As in teacher perspective, this puzzle is pretty straightforward. By using the ratio of the bicycle's height to that of the big soup can, we can measure the corresponding position of the small soup can when lying flat. It is approximately at half the height of the 'P' letter and perpendicular to the ground. This proportion helps calculate the dimension ratio between the small soup can and the giant soup can using the scale, and subsequently, we can use the volume formula to approximate the tank's water capacity.
When I consider this problem from a student's perspective, I realize that it is far from simple. First, I need to comprehend the feasibility of enlarging the proportions. Moreover, I must understand that volume cannot be simply scaled by a proportion of length, which is an error I have commonly observed in many of my past students. Furthermore, I would need to be aware that the soup can is a cylinder, and its volume is calculated using the formula of the square of the radius multiplied by π and then by the height. Understanding this formula would also require prior knowledge of what π represents.
The one approach of me as a student: base on the online information, the normal soup can has 6 inches as height and 2.5 inches as radius, we get a ratio of 6 and 2.5; assume the bike is standard length 1.75m, and the height of the giant soup can is 3.6 multiples length of it, then the dimension of the giant soup can would be: 1.75m*3.6= 6.3 m, with the 6:2.5 ratio, the radius of the giant soup can would be 6.3m/6*2.5=2.625 m. And so the volume of the giant soup can would be 6.3*2.625^2*π ≈136.38m^3
The application of real-life examples in teaching holds significant meaning. I have a friend whose struggle with mathematics, mainly after the 8th grade, was primarily due to the sudden abstraction in the teaching approach. Thus, I believe that for children whose abstract thinking is not fully developed, utilizing tangible objects in teaching can help them establish a more direct connection between mathematics and reality.
An example that left a profound impression on me was from a video I once watched. A young girl asked her brother how to equally divide a quarter-damaged square cake to share with her four best friends while maintaining the same appearance.
Pausing the video, I spent two minutes contemplating how to solve it. Eventually, I realized that the remaining 3/4 of the L-shaped cake needed to be further divided into four equal parts each, totaling 12 pieces. Then, I rearranged them as a puzzle, forming four identical L-shaped cakes. This process involved introducing the concept of fractions and engaging in a puzzle game, making the idea quite captivating.
（reference video: https://www.youtube.com/shorts/hgp-BzhkF8Y)
Another brain-teasing puzzle that astonished me was how to divide a circular cake into eleven equal parts without a protractor. Although I didn't come up with a mathematical proof myself in a short time, the solution was super amazing and incredibly surprising!
Indeed, we are aware that using a protractor can relatively accurately divide a circle into any factor of 360, or the method of bisecting to divide a circle into powers of 2. However, with the prime number 11, which is quite hard without measurement, but a clock with fixed rotating dials provides a useful analogy. Since the minute hand of a clock completes 12 full rotations before aligning with the hour hand, and, remarkably, the 12th alignment coincides with the initial one, indicating that in a full rotation of hour hand aligns with the minute hand in 11 distinct positions. Consequently, by manipulating the minute hand of a clock, we can identify these 11 positions of alignment, mark their directions, and connect the centers of the clock's hour and minute hands to divide a circle into 11 equal parts!
Hi You. A few things here: (1) You've said something about how you would solve the soup can puzzle, but you haven't actually showed a solution (i.e., your 'student bird' point of view); (2) You've done some work toward finding some interesting further puzzles, but (a) the 'cake' puzzle is not very challenging, as far as I can see! You are just cutting each of the three pieces into four quarters, and leaving them where they are...so what's the puzzle?? (b) I REALLY don't get the 11 slices of moon cake puzzle! The clock is divided into 12 segments (of 5 minutes each), NOT 11. I watched the video, and it didn't make sense to me at all. Maybe I'm missing something? But also, you were asked to create your own puzzle, from something YOU have observed in life, with a photo you have taken. There are lots of puzzles online, but this was supposed to be an original one from you yourself!
ReplyDeleteIn any case, this post needs some revision: (1) Please add your solution of the soup can problem, and (2) Please add a puzzle of your own, based on your own observations and using a photo you have taken of the situation that prompted your puzzle. Let me know when you have completed this so that I can check it and mark this as complete!