Soup Can Response

Response to the questions asked

First of all, I responded to the question asked on the blog. I concluded that there would be enough water to put out a house fire.

Teacher bird, student bird

In responding to the question, I noticed early on that I had a plan. The questions about dimensions and volume are straightforward enough; however, the openness in the question is where a lot of ambiguity lies.

I first realised that I needed to establish a scale of some sort. This is where the assumptions (and research) started. I looked up bikes (and asked someone who knows a lot more about bike sizes than I do) and chose to work with 26" wheels. I measured the picture to get a reference of 3 cm for the 26". So in establishing a scale, I needed to research, make an assumption, and measure relevant pieces of information. I also needed to choose which dimension to use in my calculation. I chose the 22 cm height of the cylinder, as I'd assumed that dimension changed the least, given the damage to the not-so-circular cylinder.

Then came the research on the proportions of the Campbell's Soup can. In conjunction with information that was provided in the question (and assumed to be true), I could use this information to establish dimensions of the cylindrical water tank. Then volume. Then capacity.

At that stage, some quick searches were done to determine how much water it takes to put out a fire on the average-sized house on Hornby Island.

So I feel the main areas for research (that I determined as I went through the question) had to do with lots of averages: bike size, can of soup, average house size, how much water is used.

The things that I knew or could determine included the steps I needed to follow, how to determine a scale, how to use proportional reasoning to provide a reasonable estimate for what I was trying to calculate, unit conversions. I didn't find that I got too stuck. For me, actually using the average values was the challenging part. I think I wanted actual numbers. Like in a textbook. Because word problems are exactly like real life!

(a) Extending the puzzle

This tension leads to the extension that I would pursue for the question itself. A question like this has many variables. And those variables contribute to ranges of information.

For example, setting aside the soup can proportions could lead to providing a minimum and maximum water capacity of the tank (it's cylindrical at one end, but the cross-section morphs into something more elliptical at the other). This could prompt a student to consider a range of values for the actual capacity. Further, questions along the lines of which value would you work from in a situation where firefighting was concerned (Will you make decisions based on the maximum projected value the tank holds? the minimum? an average?) This range strategy could be applied to most of the researched information: bike size, average house size on Horby Island (maybe consider median house size?), even the soup can sizes vary. So, I would try to develop a project where students needed to prepare a proposal for the town council regarding how much water is actually available and whether they may be prepared for a bad fire season.