Teacher guide reSolve: Polygon Pieces

TLF ID M025320

This lesson explores the geometry of cutting polygons in different ways and using algebra to express subsequent findings. Students use one straight cut to divide a convex polygon into two new polygons. They make generalisations about the total number of sides of the two new polygons, and about the number of different combinations of polygons that can be made. Students are then asked to express the number of sides that can be created algebraically, given a convex polygon with n sides. The lesson is 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 of value for the year 8 mathematics content description about establishing properties of quadrilaterals and solving related numerical problems using reasoning. Students are challenged to use a straight cut to divide a convex polygon into two new polygons, investigate the properties of the resulting shapes and use mathematical reasoning to explore their findings.
  • The resources is also valuable for the year 8 mathematics content description about simplifying algebraic expressions involving the four operations. As the students explore the properties of their resultant polygons, they record their data and use this to make generalisations. They are challenged to express their generalisations algebraically and to simplify their generated expressions.
  • This resource also offers opportunities to link to the Numeracy General capability, as it engages students in identifying trends using number rules and relationships and in visualising, describing and applying their understanding of the features and properties of 2D shapes.
  • 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
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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.