Task of the week: Old City Hall of Michelstadt
Our new task of the week takes us to Michelstadt in the beautiful Odenwald, Germany. Here math teacher Alexander Strache created the task “Altes Michelstädter Rathaus” (engl.: “Old City Hall of Michelstadt”). In the interview he talks about his experiences with MathCityMap.
How did you get to know MathCityMap project? How do you use MCM?
I came across MCM during my studies at the Goethe University Frankfurt. At first through flyers and “advertising” for it in a lecture, then through attending a seminar on it. At the university I also created my first two assignments for MCM. At the moment I am a teacher in the preparatory service and start to build the first math trail for my school.
Describe your task. How can it be solved?
The task is to estimate the area of the roof of the historical Michelstadt town hall as good as possible. On the one hand, many sizes cannot be measured directly, because the roof hangs far above the heads of the students, on the other hand, the dimensions of the ground plan can be walked/measured and other sizes can be estimated well (advanced students can even determine certain vertical distances quite well using a ray set figure). The comparison with neighbouring buildings and counting the floors can be helpful for a rough approximation. For the creation of the sample solution I worked with a craft sheet and looked at the respective surfaces as exactly as possible – on site working with triangles and rectangles is fully sufficient.
What didactic goals do you pursue with this task?
On the one hand, it is about training an eye for simple geometric figures in architecture and, if necessary, to abstract them to even simpler ones: the surface area of many trapezoids, but also general polygons can be approximated by parallelograms or rectangles. Of course, many simplifications have to be made for the small-scale roof surface, but here the mathematical modelling is trained: What can I neglect and simplify without distorting the overall result too much? It is a matter of cleverly estimating non-measurable quantities by “educated guesses”: If I know that the depth of the building is about 10m, how high could the roof be? And of course, as always by using MCM, interdisciplinary skills such as teamwork are trained.
Further comments on MCM?
I think it’s great that a digital tool has been developed here that doesn’t lead to children sitting in front of the screen longer and longer, but that exercise, fresh air, training in local knowledge and an eye for mathematical phenomena in the “real world” play a major role. Furthermore, the competence of modelling is in the foreground, which is very important for me. Even if the development of a good task takes some time and work, it can be used again and again. MCM is therefore ideal for a student council that develops tasks cooperatively.