Network Connections Overview

Year Level

Year 12 Mathematics (Australian Curriculum v9)

Unit Title

Exploring Network Connections

Lesson Title

Introduction to Networks

Duration

60 minutes

Class Size

10 students

Curriculum Alignment

Australian Curriculum (v9) - Mathematics - Year 12

Content description:
Understanding networks as systems of interconnected objects, interpreting network diagrams including vertices and edges, and analysing properties such as the degree of vertices.
(Note: While specific AC content codes were not directly retrieved for networks at Year 12, this unit aligns with mathematical modeling, graph theory, and discrete mathematics topics suitable for senior students exploring connections and structures in mathematics.)

Learning Objectives

By the end of this lesson, students will be able to:

Define a network as a system of interconnected objects (nodes/vertices and edges).
Identify vertices and edges in different network diagrams.
Explain the concept of the degree of a vertex and how to calculate it.
Recognise and discuss real-life examples of networks such as maps, social media connections, transport routes, or communication networks.
Create simple network diagrams and label vertices, edges, and vertex degrees.

Key Terminology

Network
Vertices (nodes)
Edges (connections/links)
Degree of a vertex

Lesson Structure

Time	Activity	Details & Resources	Purpose
0-10 min	Introduction & Hook	- Present real-life network examples: social media, maps, transport routes. - Use visuals (images or projected slides showing a social network graph and a city map network).	Engage students with familiar examples and stimulate curiosity.
10-20 min	Concept Explanation and Vocabulary	- Define 'network', 'vertex', and 'edge'. - Introduce 'degree of a vertex' with simple diagrams. - Show how to read network diagrams.	Establish foundational concepts and vocabulary aligned with the curriculum.
20-35 min	Guided Practice: Identifying Networks	- Provide students with printed network diagrams. - In pairs/small groups, identify vertices, edges, and calculate degrees. - Include maps and social connection diagrams.	Reinforce concepts through hands-on identification and calculation.
35-45 min	Class Discussion: Networks in Daily Life	- Facilitate discussion on networks experienced daily. - Examples: how Facebook friends form a network, transport systems in cities, communication networks. - Prompt questions about how networks help organise information and decision-making.	Connect concepts to wider contexts and develop critical thinking.
45-55 min	Independent Task: Create Your Own Network	- Students create a simple network diagram related to a chosen theme (e.g., school friendship network, transport routes between places, or a fictional network). - Label vertices, edges, and indicate degrees for selected vertices.	Apply understanding creatively and personally contextualise learning.
55-60 min	Wrap-Up and Review	- Summarise key points. - Quick Quiz: verbal Q&A to identify vertices, edges, and vertex degrees from sample diagrams. - Homework prompt: Observe a network around them and describe it.	Consolidate learning, check understanding, and extend thinking beyond class.

Resources Needed

Projector or interactive whiteboard for visuals.
Handouts with network diagrams (varying complexity).
Paper, coloured pens/pencils for drawing.
Example images: social media network graph, city transport map.

Differentiation

For students needing additional support: provide simpler diagrams with clear labels and fewer vertices/edges.
For advanced students: challenge them to consider directed networks or weighted edges informally.

Assessment and Feedback

Formative assessment through observation during pair work and class discussion.
Quick verbal quiz at the end to assess understanding of vertices, edges, and degree.
Review the students’ independent network diagrams for accuracy and completeness.
Homework observation task allows informal assessment of applying concepts to their environment.

Cross-curricular Links and General Capabilities

Information and Communication Technology (ICT): Using digital tools or apps to explore networks.
Critical and Creative Thinking: Analysing properties of networks and real-life applications.
Literacy: Using mathematical language precisely.
Ethical Understanding: Consideration of social networks and connectivity impact.

Notes for Teachers

Encourage students to see networks beyond the math — social, physical, and digital worlds are full of networks. This connection enhances engagement and relevance.
Use a variety of examples to cater to different interests—sports, gaming, social media, or transport can all illustrate networks vividly.
The lesson sets the foundation for more advanced network theory explorations in later lessons, such as shortest paths, connectivity, and network optimisation.

This lesson plan provides a richly contextualised, Australian Curriculum aligned introduction to networks for Year 12 mathematics students, building foundational understanding and engagement with this important mathematical area.

Teaching Instructions