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# How many possible ways?

Factors are pairs of counting numbers that multiply to give another counting number.

Constraining the number of tiles and building different rectangular arrays develops the concept of factors and the commutative property of multiplication.

Pose the following situation:

**I made an array with 24 tiles. What might it look like? Close your eyes and picture it. Open your eyes and make what you saw.**

**Top Drawer Teachers: Possible Arrays**from

**The Australian Association of Mathematics Teachers (AAMT) Inc.**

You can view and download the *Possible Arrays* slide presentation.

Note the way the students work out the different arrays. Do they recognise that by rotating the structure they generate another arrangement?

Students share the different possibilities and draw them on the board or interactive whiteboard.

**What is the same about all the arrays?****What is different?****What do you notice about the number of rows and number of tiles in each row?**

Pose extension problems such as:

**I wonder if another number such as 36 would have as many different possible arrays as 24?**