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, 16 students study French, 17 study Spanish, and 8 study both languages. How many students study at least one of these languages?
16 s · 17 s · 8 s · Set overlap & Venn totals
2. In a group, 22 students study French, 25 study Spanish, and 7 study both languages. How many students study at least one of these languages?
22 s · 25 s · 7 s · Set overlap & Venn totals
3. In a group, 22 students study French, 22 study Spanish, and 12 study both languages. How many students study at least one of these languages?
22 s · 22 s · 12 s · Set overlap & Venn totals
4. In a group, 23 students study French, 16 study Spanish, and 6 study both languages. How many students study at least one of these languages?
23 s · 16 s · 6 s · Set overlap & Venn totals
5. In a group, 21 students study French, 10 study Spanish, and 5 study both languages. How many students study at least one of these languages?
21 s · 10 s · 5 s · Set overlap & Venn totals
6. In a group, 25 students study French, 30 study Spanish, and 12 study both languages. How many students study at least one of these languages?
25 s · 30 s · 12 s · Set overlap & Venn totals
7. In a group, 16 students study French, 23 study Spanish, and 6 study both languages. How many students study at least one of these languages?
16 s · 23 s · 6 s · Set overlap & Venn totals
8. In a group, 23 students study French, 26 study Spanish, and 11 study both languages. How many students study at least one of these languages?
23 s · 26 s · 11 s · Set overlap & Venn totals
9. In a group, 19 students study French, 17 study Spanish, and 8 study both languages. How many students study at least one of these languages?
19 s · 17 s · 8 s · Set overlap & Venn totals
10. In a group, 14 students study French, 19 study Spanish, and 4 study both languages. How many students study at least one of these languages?
14 s · 19 s · 4 s · Set overlap & Venn totals
11. In a group, 15 students study French, 21 study Spanish, and 3 study both languages. How many students study at least one of these languages?
15 s · 21 s · 3 s · Set overlap & Venn totals
12. In a group, 7 students study French, 14 study Spanish, and 2 study both languages. How many students study at least one of these languages?
7 s · 14 s · 2 s · Set overlap & Venn totals

12 questions · Seed 42 · 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, 16 students study French, 17 study Spanish, and 8 study both languages. How many students study at least one of these languages?
25
By inclusion-exclusion: 16 + 17 − 8 = 25 students.
2. In a group, 22 students study French, 25 study Spanish, and 7 study both languages. How many students study at least one of these languages?
40
By inclusion-exclusion: 22 + 25 − 7 = 40 students.
3. In a group, 22 students study French, 22 study Spanish, and 12 study both languages. How many students study at least one of these languages?
32
By inclusion-exclusion: 22 + 22 − 12 = 32 students.
4. In a group, 23 students study French, 16 study Spanish, and 6 study both languages. How many students study at least one of these languages?
33
By inclusion-exclusion: 23 + 16 − 6 = 33 students.
5. In a group, 21 students study French, 10 study Spanish, and 5 study both languages. How many students study at least one of these languages?
26
By inclusion-exclusion: 21 + 10 − 5 = 26 students.
6. In a group, 25 students study French, 30 study Spanish, and 12 study both languages. How many students study at least one of these languages?
43
By inclusion-exclusion: 25 + 30 − 12 = 43 students.
7. In a group, 16 students study French, 23 study Spanish, and 6 study both languages. How many students study at least one of these languages?
33
By inclusion-exclusion: 16 + 23 − 6 = 33 students.
8. In a group, 23 students study French, 26 study Spanish, and 11 study both languages. How many students study at least one of these languages?
38
By inclusion-exclusion: 23 + 26 − 11 = 38 students.
9. In a group, 19 students study French, 17 study Spanish, and 8 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 19 + 17 − 8 = 28 students.
10. In a group, 14 students study French, 19 study Spanish, and 4 study both languages. How many students study at least one of these languages?
29
By inclusion-exclusion: 14 + 19 − 4 = 29 students.
11. In a group, 15 students study French, 21 study Spanish, and 3 study both languages. How many students study at least one of these languages?
33
By inclusion-exclusion: 15 + 21 − 3 = 33 students.
12. In a group, 7 students study French, 14 study Spanish, and 2 study both languages. How many students study at least one of these languages?
19
By inclusion-exclusion: 7 + 14 − 2 = 19 students.

12 questions · Seed 42 · 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, 16 students study French, 17 study Spanish, and 8 study both languages. How many students study at least one of these languages?
16 s · 17 s · 8 s · Set overlap & Venn totals
2. In a group, 22 students study French, 25 study Spanish, and 7 study both languages. How many students study at least one of these languages?
22 s · 25 s · 7 s · Set overlap & Venn totals
3. In a group, 22 students study French, 22 study Spanish, and 12 study both languages. How many students study at least one of these languages?
22 s · 22 s · 12 s · Set overlap & Venn totals
4. In a group, 23 students study French, 16 study Spanish, and 6 study both languages. How many students study at least one of these languages?
23 s · 16 s · 6 s · Set overlap & Venn totals
5. In a group, 21 students study French, 10 study Spanish, and 5 study both languages. How many students study at least one of these languages?
21 s · 10 s · 5 s · Set overlap & Venn totals
6. In a group, 25 students study French, 30 study Spanish, and 12 study both languages. How many students study at least one of these languages?
25 s · 30 s · 12 s · Set overlap & Venn totals
7. In a group, 16 students study French, 23 study Spanish, and 6 study both languages. How many students study at least one of these languages?
16 s · 23 s · 6 s · Set overlap & Venn totals
8. In a group, 23 students study French, 26 study Spanish, and 11 study both languages. How many students study at least one of these languages?
23 s · 26 s · 11 s · Set overlap & Venn totals
9. In a group, 19 students study French, 17 study Spanish, and 8 study both languages. How many students study at least one of these languages?
19 s · 17 s · 8 s · Set overlap & Venn totals
10. In a group, 14 students study French, 19 study Spanish, and 4 study both languages. How many students study at least one of these languages?
14 s · 19 s · 4 s · Set overlap & Venn totals
11. In a group, 15 students study French, 21 study Spanish, and 3 study both languages. How many students study at least one of these languages?
15 s · 21 s · 3 s · Set overlap & Venn totals
12. In a group, 7 students study French, 14 study Spanish, and 2 study both languages. How many students study at least one of these languages?
7 s · 14 s · 2 s · Set overlap & Venn totals

12 questions · Seed 42 · 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, 16 students study French, 17 study Spanish, and 8 study both languages. How many students study at least one of these languages?
25
By inclusion-exclusion: 16 + 17 − 8 = 25 students.
2. In a group, 22 students study French, 25 study Spanish, and 7 study both languages. How many students study at least one of these languages?
40
By inclusion-exclusion: 22 + 25 − 7 = 40 students.
3. In a group, 22 students study French, 22 study Spanish, and 12 study both languages. How many students study at least one of these languages?
32
By inclusion-exclusion: 22 + 22 − 12 = 32 students.
4. In a group, 23 students study French, 16 study Spanish, and 6 study both languages. How many students study at least one of these languages?
33
By inclusion-exclusion: 23 + 16 − 6 = 33 students.
5. In a group, 21 students study French, 10 study Spanish, and 5 study both languages. How many students study at least one of these languages?
26
By inclusion-exclusion: 21 + 10 − 5 = 26 students.
6. In a group, 25 students study French, 30 study Spanish, and 12 study both languages. How many students study at least one of these languages?
43
By inclusion-exclusion: 25 + 30 − 12 = 43 students.
7. In a group, 16 students study French, 23 study Spanish, and 6 study both languages. How many students study at least one of these languages?
33
By inclusion-exclusion: 16 + 23 − 6 = 33 students.
8. In a group, 23 students study French, 26 study Spanish, and 11 study both languages. How many students study at least one of these languages?
38
By inclusion-exclusion: 23 + 26 − 11 = 38 students.
9. In a group, 19 students study French, 17 study Spanish, and 8 study both languages. How many students study at least one of these languages?
28
By inclusion-exclusion: 19 + 17 − 8 = 28 students.
10. In a group, 14 students study French, 19 study Spanish, and 4 study both languages. How many students study at least one of these languages?
29
By inclusion-exclusion: 14 + 19 − 4 = 29 students.
11. In a group, 15 students study French, 21 study Spanish, and 3 study both languages. How many students study at least one of these languages?
33
By inclusion-exclusion: 15 + 21 − 3 = 33 students.
12. In a group, 7 students study French, 14 study Spanish, and 2 study both languages. How many students study at least one of these languages?
19
By inclusion-exclusion: 7 + 14 − 2 = 19 students.

12 questions · Seed 42 · Age guidance, not curriculum certification