ReasoningAges 10-12

Set overlap & Venn totals

Use inclusion-exclusion reasoning to find the total number of members across two overlapping sets. Review suitability for your learners before teaching.

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Age band:Ages 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Set overlap & Venn totals

Take your time. Show your thinking.

1. In a group, 23 students study French, 18 study Spanish, and 10 study both languages. How many students study at least one of these languages?
23 s · 18 s · 10 s · Set overlap & Venn totals
2. In a group, 23 students study French, 15 study Spanish, and 8 study both languages. How many students study at least one of these languages?
23 s · 15 s · 8 s · Set overlap & Venn totals
3. In a group, 24 students study French, 26 study Spanish, and 11 study both languages. How many students study at least one of these languages?
24 s · 26 s · 11 s · Set overlap & Venn totals
4. In a group, 16 students study French, 13 study Spanish, and 2 study both languages. How many students study at least one of these languages?
16 s · 13 s · 2 s · Set overlap & Venn totals
5. In a group, 17 students study French, 23 study Spanish, and 5 study both languages. How many students study at least one of these languages?
17 s · 23 s · 5 s · Set overlap & Venn totals
6. In a group, 5 students study French, 12 study Spanish, and 2 study both languages. How many students study at least one of these languages?
5 s · 12 s · 2 s · Set overlap & Venn totals
7. In a group, 25 students study French, 11 study Spanish, and 8 study both languages. How many students study at least one of these languages?
25 s · 11 s · 8 s · Set overlap & Venn totals
8. In a group, 19 students study French, 12 study Spanish, and 2 study both languages. How many students study at least one of these languages?
19 s · 12 s · 2 s · Set overlap & Venn totals
9. In a group, 16 students study French, 14 study Spanish, and 2 study both languages. How many students study at least one of these languages?
16 s · 14 s · 2 s · Set overlap & Venn totals
10. In a group, 10 students study French, 23 study Spanish, and 5 study both languages. How many students study at least one of these languages?
10 s · 23 s · 5 s · Set overlap & Venn totals
11. In a group, 15 students study French, 22 study Spanish, and 11 study both languages. How many students study at least one of these languages?
15 s · 22 s · 11 s · Set overlap & Venn totals
12. In a group, 18 students study French, 19 study Spanish, and 7 study both languages. How many students study at least one of these languages?
18 s · 19 s · 7 s · Set overlap & Venn totals

12 questions · Seed 104729 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Set overlap & Venn totals

Answers and reasoning. Review before teaching.

1. In a group, 23 students study French, 18 study Spanish, and 10 study both languages. How many students study at least one of these languages?
31
By inclusion-exclusion: 23 + 18 − 10 = 31 students.
2. In a group, 23 students study French, 15 study Spanish, and 8 study both languages. How many students study at least one of these languages?
30
By inclusion-exclusion: 23 + 15 − 8 = 30 students.
3. In a group, 24 students study French, 26 study Spanish, and 11 study both languages. How many students study at least one of these languages?
39
By inclusion-exclusion: 24 + 26 − 11 = 39 students.
4. In a group, 16 students study French, 13 study Spanish, and 2 study both languages. How many students study at least one of these languages?
27
By inclusion-exclusion: 16 + 13 − 2 = 27 students.
5. In a group, 17 students study French, 23 study Spanish, and 5 study both languages. How many students study at least one of these languages?
35
By inclusion-exclusion: 17 + 23 − 5 = 35 students.
6. In a group, 5 students study French, 12 study Spanish, and 2 study both languages. How many students study at least one of these languages?
15
By inclusion-exclusion: 5 + 12 − 2 = 15 students.
7. In a group, 25 students study French, 11 study Spanish, and 8 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 25 + 11 − 8 = 28 students.
8. In a group, 19 students study French, 12 study Spanish, and 2 study both languages. How many students study at least one of these languages?
29
By inclusion-exclusion: 19 + 12 − 2 = 29 students.
9. In a group, 16 students study French, 14 study Spanish, and 2 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 16 + 14 − 2 = 28 students.
10. In a group, 10 students study French, 23 study Spanish, and 5 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 10 + 23 − 5 = 28 students.
11. In a group, 15 students study French, 22 study Spanish, and 11 study both languages. How many students study at least one of these languages?
26
By inclusion-exclusion: 15 + 22 − 11 = 26 students.
12. In a group, 18 students study French, 19 study Spanish, and 7 study both languages. How many students study at least one of these languages?
30
By inclusion-exclusion: 18 + 19 − 7 = 30 students.

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Set overlap & Venn totals

Take your time. Show your thinking.

1. In a group, 23 students study French, 18 study Spanish, and 10 study both languages. How many students study at least one of these languages?
23 s · 18 s · 10 s · Set overlap & Venn totals
2. In a group, 23 students study French, 15 study Spanish, and 8 study both languages. How many students study at least one of these languages?
23 s · 15 s · 8 s · Set overlap & Venn totals
3. In a group, 24 students study French, 26 study Spanish, and 11 study both languages. How many students study at least one of these languages?
24 s · 26 s · 11 s · Set overlap & Venn totals
4. In a group, 16 students study French, 13 study Spanish, and 2 study both languages. How many students study at least one of these languages?
16 s · 13 s · 2 s · Set overlap & Venn totals
5. In a group, 17 students study French, 23 study Spanish, and 5 study both languages. How many students study at least one of these languages?
17 s · 23 s · 5 s · Set overlap & Venn totals
6. In a group, 5 students study French, 12 study Spanish, and 2 study both languages. How many students study at least one of these languages?
5 s · 12 s · 2 s · Set overlap & Venn totals
7. In a group, 25 students study French, 11 study Spanish, and 8 study both languages. How many students study at least one of these languages?
25 s · 11 s · 8 s · Set overlap & Venn totals
8. In a group, 19 students study French, 12 study Spanish, and 2 study both languages. How many students study at least one of these languages?
19 s · 12 s · 2 s · Set overlap & Venn totals
9. In a group, 16 students study French, 14 study Spanish, and 2 study both languages. How many students study at least one of these languages?
16 s · 14 s · 2 s · Set overlap & Venn totals
10. In a group, 10 students study French, 23 study Spanish, and 5 study both languages. How many students study at least one of these languages?
10 s · 23 s · 5 s · Set overlap & Venn totals
11. In a group, 15 students study French, 22 study Spanish, and 11 study both languages. How many students study at least one of these languages?
15 s · 22 s · 11 s · Set overlap & Venn totals
12. In a group, 18 students study French, 19 study Spanish, and 7 study both languages. How many students study at least one of these languages?
18 s · 19 s · 7 s · Set overlap & Venn totals

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Set overlap & Venn totals

Answers and reasoning. Review before teaching.

1. In a group, 23 students study French, 18 study Spanish, and 10 study both languages. How many students study at least one of these languages?
31
By inclusion-exclusion: 23 + 18 − 10 = 31 students.
2. In a group, 23 students study French, 15 study Spanish, and 8 study both languages. How many students study at least one of these languages?
30
By inclusion-exclusion: 23 + 15 − 8 = 30 students.
3. In a group, 24 students study French, 26 study Spanish, and 11 study both languages. How many students study at least one of these languages?
39
By inclusion-exclusion: 24 + 26 − 11 = 39 students.
4. In a group, 16 students study French, 13 study Spanish, and 2 study both languages. How many students study at least one of these languages?
27
By inclusion-exclusion: 16 + 13 − 2 = 27 students.
5. In a group, 17 students study French, 23 study Spanish, and 5 study both languages. How many students study at least one of these languages?
35
By inclusion-exclusion: 17 + 23 − 5 = 35 students.
6. In a group, 5 students study French, 12 study Spanish, and 2 study both languages. How many students study at least one of these languages?
15
By inclusion-exclusion: 5 + 12 − 2 = 15 students.
7. In a group, 25 students study French, 11 study Spanish, and 8 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 25 + 11 − 8 = 28 students.
8. In a group, 19 students study French, 12 study Spanish, and 2 study both languages. How many students study at least one of these languages?
29
By inclusion-exclusion: 19 + 12 − 2 = 29 students.
9. In a group, 16 students study French, 14 study Spanish, and 2 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 16 + 14 − 2 = 28 students.
10. In a group, 10 students study French, 23 study Spanish, and 5 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 10 + 23 − 5 = 28 students.
11. In a group, 15 students study French, 22 study Spanish, and 11 study both languages. How many students study at least one of these languages?
26
By inclusion-exclusion: 15 + 22 − 11 = 26 students.
12. In a group, 18 students study French, 19 study Spanish, and 7 study both languages. How many students study at least one of these languages?
30
By inclusion-exclusion: 18 + 19 − 7 = 30 students.

12 questions · Seed 104729 · Age guidance, not curriculum certification