One of the Year 10 Mathematics groups already wrote their IGCSE Mathematics exams and have hence started an Additional Mathematics course. To emphasise that Mathematics is a creative subject, we have chosen to use 10 periods for a project titled ‘Around the corner’.
As an added bonus, this also allows the students to practise their mathematical writing skills, which they will need later: for every IB course in the subject 20% of the final exam grade is obtained through project work.
The students started their research with the question whether a piano of 1,54m long and 0,60m wide can be moved around the corner in a corridor of width 1m and then next, whether a rectangular sofa of dimensions 1,36m by 0,78m would fit.
The students have been very creative, constructing actual corridors for experiments, and coming up with little side-conjectures to prove or disprove. And that’s where the real mathematics come in:
- how can you (dis)prove that a rectangle that you move around the corridor describes an area bounded by a circle that seems to have the rectangle length as its radius?
- how can you prove that the longest stick that fits through is determined by the diagonal that makes a 45o angle with the walls and just touches the inner corner?
It even turns out that the final question ’What is the largest object that you can get through the corridor?‘ is actually an unsolved mathematical problem! And what does ‘largest’ mean? Is it the object with largest area, or with largest circumference, or is there another measure that would make sense?
Our Year 10 students are not likely to solve this problem, but they are supposed to remember that mathematics is not just about questions with known answers.
And that some practical daily-life problems relate to great unsolved mathematical questions.