Recently the students in the Year 12 IB Higher Level course designed some interesting liqueur bottles using Volumes of Revolution which is one of the topics they study in Calculus.
The task is an example of a rich task which is likely to capture the interest and curiosity of students. It inspires the students, enabling them to harness their ability to be creative and solve problems while engaging in deeper learning of mathematics. No marks or grades were given for this task, but the end product and achievement is reward enough. It is an example of a formative task for learning.
The students were asked to choose between three and five kinds of functions (for example, logarithmic, exponential, trigonometric, polynomial or rational) to combine so that by revolving them around an axis, they could make an interesting and realistic bottle which would hold 700mls.
The mathematics involved is challenging and extensive. Their results were impressive as the example ‘bottles’ shown below, by Deborah Lam and Ivan Hu, would both hold 700mls correct to the second decimal place! The diagrams are computer representations, using the computer package, Autograph.
Robyn Gregory | Head of Mathematics