Year level: 10

Strand: Space / Algebra

Lesson length: 60 mins

In this lesson students are introduced to the concept of a network through an airline route map. The task extends into a detailed mathematical modelling activity with students exploring in teams how to re-design the network map to improve the airline’s profitability. This lesson is in two parts and is followed by Capital Airways: Part 2.

### Achievement standard

Students interpret networks used to represent practical situations and describe connectedness and use mathematical modelling to solve problems in financial and other applied situations, applying linear functions as appropriate.

### Content descriptions

• Students interpret networks and network diagrams used to represent relationships in practical situations and describe connectedness. AC9M10SP02
• Students use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings. AC9M10A04

### General capabilities

Numeracy

• Number patterns and algebraic thinking (Level 9)

Critical and creative thinking

• Consider alternatives (Level 6)
• Identify, process and evaluate information (Level 6)
• Interpret concepts and problems (Level 6)
• Draw conclusions and provide reasons (Level 6)

The following formative assessment opportunity is described below.

Provide the link for the interactive quiz to the class and have students complete the questions. Alternatively, use slides 7–9 where students answer the same questions in their exercise books for your review and feedback.

Prior to this lesson, it is assumed that students have some knowledge of:

• basic spreadsheet functionality including cell referencing and performing calculations using symbols such as = * and /
• personal experience or understanding of the airline business, although no specialist knowledge is assumed
• language important for this lesson including node, vertex, edge, connected network, degree.
• Some students may have limited knowledge about the airline industry and struggle to identify potential model inputs and variables – use slide 5 from the teacher’s slides as a stimulus with questioning, for example: ‘Why do you think it would be useful to know what routes competitors fly and what they charge?’
• Some believe that network maps must accurately reflect the position of people, places and things – refer to local examples such as train and bus maps or circuit diagrams that are not drawn to scale and discuss why this is the case.
• Some students have gaps in spreadsheet skills or knowledge – explicitly demonstrate and explain the key features and operation of spreadsheets. Use the provided Excel model and encourage students to interrogate formulae in cells to understand how the calculations have been derived. For students creating their own models, encourage use of online help videos.