Instead of relying on trial and error, learners count the degree of each vertex and use the number of odd vertices to predict whether a drawing is possible. They then decide where a successful route must begin and end.

This lesson explores:

• representing drawings as graphs;
• counting odd- and even-degree vertices;
• deciding whether a one-stroke drawing is possible;
• choosing the correct starting and finishing vertices;
• distinguishing crossings from marked vertices;
• explaining failed attempts mathematically;
• repairing and designing one-stroke drawings.

The download includes the main printable lesson together with additional examples, answer checks and complete model solutions.

Suitable for learners aged 10 and over. Familiarity with vertices, edges and degrees is recommended.

This is Lesson 4 of the six-part Beyond Curriculum: Graphs course.

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This resource is completely free. If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi .

The challenge sounds simple: can you walk through the city and cross each of its seven bridges exactly once? Learners replace areas of land with vertices and bridges with edges, turning a complicated map into a much simpler mathematical graph.

This lesson develops:

• translating maps and routes into graphs;
• counting the degree of each vertex;
• recognising the importance of odd and even degrees;
• testing possible routes systematically;
• explaining why some route puzzles are impossible;
• mathematical reasoning through a famous historical problem.

The download also includes further practice and worked solutions in the supplementary examples booklet.

Suitable for learners aged 10 and over. Lesson 1 is helpful but not essential.

This is Lesson 2 of the six-part Beyond Curriculum: Graphs course.

☕ Free to download

This resource is completely free. If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi .

In this introductory lesson, learners discover how graphs can represent connections between places, people and objects. They learn the meanings of vertex, edge and degree, practise translating everyday situations into graphs, and investigate how the structure changes when edges are added or removed.

This lesson includes:

• a clear introduction to vertices and edges;
• practice counting vertices, edges and degrees;
• real-world examples of networks;
• opportunities to draw and interpret graphs;
• answers and discussion;
• a supplementary booklet containing further examples and worked solutions.

Suitable for learners aged 10 and over. No previous knowledge of graph theory is required.

This is Lesson 1 of the six-part Beyond Curriculum: Graphs course.

☕ Free to download

This resource is completely free. If you find it useful and would like to support the creation of more free mathematics resources, you can support Sumthing Else on Ko-fi .