When I first approached this problem, I spent a ridiculous amount of time trying to identify the bike pictured in the photo (it's a sickness) :-) I’m not entirely sure what lesson can be gleaned from this, except that bikes can be quite fixating! After some research, I settled on it being a 2005-2010 Norco Citadel women’s version. At one point, I considered using the standover height for scaling, but that would have been more of a way to show off my bike knowledge than to help solve the problem. Ultimately, I stuck with the 26-inch wheel size, which was more consistent and reliable.
Initially, I considered switching to meters for my measurements. Still, since all the dimensions of the Campbell’s soup can were in inches, I figured it would be easier to keep everything in the same units and convert to gallons when needed.
Researching the standard dimensions of a soup can was more challenging than I expected, but I eventually settled on 4.25 inches for the height and 2.6 inches for the diameter.
I started the problem by framing it according to the “Thinking Mathematically” suggestions: I identified what I knew, wanted, and could introduce. This provided a structured approach.
I used the wheel height (26”) to find a scale and measured its pixel height in the photo (I used the Mac CMD-SHIFT-4 for pixel measurement), creating a pixels-to-inches ratio of 6.15 pixels per inch. I then measured the diameter of the cylinder in pixels, as that seemed to be the most reliable dimension given the partial framing and slight “fold” in the image.
The pixel diameter I found was 575 pixels. Dividing this by the scale (6.15 px/inch), I calculated the real-world diameter to be 93.5 inches. Next, I calculated the tank's volume and came up with 1,049,833.9 cubic inches.
Finally, I converted this volume to gallons using a conversion factor I looked up: 1 cubic inch = 0.004329 gallons. This gave me approximately 4,545 gallons. Considering that an average house fire can be fought with around 3,000 gallons, the Hornby tank seemed to suffice.
Teacher Perspective
From a teaching standpoint, I can see how this real-world problem would captivate students and relate directly to their experiences. My personal connection to Hornby Island added an extra layer of interest and motivation for me.
This problem offered a fun and practical way to teach proportions and scaling, making it a perfect lesson in understanding ratios. The exercise also conveyed the value of estimation. Taking an object with known dimensions and scaling it up to real-life proportions can empower students, showing them the tangible benefits. Though, I think if I were giving this problem in a secondary class I think I'd strongly that they only need to focus on a "rough estimate" as I think it's easy to get bogged down in the details.
Reflecting on what parts of the process proved challenging for students would be a good way to pinpoint areas that may need more instructional focus. For instance, some students might struggle with breaking down the problem, applying proportions, or performing unit conversions. Understanding these struggles can help tailor future lessons for better comprehension and skill-building.
For an extension to this activity, students could be given the actual size of the tank to explore why their initial estimates were either too low or too high. They could examine factors such as the accuracy of the bike wheel size, the proportions of the soup can, the camera's distance from the bike, and the distance between the bike wheel and the tank. This would let student connect their estimations and have them critically assess their methods. I think my estimate was highly impacted by the camera's distance to the bike and the distance of the bike to the tank. Exploring this further with the actual size of the tank might be a natural extension.
It might also be cool for students to calculate how long it would take for someone to ride a bike to the Hornby Island Co-op and back to retrieve enough water to fill half of the fire department's water tank. This scenario would include a known rate of water dispensing (in gallons per hour) and the average speed of the bike, adding an additional layer of applied mathematics and real-world connection. I like this idea because you can incorporate it into a real-world activity, where the class can collect water on foot and associate how heavy even a small amount of water is. This hands-on experience could provide students with an appreciation for water access and usage complexities.
It's interesting how general knowledge can play a role in solving problems! Personally, I'm not particularly interested in bikes, but when I saw the bike in the photo, I immediately decided to use its length as a practical reference to estimate the tank dimensions. As a teacher, how would you guide students to avoid spending too much time on irrelevant parts of a word problem, like focusing on identifying the exact bike model, and instead direct their attention to the aspects that are most useful for solving the problem? What strategies would you recommend to help them balance curiosity with efficiency? At the same time, don’t you think it could be an opportunity for students to learn more about bikes and explore related topics? Why not let this curiosity enhance their learning experience in a meaningful way?
ReplyDeleteMy deep dive into identifying the bike model lightly illustrates how interests can inform problem solving, but I recognize that it’s a delicate balance. It’s probably necessary to draw a line between problem-solving content and student curiosity. They’re interrelated, but it would be healthy (read: efficient) to make the distinction. As you suggest, if curiosity and interest increase the student’s engagement, then by all means.
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