Data and charts · Ages 7–8

Sorting with Venn and Carroll diagrams worksheet

Part of: Pictograms and block charts

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Data and charts · Ages 7–8

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.How many numbers in the Venn diagram are outside both rings?
Answer:
2.How many numbers in the Carroll diagram fit neither rule?
Answer:
3.How many numbers are inside the left ring of the Venn diagram, the overlap included?
Answer:
4.How many numbers in the Venn diagram fit both rules?
Answer:

13.A box of blocks is sorted into a Carroll diagram by red / not red and square / not square: 4 red squares, 6 red but not square, 6 squares that aren't red, 5 neither red nor square. How many squares are there in all?
Working:
Answer:
14.Of 24 children, 11 keep a cat and 9 keep a dog, and 1 of them keep both. How many keep a cat but no dog?
Working:
Answer:
15.A tour group has 19 people. 8 have been to Japan and 6 to Taiwan, and 3 of them to both. How many have been to neither?
Working:
Answer:
16.In a group, 10 people like pears and 6 like apples, and 5 of them like both. How many like pears or apples (or both)?
Working:
Answer:
17.A box of blocks is sorted into a Carroll diagram by red / not red and square / not square: 5 red squares, 3 red but not square, 3 squares that aren't red, 8 neither red nor square. How many squares are there in all?
Working:
Answer:
18.A tour group has 17 people. 10 have been to Japan and 8 to Taiwan, and 6 of them to both. How many have been to neither?
Working:
Answer:

Show the answers and working

Sorting with Venn and Carroll diagrams worksheet: Answers and working

1. 1
Numbers outside fit neither rule. Count how many sit outside both rings.
The numbers outside fit neither rule: count them, 1.
2. 0
Numbers that fit neither rule go in the cell where the two “not” labels cross. Count how many are in it.
Numbers fitting neither rule sit bottom right, where the two “not” rows cross: 0.
3. 3
The left ring includes the part only in it and the overlap: count both parts.
The left ring holds 2 in it alone and 1 in the overlap: 2 + 1 = 3.
4. 1
Numbers fitting both rules go where the rings overlap. Count how many are there.
Numbers fitting both rules sit where the rings overlap: count them, 1.

5. C. In the left ring only
Ask rule by rule: does 28 fit the left ring's rule? Does it fit the right ring's rule?
Ask rule by rule: does 28 fit the left rule? The right? Both: the overlap; one: that ring; neither: outside.
6. B. Where the rings overlap
Ask rule by rule: does 24 fit the left ring's rule? Does it fit the right ring's rule?
Ask rule by rule: does 24 fit the left rule? The right? Both: the overlap; one: that ring; neither: outside.
7. C. In the right ring only
Ask rule by rule: does 30 fit the left ring's rule? Does it fit the right ring's rule?
Ask rule by rule: does 30 fit the left rule? The right? Both: the overlap; one: that ring; neither: outside.
8. C. Bottom right
First see which column's rule 36 fits, then which row's.
Find the column whose rule 36 fits, then the row: the cell where they cross is the one.
9. B. Top right
First see which column's rule 38 fits, then which row's.
Find the column whose rule 38 fits, then the row: the cell where they cross is the one.
10. False
The overlap needs both rules to fit. Check 2 against each rule in turn.
The overlap needs both rules to fit: check 2 against each.
11. False
The overlap needs both rules to fit. Check 20 against each rule in turn.
The overlap needs both rules to fit: check 20 against each.
12. False
The overlap needs both rules to fit. Check 5 against each rule in turn.
The overlap needs both rules to fit: check 5 against each.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 10 blocks
The squares fill the “square” row, red or not: count both.
The squares fill the “square” row, red or not: 4 + 6 = 10.
14. 10 children
Of the 11 with a cat, 1 keep a dog as well. Those who keep only a cat don't include them.
Of the 11 with a cat, 1 sit in the overlap; in the cat ring alone are 11 − 1 = 10.
15. 8 people
First work out how many have been to at least one place, without counting the 3 who went to both twice.
Inside the rings are 8 + 6 − 3; the rest are outside: 19 − (8 + 6 − 3) = 8.
16. 11 people
How many times does 10 + 6 count the people who like both? Draw a Venn diagram to see.
10 + 6 counts the 5 who like both twice, so take them off once: 10 + 6 − 5 = 11.
17. 8 blocks
The squares fill the “square” row, red or not: count both.
The squares fill the “square” row, red or not: 5 + 3 = 8.
18. 5 people
First work out how many have been to at least one place, without counting the 6 who went to both twice.
Inside the rings are 10 + 8 − 6; the rest are outside: 17 − (10 + 8 − 6) = 5.

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