## Lesson abstract

This lesson generalises the repeated doubling strategies of Lesson 1 to flexible use of the properties for multiplication. Students find the number of cupcakes in 40 trays by multiplying by its factors (first 4 and then 10). This is a practical use of the associative property of multiplication. In a second inquiry, students again find, present and compare strategies and undertake consolidation exercises based around making multiplication easy by flexibly multiplying by factors in turn.

## Mathematical purpose (for students)

Splitting numbers into their factors can help with multiplying.

## Mathematical purpose (for teachers)

The central idea in this lesson is that multiplying by a number can be done by multiplying by its factors, so for example, multiplying by 40 is the same as multiplying by 4 and then by 10. This principle is illustrated by arrays (now in grid form) and revealed in two inquiries, one calculating 24 x 40 in various ways and the next calculating 32 x 25. There are applications to making mental multiplication easy (e.g. the easy way to multiply by 25).

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