Deutsche Version

Making Networks Visible

Starting point is a task, as is the case in many textbooks.

A largest possible circle is inscribed in an equilateral triangle. What percentage of the area of the triangle is occupied by the circle? incircle

Possible solutions are not supposed to be dealt here further. You can refer to the suggestion proposed by Volker Ulm, Mathematics lessons for individualised learning (see below) or even develop a solution by yourself on the basis of the following chart.
The following task can initiate a reflection upon the selected solutions:

Which mathematical terms and concepts have we used in the processing of the task?
Represent it clearly in a chart!

A joint brainstorming session with the class to gather as many ideas as possible is recommended.
Below you see a possible networking chart. It does not contain all conceivable networks due to reasons of clarity.

Networks

A mouse click leads to enlargement of the image.

The example comes from "Mathematics lessons for individualised learning" by V. Ulm, Kallmeyer 2004.