Categorise examples of real-world networks as either social, biological, transport or infrastructure-based, or
Recall and organise network terminology, types of networks and examples of real-world networks
Recognise and define examples of network features and types of networks (weighted, directed)
Draw a network diagram with locations (animal enclosures) connected by edges (roads)
Develop contextual questions about their network diagram
Respond to student-developed questions about network diagrams using network terminology
N1.1 Networks
Students:
identify and use network terminology: vertices, edges, paths, the degree of a vertex, directed networks and weighted edges
solve problems involving network diagrams AAM
recognise circumstances in which networks could be used, e.g. the cost of connecting various locations on a university campus with computer cables
given a map, draw a network to represent the map, e.g. travel times for the stages of a planned journey
Sort examples of real-world networks into categories (Understanding)
Recall network terminology and examples of networks (Fluency, Communicating)
Recognise and define features or types of network diagrams (Fluency)
Represent networks in graphical form given real-world maps (Communicating)
Identify appropriate vertices and edges from descriptions of networks (Fluency, Understanding)
Assign weight values to edges in a network using map information (Fluency, Understanding)
Justify how an optimal path in a network was found (Problem-Solving, Justification)
Explain why it is inefficient to connect each vertex to every other vertex in a network (Understanding, Justification)
Network Systems Table or Post-It Notes (see Orientation)
Whiteboard and Whiteboard Markers
Taronga Zoo Map, A3 Paper, Coloured Markers, Rulers (see Body)
Padlet, Phones (Camera) (see Orientation, Conclusion, Homework/Follow-up)
Blank A4 Paper (see Conclusion)
Categorisation
Affinity Mapping
Literacy Activity (images & definitions)
Group Work
Student-Developed Questions
ICT (Padlet)
Peer Feedback
Working Mathematically: Fluency, Understanding, Communicating
Categorisation (5 min) [LIT]
Give students the Network Examples Table and ask them to categorise the different networks into the four categories they have studied about networks prior to this lesson: Social, Biological, Transport and Infrastructure.
Ask students to quickly call out which category each network belongs to (AFL).
ALTERNATIVE ACTIVITY:
Affinity Map (15 min) [LIT, ICT] (Combine with Introduction activity)
Students are split off into groups and each given Post-It notes of different colours to write on. They should write down words (or draw pictures) that come to their minds as they think back to what they have learnt in Networks and Paths.
Students then collate their group's Post-It notes and categorise them into categories (for instance, terminology, types of networks, real-world examples of networks).
Their work should be photographed and uploaded onto Padlet (AFL).
Working Mathematically: Fluency
Matching Activity (10 min) [LIT]
To refresh student knowledge of the vocabulary covered thus far, students will be given diagrams that they have to identify the correct terminology and definition for.
While students are completing the Orientation activity, draw the following on the board: a vertex (point); two vertices and an edge connecting the two; three vertices connected together with their degree numbers written; two vertices connected together, with one having a loop; two vertices connected together by multiple edges; two vertices connected with a directed edge; two vertices connected with a weighted edge
Students should write down in their workbooks what aspect of a network the diagram is showing, as well as an accompanying definition. Definitions should be written without aid from their book or textbook. Take the time to check each student's workbook and ensure they are correctly identifying the images (AFL).
If students need assistance, encourage them to discuss it with a nearby peer rather than referring them to their workbook.
Working Mathematically: Fluency, Communicating, Understanding, Justification, Problem-Solving
Group Zoo Activity (40 min) [NUM]
Students will work in their table groups for this activity. They will plan a visit to Taronga Zoo Sydney by first selecting six different animals they would like to look at (show students the list of animals in Taronga Zoo's care).
Once students have decided, give each group a map of the zoo for students to continue on with the next part of the activity:
Students identify the enclosure locations of the six animals they have selected.
The information is transferred onto an A3 sheet of paper by using vertices to represent the enclosures and edges to represent the roads connecting the enclosures together.
The six animal enclosures must be clearly marked and labelled on their sheet.
Students are then tasked with creating a weighted network and a path the students can take to visit all of the exhibits
Students must ensure that they use real-life distances when assigning weights (distance) to the edges by using the scale provided on the map and a ruler. Students may need some assistance here; demonstrate on the board how students should use the scale when they reach this point.
Once completed, students should also include questions that their peers can answer by analysing their network diagram.
When finished, students should swap their group network diagram with other groups to analyse and answer each other's questions.
Throughout this activity, the teacher should be monitoring students' diagrams to ensure they're accurate (i.e. students are doing proper measurements and using the scale correctly) and clearly drawn (i.e. enclosures are labelled correctly) (AFL). If students are stuck on developing questions for their peers, offer some suggestions (see the Example Questions). Also check the strategies students are using to solve their peer's questions (e.g. trial-and-error), and ask students to justify their choice of strategy (AFL).
What is the total distance that one would have to travel to visit all of the enclosures?
In your opinion, what is the best ordering for seeing the six different animal enclosures? Why?
Is there a more efficient path? If so, in what order should the animal enclosures be visited in?
Is it possible to visit all of the enclosures without using the same road twice?
If not, where does an extra road need to be made?
Which of these three possible routes should be taken from enclosure A to enclosure B? Why?
Would it be better to build a road connecting every enclosure to every other enclosure? Why or why not?
Working Mathematically: Fluency, Understanding
Gallery Walk (5 min)
Students display their group network diagrams around the classroom (with a blank A4 sheet of paper for feedback). Each group walks around to see what other groups have created. As students are visiting each network diagram, they should think of feedback or comments they can give.
Before the end of the lesson, students must ensure they take a photo of their work, as well as any feedback or comments they received.
Students upload their photos from the lesson onto Padlet. At home, students must comment on at least one other group's photo, pointing out or analysing the mathematics involved.
Additionally, students should respond to any feedback or comments they received for their own network diagram.