Task of the Week: The Ring
Dominik Enders, a student of the German grammer school (Gymnasium) in Bad Neustadt, created our new Task of the Week (the task “Ring”). In the interview, he explains why the students at his school create their own MCM tasks.
How do you use MCM and why?
I participate in a project, led by teacher Ms Gleichmann, in which we create math trails for pupils from younger classes, which you can tackle in your free time or on hiking days.
Describe your task. How can it be solved?
My problem is about a ring-shaped piece of sports equipment on a playground, of which you are supposed to find the area of the upper side. Assume that the edges of the ring are smooth, i.e. without indentations.
First you have to calculate the area of the circle up to the outer edge of the ring (tape measure/inch stick and pocket calculator are required) by determining the radius and then
calculate the area of the circle. Using the same procedure, calculate the smaller area of the circle enclosed by the inner edge of the ring. Then you only have to subtract the smaller area from the larger one to get the area of the top of the ring.
What didactic goals do you pursue with the task?
The task refers to the teaching content of the 8th grade and represents an application of the pupils’ knowledge on the topic of the area of a circle. The circle-ring is more demanding, but this can be mastered by using the area formula for two circles. The reference of mathematics in the 8th grade to a piece of sports equipment on a playground, which the pupils know from their everyday experience, should be motivating. By measuring lengths (radii), the topic of sizes from Year 5 is also addressed, as well as the importance of measuring accuracy.