I know it’s probably an unpopular opinion, but I really love spreadsheets. The way you can set them up to adjust one value and have everything change, or manipulate a formula to adjust a fairly large (but manageable) set of data, really makes the calculations much more interesting and less tedious, and lets one start to make sense of some nice patterns. Spreadsheets are also (at least currently) still a part of the professional world, and properly writing an expression in the formula bar is a good and basic introduction to the syntax of programming languages. I don’t do it as often as I would like, but when the opportunity to incorporate a spreadsheet into a lesson presents itself as a good tool to simplify the calculations and get at the interesting math and conclusions, I jump at the chance.
Dan Meyer’s 3 act lesson, Dandy Candies, is an excellent way to explore basic surface area and volume comparisons. But what if we take it a step further?
In case you aren’t familiar with the premise, the lesson starts with a short video of 24 candies being packaged into various boxes, all with integer dimensions and a volume of 24 cubic candy units (where 1 candy = 1 cubic candy unit). Students then need to calculate the surface areas of the boxes and the length of ribbon required. But that’s about where the original problem ends. And this is where mine begins.
Students develop formulas for both surface area and ribbon length, and then create a spreadsheet in which they enter various dimensions for length, width, and height. They can then play around with different combinations to try to find some patterns that minimize both surface area and ribbon length. The next step, of course, is to minimize the actual cost. Students then must research (or be given) costs for cardboard and ribbon. For simplicity sake, we assume that 1 cubic candy unit is 1 cubic inch, meaning that we are looking for square inches of cardboard and inches of ribbon.
This gives another opportunity for some more formulas to find cost of cardboard for each configuration, cost of ribbon for each configuration, and their sum, the total cost of packaging for each box. I have a screenshot of one part of a student spreadsheet, to give an idea of what this (basically) looks like. We used Google Sheets, but this can be done in any other spreadsheet.
As a result of the extra spreadsheet work, along with some additional research time, we now take about two full class periods on this assignment, but the amount of practice that students get with spreadsheets, spatial thinking, and applying a variety of skills makes this extra time well spent. Plus, I show a few clips from Charlie and the Chocolate Factory just to remind my students of the genius of Gene Wilder.