I began to see the huge potential for the use of Venn Diagrams as a rich task from my constant source of inspiration – the amazing Median Maths Blog, by Don Steward. Don created a lovely Straight Line Graphs Venn Diagrams task that you can access here. Since then, I have become Venn Diagram obsessed.

In Chapter 10 of my book, “How I wish I’d taught maths: Lessons learned from research, conversations with experts, and 12 years of mistakes“, I described the concept of Purposeful Practice, whereby students are able to get crucial practice of a given skill or concept, but in a way that provides opportunity for them to think deeper. Venn Diagrams are one of my favourite sources of this Purposeful Practice, and I want this site to grow into the world’s largest collection, so everyone can benefit.

Why I flipping love a Venn Diagram

Here is why I love Venn Diagram activities so much:
1) Students can always make a start. If they can think of a number/expression/object or whatever it might be, it has to go in one of the regions on the diagram, so they are up and running. This early taste of success is so crucial.
2) The more regions student find, the more challenging the task gets, which adds a nice element of differentiation
3) As I hope you see on this website, they are incredibly versatile, and can be used for almost all maths topics for all ages and abilities
4) They are very quick to create and require no special resources. You don’t even need to print them out, as students can draw 2 or 3 circles in their books and they are away.
5) They are easy to tweak by simply changing one of the circle labels if you find they are too difficult/easy
6) Students can create their own – including with some challenging constrains – as a lovely extension task

Starting off the activity

I like to start off any Venn Diagram activity by ensuring students understand the structure of the activity. I cannot have this getting in the way of the Purposeful Practice that follows.

For example, imagine I was starting the following averages and range Venn Diagram (which is one of my favourites, by the way).

I would begin by asking five students to each pick a number between 1 and 9. Say the numbers they chose were 5, 7, 2, 1, 4. I would then ask the class to calculate the mean, median, mode and range of this set of numbers. After checking there answers to these, I would write them on the board:

Mean = 3.8
Median = 4
Mode = no mode
Range = 6

I would then present the Venn Diagram and ask students to think for 30 seconds which region the set of numbers belongs in. Then I would ask them to discuss their answer with their partner, before finally having a class discussion. This way I can ensure that students understand the structure of the activity, and have experienced that all important early taste of success, before I set them off on a mission to find sets of data that could fit into the remaining 8 regions. And if a student gets stuck, it is simply a case of asking them to think of another set of 5 numbers (or having a set to hand), asking them to carry out the same 4 calculations, and seeing where the numbers fit.

Venn Diagram Challenges

These are some of the challenges I like to set my students when they are attempting Venn Diagrams:

• Describe your strategy for filling in the regions
• Which was the easiest region to complete, and which was the hardest?
• Which region has the most possible examples, and which has the fewest?
• If you think it is impossible to find an example for a particular region, convince me why
• What would you change a circle label to, to make the task easier/harder?
• Can you think of another example for region A? How about another? How about another?
• What is the most interesting example you can think of for region A?
• Can you change one thing about your example in region A so now it belongs in region D?
• Can you create your own Venn Diagram on this topic where it is possible to fill in all the regions?
• Can you create your own Venn Diagram on this topic when it is impossible to fill in just 1 of the regions? How about one where it is impossible to fill in 2, 3, 4, etc regions?
• Can you create a quadruple Venn Diagram for this topic?

Note: if you want some blank templates to print off for your students so they can create their own Venn Diagrams, you can download them by clicking this link.

Venn Diagram assessment

As students will have come up with lots of different examples – some correct, others not – it is impossible to simply project up the answers. Instead, I ask students to swap their completed Venn Diagram with their partner and mark it. The direction I give students is:

If you are happy that an example belongs in a region, tick it. If not, place a question mark and then discuss it with your partner when they are ready. Any disputes you can’t resolve, let me know and we will discuss them as a class.

You can guarantee these examples will expose misunderstandings or misconceptions, so be the very examples we want to discuss with students.

It is also a good idea to take 2 or 3 examples from the class for each region when going through the Venn Diagram as it allows for the possibility of generalisation and strategy to be discussed.

What does it look like in students’ books?

I am obviously ridiculously biased, but I think it looks lovely. Here are some photos from my Year 8’s work:

Get involved

Feeling inspired? Do you have a Venn Diagram to share? Of course you do! And this site can only keep growing with your Venn-related contributions. Click here to see how you can submit your masterpiece.