Close message Scootle will be undergoing maintenance between 17:00 to 19:00 on 25 September 2023. You may experience intermittent connection during this time. We apologize for any inconvenience caused.

Teacher guide reSolve: Fibonacci Miles

TLF ID M025820

This lesson introduces students to a trick for quick conversion between miles and kilometres using the Fibonacci sequence. Students are challenged to explain why the trick works. They investigate using their knowledge of ratio and discover that the miles/kilometres conversion rate is close to the golden ratio. The lesson is outlined in detail including curriculum links, materials needed, discussion points, a slide show and student resources. This sequence is part of the reSolve: Maths by Inquiry program.

Educational details

Educational value
  • This resource is valuable for the year 8 mathematics content description about solving problems involving rates and ratios, with and without digital technologies. During the lesson, students investigate deriving the golden ratio from part of the Fibonacci sequence and how using this ratio can help approximate converting between miles and kilometres.
  • The resource is also very valuable for supporting the Numeracy general capability. The lesson provides multiple opportunities for students to apply proportional thinking, by visualising and describing the proportions and ratios in the context of number sequences and conversion problems.
  • This resource is also of pedagogical value as it supports teachers in building an inquiry-focused learning environment with authentic application of mathematical skills and understandings. The unit aims to develop content knowledge as well as assisting students to understand the process of inquiry.
Year level


Other details

  • Contributor
  • Name: Education Services Australia
  • Organization: Education Services Australia
  • Description: Data manager
  • Address: VIC, AUSTRALIA
  • URL:
  • Copyright Holder
  • Name: Australian Government Department of Education and Training
  • Organization: Australian Government Department of Education and Training
  • Publisher
  • Name: Australian Academy of Science
  • Organization: Australian Academy of Science
  • Description: Publisher
  • URL:
  • Resource metadata contributed by
  • Name: Education Services Australia Ltd
  • Organisation: Education Services Australia Ltd
  • Address: AUSTRALIA
  • URL:
Access profile
  • Unknown
Learning Resource Type
  • Online
  • © Australian Government Department of Education and Training 2017. Unless otherwise indicated, this material may be used in accordance with the Creative Commons Attribution 4.0 International (CC BY 4.0) licence.