Pupils investigate graphs and networks, with a focus on whether a network is traversable. The resource will do the heavy lifting, and with minimal explanation pupils will be able to work through tasks which build to the Königsberg bridge problem.

No prior knowledge required.

Watch the introduction video if you are not familiar with Eulerian graphs. This video, in less than 3 minutes, explains the rules for traversability.

It is provided for teachers.

Do not play this video for pupils.

1. Print one copy of the attached A3 Teacher Sheet for your reference.

2. You may want to remind pupils beforehand of the definition of edges and vertices. This task does not consider edges which connect vertices to themselves, so I suggest before pupils start that you draw a very simple graph on the board and make the point (perhaps not explicitly) that every time you add an edge to the graph it is changing the valency of two vertices.

3. Distribute one copy of the A3 sheet to each pupil, and allow them to work through at their own pace.