Mathematical tasks connected to real world problem solving have the potential of building mathematical identity and increasing “engagement and motivation in mathematics”(as cited in NCTM, 2014, p.17).
As consumers, we can use mathematics to explore multiple factors before making a purchase. Comparing the cost of different items is a valuable skill directly related to mathematical understanding and quantitative literacy.
Smartphones and tablets have become a part of our everyday lives, which means we often have to decide which data plan to purchase along with these devices. We may consider:
- the number of people sharing the data plan,
- the type of internet-related and app-based activities used
- upfront costs and fees
Let’s say Herizon Wireless offered two data plans. Which plan would be the most reasonable choice, and why?
- The Pay-Go Plan costs $30 per gigabyte but has no monthly charge
- The Select Plan has a monthly fee of $100 but you only pay $15 per gigabyte
As I began to think through this situation, I considered these questions:
- Will the data plan with the lowest monthly charge always be the best option?
- Is there a point where the cost per gigabyte will outweigh the monthly charge when determining the overall value of a data plan?
We can compare the cost of each phone plan using a spreadsheet. In an earlier blog, I discuss the reasons why spreadsheets are useful mathematical action technology tools (Biegie, 2017; Dick & Hollebrands, 2011). In this investigation, analyzing the data within a spreadsheet will help us to predict the most cost-effective plan, develop generalizations based on our reasoning, and justify our decisions given the calculated values.
Spreadsheets for Extending Patterns
I started by using Columns A, B, and C in a spreadsheet to represent the number of gigabytes purchased, the Pay-Go and Select plans respectively. The data within this worksheet is the cost of both plans for 1 month. (Picture 1)
In the “Gigabytes” column, I started with 0 and increased the value in each row by 1, since gigabytes are not sold in a fractions of a gigabyte. To do this within a spreadsheet, I could enter each successive value in a new row (i.e. 0, 1, 2, 3), but there is another option within a spreadsheet application which can accomplish this task in a faster way. First, I entered “0” in cell A2 and “1” in cell A3, then highlighted both cells to identify this as the number pattern I wanted to extend to other rows. In the bottom right-hand corner of the highlighted cells, is a small white square. A previously established pattern can be extended by clicking then holding the mouse on this square and dragging the square to highlight a select group of empty cells.
Because Columns B and C represent the costs of the Pay-Go and Select plans, I changed the data format to currency. To determine the cost of the Pay-Go Plan, I entered “0” in cell B2, and “30” in cell B3 because the cost for 1 gigabyte of data is $30. Since the cost increases by $30 for each gigabyte, I wanted to establish and extend a pattern to determine the cost of multiple gigabytes. The recursive formula I used to represent this pattern involved adding $30 to the value in the previous cell. Mathematically, the pattern could be represented as:
Much like the process of filling down the values in the Gigabytes column, I filled this formula down the remaining cells of Column B. (Picture 2)
Next, when determining the cost of the Select Plan, I started by entering “100” in cell C2. The cost of this plan starts at $100, and with each gigabyte of data, the cost increases by $15. The recursive formula I used to represent this pattern involved adding $15 to the value in the previous cell. Mathematically, the pattern could be represented as:
Much like the process of filling down the values in the Pay-Go column, I filled this formula down the remaining cells of Column C. (Picture 3)
Comparing the Plans
Looking at the data in my spreadsheet, I was able to compare the monthly cost for each data plan. For up to 6 gigabytes, the cost of the Pay-Go plan is less expensive than the Select Plan. When 7 gigabytes are purchased, the cost of the Pay-Go plan increases to $210 and the cost of the Select Plan only increases to $205. At this point, the cost of the Pay-Go plan continues to exceed that of the Select plan. We can conclude that if you plan to purchase no more than 6 gigabytes, the Pay-Go plan would be the better buy. If you plan to purchase 7 or more gigabytes of data, the Select plan is the better buy.
Wait, there’s more!
What if Herizon Wireless introduces a new Unlimited Plan which costs $240 per month for as much data as you wish to use? How does this data plan compare to the Pay-Go and Select plans?
I used Column D of the spreadsheet to represent the Unlimited plan. Mathematically, the values in this column could be represented with this equation:
After formatting the column as currency, I entered 240 into cell D2 and filled the value down the entire column (Picture 4).
According to the spreadsheet, the cost of the Pay-Go and Unlimited plans are the same when 8 gigabytes of data are purchased. When 10 or more gigabytes are purchased, the cost of the Pay-Go and Select plans exceed the Unlimited plan. With this data, we can conclude the Unlimited plan would be a best buy if you would like to purchase 10 or more gigabytes of data. From evaluating the monthly plan cost data created within this spreadsheet, we can now see that each plan could be consider a “best buy” depending on how many gigabytes you want to purchase.
The Chronicles of Algebrea 