Data and charts · Ages 9–10
Venn and Carroll diagrams worksheet
Part of: Bigger bar charts and rounding
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Venn and Carroll diagrams worksheet
Data and charts · Ages 9–10
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The Venn diagram shows how many children in a group like swimming (A) and running (B). How many like both?
Answer:
2.The Venn diagram shows how many children in a group like swimming (A) and running (B). How many like swimming altogether?
Answer:
3.The Venn diagram shows how many children in a group like swimming (A) and running (B). How many children are in the group?
Answer:
4.The Venn diagram shows how many children in a group like swimming (A) and running (B). How many like running but not swimming?
Answer:
5.The Venn diagram shows how many children in a group like swimming (A) and running (B). How many like at least one of them?
Answer:
Part B: Choose, or true or false (2 marks each)
6.The numbers 1 to 30 go in a Venn diagram: ring A is even numbers, ring B is multiples of 3. Where does 12 go?
- A. In B only
- B. Outside both rings
- C. In A only
- D. Where the rings overlap
Choose the right answer
Answer:
7.The Venn diagram shows how many children in a group like swimming (A) and running (B). More children like swimming than running.
True or false?
Answer:
8.The numbers 1 to 30 go in a Venn diagram: ring A is even numbers, ring B is multiples of 3. Where does 13 go?
- A. In A only
- B. Outside both rings
- C. In B only
- D. Where the rings overlap
Choose the right answer
Answer:
9.The numbers 1 to 30 go in a Venn diagram: ring A is even numbers, ring B is multiples of 3. Where does 19 go?
- A. In A only
- B. In B only
- C. Outside both rings
- D. Where the rings overlap
Choose the right answer
Answer:
10.The numbers 1 to 30 go in a Venn diagram: ring A is even numbers, ring B is multiples of 3. Where does 9 go?
- A. In B only
- B. Outside both rings
- C. Where the rings overlap
- D. In A only
Choose the right answer
Answer:
11.The numbers 1 to 30 go in a Venn diagram: ring A is even numbers, ring B is multiples of 3. Where does 21 go?
- A. Outside both rings
- B. Where the rings overlap
- C. In B only
- D. In A only
Choose the right answer
Answer:
12.The numbers 1 to 30 go in a Venn diagram: ring A is even numbers, ring B is multiples of 3. Where does 15 go?
- A. Where the rings overlap
- B. Outside both rings
- C. In B only
- D. In A only
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.In a group of 21, 9 wear glasses, 12 are boys, and 5 boys wear glasses. How many girls wear glasses?
Working:
Answer:
14.Of 37 people, 14 like cats, 14 like dogs, and 4 like both. How many like neither?
Working:
Answer:
15.The Venn diagram shows how many children in a group like swimming (A) and running (B). How many like exactly one of them?
Working:
Answer:
16.Of 38 people, 20 like cats, 19 like dogs, and 6 like both. How many like neither?
Working:
Answer:
17.In a group of 30, 16 wear glasses, 12 are boys, and 1 boys wear glasses. How many girls wear glasses?
Working:
Answer:
18.Of 36 people, 6 like cats, 9 like dogs, and 4 like both. How many like neither?
Working:
Answer:
Show the answers and working
Venn and Carroll diagrams worksheet: Answers and working
Part A: Working out and filling in
1. 6 children
Liking both means being inside ring A and ring B at once.
Those who like both are where the rings overlap: 6.
2. 22 children
Everyone who likes swimming is inside ring A, and that includes the overlap.
Everyone in ring A likes swimming: 10 in A only plus 12 in the overlap, 22.
3. 33 children
Every child is in one part of the diagram, including outside both rings.
Add all four parts: 15 + 8 + 5 + 5 = 33 (those outside the rings too).
4. 14 children
Running fans are in ring B; not liking swimming means being outside ring A.
In ring B but outside ring A: 14.
5. 30 children
At least one means inside either ring; leave out those outside both.
Everyone inside the rings, but not outside: 10 + 9 + 11 = 30.
Part B: Choose, or true or false
6. D. Where the rings overlap
Check whether 12 divides exactly by 2, and whether it divides exactly by 3.
Check each: is 12 even? Is it a multiple of 3? Both: the overlap; neither: outside.
7. True
Swimming is all of ring A and running all of ring B; both include the overlap.
Swimming: 14 + 1 = 15; running: 1 + 13 = 14. Compare them.
8. B. Outside both rings
Check whether 13 divides exactly by 2, and whether it divides exactly by 3.
Check each: is 13 even? Is it a multiple of 3? Both: the overlap; neither: outside.
9. C. Outside both rings
Check whether 19 divides exactly by 2, and whether it divides exactly by 3.
Check each: is 19 even? Is it a multiple of 3? Both: the overlap; neither: outside.
10. A. In B only
Check whether 9 divides exactly by 2, and whether it divides exactly by 3.
Check each: is 9 even? Is it a multiple of 3? Both: the overlap; neither: outside.
11. C. In B only
Check whether 21 divides exactly by 2, and whether it divides exactly by 3.
Check each: is 21 even? Is it a multiple of 3? Both: the overlap; neither: outside.
12. C. In B only
Check whether 15 divides exactly by 2, and whether it divides exactly by 3.
Check each: is 15 even? Is it a multiple of 3? Both: the overlap; neither: outside.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 4 girls
Draw a Carroll diagram: the 9 with glasses split into a boys' cell and a girls' cell.
In the Carroll diagram, the 9 with glasses split into 5 boys and the girls: 9 − 5 = 4.
14. 13 people
First find how many like at least one: 14 + 14 counts those who like both twice.
At least one: 14 + 14 − 4 (counting both once); 37 less that is neither: 13.
15. 16 children
Exactly one means inside a ring but not in the overlap.
3 in A only plus 13 in B only: 16.
16. 5 people
First find how many like at least one: 20 + 19 counts those who like both twice.
At least one: 20 + 19 − 6 (counting both once); 38 less that is neither: 5.
17. 15 girls
Draw a Carroll diagram: the 16 with glasses split into a boys' cell and a girls' cell.
In the Carroll diagram, the 16 with glasses split into 1 boys and the girls: 16 − 1 = 15.
18. 25 people
First find how many like at least one: 6 + 9 counts those who like both twice.
At least one: 6 + 9 − 4 (counting both once); 36 less that is neither: 25.
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