My Solution:
I started off by estimating the size of the medium-sized hybrid bike's frame to be 43cm, which falls in the range of the suggested hybrid bike frame size for a medium sized bike. Then, measuring the scaled length of 43 cm, we can use it as a scale factor to estimate the potential size of the giant soup can. Once we measure to scale, we can use the volume of the giant soup can to calculate the amount of volume of water, and compare with the amount of water needed to put out a house fire.
Extension:
One extension to this problem is to look at the amount of pain needed to paint this water tank. Maybe even go deeper into how long would it have taken to dry the paint depending on the angle of the sun on Hornby Island. This would be a question that, just like the original question, requires some research and connection to science within math. It will require lots of estimations and assumptions, focusing on the different methods that students can use to approach this question. This can be a good math question where teachers can promote math-thinking and communication where there are no correct answers (however there could be a range where reasonable answers should fall).
You’ve got a clean, logical entry point here — anchoring everything to one measurable element (the frame size) is exactly the kind of disciplined estimation we want students to learn. And your extension is fun in the right way: interdisciplinary, open-ended, and full of space for mathematical thinking rather than chasing a single “right” answer.
ReplyDeleteThe one place you could push this further is by letting us see how your scaling played out — even one or two numbers or quick ratio checks would make your reasoning feel more grounded and give students a model of what mathematically accountable estimation looks like.