# Venn diagrams

## What is a Venn diagram?

A Venn diagram is a graphic organiser for sorting data. The Venn diagram itself is made up of two or three circles which overlap in the middle and it is used to demonstrate the properties of items in set: numbers, shapes, objects, etc. Each circle in the Venn diagram represents a rule or property - e.g. prime numbers, two legs, a pair of parallel sides. For example:

## How to use a Venn diagram

Simple Venn diagrams use just two circles which overlap in the middle (this part of the diagram is called the intersection). Items from the group are sorted into the diagram based on whether they demonstrate the property that each circle represents. If an item does not have either property represented by the circles, then it is placed outside of the Venn diagram. If an item has both properties, then it is placed in the intersection where the circles overlap. For example:

## Why use a Venn diagram?

Venn diagrams are a great way to sort data and to encourage flexible thinking. They can convey complicated information about groups of items in a much simpler, visual way. Also, the process of sorting items like this can help children spot patterns or shared characteristics which they might otherwise miss.

Using Venn diagrams in the classroom often leads to rich discussion and a deeper understanding of the topic at hand as children consider and justify how to sort and place the items in their set.

Although Venn diagrams are particularly well-suited to Maths and Science, the power of using these in foundation subjects such as Geography and History should not be overlooked. Here, for example, they can be a very effective way to develop children's locational knowledge and their understanding of historical causes.

## Venn diagrams at KS1

Venn diagrams are great for encouraging discussion about the properties of numbers, shapes and objects. They are also a useful tool to help children learn how to sort items by their characteristics.

When first introducing Venn diagrams to children, ask children to sort shapes or objects into hula hoops or sorting hoops. To start with, just use one hula hoop and give it a rule or property e.g. red items. Ask children to put all of the red items from their set into the circle.

Next, you can introduce two hoops, side-by-side, each with their own rule. Again, ask children to sort all the items that meet these rules into the correct circle. Children may point out that some items can be placed in both hoops. At this stage, you can ask children for their suggestions about how to solve the problem and introduce the concept of overlapping circles.

Make sure to explicity teach how to use the intersection of the venn diagram as well as how to record non-examples by positioning these items outside of the diagram.

## Venn diagrams at KS2

Children in KS2 should be able to use a Venn diagram with two overlapping circles with confidence. At this stage, you can introduce more complicated versions of Venn diagrams which use three overlapping circles, or even a circle embedded within a circle (a useful one for exploring times tables).

For a low ceiling, high threshold activity, ask children to create their own Venn diagrams for a given group of items or numbers. This activity is accessible to all, child-led and low preparation so it's an all round winner! You will be surprised as to how sophisticated children's suggestions can be.

Extend children's understanding by asking them to create a set of examples and non-examples for their partner to sort onto a Venn digram with given rules. This can be a good revision exercise in the lead up to those dreaded SATS!

## Misconceptions

Remember to explicitly teach children how to record non-examples on their Venn diagram. Non-examples are any items in the sorting set which do not meet any of the criteria set out in the Venn diagram. These items should be placed outside of the diagram.

Additionally, some children may struggle to accurately position items in the intersections of more cognitively challenging Venn diagrams (e.g. a Venn diagram which uses three overlapping circles). Offer children plenty of modelled examples and ask them to spot mistakes you have made (deliberately, of course!) when sorting a set of items onto a three-way venn diagram.