Graphs
Venn and Carroll diagrams
Venn and Carroll diagrams are two ways to sort and group data using rules. A Venn diagram uses circles inside a box; a Carroll diagram uses a grid of rows and columns.
Venn diagrams
A Venn diagram uses circles inside a box. Each circle is one rule, such as 'multiples of 2'. ā¢ If a thing fits one rule, it goes in that circle. ā¢ If it fits both rules, it goes in the overlap where the circles cross. ā¢ If it fits neither rule, it goes in the box, outside the circles.
Carroll diagrams
A Carroll diagram is a grid. One rule and its opposite make the columns (for example 'even' and 'not even'); another rule and its opposite make the rows. To sort a number, check each rule, then put it in the box where the correct row and column meet.
Sorting carefully
Check every rule for each thing before you place it. Then check you have used every item exactly once ā crossing them off a list helps. Both diagrams let you see what is the same and what is different in your data.
Worked examples
Venn: the overlap (both rules)
- Sort 6 into a Venn diagram of 'multiples of 2' and 'multiples of 3'.
- Is 6 a multiple of 2? Yes.
- Is 6 a multiple of 3? Yes.
- Both rules are true.
Answer: 6 goes in the overlap where the circles cross.
Venn: one circle only
- Sort 9 into the same Venn diagram.
- Is 9 a multiple of 2? No, it is odd.
- Is 9 a multiple of 3? Yes.
- Only one rule is true.
Answer: 9 goes in the 'multiples of 3' circle only.
Venn: the box (neither rule)
- Sort 7 into the same Venn diagram.
- Is 7 a multiple of 2? No.
- Is 7 a multiple of 3? No.
- Neither rule is true.
Answer: 7 goes in the box, outside both circles.
Carroll: finding the box
- Sort 18 into a Carroll diagram (Even/Not even and Multiple of 3/Not).
- Is 18 even? Yes ā the 'Even' row.
- Is 18 a multiple of 3? Yes ā the 'Multiple of 3' column.
- Find where that row and column meet.
Answer: 18 goes in the 'Even and multiple of 3' box.
Where you see this in real life
- Sorting numbers into groups like odd numbers and multiples of 5.
- Grouping shapes by whether they are 2D or have vertices.
- Sorting a class by who has a pet and who walks to school.
Key words
- Venn diagram
- A way to sort data using circles inside a box; the overlap shows things in both groups.
- Carroll diagram
- A grid that sorts data using a rule and its opposite for the rows and columns.
- Overlap
- The part of a Venn diagram where the circles cross ā for things in both groups.
- Set
- A group of things that follow the same rule.
- Sort
- To put things into groups using rules.