Multiplication: Cartesian Product

Australian curriculum number (ACMNA075; ACMNA076)

Students are introduced to the key idea of multiplication as a Cartesian product, using the language of “for each”. 

This sequence is for students who:

  • have previously used arrays to help solve multiplication problems.
  • are building their recall of multiplication facts up to 10 x 10.
  • ideally have worked on multiplication problems that involve multiplying three or four numbers together and questions that use at least one multidigit number.


Lesson 1: What is a Plocoroo?

Students explore the number of animals it is possible to make using a mix-and-match book. The book contains 10 different animals that have each been divided into three parts: head, body and tail. To help solve the larger problem, students are encouraged to use a simpler problem. They use a tree diagram in their working.

Lesson 2: Making Avatars

Students design their own avatar by choosing options from a set of features. The class is asked to consider if all possible avatars have been made, given the different features that can be selected. Students use an array and are then introduced to a tree diagram to explore the Cartesian product for multiplication.


Last updated June 19 2020.