Teacher guide reSolve: Authentic Problems: Expanded Square

TLF ID M024876

This sequence of four lessons explores concepts around informal area and symmetry. Students design an 'expanded square' where approximately half the area of the original square is flipped to the outside. The lessons provide opportunities for students to devise and use methods to informally measure area, record their mathematical thinking and justify their designs. 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 special topic 'Authentic Problems'.

Educational details

Educational value
  • This resource is very valuable for the year 4 mathematics content descriptions about the areas of regular and irregular shapes, describing and comparing shapes and creating symmetrical objects. Students are engaged in an investigation of the Japanese art of Notan, exploring the symmetry of the shapes, comparing the area of the dark and light areas, and creating their own expanded squares using mathematical processes.
  • This resource is also of value for the year 4 content descriptions about equivalent fractions as students use fractions to describe and compare areas of the shapes they create.
  • The resource is also valuable for supporting the Numeracy general capability. The lessons provide opportunities for students to visualise, identify and sort shapes and objects, describing their key features.
  • The resource provides opportunities for students to develop Critical and Creative Thinking as they generate different designs by cutting and rearranging parts of squares.
  • 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 uses a learning and teaching model with four phases: Discover, Devise, Develop and Defend. 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 2018. Unless otherwise indicated, this material may be used in accordance with the Creative Commons Attribution 4.0 International (CC BY 4.0) licence.