The same company that makes Fruit Roll Ups® also makes a product called Fruit by the Foot®. Both packages have about the same net weight and cost about the same amount of money. The ingredient lists on both packages list the same items and the nutrition labels are the same, except that a serving of Fruit Roll Ups® is 2 packages instead of 1.
I would like you to compare the 2 products and write a note to the manufacturer telling them which one you find to be the better deal. Which one provides the greatest number of bites and lasts the longest? In other words, which has the greatest "pleasure measure"?
Which one has the most "environmentally friendly" packaging (has the lowest ratio of packaging material to packed material)?
Give the manufacturer specific, detailed information and make a recommendation to the company based on your findings. Should they continue to offer both products? Should they change their packaging?
We were having a conversation during snack time about the various fruit leather snacks students were eating. I was amazed at the wide variety in presentation of essentially the same food product. On my next trip to the grocery store, I perused the fruit snack aisle and found these two products, manufactured by the same company, with the same unit price. Both seemed to be over packaged and offered only a tiny amount of food beneath all that wrapping. Not one to pass up a teachable moment, I designed this task. On one level I hoped that this task would create more aware consumers. There are also many decision-making and math skills required to complete this task. The student must first decide on a focus for comparison. Will s/he compare the relative amount of food product in the boxes? The relative amount of wrapping in the boxes? Or both? The student then must decide on the advice to be given to the manufacturer.
This task required about two hours of structured class time and additional homework time to complete the written portion of the solution. It would be important to teach students how to find surface area and volume prior to presenting this task. The fruit is rolled so thin that students decided to measure just length and width as the height was slightly less than one millimeter and we did not have precise enough tools to measure the actual thickness of either fruit product.
You might present one product per class and have students measure the amount of food product and wrapping in a package for each separately to avoid confusion in keeping track of data.
I had students work in teams to keep the material expenses down. You might get a grocer to underwrite this project by giving you enough of the products to conduct the investigation.
- Have enough packages of the two fruit products to have one individual package for each pair of students (keep the outer boxes available for measuring and for label information).
- Rulers
- Calculators
- A third type of fruit leather product for extension comparisons*
*I had Fruit String Things® by the same manufacturer, they were difficult to measure. Students were surprised to discover that the individual packages for Fruit Roll Ups® represented one-half of a serving. They thought (and I agreed) that there is no reason to use twice as much wrapping when doubling the thickness would be so easy. There appeared to be slightly more product in the Fruit Roll Ups® packages, but more non-recyclable wrapping as well. Both boxes had more cardboard than necessary, so it was possible to pack more servings into a single box than is being done presently. There will be many variations on the solution depending on how and what the student measures. The important point is that students arrive at the ratio of fruit to wrapping, discover that neither of these products is particularly environmentally friendly, and that they are spending more for wrapping than food. The actual measurements in the Practitioner benchmark are extremely close to my measurements. The Expert benchmark has an error in computation on both cardboard areas, but was still chosen as Expert, as this error does not change the solution. This student did a good job of explaining the process of comparing the two products and then comparing the "String Thing" product as well.
These students either did no measurements or did them poorly and did not compare the two products accurately. They had little or no mathematics in their solutions, used no mathematical representations, and presented weak arguments for their points of view. The exemplar includes very little measurement and bases the comparison on nutritional labeling, rather than solving the problem as it was presented.
For the most part these students understood what was asked of them in the task. They did take appropriate measurements, but were often inaccurate in their findings. They got confused between the two products and that led them to faulty assumptions. They did attempt to use mathematical language and representations in their presentation and attempted to convince the manufacturer of their point of view.
The exemplar student found the measurements for one individually wrapped portion of the fruit and its wrappers, but did not multiply that figure by the number of packages in the box for either product. The area of cardboard is close to accurate, given the difficulty in measuring the entire area of all the flaps. The student does make some unfounded statements as indicated in the annotations in the exemplar.
These students understood the task, did the measurements - usually with good accuracy - and made some comparisons. They often left out some aspect of the solution, made faulty comparisons or simply stopped too soon. The exemplar of this group had excellent mathematical language, much of it symbolic, but could have enhanced the solution with diagrams of the measurements written about. This student does have a good table to compare the two products from all aspects.
The Experts solved the problem efficiently and communicated their solutions clearly. Many included the extension product comparison. All of these students wrote their solution to include the letter to the manufacturer, summarizing their findings as instructed in the task. Their mathematical language was accurate, as were their representations. They may even make informed decisions in the grocery store as well!
The exemplar used diagrams to demonstrate the measurements of the fruit products and the packaging. This student made good comparisons of the ratios of food to waste in these two products, considered a third product made by the same manufacturer, and found it to contain less food per amount of waste. The advice to the manufacturer is accurate and well stated.
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