Using arrays to teach multiplication and division skills is a great way to give children useful mental images. In this fun outdoor maths activity, children use digital cameras or tablets to record the arrays they find all around them, and those that they create for themselves.

## For this outdoor maths activity you will need:

• Some prepared photographs of objects that show arrays
• Tablets and digital cameras (ideally one per pair or small group)

It is a good idea to start the session by showing the children some examples of “real-life” mathematical arrays.

Some good examples are:

• Games boards (Chess, Connect Four, Tic Tac Toe)
• Classroom trays
• Brick walls

Discuss how the objects are arranged in rows and columns. Model how to carefully count the number of trays (or similar object) in a row. Write the number sentence next to the arrays as repeated addition and multiplication.

4+4+4+4=16

4 x 4 =16

Explain to the children that you will be going outdoors to look for arrays; these can often be spotted in patterns. Then they will be making some arrays of their own.

Divide the children into pairs or small working groups, depending on your class and the equipment available.

Challenge one is to find and photograph arrays in the environment.  (It is a good idea to have identified a few around the site to get them going).

Challenge two is to create their own arrays using natural materials (depending what you have available, for example pebbles, wooden pieces, building equipment)

Children use the tablets or cameras to record the arrays and patterns they find and make. They can annotate the arrays with number sentences in a variety of ways.  For example they could use individual whiteboards, or chalk on the playground.

Back in class, the pictures can be shared on the Interactive Whiteboard and discussed. After the lesson, they can be printed out and used to make an “Array Display”. This can be made interactive by adding practical equipment, such as bun trays or laminated grids and counters for children to make their own arrays.

## Extension Ideas

• Print sheets with several different arrays the children found and made, and ask them to record the number sentence.
• Laminate the printed pictures to make a matching game where children match the array to the appropriate number sentence.
• Use the arrays as inspiration for looking at patterns in art, for example Andy Warhol’s Soup Cans  or Damien Hirst’s Spot paintings.
• Use the arrays to teach division by demonstrating how they can be broken down in different ways.

Arrays are very powerful visual models for multiplication and division. Their layout makes it clear how a number is built from its factors. Children can easily make them using concrete materials or spot them in patterns in their environment.

The nrich website has two excellent articles which explain in more detail the theory and how to use them to teach multiplication and division:

Arrays, Multiplication and Division

Illustrating Number Properties with Arrays

## Key Misconceptions

This activity is good for addressing a few of the most common misconceptions about multiplication.

• Some children are not confident using the vocabulary of multiplication. The clear layout demonstrates the meaning of words such as “group”, “row” and “column”. Model using the vocabulary and refer back to the visual images to help the children become confident in using it.
• Some children will find it difficult to organise objects into an array – providing a grid can help.  Small objects can be placed in arrays using numicon plates or in bun tins, for example.
• The layout clearly shows that each row/column has the same number and helps children to see that they do not need to count each one again. (E.g. This group of 4 has the same number of objects as that group of 4.)
• Using arrays clearly shows that division is the inverse of multiplication, which is a concept many children find difficult.

## Learning Outcomes

This activity covers the following areas of the National curriculum 2014:

Year 1 – Pupils should be taught to: solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Year 2 – Pupils should be taught to: solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

## This post was written By Sam Collins

Sam teaches in Devon, and has over 20 years experience in primary education teaching Early Years, KS1 and KS2.

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