A Fruit Roll Up weighs 0.5 oz & is a 12.5 by 11 cm parallelogram.
A Fruit by the Foot weighs 0.75 oz & is rectangular. One dimension of this rectangle is 2.2 cm. What is the other dimension?
(Be sure to state your assumptions, and any other information you draw upon in your solution.)
There are now Cheez-Its BIG. They claim to be “Twice as Big” as ordinary Cheez-Its. One serving of regular Cheez-Its consists of 27 crackers and weighs 30 grams. One serving of BIG Cheez-Its also weighs 30 grams.
(A) How many crackers should one serving of BIG Cheez-Its contain?
(B) How many does it contain?
Problem 1: insufficient information. What is the thickness of each product?
Indeed, gasstation. I have revised the task to include a call for stating assumptions in the solution. In fact, one could give an algebraic expression as a solution, where the independent variable expresses the relative thicknesses (and/or densities) of the two products.
As an additional observation, it is my experience that only textbook math problems come along with all of the information necessary to solve definitively. All other uses of mathematics in my life (including in the grocery store) have required that I make some assumptions or gather further information.
In fact, those are the problems I am usually much more interested in solving than the neat and tidy textbook ones.
You can imagine that there is a certain breed of student who finds this characteristic in a teacher to be frustrating.
Word. A popular quote from my classes this past year, “That’s doing too much, Mr. P.” …better than not enough, I always said.
I don’t mind insufficient-information problems, as long as students are warned about them. If they are regularly used in your class, that may be sufficient warning, but initially it is probably better to scaffold the reasoning a little more—not just “state your assumptions”, but “what other data would you need to answer this question? Make some reasonable guesses at that information, and state them clearly.”
I did the fruit roll-up exercise yesterday. My students had eaten them before but we didn’t have any available here in Japan. So in addition to assuming the thickness of each product to be equal, we assumed the density to be equal (slightly different ingredients). Also, the students assumed the parallelogram’s dimensions to be base and height, not lengths of sides. Otherwise, they couldn’t come up with the area.
As has been mentioned, stating assumptions and thinking about what additional information would be helpful, are a big part of math. We also ended up talking about how many decimal places it made sense to include in the students’ answers.
Thanks for the fun exercise!
Christopher, You asked on twitter about my students answers and thinking. They got about 94 cm for the length of the Fruit by the Foot. Then they thought that should be converted to feet because of the product name, and ended up calling it three feet. Different groups came to that answer differently, but the group I observed the most calculated the area of the Fruit Roll-Up. multiplied by 1.5, then divided by 2.2.
Inspired by your recent posts, I did some more grocery store math with four different sales units of snickers bars. If I get a chance, I’ll blog about it and link here.