# Year 4 - Multiplicative Thinking: Cartesian Product (Trial)

Australian curriculum number (ACMNA075: ACMNA076)

## Who is this Sequence for?

This sequence is designed for students in Year 4. It is assumed that students have used arrays to help solve multiplication problems and that they are building their recall of multiplication facts up to 10 x 10. It would also be helpful if students have worked on multiplication problems that involve multiplying three or four numbers together and questions that use at least one multi-digit number.

## Summary of learning goals

The sequence introduces the key idea of multiplication as a Cartesian product, using the language of “for each”. In the first task, students 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 then they learn how to create a tree diagram. The second task, students build their skills in using a tree diagram to find the number of possible combinations that can be made in an animal mix and match book. Students learn how a simpler problem can be used to help solve a larger, more complex problem.