge (and the charge) for data in the table/equation/graph?
- How does the table/equation/graph help us understand how the cost is changing over time?
- How can this help us make a decision about which plan to purchase?
Help students make the connection that the slope of the line shows us the rate of change. Use the example of Republic to bring out the idea of slope or rate of change. Initially the cost of Verizon and Metro does not change with an increase in data usage, so there is no slope. However, the cost of the Verizon plan changes faster once you use more than 8 GB and the graph shows this with a steeper slope than that of Republic.
If no one has used equations, you can build on their solutions to introduce how to write equations for the total cost (c) as a function of monthy charge plus per GB data charges (x):
Metro: c = 70
Republic: c = 15 + 5x
Verizon: c = 45 when x <=8; c = 45 + 15 (x-8)
You may want to note that if charges are billed at the end of each month, this is a step-wise rather than a continuous function.
Through analyzing the three functions through these various representations and solutions, students should eventually agree that it depends on how much data your friend uses:
- If 6GB or less are used, Repuplic costs the least.
- Between 6 and 9 GB, Verizon costs the least.
- Between 9 and 11 GB, Republic costs the least
- If more than 11 GB are used, Metro costs the least.
You can extend this problem by adding further constraints, more plans, more complex plans, or pay-as-you go contracts.
Comments
(no comments)