Networks: Year 10: Planning tool

Expected level of development

Australian Curriculum Mathematics V9: AC9M10SP02

Numeracy Progression: n/a

At this level, students develop the ability to use visual representations to solve problems. Networks is a new area for Year 10 and may be unfamiliar to many teachers. Also called 'graph theory', networks and network diagrams are ways of displaying and describing relationships and modelling connections. Networks serve as a model for decision making, much like a flowchart, and enable users to follow a sequence of tasks that show clear connections between them.

It’s important to demonstrate how networks work and how they apply in the real world. Ensure students are introduced to common vocabulary such as 'nodes', 'vertices' and 'edges', and use these terms when they are working and describing. It is important to emphasise that the order of events is important so that a pathway may be taken, and that the diagram is not just a set of visual of nodes that are unrelated. Spend time on the elements of networks and how to draw them, so that students may equally interpret a diagram when they are presented with one.

Networks may be drawn by hand in order to understand and design them, but appropriate dynamic geometric software can add complexity and engagement as students make sense of the topic. Furthermore, engagement may be enhanced by talking about the Konigsberg problem alongside referencing the application in the real world; for example, social networking, electrical diagrams and travel.

Teaching and learning summary:

Demonstrate how to draw a network diagram.
Use the bridges of Konigsberg problem as an example.
Discuss Euler’s formula: F + V = E + 2.
Introduce the terminology of networks:
- node (or vertex) – a point, which could be a person, place, activity
- edge (or arc) – this is a line joining nodes, which could represent a route, cost, activity
- degree – the number of edges at a node
- weight – this represents the cost of using the edge
- graph – a group of nodes and edges.
Investigate where networks can be used to model authentic situations – travel, social networks, electrical diagrams, distribution.

Students:

can draw a diagram to model a network
understand and use the terminology of networks
interpret networks and network diagrams modelling relationships and connectedness
know where networks can be used to model authentic situations.

Some students may:

have difficulty constructing a network diagram that is based on a sequenced set of events
assume that a pathway may only go in one direction when some pathways go backwards, which leads to misinterpreting a network diagram.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

We are learning to think about networks as a sequence to follow.
We are thinking about networks as a series of connections.

Why are we learning about this?

Giving instructions can be complex and sometimes involves many interrelated connections. Sometimes we need to give complex instructions to others, machines, software programs or mapping programs so that the sequence and connections are recorded, and can be followed or checked or provide a way of understanding in our complex world.

What to do

Below are two resources for you to learn more with your family. The first is an explanatory resource that helps you figure out what basic networks encompass.

The second resource is an interactive you can use on your device. The great thing about interactives is that you are more engaged with learning, can re-do it continually, connect what you have just learnt and experience how it works.

Basic network

Read through this resource , which gives a simple, clear explanation of nodes, edges and weights.
Make a mini-notebook to use use as a reference guide so that each page is a new term, definition and explanation. Give examples where you can.

Moving through a network

3. Use the interactive to take learning further by demonstrating differences between paths, walks, trials and circuits.

Success criteria

I can understand networks and use the right vocabulary.
I can make or follow pathways and see how a complex system is connected and interconnected.

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Planning tool

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