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.

New variation Try interactive challenge Browse templates

Age band:Ages 10-12 Ages 13-15

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Set overlap & Venn totals

Take your time. Show your thinking.

1. In a group, 22 students study French, 24 study Spanish, and 12 study both languages. How many students study at least one of these languages?
22 s · 24 s · 12 s · Set overlap & Venn totals
2. In a group, 12 students study French, 12 study Spanish, and 8 study both languages. How many students study at least one of these languages?
12 s · 12 s · 8 s · Set overlap & Venn totals
3. In a group, 8 students study French, 16 study Spanish, and 3 study both languages. How many students study at least one of these languages?
8 s · 16 s · 3 s · Set overlap & Venn totals
4. In a group, 18 students study French, 18 study Spanish, and 9 study both languages. How many students study at least one of these languages?
18 s · 18 s · 9 s · Set overlap & Venn totals
5. In a group, 22 students study French, 24 study Spanish, and 11 study both languages. How many students study at least one of these languages?
22 s · 24 s · 11 s · Set overlap & Venn totals
6. In a group, 18 students study French, 27 study Spanish, and 9 study both languages. How many students study at least one of these languages?
18 s · 27 s · 9 s · Set overlap & Venn totals
7. In a group, 16 students study French, 9 study Spanish, and 4 study both languages. How many students study at least one of these languages?
16 s · 9 s · 4 s · Set overlap & Venn totals
8. In a group, 17 students study French, 23 study Spanish, and 11 study both languages. How many students study at least one of these languages?
17 s · 23 s · 11 s · Set overlap & Venn totals
9. In a group, 16 students study French, 27 study Spanish, and 9 study both languages. How many students study at least one of these languages?
16 s · 27 s · 9 s · Set overlap & Venn totals
10. In a group, 22 students study French, 15 study Spanish, and 6 study both languages. How many students study at least one of these languages?
22 s · 15 s · 6 s · Set overlap & Venn totals
11. In a group, 17 students study French, 20 study Spanish, and 7 study both languages. How many students study at least one of these languages?
17 s · 20 s · 7 s · Set overlap & Venn totals
12. In a group, 11 students study French, 11 study Spanish, and 6 study both languages. How many students study at least one of these languages?
11 s · 11 s · 6 s · Set overlap & Venn totals

12 questions · Seed 43 · 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, 22 students study French, 24 study Spanish, and 12 study both languages. How many students study at least one of these languages?
34
By inclusion-exclusion: 22 + 24 − 12 = 34 students.
2. In a group, 12 students study French, 12 study Spanish, and 8 study both languages. How many students study at least one of these languages?
16
By inclusion-exclusion: 12 + 12 − 8 = 16 students.
3. In a group, 8 students study French, 16 study Spanish, and 3 study both languages. How many students study at least one of these languages?
21
By inclusion-exclusion: 8 + 16 − 3 = 21 students.
4. In a group, 18 students study French, 18 study Spanish, and 9 study both languages. How many students study at least one of these languages?
27
By inclusion-exclusion: 18 + 18 − 9 = 27 students.
5. In a group, 22 students study French, 24 study Spanish, and 11 study both languages. How many students study at least one of these languages?
35
By inclusion-exclusion: 22 + 24 − 11 = 35 students.
6. In a group, 18 students study French, 27 study Spanish, and 9 study both languages. How many students study at least one of these languages?
36
By inclusion-exclusion: 18 + 27 − 9 = 36 students.
7. In a group, 16 students study French, 9 study Spanish, and 4 study both languages. How many students study at least one of these languages?
21
By inclusion-exclusion: 16 + 9 − 4 = 21 students.
8. In a group, 17 students study French, 23 study Spanish, and 11 study both languages. How many students study at least one of these languages?
29
By inclusion-exclusion: 17 + 23 − 11 = 29 students.
9. In a group, 16 students study French, 27 study Spanish, and 9 study both languages. How many students study at least one of these languages?
34
By inclusion-exclusion: 16 + 27 − 9 = 34 students.
10. In a group, 22 students study French, 15 study Spanish, and 6 study both languages. How many students study at least one of these languages?
31
By inclusion-exclusion: 22 + 15 − 6 = 31 students.
11. In a group, 17 students study French, 20 study Spanish, and 7 study both languages. How many students study at least one of these languages?
30
By inclusion-exclusion: 17 + 20 − 7 = 30 students.
12. In a group, 11 students study French, 11 study Spanish, and 6 study both languages. How many students study at least one of these languages?
16
By inclusion-exclusion: 11 + 11 − 6 = 16 students.

12 questions · Seed 43 · 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, 22 students study French, 24 study Spanish, and 12 study both languages. How many students study at least one of these languages?
22 s · 24 s · 12 s · Set overlap & Venn totals
2. In a group, 12 students study French, 12 study Spanish, and 8 study both languages. How many students study at least one of these languages?
12 s · 12 s · 8 s · Set overlap & Venn totals
3. In a group, 8 students study French, 16 study Spanish, and 3 study both languages. How many students study at least one of these languages?
8 s · 16 s · 3 s · Set overlap & Venn totals
4. In a group, 18 students study French, 18 study Spanish, and 9 study both languages. How many students study at least one of these languages?
18 s · 18 s · 9 s · Set overlap & Venn totals
5. In a group, 22 students study French, 24 study Spanish, and 11 study both languages. How many students study at least one of these languages?
22 s · 24 s · 11 s · Set overlap & Venn totals
6. In a group, 18 students study French, 27 study Spanish, and 9 study both languages. How many students study at least one of these languages?
18 s · 27 s · 9 s · Set overlap & Venn totals
7. In a group, 16 students study French, 9 study Spanish, and 4 study both languages. How many students study at least one of these languages?
16 s · 9 s · 4 s · Set overlap & Venn totals
8. In a group, 17 students study French, 23 study Spanish, and 11 study both languages. How many students study at least one of these languages?
17 s · 23 s · 11 s · Set overlap & Venn totals
9. In a group, 16 students study French, 27 study Spanish, and 9 study both languages. How many students study at least one of these languages?
16 s · 27 s · 9 s · Set overlap & Venn totals
10. In a group, 22 students study French, 15 study Spanish, and 6 study both languages. How many students study at least one of these languages?
22 s · 15 s · 6 s · Set overlap & Venn totals
11. In a group, 17 students study French, 20 study Spanish, and 7 study both languages. How many students study at least one of these languages?
17 s · 20 s · 7 s · Set overlap & Venn totals
12. In a group, 11 students study French, 11 study Spanish, and 6 study both languages. How many students study at least one of these languages?
11 s · 11 s · 6 s · Set overlap & Venn totals

12 questions · Seed 43 · 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, 22 students study French, 24 study Spanish, and 12 study both languages. How many students study at least one of these languages?
34
By inclusion-exclusion: 22 + 24 − 12 = 34 students.
2. In a group, 12 students study French, 12 study Spanish, and 8 study both languages. How many students study at least one of these languages?
16
By inclusion-exclusion: 12 + 12 − 8 = 16 students.
3. In a group, 8 students study French, 16 study Spanish, and 3 study both languages. How many students study at least one of these languages?
21
By inclusion-exclusion: 8 + 16 − 3 = 21 students.
4. In a group, 18 students study French, 18 study Spanish, and 9 study both languages. How many students study at least one of these languages?
27
By inclusion-exclusion: 18 + 18 − 9 = 27 students.
5. In a group, 22 students study French, 24 study Spanish, and 11 study both languages. How many students study at least one of these languages?
35
By inclusion-exclusion: 22 + 24 − 11 = 35 students.
6. In a group, 18 students study French, 27 study Spanish, and 9 study both languages. How many students study at least one of these languages?
36
By inclusion-exclusion: 18 + 27 − 9 = 36 students.
7. In a group, 16 students study French, 9 study Spanish, and 4 study both languages. How many students study at least one of these languages?
21
By inclusion-exclusion: 16 + 9 − 4 = 21 students.
8. In a group, 17 students study French, 23 study Spanish, and 11 study both languages. How many students study at least one of these languages?
29
By inclusion-exclusion: 17 + 23 − 11 = 29 students.
9. In a group, 16 students study French, 27 study Spanish, and 9 study both languages. How many students study at least one of these languages?
34
By inclusion-exclusion: 16 + 27 − 9 = 34 students.
10. In a group, 22 students study French, 15 study Spanish, and 6 study both languages. How many students study at least one of these languages?
31
By inclusion-exclusion: 22 + 15 − 6 = 31 students.
11. In a group, 17 students study French, 20 study Spanish, and 7 study both languages. How many students study at least one of these languages?
30
By inclusion-exclusion: 17 + 20 − 7 = 30 students.
12. In a group, 11 students study French, 11 study Spanish, and 6 study both languages. How many students study at least one of these languages?
16
By inclusion-exclusion: 11 + 11 − 6 = 16 students.

12 questions · Seed 43 · Age guidance, not curriculum certification