Resources

• Projector and Directed Network Images (see Orientation)

• Laptops (see Body 1)

• Food Chain Passages (see Body 2)

• Exit Slips (see Conclusion)

Orientation

Working Mathematically: Understanding, Fluency

Collect students' homework from the last lesson. Check whether students have an understanding of connected networks (AFL).

Think-Pair-Share (10 min) [LIT]

Project the Directed Network Images onto the board. Instruct students to engage in Think-Pair-Share to discuss each of the images.

• • Think: Students individually analyse the images, brainstorming factors that might be of interest

    • • If students need help, remind students to consider the terminology they have covered in previous lessons

  • Pair: Students converse with a partner and share their ideas

  • Share: Students discuss and refine their responses with their table groups

Conduct a verbal class discussion to gain insight into the ideas students have collated (AFL). Ask students what all of the images have in common, and what particular images are showing.

• Expected answers: "all these networks show one-way systems"; "mostly natural networks/systems"; "branches"

Introduction

Working Mathematically: Communicating, Fluency, Understanding

Group Network Modelling (10 min)

From the Orientation images, choose one to model into a directed network.

For instance, show that the directed network mapping of a river system starts at the source and makes its way to an ocean, lake or bigger river. Ensure that students understand that the arrowhead for directed edges can be placed either in the middle or at the end of the edge.

Instruct students (in groups) to select one of the images from the Orientation activity to draw as a directed network. Provide each group with a printed copy of their selected image, monitor their progress and ask the following questions (AFL):

• What did you notice about your network drawing?

• Does the network flow in one general direction?

• What does this indicate about the network as a whole?

Body 1

Working Mathematically: Communicating, Fluency

Online Graph Drawing (20 min) [ICT]

Ask students to open the Directed Graph Editor website and show them how to use the available tool.

• • Add in enough vertices and edges so that five vertices connect together to make a pentagon with a sixth node inside the pentagon.

  • There should be edges connecting the outer nodes together to create the pentagon shape, and edges extending from the inner vertex to the outer vertex.

  • Each edge should have an arrow extending from either the central vertex out towards the outer vertices, or extending from the the outer vertices inwards to the centre vertex.

Describe this directed network using explicit vocabulary (edge, vertex, direction, one-way, two-way). Afterwards, instruct students to explore the website in pairs using their laptops, experimenting with as many vertices, edges and arrows as they want. Once students are content with their creation, they should draw it into their workbook and write down how many edges and vertices there are, as well as how many one-way or two-way edges there are. Monitor students' work and check that their final drawings are clear and correctly labelled (AFL).

Ask students to answer the following question (AFL): Suppose I was standing at any vertex on your network diagram, and I wanted to move to another vertex by travelling along the edges. What is the difference between a one-way and a two-way directed edge?

Body 2

Working Mathematically: Communicating, Understanding, Reasoning

Food Web Passage Construction (10 min) [LIT]

Explain to students that directed networks may sometimes show the (one-way) relationship between two things. Show students the food web image from the Orientation activity, and discuss briefly what each tier in the food web hierarchy corresponds to:

• producers (e.g. plants), first-order consumers, second-order consumers

• Alternatively: plants, herbivores/omnivores, predators, apex predators; depends on the scientific literacy of the class

Explain that organisms are connected by arrows if one is eaten by the other (i.e. A --> B if A is eaten by B).

Provide students with the Food Chain Passage that details an example ecosystem, and instruct them to read it then to draw the food web that is being described. Afterwards, have a student (or group) draw the network on the whiteboard, and ensure everyone has a matching diagram (AFL). Ask the following questions to the class (AFL):

• In a scientific sense, what might the arrow represent in this directed network?

• What else could arrows represent if we had different vertices, e.g. people or places?

• Were there organisms that had arrows only leaving or arrows only leading into it? What does this represent?

• What happens if we were to remove one or more of the organisms from the ecosystem?