Introduction to networks (Path)
Mathematics K–10 (2022) · Stage 5 · View this focus area on the NESA NSW Curriculum website ↗
Outcomes
MA5-NET-P-01 solves problems involving the characteristics of graphs/networks, planar graphs and Eulerian trails and circuits (Path: Stn)Content dot points
Each dot point has its own page with resources matched to it.
Examine and describe a graph/network
- Describe a network as a collection of objects (nodes or vertices) interconnected by lines (edges) that can represent systems in the real world 1 resource · 1 interactive/game
- Examine real-world applications of networks such as social networks, supply chain networks and communication infrastructure, and explore other applications of networks
- Explain that the terms graph and network are interchangeable
- Identify and define elements of a graph including vertex, edge and degree 2 resources · 2 interactive/game
- Explain that a given graph can be drawn in different ways
Define a planar graph and apply Euler’s formula for planar graphs
- Define a planar graph as any graph that can be drawn in the plane so that no 2 edges cross 2 resources · 2 interactive/game
- Define a non-planar graph as a graph that can never be drawn in the plane without some edges crossing
- Demonstrate that some graphs that have crossing edges are still planar if they can be redrawn so that no 2 edges cross 1 resource · 1 interactive/game
- Identify the number of faces in a planar graph 1 resource · 1 interactive/game
- Describe and apply Euler’s formula for planar graphs: v - e + f = 2, where v = vertices, e = edges and f = faces 1 resource · 1 interactive/game
Explain the concept of Eulerian trails and circuits in the context of the Königsberg bridges problem
- Explain that a connected graph is a graph that is in one piece, so that any 2 vertices are connected by a path
- Define a walk on a graph to be a sequence of vertices and edges of a graph
- Explain the difference between trail, circuit, path and cycle
- Relate the definition of a trail to an Eulerian trail as a walk in which every edge in the graph is included exactly once 3 resources · 2 interactive/game
- Relate the definition of a circuit to an Eulerian circuit that is defined as an Eulerian trail that ends at its starting point 1 resource · 1 interactive/game
- Relate Euler’s Seven Bridges of Königsberg network problem to the definition of an Eulerian trail or circuit 3 resources · 3 interactive/game
Focus area resources
- Unit/PlanningSample unit – Stage 5: introduction to networks
- Unit/PlanningStage 5 Unit 1 – geometric representations (sample unit of learning)
Stage 5 planning resources
Stage- or course-wide documents (scope and sequences, guides) that cover this focus area alongside others.
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 03)
- Unit/PlanningSample scope and sequence: Stages 4–5 core and selected paths (NESA no. 04)
- Unit/PlanningSample scope and sequence: Stage 5 core and all paths (NESA no. 05)
- Unit/PlanningSample scope and sequence: Stage 5 core (NESA no. 02)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 06)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 01)
- Unit/PlanningSample scope and sequence: Stages 4–5 stage based (NESA no. 08)
- Unit/PlanningStage 5 – sample scope and sequence
- Unit/PlanningStage 5 – stage based – sample scope and sequence