ReasoningAges 10-12

Symbol equation puzzles

Deduce the value of a repeated mystery symbol in a two-step arithmetic equation. Review suitability for your learners before teaching.

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Age band:Ages 7-9 Ages 10-12

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Worksheet StudioPractice pack · Ages 10-12

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 6 × ★ + 9 = 69, what number does ★ stand for?
6 · 9 · 69 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 5 × ★ + 10 = 45, what number does ★ stand for?
5 · 10 · 45 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 2 = 107, what number does ★ stand for?
7 · 2 · 107 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 18 = 82, what number does ★ stand for?
8 · 18 · 82 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 16 = 38, what number does ★ stand for?
2 · 16 · 38 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 2 = 12, what number does ★ stand for?
2 · 2 · 12 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 16 = 48, what number does ★ stand for?
4 · 16 · 48 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 20 = 95, what number does ★ stand for?
5 · 20 · 95 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 18 = 67, what number does ★ stand for?
7 · 18 · 67 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 11 = 43, what number does ★ stand for?
4 · 11 · 43 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 11 = 86, what number does ★ stand for?
5 · 11 · 86 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 9 = 86, what number does ★ stand for?
7 · 9 · 86 · Symbol equation puzzles

12 questions · Seed 71 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 6 × ★ + 9 = 69, what number does ★ stand for?
10
Subtract 9 from 69 to get 60, then divide by 6: ★ = 10.
2. If ★ represents the same whole number each time and 5 × ★ + 10 = 45, what number does ★ stand for?
7
Subtract 10 from 45 to get 35, then divide by 5: ★ = 7.
3. If ★ represents the same whole number each time and 7 × ★ + 2 = 107, what number does ★ stand for?
15
Subtract 2 from 107 to get 105, then divide by 7: ★ = 15.
4. If ★ represents the same whole number each time and 8 × ★ + 18 = 82, what number does ★ stand for?
8
Subtract 18 from 82 to get 64, then divide by 8: ★ = 8.
5. If ★ represents the same whole number each time and 2 × ★ + 16 = 38, what number does ★ stand for?
11
Subtract 16 from 38 to get 22, then divide by 2: ★ = 11.
6. If ★ represents the same whole number each time and 2 × ★ + 2 = 12, what number does ★ stand for?
5
Subtract 2 from 12 to get 10, then divide by 2: ★ = 5.
7. If ★ represents the same whole number each time and 4 × ★ + 16 = 48, what number does ★ stand for?
8
Subtract 16 from 48 to get 32, then divide by 4: ★ = 8.
8. If ★ represents the same whole number each time and 5 × ★ + 20 = 95, what number does ★ stand for?
15
Subtract 20 from 95 to get 75, then divide by 5: ★ = 15.
9. If ★ represents the same whole number each time and 7 × ★ + 18 = 67, what number does ★ stand for?
7
Subtract 18 from 67 to get 49, then divide by 7: ★ = 7.
10. If ★ represents the same whole number each time and 4 × ★ + 11 = 43, what number does ★ stand for?
8
Subtract 11 from 43 to get 32, then divide by 4: ★ = 8.
11. If ★ represents the same whole number each time and 5 × ★ + 11 = 86, what number does ★ stand for?
15
Subtract 11 from 86 to get 75, then divide by 5: ★ = 15.
12. If ★ represents the same whole number each time and 7 × ★ + 9 = 86, what number does ★ stand for?
11
Subtract 9 from 86 to get 77, then divide by 7: ★ = 11.

12 questions · Seed 71 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 6 × ★ + 9 = 69, what number does ★ stand for?
6 · 9 · 69 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 5 × ★ + 10 = 45, what number does ★ stand for?
5 · 10 · 45 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 2 = 107, what number does ★ stand for?
7 · 2 · 107 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 18 = 82, what number does ★ stand for?
8 · 18 · 82 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 16 = 38, what number does ★ stand for?
2 · 16 · 38 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 2 = 12, what number does ★ stand for?
2 · 2 · 12 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 16 = 48, what number does ★ stand for?
4 · 16 · 48 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 20 = 95, what number does ★ stand for?
5 · 20 · 95 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 18 = 67, what number does ★ stand for?
7 · 18 · 67 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 11 = 43, what number does ★ stand for?
4 · 11 · 43 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 11 = 86, what number does ★ stand for?
5 · 11 · 86 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 9 = 86, what number does ★ stand for?
7 · 9 · 86 · Symbol equation puzzles

12 questions · Seed 71 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 6 × ★ + 9 = 69, what number does ★ stand for?
10
Subtract 9 from 69 to get 60, then divide by 6: ★ = 10.
2. If ★ represents the same whole number each time and 5 × ★ + 10 = 45, what number does ★ stand for?
7
Subtract 10 from 45 to get 35, then divide by 5: ★ = 7.
3. If ★ represents the same whole number each time and 7 × ★ + 2 = 107, what number does ★ stand for?
15
Subtract 2 from 107 to get 105, then divide by 7: ★ = 15.
4. If ★ represents the same whole number each time and 8 × ★ + 18 = 82, what number does ★ stand for?
8
Subtract 18 from 82 to get 64, then divide by 8: ★ = 8.
5. If ★ represents the same whole number each time and 2 × ★ + 16 = 38, what number does ★ stand for?
11
Subtract 16 from 38 to get 22, then divide by 2: ★ = 11.
6. If ★ represents the same whole number each time and 2 × ★ + 2 = 12, what number does ★ stand for?
5
Subtract 2 from 12 to get 10, then divide by 2: ★ = 5.
7. If ★ represents the same whole number each time and 4 × ★ + 16 = 48, what number does ★ stand for?
8
Subtract 16 from 48 to get 32, then divide by 4: ★ = 8.
8. If ★ represents the same whole number each time and 5 × ★ + 20 = 95, what number does ★ stand for?
15
Subtract 20 from 95 to get 75, then divide by 5: ★ = 15.
9. If ★ represents the same whole number each time and 7 × ★ + 18 = 67, what number does ★ stand for?
7
Subtract 18 from 67 to get 49, then divide by 7: ★ = 7.
10. If ★ represents the same whole number each time and 4 × ★ + 11 = 43, what number does ★ stand for?
8
Subtract 11 from 43 to get 32, then divide by 4: ★ = 8.
11. If ★ represents the same whole number each time and 5 × ★ + 11 = 86, what number does ★ stand for?
15
Subtract 11 from 86 to get 75, then divide by 5: ★ = 15.
12. If ★ represents the same whole number each time and 7 × ★ + 9 = 86, what number does ★ stand for?
11
Subtract 9 from 86 to get 77, then divide by 7: ★ = 11.

12 questions · Seed 71 · Age guidance, not curriculum certification