Teacher guide reSolve: Quarter Cartons

TLF ID M025819

This lesson challenges students to use algebra and proportional reasoning to investigate how changing the size of a paper square or rectangle impacts the dimensions of a box folded from that paper. Students apply knowledge about nets of 3D objects and explore algebraic relationships through a set of hands-on activities making origami boxes. The context of paper folding encourages students to physically manipulate objects to investigate relationships and demonstrate their findings. The sequence could serve as an introduction to geometric proofs. Each lesson is outlined in detail including curriculum links, vocabulary, materials needed, 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 valuable for the year 8 mathematics content description about applying formulas for volumes of rectangular prisms and using formulas to solve problems involving volume. Students are challenged to create a series of origami boxes and investigate relationships between the dimensions of their paper and the resulting volume of the box. They record the dimensions of the boxes and apply the prism formula to calculate their volumes as an integral part of the investigation.
  • This resource is also valuable for the year 8 mathematics content description about establishing properties of quadrilaterals and solving related numerical problems using reasoning. Students explore how changing the lengths of the sides of their paper affects the resulting area, and identify features of the folds within the quadrilateral that will help them in calculating the size of their new box.
  • This resource is also of value for the year 8 mathematics content descriptions about simplifying and factorising algebraic expressions. As students investigate the relationships between the dimensions of their boxes and the resultant volumes, they use algebraic formulae for volumes of prisms to express their own relationships for the ratios of the volumes.
  • The resource is also valuable for supporting the Numeracy general capability. The lesson provides multiple opportunities for students to visualise, describe and apply their understanding of the features and properties of 2D shapes and 3D objects and create and interpret 2D and 3D models and diagrams.
  • 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.