This sequence introduces the key idea of multiplication as a Cartesian product, using the language of “for each”. Students explore the total number of different robots that can be made using three heads, three bodies and three feet. The students represent the different combinations for the robots as an array.

This sequence is for students who:

- have some familiarity with multiplication concepts and early strategies for solving multiplication problems.
- understand that multiplication can be represented as equal groups, repeated addition and also in an array formation.

Students will apply and build on this knowledge and create connections to multiplication as a Cartesian product.

### Lesson 1: Robot, Go Fish

In this task students think about the number of robots it is possible to make with three heads, three bodies and three sets of legs. Students start by making one robot and checking whether anyone else has made the same robot as them. They then play a game that shows that many unique robots can be made.

### Lesson 2: How Many Robots

In this task students are asked to consider how many different robots can be made using three heads, three bodies and three sets of legs. Students sort and classify their robot cards according to their body parts. From here, an array structure is introduced. Students will see that for each head there are three bodies and for each body there are three sets of legs. This means that for each head, nine unique robots can be made.

Last updated January 15 2018.