Year 10 Mathematics · AC9M10SP02

Networks and Connectedness

Networks simplify real relationships into vertices and edges so routes, connections and structural properties can be analysed without unnecessary physical detail

Ready to project and teach

Learning goalsSay it simply

explain the central idea: Interpret networks as vertices and edges, analyse connectedness and use network diagrams in practical situations.
choose and apply an appropriate method without relying on keyword matching
check results using units, substitution, estimation, a second representation or contextual reasonableness
justify a conclusion and communicate limitations where the context requires them

Key conceptTeach from the board

A vertex represents an entity/location and an edge represents a relationship/connection. A network is connected if every vertex can be reached from every other through some path. Always state what the vertices and edges mean in the real context.

Vocabulary

Vertex/node, edge/link, path, degree, connected component.

Connected

There is a path between every pair of vertices.

Degree

Number of edges incident to a vertex.

Euler polyhedra

For convex polyhedra: V−E+F=2, equivalently F+V=E+2.

Worked examplesWe do

Worked examples

AC9M10SP02 - Networks and Connectedness

Example 1

Vocabulary Vertex/node, edge/link, path, degree, connected component.

Example 2

Connected There is a path between every pair of vertices.

Example 3

Degree Number of edges incident to a vertex.

Example 4

Euler polyhedra For convex polyhedra: V−E+F=2, equivalently F+V=E+2.

Curriculum examplesCopied content

Australian Curriculum: AC9M10SP02 — Year 10 Space. Interpret networks as vertices and edges, analyse connectedness and use network diagrams in practical situations.

Victoria: VC2M10SP02 — Level 10 Space

NSW: Stage 5 Path — Introduction to networks

Alignment explanation: The explicit teaching and worked examples address the Australian Curriculum concept directly. The Victorian mapping follows the current Version 2.0 descriptor structure; where Victoria combines or extends content, that difference is stated rather than hidden. NSW uses a Stage 5 Core–Paths structure, so this page maps to the relevant content group(s) and Working mathematically processes instead of inventing a Year 10 one-to-one code.

Lesson component	Australian Curriculum	Victoria	NSW
Explicit concept teaching and worked examples	AC9M10SP02	VC2M10SP02 — Level 10 Space	Stage 5 Path — Introduction to networks
Guided and independent practice	Builds fluency and application for AC9M10SP02	Practises the mapped Level 10/10A knowledge as applicable	Practises the mapped Stage 5 Core/Path content
Reasoning and assessment tasks	Applies reasoning/problem solving in the descriptor context	Supports Victorian reasoning and modelling expectations	Embeds Working mathematically: reasoning, problem solving and communication

Australian Curriculum elaborations

AC9M10SP02: interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness.

E1: model authentic situations and identify meanings of vertices/edges. Examples 1,6,8.
E2: analyse connectedness, including Seven Bridges. Examples 2,4.
E3: represent polyhedra as networks and demonstrate Euler F+V=E+2. Example 5.
E4: model social, LAN, electrical or wireless networks and practical connection/router problems. Example 6.
E5: represent travel, food webs, metabolic or biological structures. Examples 8–9.
E6: represent First Nations Australians’ kinship systems and significance of Country/Place relationships using culturally authoritative material. Example 10.

Questions and answersWith answers

Define vertex and edge for a flight network.: Airports=vertices; direct flights=edges.
What does connected mean?: Every vertex can be reached from every other by some path.
Find degree of a node with 5 incident edges.: 5.

Practice and reviewReady for practice

Not defining what vertices/edges represent.
Assuming physical drawing distance equals an edge weight.
Confusing connected with complete: connected does not mean every vertex links directly to every other.
Applying Euler's polyhedron formula to an inappropriate network.
Flattening culturally specific relationships into invented generic categories.

Classroom View Homework Practice Test

Curriculum alignmentStart here

explain the central idea: Interpret networks as vertices and edges, analyse connectedness and use network diagrams in practical situations.
choose and apply an appropriate method without relying on keyword matching
check results using units, substitution, estimation, a second representation or contextual reasonableness
justify a conclusion and communicate limitations where the context requires them

Official wording is paraphrased on SkillrHub; use the linked curriculum sites as the source of record.

Other curriculum comparisons retained

Networks are less uniformly placed internationally; closest alignments occur in discrete mathematics, graph theory, computational thinking and modelling strands in Australian states, UK/Canadian/NZ secondary mathematics and enrichment curricula.

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