Venn and Carroll diagrams
🎯 In this topic you will
- Record, organise, and present data using Venn and Carroll diagrams.
- Interpret data by identifying similarities and differences, and ask and answer questions based on the information.
🧠 Key Words
- Carroll diagram
- Venn diagram
Show Definitions
- Carroll diagram: A table used to sort items or data according to two different properties or categories.
- Venn diagram: A diagram that uses overlapping circles to show how groups are similar and how they differ.
Understanding Venn Diagrams
A Venn diagram shows a lot of information in a simple visual way. It is made using circles that overlap inside a box, and you place data inside the circles to show how groups are related.
Showing Relationships Between Groups
A Venn diagram shows the relationship between a group of different things, called a set, by showing which items are shared and which are different.
What a Carroll Diagram Does
A Carroll diagram is used to organise and group data by sorting items according to rules or properties.
❓ EXERCISES
1.
a. Complete this Venn diagram for the numbers $1$ to $20$. Cross out the numbers to make sure that you have used them all.
a. Choose a set of $12$ numbers. Draw a Venn diagram. Label it and sort your numbers.
👀 Show answer
Multiples of $3$ only: $3,9,15$.
Multiples of both $2$ and $3$: $6,12,18$.
Not multiples of either: $1,5,7,11,13,17,19$.
For the second part, answers will vary depending on the chosen set of $12$ numbers.
2. Use the numbers in the list and fill the Carroll diagram.
$15,\;11,\;10,\;16,\;18,\;21,\;20,\;22,\;12,\;24,\;17,\;23$
| Even | Not even | |
|---|---|---|
| Multiple of $3$ | ||
| Not a multiple of $3$ |
b. Choose a set of $12$ numbers. Draw a Carroll diagram. Label it and sort your numbers.
👀 Show answer
Multiple of $3$ and not even: $15,21$.
Not a multiple of $3$ and even: $10,16,20,22$.
Not a multiple of $3$ and not even: $11,17,23$.
For part b, answers will vary depending on the chosen set.
3. Work as a group of four to make a Venn diagram.
a. Decide on a question to ask each other.
b. Join with another group of four. Ask everyone the same question.
c. Collect the data that you need from both groups.
d. Show the data in a Venn diagram.
e. Write three things that you can find out from the diagram.
👀 Show answer
4. The monsters have arrived. They are your data. With a partner, organise and group the monsters into the Carroll diagram.
👀 Show answer
🧠 Think like a Mathematician
Make a poster to show what Venn diagrams and Carroll diagrams are. Use pictures and simple words.
Show Answers
- A Venn diagram can be shown as two overlapping circles that group items and show similarities and differences.
- A Carroll diagram can be shown as a table that sorts items using two rules.
- The poster should include clear labels, simple examples, and pictures of each diagram.