**As a primary specialist for White Rose Maths, I am often asked by teachers how they can teach place value and the four operations in autumn term, without the need to revisit later.**

Teachers panic that children will forget the basics as they cover the many other areas of the curriculum. They refer back to the National Strategies, which saw children recovering content every term with a cyclical approach.

However, my advice is not to panic. As well as revisiting key skills on a daily basis, be reassured that you don’t just leave place value and the four operations behind. You in fact use them in other areas and can apply understanding across the curriculum. The national curriculum states:

*The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems.*

With this in mind, here I focus on perimeter and look at how we can encourage KS2 children to develop rich connections and deepen their understanding.

Perimeter lends itself perfectly to applying the four operations. Take this question from the White Rose Maths Y4 module:

Work out the perimeter of the rectangles.

Here, children are working with numbers they can calculate mentally. Working out simple perimeters gives the perfect opportunity to share different methods and reason about why each method works.

For example, one method is adding the length and width together and doubling this. Another is to label all the sides of the rectangle (opposite sides are equal), then add all four sides together.

Ask the children which method is more effective. Would you change your method if the length and width were 7.82m and 4.38m? Why? Delving deeper into children’s methods ensures they are confident in why the method works and why it is the most efficient.

This question can also be used to look at the difference between the perimeters of the rectangles. Children can reason about why the green rectangle is double the perimeter of the yellow rectangle.

They may then explore if, when you double both side lengths, the perimeter doubles as well. This shows how a fluency question can be extended through deeper questioning to encourage children to start to reason about a topic.

Using multiplication and their knowledge of shape, children can calculate perimeter where only one side length is given.

Within Y4, they can focus on squares. However, as they move into Y5 and learn about regular polygons, this can be consolidated by using times table knowledge to calculate the perimeter of regular pentagons, hexagons and octagons, for example.

Building on their knowledge of inverse, here is an example of a question that draws on understanding of shape and division: The perimeter of a square is 16cm. How long is each side?

Children need to understand that all the sides are equal in order to realise they need to divide by four. In order to use short division, children could be given the same question but with a larger perimeter, perhaps 532mm.

Ask children to convert from millimetres to centimetres to bring the skill of dividing by 10 into the mix.

Drawing these skills together, here is a question taken from the White Rose Problem of the Day collection:

Here is a rectangle.

A new shape is made up of three of these rectangles.

What is the perimeter of the new shape?

Finding the perimeter of one rectangle is simple. However, children need to reason in order to calculate the lengths of the sides where the rectangles join together.

Consider using a number line to support this understanding, once again drawing other aspects of the curriculum together.

Moving on to other rectilinear shapes, I was recently inspired when working with a Y4 team at Lily Lane Primary in Manchester.

We were discussing ways to help children understand why we can use our understanding of the perimeter of rectangles to support calculating the perimeter of other rectilinear shapes.

We planned an investigation where the children had to find the perimeter of Numicon shapes. They could start by using each individual square as a unit, eg the number 10 Numicon has a length of five and width of two, therefore the perimeter is 14 units.

Developing this further, if you measure the length of one of the squares, the children can use multiplication to calculate the perimeter in centimetres as well as converting to millimetres.

Comparing the perimeter of different Numicon shapes will help children to uncover that some of the Numicon pieces have the same perimeter as each other even though they are different shapes. This can then lead children to look at a variety of rectilinear shapes.

Open-ended questions regarding perimeter give teachers the perfect chance to draw on knowledge from many areas of the curriculum. Take this question from the Y5 perimeter module of White Rose Maths:

How many rectangles can you draw where the length and width have a difference of five centimetres? What is the perimeter of each rectangle?

To begin with, children may focus on whole numbers (eg 12 centimetres and seven centimetres). However, teacher questioning can then encourage children to think more deeply about the length and width they can use:

- Will the length and width ever both be odd numbers? Will the length and width ever both be even numbers? Can you explain why?
- If the width of the rectangle is 34.5 centimetres, what will the length be? Can you write the length and width as a fraction?
- If the length of the rectangle is 21 centimetres, what will the width be? Can you write the perimeter as a decimal?
- The perimeter of the rectangle is 35 centimetres. The length and width have a difference of five centimetres. What is the length and width of the rectangle? Explain how you found your answer. Can you use a bar model to show your working?

These extension prompts show how teachers can take a single question for their whole class and use questioning to extend children’s thinking.

Children will draw on other areas of the curriculum and recap key skills in a different context, strengthening their understanding.

In conclusion, perimeter can be used to draw together number from across the curriculum. However, the same can be done with many other areas.

It is important that teachers plan for these links so that children are able to use, apply and deepen skills in all areas of the maths curriculum.

**Beth Smith is senior primary maths specialist for whiterosemaths.com. Follow her on Twitter at @beth_89.**

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