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Venn diagrams

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visibility 52update a month agobookmarkshare

🎯 In this topic you will

Record, sort and present data using Venn diagrams.
Describe and interpret data clearly.
Discuss and evaluate the results obtained from data.

🧠 Key Words

fewer
more
Venn diagram

Show Definitions

fewer: A comparative term used to describe a smaller number of countable items.
more: A comparative term used to describe a greater number or amount of items.
Venn diagram: A diagram that uses overlapping circles to show relationships and shared properties between sets of data.

Organising Data with Venn Diagrams

A Venn diagram helps you to organise data. It can help you to compare different groups of things. We need to know about sorting into sets so that we can organise objects that fit together. When we sort, we look for things that are the same.

📘 Worked example

Look at the stars.
Some have 5 points. Some do not.
Sort the stars by writing the letters in the correct part of the Venn diagram.
What do you notice?

Answer:

The stars that do not have 5 points go outside the circle. All the stars in the circle have 5 points.

❓ EXERCISES

1. Work with your partner. Here is a group of shapes. Sort the shapes by writing the letters into the correct part of the Venn diagram.

👀 Show answer

Shapes with all faces flat go inside the circle: $B$, $F$, $G$, $H$, $I$. Cylinders $A$, $C$, $D$, $E$ stay outside because they have curved surfaces.

2. Sort the balloons by writing the letters into the correct part of the Venn diagram.

👀 Show answer

Balloons that are not orange go inside the circle: $B$, $E$, $F$, $G$. Orange balloons $A$, $C$, $D$, $H$, $I$ stay outside.

3. Sort the shapes by writing the letters into the correct part of the Venn diagram. How many shapes are squares? How many shapes are stripy? How many stripy squares do you have? Draw a ring around the correct word to complete each sentence. There are more stripy shapes / square shapes. There are fewer stripy shapes / square shapes.

👀 Show answer

Squares: $D$, $E$, $F$ → total $3$. Stripy shapes: $A$, $C$, $E$, $F$ → total $4$. Stripy squares: $E$, $F$ → total $2$. There are more stripy shapes. There are fewer square shapes.

4. Sort the animals by writing the letters into the correct part of the Venn diagram.

👀 Show answer

Animals that cannot fly go inside the circle: $A$, $B$, $D$, $E$, $G$. Animals that can fly ($C$, $F$, $H$) stay outside.

5. Work with a partner. How can you find and record your favourite food? Talk to your partner about what you like to eat. Draw or write things you like in your circle. Draw or write things you don’t like outside your circle. Your partner should do the same in their book. Now compare your answers with your partner’s. What did you both like most? Were they the same or different? What did you both like the least? Were they the same or different?

👀 Show answer

Answers will vary. Students should compare their circles and discuss similarities and differences.

6. Draw a ring around each mistake in the Venn diagram.

👀 Show answer

There are $4$ mistakes. Any clothes without spots inside the circle are incorrect, and any spotted clothes outside the circle are also incorrect.

🧠 Think like a Mathematician

Task: Look at this group of bugs.

Sort the bugs into a Venn diagram in $2$ different ways.

Work on your own and talk about the different ways you found.

Do you think there are more than $2$ ways to sort the bugs? Find $2$ more different ways.

Use these labels.

Draw or write what you think. Don’t forget to label your diagram.

Follow-up Questions:

1. Give one possible way to sort the bugs.

2. Give another different way to sort the bugs.

3. Explain how you know there can be more than $2$ ways.

Show Answers

1: Example: sort bugs into groups such as “has wings” and “no wings”.
2: Example: sort bugs by “number of legs” or by “has a shell” and “no shell”.
3: Because bugs can be grouped by many different properties (such as legs, wings, colour, or body type), there are many possible ways to sort them.

📘 What we've learned

We learned how to record, sort and show data using Venn diagrams.
We practiced describing and comparing groups of objects using sorting rules.
We learned that items inside a Venn circle share the same property.
We used the ideas of $\text{more}$ and $\text{fewer}$ to compare groups.

Venn diagrams

🎯 In this topic you will

🧠 Key Words

Organising Data with Venn Diagrams

❓ EXERCISES

🧠 Think like a Mathematician

📘 What we've learned

Related Past Papers

Related Tutorials

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