Lately I have been buying toilet paper made from recycled paper at an environmental store, but last night we ran out, so I stopped at the local grocery store to pick up a roll. It has been a while since I shopped in the "bath tissue" aisle of a supermarket and I was unprepared for the number of choices available! I used to buy Charmin® brand and I was surprised to discover that it is now possible to buy white Charmin® in 8 different packages. I have listed the choices below. Please help me decide which is the best choice, as I was overwhelmed! 4-Roll Packages:
Ultra Charmin®: 2-ply with 170 sheets per roll costs $1.29/pkg.
Ultra Charmin®: 1-ply with 560 sheets per roll costs $2.49/ pkg.
Ultra Charmin® Double: 2-ply with 340 sheets per roll costs $2.49/ pkg.
6-Roll Packages:
Charmin® Free: 1-ply with 280 sheets per roll costs $1.98/ pkg.
Charmin® Plus: 1-ply with 170 sheets per roll costs $1.98/ pkg.
Charmin® Ultra: 1-ply with 170 sheets per roll costs $1.98/ pkg. 9-Roll Packages:
Charmin® Big Squeeze: 2-ply with 420 sheets per roll costs $4.59/pkg.
Charmin® Ultra Big Squeeze: 2-ply with 260 sheets per roll costs $4.59/pkg.
We had just finished a week of studying ratios and proportions. I wanted to assess the students' ability to apply these concepts in real life situations. We had done a few problems that asked for unit rates, but had not discussed unit pricing. I wanted to see if students could transfer their learning to this area. I was looking for a subject with universal appeal and it seems that this hit the spot. The students loved it! Cruising the bath tissue aisle of the grocery store really was an eye opener for me.
This task gave the students an opportunity to use the skills of problem solving by setting up proportions, practice their division of decimals, and decision making in a problem-solving setting. Students first determined the price per roll and then the price per sheet of the various papers. They then could apply their personal preferences in choosing from packages whose prices were comparable. This task offers the opportunity to make a variety of mathematical representations for comparing the prices of the various packages. 45 minutes We were conducting a unit on media advertising at the time we did this task. We talked about how many students used this brand of tissue and why. Most of them did use this brand and when they went home to discuss it, discovered that the reason was TV advertising and brand loyalty. Just about every student knew "Mr. Whipple".
Students needed very little assistance with this task. They worked alone and the only equipment needed was a calculator. They did the main work of the task in one 45-minute period and then went home to do final write-ups and final representations as many of them chose to use computers for this task.
- Calculators
- Toilet paper samples (optional)
According to the unit prices found on the grocery shelf, the four-pack of 1-ply paper is the cheapest at $0.00111 per sheet. The most expensive are the Charmin® Plus and Charmin® Ultra, both in the six packs. See the Expert student's graph for complete cost comparisons. There is a lot of room for applying special factors in this task. Perhaps you have limited storage space so nine packs are impractical (and surprisingly not the cheapest way to buy toilet paper). Or maybe you need fragrance-free paper, or want the luxury of aloe added to your paper and are willing to pay for this additive. I was personally surprised to discover that the four-pack was so much cheaper than the same paper in a six pack. Some students considered that you might use twice as much 1-ply as 2-ply and compared costs based on this assumption. I am not convinced that there is one correct solution to this task, which is one of its appeals for me.
This student did have an idea of what was being asked, but did not carry out what was started. S/he claims that Big Squeeze is the best buy, but never shows the calculations for this choice. S/he also bases his/her conclusion on the per roll price which is not the best strategy, as there is a wide variety of number of sheets per roll. There is practically no mathematical language and there is no attempt at mathematical representation by this student. S/he was clearly not engaged in finding the solution of this task.
This student had some idea of how to begin to solve this task. S/he got off to a good start in finding the cost per roll, but describes this process incorrectly. S/he divided the cost per package by the number of rolls, not the "toilet paper" by "how many rolls are in the package." His/her error on page two came from dividing the number of sheets by the cost per roll instead of the other way around. S/he did not see that $.05 per sheet was too expensive to make sense. On page three the student states that Charmin® Free is the best buy and that does make some sense as there are more sheets per roll for that brand. But, the student ignores the price per sheet information from page two in his/her final decision making. Mathematical language is lacking and the comparison data is not well organized into charts or tables. I believe many of the errors in this piece would have been spotted if the student had checked his/her work or tried to verify his/her solution.
This student showed some excellent reasoning in his/her solution. The decision about one vs. two-ply paper is very interesting and well founded. S/he does a good job of informing the reader of his/her thought processes, although his/her mathematical language is rather weak. The mathematical representation is well done and complete. There are some calculation errors to be found in the chart. However, while brief, this solution does accomplish the task as assigned and is clear in presentation.
This student used technology to his/her advantage in representing his/her solution in an easy to read manner. S/he took a straightforward approach to the solution and applied no special factors to her approach. It is not the most creative solution I received, but it is the clearest. The student clearly articulates his/her reasoning throughout the narrative. The chart is clearly organized, easy to read and makes it easy to compare the costs. The graph provides a clear visual comparison of the prices of the various packages. This graph is representational of many done by students in the class using computer technology.
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