skip to main content
NSW Syllabuses

Stage 5 - Activity 1

Best airfare deals

Description of activity

Students ‘consider the best value fare given the price of nine return airfares from Sydney, and suggest an appropriate fare for a new journey, given the distance’.
Students will complete the attached worksheet.
Possible prompts to assist student engagement:

  • Is there a pattern in the table?
  • Can you compare two fares to get started?
  • Compare the costs for travel to Darwin and Perth. Which is the best value?
  • If you double the distance, does the price double?
  • How much does it cost for each kilometre travelled on the flight to Adelaide?

(Material developed by Dr Doug Clarke for the NSW Government.)


This assessment activity could be presented to students at the end of a unit on Ratios and Rates, where students have been investigating real-life situations and applying their knowledge, skills and understanding in a variety of contexts.


  • develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning
  • develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation


MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions
MA5.2-2WM interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems
MA5.3-1WM uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures
MA5.3-2WM generalises mathematical ideas and techniques to analyse and solve problems efficiently
MA5.3-3WM uses deductive reasoning in presenting arguments and formal proofs
MA5.2-5NA recognises direct and indirect proportion, and solves problems involving direct proportion
MA5.3-4NA draws, interprets and analyses graphs of physical phenomena


Criteria for assessing learning

(These criteria would normally be communicated to students with the activity.)
Students will be assessed on their ability to:

  • analyse a real-life situation and apply appropriate problem-solving strategies
  • give clear and appropriate explanations.

Graded student work samples

Grade AGrade C
Grade D