ReasoningAges 13-15

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 13-15

Set overlap & Venn totals

Take your time. Show your thinking.

1. In a group, 9 students study French, 18 study Spanish, and 5 study both languages. How many students study at least one of these languages?
9 s · 18 s · 5 s · Set overlap & Venn totals
2. In a group, 26 students study French, 21 study Spanish, and 12 study both languages. How many students study at least one of these languages?
26 s · 21 s · 12 s · Set overlap & Venn totals
3. In a group, 18 students study French, 6 study Spanish, and 2 study both languages. How many students study at least one of these languages?
18 s · 6 s · 2 s · Set overlap & Venn totals
4. In a group, 18 students study French, 29 study Spanish, and 11 study both languages. How many students study at least one of these languages?
18 s · 29 s · 11 s · Set overlap & Venn totals
5. In a group, 27 students study French, 17 study Spanish, and 12 study both languages. How many students study at least one of these languages?
27 s · 17 s · 12 s · Set overlap & Venn totals
6. In a group, 19 students study French, 15 study Spanish, and 6 study both languages. How many students study at least one of these languages?
19 s · 15 s · 6 s · Set overlap & Venn totals
7. In a group, 14 students study French, 24 study Spanish, and 11 study both languages. How many students study at least one of these languages?
14 s · 24 s · 11 s · Set overlap & Venn totals
8. In a group, 24 students study French, 22 study Spanish, and 7 study both languages. How many students study at least one of these languages?
24 s · 22 s · 7 s · Set overlap & Venn totals
9. In a group, 20 students study French, 30 study Spanish, and 12 study both languages. How many students study at least one of these languages?
20 s · 30 s · 12 s · Set overlap & Venn totals
10. In a group, 18 students study French, 25 study Spanish, and 12 study both languages. How many students study at least one of these languages?
18 s · 25 s · 12 s · Set overlap & Venn totals
11. In a group, 20 students study French, 15 study Spanish, and 9 study both languages. How many students study at least one of these languages?
20 s · 15 s · 9 s · Set overlap & Venn totals
12. In a group, 23 students study French, 17 study Spanish, and 6 study both languages. How many students study at least one of these languages?
23 s · 17 s · 6 s · Set overlap & Venn totals

12 questions · Seed 44 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Set overlap & Venn totals

Answers and reasoning. Review before teaching.

1. In a group, 9 students study French, 18 study Spanish, and 5 study both languages. How many students study at least one of these languages?
22
By inclusion-exclusion: 9 + 18 − 5 = 22 students.
2. In a group, 26 students study French, 21 study Spanish, and 12 study both languages. How many students study at least one of these languages?
35
By inclusion-exclusion: 26 + 21 − 12 = 35 students.
3. In a group, 18 students study French, 6 study Spanish, and 2 study both languages. How many students study at least one of these languages?
22
By inclusion-exclusion: 18 + 6 − 2 = 22 students.
4. In a group, 18 students study French, 29 study Spanish, and 11 study both languages. How many students study at least one of these languages?
36
By inclusion-exclusion: 18 + 29 − 11 = 36 students.
5. In a group, 27 students study French, 17 study Spanish, and 12 study both languages. How many students study at least one of these languages?
32
By inclusion-exclusion: 27 + 17 − 12 = 32 students.
6. In a group, 19 students study French, 15 study Spanish, and 6 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 19 + 15 − 6 = 28 students.
7. In a group, 14 students study French, 24 study Spanish, and 11 study both languages. How many students study at least one of these languages?
27
By inclusion-exclusion: 14 + 24 − 11 = 27 students.
8. In a group, 24 students study French, 22 study Spanish, and 7 study both languages. How many students study at least one of these languages?
39
By inclusion-exclusion: 24 + 22 − 7 = 39 students.
9. In a group, 20 students study French, 30 study Spanish, and 12 study both languages. How many students study at least one of these languages?
38
By inclusion-exclusion: 20 + 30 − 12 = 38 students.
10. In a group, 18 students study French, 25 study Spanish, and 12 study both languages. How many students study at least one of these languages?
31
By inclusion-exclusion: 18 + 25 − 12 = 31 students.
11. In a group, 20 students study French, 15 study Spanish, and 9 study both languages. How many students study at least one of these languages?
26
By inclusion-exclusion: 20 + 15 − 9 = 26 students.
12. In a group, 23 students study French, 17 study Spanish, and 6 study both languages. How many students study at least one of these languages?
34
By inclusion-exclusion: 23 + 17 − 6 = 34 students.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Set overlap & Venn totals

Take your time. Show your thinking.

1. In a group, 9 students study French, 18 study Spanish, and 5 study both languages. How many students study at least one of these languages?
9 s · 18 s · 5 s · Set overlap & Venn totals
2. In a group, 26 students study French, 21 study Spanish, and 12 study both languages. How many students study at least one of these languages?
26 s · 21 s · 12 s · Set overlap & Venn totals
3. In a group, 18 students study French, 6 study Spanish, and 2 study both languages. How many students study at least one of these languages?
18 s · 6 s · 2 s · Set overlap & Venn totals
4. In a group, 18 students study French, 29 study Spanish, and 11 study both languages. How many students study at least one of these languages?
18 s · 29 s · 11 s · Set overlap & Venn totals
5. In a group, 27 students study French, 17 study Spanish, and 12 study both languages. How many students study at least one of these languages?
27 s · 17 s · 12 s · Set overlap & Venn totals
6. In a group, 19 students study French, 15 study Spanish, and 6 study both languages. How many students study at least one of these languages?
19 s · 15 s · 6 s · Set overlap & Venn totals
7. In a group, 14 students study French, 24 study Spanish, and 11 study both languages. How many students study at least one of these languages?
14 s · 24 s · 11 s · Set overlap & Venn totals
8. In a group, 24 students study French, 22 study Spanish, and 7 study both languages. How many students study at least one of these languages?
24 s · 22 s · 7 s · Set overlap & Venn totals
9. In a group, 20 students study French, 30 study Spanish, and 12 study both languages. How many students study at least one of these languages?
20 s · 30 s · 12 s · Set overlap & Venn totals
10. In a group, 18 students study French, 25 study Spanish, and 12 study both languages. How many students study at least one of these languages?
18 s · 25 s · 12 s · Set overlap & Venn totals
11. In a group, 20 students study French, 15 study Spanish, and 9 study both languages. How many students study at least one of these languages?
20 s · 15 s · 9 s · Set overlap & Venn totals
12. In a group, 23 students study French, 17 study Spanish, and 6 study both languages. How many students study at least one of these languages?
23 s · 17 s · 6 s · Set overlap & Venn totals

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Set overlap & Venn totals

Answers and reasoning. Review before teaching.

1. In a group, 9 students study French, 18 study Spanish, and 5 study both languages. How many students study at least one of these languages?
22
By inclusion-exclusion: 9 + 18 − 5 = 22 students.
2. In a group, 26 students study French, 21 study Spanish, and 12 study both languages. How many students study at least one of these languages?
35
By inclusion-exclusion: 26 + 21 − 12 = 35 students.
3. In a group, 18 students study French, 6 study Spanish, and 2 study both languages. How many students study at least one of these languages?
22
By inclusion-exclusion: 18 + 6 − 2 = 22 students.
4. In a group, 18 students study French, 29 study Spanish, and 11 study both languages. How many students study at least one of these languages?
36
By inclusion-exclusion: 18 + 29 − 11 = 36 students.
5. In a group, 27 students study French, 17 study Spanish, and 12 study both languages. How many students study at least one of these languages?
32
By inclusion-exclusion: 27 + 17 − 12 = 32 students.
6. In a group, 19 students study French, 15 study Spanish, and 6 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 19 + 15 − 6 = 28 students.
7. In a group, 14 students study French, 24 study Spanish, and 11 study both languages. How many students study at least one of these languages?
27
By inclusion-exclusion: 14 + 24 − 11 = 27 students.
8. In a group, 24 students study French, 22 study Spanish, and 7 study both languages. How many students study at least one of these languages?
39
By inclusion-exclusion: 24 + 22 − 7 = 39 students.
9. In a group, 20 students study French, 30 study Spanish, and 12 study both languages. How many students study at least one of these languages?
38
By inclusion-exclusion: 20 + 30 − 12 = 38 students.
10. In a group, 18 students study French, 25 study Spanish, and 12 study both languages. How many students study at least one of these languages?
31
By inclusion-exclusion: 18 + 25 − 12 = 31 students.
11. In a group, 20 students study French, 15 study Spanish, and 9 study both languages. How many students study at least one of these languages?
26
By inclusion-exclusion: 20 + 15 − 9 = 26 students.
12. In a group, 23 students study French, 17 study Spanish, and 6 study both languages. How many students study at least one of these languages?
34
By inclusion-exclusion: 23 + 17 − 6 = 34 students.

12 questions · Seed 44 · Age guidance, not curriculum certification