When I first saw the problem, I immediately thought about using proportions and I was able to link it to Math 9 BC curriculum. I knew that since the water tank was in the same proportion as the soup can, scaling up from the can’s dimensions would let me estimate the tank’s dimensions. Right away, I could recognize the problem as a blend of practical scaling and real-life math applications, which made it feel engaging and approachable.
I decided to start by determining the dimensions of the soup can. A quick google search revealed that it’s about 10 cm tall with a 6.5 cm diameter. Next. I needed the dimensions of the bike. Since, I'm not very well versed in the types of bikes, I went with the average 27 inches or 68 cm diameter of the wheel of the bike. Letting go of perfection was a little challenging for mw in this step as I have always focused on accuracy in math. Once I had dimensions for both the soup can and an estimated bike height, I found the scale factor by dividing the tank height by the soup can height. Applying the scale factor to the soup can’s radius and height gave the water tank’s dimensions. At this stage, I realized that I needed to be careful with the units to avoid simple but easy-to-make mistakes, like mixing up diameter and radius. Then, to calculate the volume of the tank, I used the formula V = πr2h. The calculations were straightforward since I already had both the radius and height for the tank.
Reflecting on this puzzle from Teacher's Perspective, I was immediately excited to see this problem because I could connect to the curriculum and I could see how it has the scope to engage students. To extend this problem, surface area could be introduced. Students could work on how many buckets of paint would be needed to paint the tank.
Another puzzle like this that would engage the students would be to use a picture of themselves next to an object of interest and use their own height and their height in the image to come up with a scale factor, then using that scale factor, students can figure out the height of the object of interest. Some students have pictures with athletes and other celebrities that they could use to find their true height.
Nice work, Manveen! Working with inexact estimates can be frustrating, I know -- and many of your classmates' estimations and assumptions differed enough that that they got an estimate of about double the volume you did! Nonetheless, your work is well justified all along and your reflections and extension are thoughtful and interesting. Thanks!
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