## Lesson abstract

This lesson uses arrays to build an understanding of the distributive property and how it relates to multiplication of two digit numbers. During an investigation comparing the areas of trays for cupcakes, students observe the convenience of partitioning the array into tens and units then using the distributive property to multiply. Students use open arrays and an area model for multiplication, and engage with equal group and rate problems.

## Mathematical purpose (for students)

How to multiply two digit numbers using an array.

## Mathematical purpose (for teachers)

In this lesson students learn to use the array structure and the distributive property to multiply two digit numbers. They first use an array on grid paper and, when ready, move to an open array. Students consolidate their ability to partition numbers appropriately for multiplication through a ‘number string’ activity (a series of related multiplications). They begin to develop fluency with two digit multiplication (still supported by partitioning an array) by calculating the possible areas of trays with length plus width equal to 50 cm. This provides an opportunity to observe patterns, work systematically, use a labelled table to organise data, explain some surprising results and test a generalisation.

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