As a teacher for over 35 years, I know that Venn Diagrams can be tricky for students to pick up and can often be found in 11 Plus exams. I have taught in independent, state and Grammar schools all over the country and most children have difficulty with this. Do not fear, we are here to help!

## What are Venn Diagrams?

A Venn diagram shows the link between groups of different things. Venn Diagrams allow us to sort information into circles that overlap in the middle. The different circles will be allocated for different rules and the overlapping part will follow both rules.

Put succinctly; Venn Diagrams are a way to segment data that have similarities and differences by putting them into overlapping circles. They are a brilliant way to summarise and compare information.

## How to solve Venn Diagrams?

In a Venn Diagram question, the amount of received data will always be different than the number of participants. Below is a step-by-step guide on how to succeed when doing Venn Diagrams.

**26 PEOPLE WERE ASKED WHETHER THEY LIKE CHIPS, FISH OR NEITHER. HOW MANY LIKE ONLY CHIPS?**

THE PEOPLE GAVE THE BELOW ANSWERS:

18 Chips

13 Fish

3 Neither

### 1. MARK UP YOUR CIRCLES

Before we start talking about the steps, it is important to fully understand the question. This means drawing the diagram properly and labelling the circles.

For this instance, label one circle chips and one circle fish.

### 2. ADDITION

As you can see, the total results are going to be considerably more than the number of people that were asked. So, let’s have a look at what has happened.

First of all, we will add up the results given.

*18 + 13 + 3 = 34*

Clearly, 34 is more than 26 that were asked, so some people have answered twice.

### 3. SUBTRACTION

Now to find who liked both fish and chips, we subtract the total number of answers given by the number of people that were asked.

*34 – 26 = 8*

This number goes into the middle where the two circles overlap as they follow both options of liking both fish and chips.

### 4. ALLOCATE THE NEITHER

We know that 3 people said that they like neither fish nor chips so you must remember to put this number outside of the two circles.

People often forget this step.

### 5. FINISH THE MATHS

Now if we look at the chips circle, we already have 8 people in it. So we go to the chip result and take away 8 answers. This will give us the number of people who just like chips.

*18 – 8 = 10*

Put 10 in the chips circle.

Then if we look at the fish circle, we have 8 people already in it. So we go to the fish result and take away 8 answers. This will give us the number of people who just like fish.

*13 – 8 = 5*

Now if we add up all the numbers written in your diagram, including those outside the circles, it will equal 26 which equates to the total number of people that had been asked.

### 6. ANSWER THE QUESTION

So now that we have sorted and correctly allocated all of the data, it is important that we go back and re-read the question so that we know what it is asking from us. We can do this by underlining the text.

Now the questions says, **How many only like chips?**

We go to the chips circle and it is not all those in the circle, ONLY those who like chips.

*Therefore the answer is 10.*

Now some questions you might be asking yourself…

#### Do Venn Diagrams have to overlap?

Most of the time but not always. If you have 2 different sets of data that you have found no similarities between, there is no need for them to overlap. For example, in the video above if no one answered twice, liking fish AND chips, there would be no overlap. The circles are then able to stand alone.

For good practice, it is still good to overlap your circles to clearly show the examiner that you know how Venn Diagrams work.

#### What do I do now?

We work on tricky problems like this all the time in our lessons. Due to the most recent government guidelines and schools being closed, I am offering free online lessons during this time with classes for Years 3 – 11. These free lessons will run daily from Monday – Friday and you will be able to see clear timings below.

The aim of these lessons is to provide students with new material to work on throughout the day while children may not receiving this from school.

We did this for both of the previous lockdowns, and it was a resounding success. It has been an honour and privilege to support parents and children during a challenging time by providing our personal support.

##### Parents can easily sign up through a sign up using the form below.

Your child’s education is precious, and we are always here to support our children and their families fully.

We will all pull together in this time of need and will keep our children learning.

### QUESTIONS

If you have any questions you would like to ask me about Venn Diagrams, please ask below in the comments.

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