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 7 × ★ + 12 = 96, what number does ★ stand for?
7 · 12 · 96 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 17 = 87, what number does ★ stand for?
7 · 17 · 87 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 8 = 50, what number does ★ stand for?
6 · 8 · 50 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 2 = 24, what number does ★ stand for?
2 · 2 · 24 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 10 = 58, what number does ★ stand for?
8 · 10 · 58 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
2 · 4 · 32 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 2 = 18, what number does ★ stand for?
2 · 2 · 18 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 11 = 67, what number does ★ stand for?
8 · 11 · 67 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 20 = 60, what number does ★ stand for?
5 · 20 · 60 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 11 = 25, what number does ★ stand for?
7 · 11 · 25 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 3 = 21, what number does ★ stand for?
6 · 3 · 21 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 4 = 39, what number does ★ stand for?
5 · 4 · 39 · Symbol equation puzzles

12 questions · Seed 58 · 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 7 × ★ + 12 = 96, what number does ★ stand for?
12
Subtract 12 from 96 to get 84, then divide by 7: ★ = 12.
2. If ★ represents the same whole number each time and 7 × ★ + 17 = 87, what number does ★ stand for?
10
Subtract 17 from 87 to get 70, then divide by 7: ★ = 10.
3. If ★ represents the same whole number each time and 6 × ★ + 8 = 50, what number does ★ stand for?
7
Subtract 8 from 50 to get 42, then divide by 6: ★ = 7.
4. If ★ represents the same whole number each time and 2 × ★ + 2 = 24, what number does ★ stand for?
11
Subtract 2 from 24 to get 22, then divide by 2: ★ = 11.
5. If ★ represents the same whole number each time and 8 × ★ + 10 = 58, what number does ★ stand for?
6
Subtract 10 from 58 to get 48, then divide by 8: ★ = 6.
6. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
14
Subtract 4 from 32 to get 28, then divide by 2: ★ = 14.
7. If ★ represents the same whole number each time and 2 × ★ + 2 = 18, what number does ★ stand for?
8
Subtract 2 from 18 to get 16, then divide by 2: ★ = 8.
8. If ★ represents the same whole number each time and 8 × ★ + 11 = 67, what number does ★ stand for?
7
Subtract 11 from 67 to get 56, then divide by 8: ★ = 7.
9. If ★ represents the same whole number each time and 5 × ★ + 20 = 60, what number does ★ stand for?
8
Subtract 20 from 60 to get 40, then divide by 5: ★ = 8.
10. If ★ represents the same whole number each time and 7 × ★ + 11 = 25, what number does ★ stand for?
2
Subtract 11 from 25 to get 14, then divide by 7: ★ = 2.
11. If ★ represents the same whole number each time and 6 × ★ + 3 = 21, what number does ★ stand for?
3
Subtract 3 from 21 to get 18, then divide by 6: ★ = 3.
12. If ★ represents the same whole number each time and 5 × ★ + 4 = 39, what number does ★ stand for?
7
Subtract 4 from 39 to get 35, then divide by 5: ★ = 7.

12 questions · Seed 58 · 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 7 × ★ + 12 = 96, what number does ★ stand for?
7 · 12 · 96 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 17 = 87, what number does ★ stand for?
7 · 17 · 87 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 8 = 50, what number does ★ stand for?
6 · 8 · 50 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 2 = 24, what number does ★ stand for?
2 · 2 · 24 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 10 = 58, what number does ★ stand for?
8 · 10 · 58 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
2 · 4 · 32 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 2 = 18, what number does ★ stand for?
2 · 2 · 18 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 11 = 67, what number does ★ stand for?
8 · 11 · 67 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 20 = 60, what number does ★ stand for?
5 · 20 · 60 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 11 = 25, what number does ★ stand for?
7 · 11 · 25 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 3 = 21, what number does ★ stand for?
6 · 3 · 21 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 4 = 39, what number does ★ stand for?
5 · 4 · 39 · Symbol equation puzzles

12 questions · Seed 58 · 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 7 × ★ + 12 = 96, what number does ★ stand for?
12
Subtract 12 from 96 to get 84, then divide by 7: ★ = 12.
2. If ★ represents the same whole number each time and 7 × ★ + 17 = 87, what number does ★ stand for?
10
Subtract 17 from 87 to get 70, then divide by 7: ★ = 10.
3. If ★ represents the same whole number each time and 6 × ★ + 8 = 50, what number does ★ stand for?
7
Subtract 8 from 50 to get 42, then divide by 6: ★ = 7.
4. If ★ represents the same whole number each time and 2 × ★ + 2 = 24, what number does ★ stand for?
11
Subtract 2 from 24 to get 22, then divide by 2: ★ = 11.
5. If ★ represents the same whole number each time and 8 × ★ + 10 = 58, what number does ★ stand for?
6
Subtract 10 from 58 to get 48, then divide by 8: ★ = 6.
6. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
14
Subtract 4 from 32 to get 28, then divide by 2: ★ = 14.
7. If ★ represents the same whole number each time and 2 × ★ + 2 = 18, what number does ★ stand for?
8
Subtract 2 from 18 to get 16, then divide by 2: ★ = 8.
8. If ★ represents the same whole number each time and 8 × ★ + 11 = 67, what number does ★ stand for?
7
Subtract 11 from 67 to get 56, then divide by 8: ★ = 7.
9. If ★ represents the same whole number each time and 5 × ★ + 20 = 60, what number does ★ stand for?
8
Subtract 20 from 60 to get 40, then divide by 5: ★ = 8.
10. If ★ represents the same whole number each time and 7 × ★ + 11 = 25, what number does ★ stand for?
2
Subtract 11 from 25 to get 14, then divide by 7: ★ = 2.
11. If ★ represents the same whole number each time and 6 × ★ + 3 = 21, what number does ★ stand for?
3
Subtract 3 from 21 to get 18, then divide by 6: ★ = 3.
12. If ★ represents the same whole number each time and 5 × ★ + 4 = 39, what number does ★ stand for?
7
Subtract 4 from 39 to get 35, then divide by 5: ★ = 7.

12 questions · Seed 58 · Age guidance, not curriculum certification