Teacher guide reSolve: Rectilinear Polygons

TLF ID M025324

In this sequence of three lessons, students use geometric reasoning to establish relationships between angles in polygons and go on to make generalisations using algebraic expressions. Students explore and enumerate right angles in a series of rectilinear polygons and generalise their findings. They then explore the number of ways they can construct a rectilinear decagon, documenting and explaining their constructions. Finally, students consider a rectilinear polygon with a large number of sides and explore strategies for generalising the combinations, including programmatically. The lessons are outlined in detail including curriculum links, vocabulary, sample answers, discussion points and student resources. This sequence is part of the reSolve: Maths by Inquiry program.

Educational details

Educational value
  • This resource is very valuable for the year 9 mathematics content description about applying the distributive law to the expansion of algebraic expressions. Throughout the learning sequence, students are challenged to generalise the relationships they discover about rectilinear polygons, and then to simplify the algebraic expressions that result, including collecting like terms of the expressions they generate.
  • The resource is also valuable for the year 9 mathematics content description about sketching linear graphs and solving linear equations. In the third lesson, students investigate the maximum possible number of right angles in polygons with a given number of sides, graph their results, then derive and simplify an algebraic expression from their graph that describes the relationship.
  • The resource is also of some value to the measurement and geometry strand in year 9 mathematics despite not directly addressing any specific content descriptions under this strand. It does challenge students to use geometric reasoning and to work with angle and shape in solving an open-ended investigation.
  • This resource also offers opportunities to link to the Numeracy General capability, as they explore how the practical application of patterns can be used to identify trends. In particular, they explore how to generalise the patterns they see in their polygon investigation and use this to make predictions in more complex contexts.
  • 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: http://www.esa.edu.au/
  • 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: https://www.science.org.au/
  • Resource metadata contributed by
  • Name: Education Services Australia Ltd
  • Organisation: Education Services Australia Ltd
  • Address: AUSTRALIA
  • URL: www.esa.edu.au
Access profile
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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.