Your task: work on this puzzle yourself, and let your 'teacher bird' and 'student bird' notice how you approach it, where you can use reasoning and where you need to research, where you get stuck and un-stuck.
Then work on either: (a) extending this puzzle, or (b) coming up with your own puzzle for secondary math students based on a real-life observation you have made (and include a photo or graphic to support it).
The teacher bird would start by analyzing the problem statement thoroughly, identifying the knowns and unknowns. Then the teacher would rely on prior knowledge about the proportions of a Campbell's Soup can and might even know the average height of a bike. Teacher would confidently make assumptions where needed, such as assuming the bike's height in relation to the tank.The teacher bird would set up proportions and equations to relate the knowns to the unknowns. Then consider the implications of the results. Then the teacher would think about how this problem could be extended or modified for different learning objectives, like introducing concepts of scale factor, volume calculations, real-world applications and so on.
If we assume the height of the bike (from the ground to the handlebars) is approximately 42 inches (3.5 feet), we can use this as a reference to estimate the height of the tank. By visually estimating, it seems the bike's height is roughly a quarter (or less) of the tank's height.
Using these assumptions:
Tank Height = 4 x 42 inches = 168 inches
Given the soup can's proportions: Can Diameter : Can Height = Tank Diameter : Tank Height
4.06 inches : 4.6 inches = Tank Diameter : 168 inches
From this proportion, we can solve for the Tank Diameter: Tank Diameter = (4.06/4.6) x 168 inches ≈ 148.3 inches
Volume = πr^2h Where r is half the diameter and h is the height. Volume ≈ π((148.3/2)^2)(168) ≈ 923701.38π cubic inches ≈ 2901893.46 cubic inches or 12562.31 gallons of water
Conclusion:
The tank can hold approximately 12562.31 gallons of water. This would be more than enough to put out multiple house fires.
The student bird might initially be overwhelmed or confused by the problem, unsure where to start. They might need to look up the dimensions of a Campbell's Soup can or ask for clarification about certain aspects of the problem. The student bird might try different approaches before finding one that works. For instance, they might struggle with setting up the correct proportions or making reasonable assumptions. They might ask a peer, teacher, or use resources like textbooks or the internet to help them understand or solve parts of the problem.
While solving this question, they may first get stuck on what the height of the bicycle is and how to construct the equation related to the can. After asking for help, they may have the equation similar to the teacher's solution.
Extended puzzle:
The Hornby Island Council wants to use the space around the water tanks to create a community art project. They plan to have local schools create large, painted tiles that will be laid out in a pattern around each tank. The tiles will be square and each side will be the same length as the diameter of the bicycle wheels.
If the bike from the provided image is used as a reference and is known to be 42 inches tall, and the height of the water tank is four times the height of the bike, calculate the following: Tile Calculation: If the diameter of the bicycle wheels is 26 inches, how many tiles will be needed to create a single row of tiles that extends from the base of the tank outwards by 10 feet?
Very nice, Sally! Good reflections and solution, and I like your extension problem. (FYI, there's only one local school on Hornby Island: the elementary school, with about 50 students...it's a small community!) I think you have interpreted the 'teacher bird' and 'student bird' differently than I intended, although it is still interesting. From what you've written, I think you have interpreted your 'teacher bird' as the confident, competent adult problem solver, and your 'student bird' as the novice problem solver lacking confidence. However, what I meant was that your 'student bird' was the part of you that wanted to dive in and DO the problem-solving, and your 'teacher bird' was the part of yourself that stood back and noticed/ reflected on your own process of problem-solving -- as you would while observing your own students' process. No problem though -- just something to keep in mind if this terminology comes up later in the course!
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