The Giant Soup Can of Hornby Island

        This specific problem challenged me to investigate geometric shapes, proportional reasoning, and real-life practical applications for volume calculations. With a little research, I know the water tank's dimensions were identical to those of a Campbell's soup can. Measuring a typical soup can, the dimensions read around 12 cm in height and 7 cm in circumference. The bicycle, which looks like an adult bike, has a saddle height of around one metre. I then calculated the tank's height by comparing the two figures, using the bike as a point of reference. I calculated the tank's height to be around 10 metres, which is like ten times taller than the bike. 

    After collecting the data, I used the equation of a cylinder to determine the water tank's volume. The volume, when substituted into the formula, is 267.34 m³, roughly around 267,300 litres, after using the metric conversion rule. It usually takes 10,000 to 20,000 litres of water to put out a conventional home fire, according to my research on firefighting. For this reason, the tank's capacity is more than enough.

    As I thought back on my procedure, I saw where I had to make assumptions and where I had to rely on logic. For example, I estimated the height of the bike and the size of the soup container. Real-world situations lack perfect data. I reviewed my data and verified the logic of my calculations when I ran into difficulties, particularly when attempting to visualize the tank's dimensions. I then began considering ways to expand the puzzle or make my own as I solved the challenging question. Examining how long the tank could support a fire hose running at a particular flow rate would be one method to expand this scenario. 

Student vs. Teacher Approaches used:

"Student Bird Approach"

• Focus on understanding the problem and analyzing the given information
• Use proportional reasoning with known dimensions (soup can and bike height)
• Make reasonable assumptions (e.g., standard bike height = 1 m)
• Apply geometry formulas to calculate volume

"Teacher Bird Approach"

• Considered how to scaffold the problem for students, such as guiding them to justify assumptions.
• Identified opportunities to teach proportional reasoning and volume concepts in real-world contexts.
• Thought about ways to engage students, such as using visuals or real-life connections.

    All things considered, this task demonstrated to me the need of applying mathematics to real-life situations. This kind of puzzle pushes me to use ideas like geometry and volume/proportions while developing my critical thinking skills because problem require a lot of thinking and planning. I also gained a deeper grasp of my problem-solving approaches.