K–10Mathematics K–10 Syllabus
The new Mathematics K–10 Syllabus (2022) is to be implemented from 2024 and replaces the Mathematics K–10 Syllabus (2012).
School sectors are responsible for implementing syllabuses and are best placed to provide schools with specific guidance and information on implementation given their understanding of their individual contexts.
Content
Stage 5
- MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
- MA5-NET-P-01
solves problems involving the characteristics of graphs/networks, planar graphs and Eulerian trails and circuits (Path: Stn)
Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.
Describe a Loading as a collection of Loading (nodes or vertices) interconnected by Loading (Loading ) that can represent systems in the real world
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 Loading and network are interchangeable
Identify and define elements of a graph including Loading , Loading and Loading
Explain that a given graph can be drawn in different ways
Define a Loading as any graph that can be drawn in the plane so that no 2 edges cross
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
Identify the number of Loading in a planar graph
Describe and apply Euler’s formula for planar graphs: , where = vertices, = edges and = faces
Explain that a Loading graph is a graph that is in one piece, so that any 2 vertices are connected by a Loading
Define a Loading on a graph to be a sequence of vertices and edges of a graph
Explain the difference between Loading , Loading , path and Loading
Relate the definition of a trail to an Eulerian trail as a walk in which every edge in the graph is included exactly once
Relate the definition of a circuit to an Eulerian circuit that is defined as an Eulerian trail that ends at its starting point
Relate Euler’s Seven Bridges of Königsberg network problem to the definition of an Eulerian trail or circuit