Venn Activities

This post is about using Venn Diagrams as a teaching tool, rather than teaching the concept of Venn Diagrams themselves.  To quote the excellent Johnny Griffiths, 'The Venn Diagram with three bubbles is the maths teacher's friend! ... To be able to fill in an eight-region diagram shows a really deep understanding of the distinctions that a good student has to be able to make, while the weaker student finds being faced with a picture such as this much less threatening than a page of exercises'.

Before we start using Venn activities in Maths lessons, let's think about whether pupils are familiar with how Venn Diagrams work. I admit to being a bit clueless about exactly what children study at primary school. The primary Maths Curriculum doesn't specifically mention Venn Diagrams, but I believe they are often used as a teaching and learning tool at Key Stage 2. Pupils are also likely to come across Venn Diagrams in other subjects, such as science, at both primary and secondary level (Physics teachers might be interested in this paper). In my experience most Year 7s have seen them before, and if not then it doesn't take long to explain the concept.

Here's some examples of how we can use Venn Diagrams in teaching secondary Maths.

Grouping Activities

I love these activities because they provide great opportunities for pair, group or class discussion. They're also quick and easy to prepare and explain (print the empty Venns onto A3 paper for pairwork, or just draw an empty Venn on the board for a whole class activity).

• My Year 10s were fully engaged in Don Steward's fantastic linear equations activity. It helped consolidate their knowledge of linear graphs and allowed me to check their understanding.
• Johnny Griffith's excellent RISPs (Rich Starting Points for A Level Core Mathematics) includes the Venn activities Risp 10 (coordinate geometry) and Risp 4 (periodic functions).  In the teacher notes for Risp 10 Johnny shares his views on the usefulness of Venns.
• A Venn activity for Solving Quadratics by Factorising by aka nka on TES. 
• A GCSE extension activity on quadratic graphs from MEI.
• I haven't tried this yet but Don Steward also gives us this lovely number activity.

Interactive Venns

Venns work well on the Interactive Whiteboard - here's some examples.

• Nrich has some interactive Venn diagrams on types of number.
• MathsPad has some lovely Venn activities (most require a subscription). I've successfully used this Factors, Primes and Multiples Activity with my Year 8s.   
• Teachitmaths.co.uk has interactive Venn activities - for example for shapes and prime factors, or you can create your own (subscription required).

Other Uses

• When I introduce complex numbers in FP1 we create a Venn Diagram during class discussion about types of numbers (real, rational, integers etc) and their Greek symbol notation.  The NCETM has a similar Venn activity in this resource sheet.
• Up until recently I used Venn Diagrams to teach Highest Common Factor and Lowest Common Multiple (method explained here), but I now prefer the simpler method described in this post.
• Quadrilaterals can be classified using a Venn Diagram like this one.  We can then answer questions such as 'Is every square a rectangle? Is every rhombus a square?' A 'family tree' also works well.

In conclusion - Venns are everywhere! But in secondary Maths they are only formally taught to those studying iGCSE (set theory) and Statistics 1 at A level (probability). I'm pleased to see that Venn Diagram methods in probability are on the new Maths GCSE Syllabus so will be more widely studied in future. But in addition to being taught as a topic in their own right, Venn Diagrams are a versatile teaching tool with numerous applications in the classroom. And they have the added bonus of being created by a British Mathematican! Well done Mr Venn.