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Teacher guide reSolve: Multiplication - Cartesian Product

TLF ID M025300

This sequence of two lessons introduces the idea of multiplication as a Cartesian product, using the language of 'for each'. Students learn to use a tree diagram to find the number of possible combinations that can be made in an animal mix and match book. They learn how a simpler problem can be used to help solve a larger, more complex problem. Students then design an avatar that has two or three different features and work as a class to find the total number of possible avatars. They look at how all combinations can be represented as an array and learn how to create a tree diagram. 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 extremely valuable for the year 4 mathematics content description about multiplication facts and related division facts. Students explore combinations of animals to make a mix and match book and use their knowledge of multiplication and division facts to calculate how many animals can be made, then extending this onto more complex combinatoric investigations.
  • The resource is also valuable for the year 4 mathematics content description about efficient mental and written strategies and appropriate digital technologies for multiplication and for division. Students use a range of strategies for investigating the problem, including tabulating combinations, using tree diagrams, and solving a simpler problem to model a complex problem.
  • The resource is of value for supporting the Numeracy general capability. The lesson provides multiple opportunities for students to identify, describe and create everyday patterns and use these patterns to model multiplication and addition to help them solve simple 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.