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 8 × ★ + 1 = 81, what number does ★ stand for?
8 · 1 · 81 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 14 = 58, what number does ★ stand for?
4 · 14 · 58 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 20 = 76, what number does ★ stand for?
7 · 20 · 76 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 4 = 95, what number does ★ stand for?
7 · 4 · 95 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 18 = 98, what number does ★ stand for?
8 · 18 · 98 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 12 = 36, what number does ★ stand for?
8 · 12 · 36 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 5 = 50, what number does ★ stand for?
3 · 5 · 50 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 18 = 46, what number does ★ stand for?
7 · 18 · 46 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 10 = 74, what number does ★ stand for?
8 · 10 · 74 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 2 = 32, what number does ★ stand for?
2 · 2 · 32 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 31, what number does ★ stand for?
3 · 4 · 31 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
3 · 9 · 24 · Symbol equation puzzles

12 questions · Seed 55 · 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 8 × ★ + 1 = 81, what number does ★ stand for?
10
Subtract 1 from 81 to get 80, then divide by 8: ★ = 10.
2. If ★ represents the same whole number each time and 4 × ★ + 14 = 58, what number does ★ stand for?
11
Subtract 14 from 58 to get 44, then divide by 4: ★ = 11.
3. If ★ represents the same whole number each time and 7 × ★ + 20 = 76, what number does ★ stand for?
8
Subtract 20 from 76 to get 56, then divide by 7: ★ = 8.
4. If ★ represents the same whole number each time and 7 × ★ + 4 = 95, what number does ★ stand for?
13
Subtract 4 from 95 to get 91, then divide by 7: ★ = 13.
5. If ★ represents the same whole number each time and 8 × ★ + 18 = 98, what number does ★ stand for?
10
Subtract 18 from 98 to get 80, then divide by 8: ★ = 10.
6. If ★ represents the same whole number each time and 8 × ★ + 12 = 36, what number does ★ stand for?
3
Subtract 12 from 36 to get 24, then divide by 8: ★ = 3.
7. If ★ represents the same whole number each time and 3 × ★ + 5 = 50, what number does ★ stand for?
15
Subtract 5 from 50 to get 45, then divide by 3: ★ = 15.
8. If ★ represents the same whole number each time and 7 × ★ + 18 = 46, what number does ★ stand for?
4
Subtract 18 from 46 to get 28, then divide by 7: ★ = 4.
9. If ★ represents the same whole number each time and 8 × ★ + 10 = 74, what number does ★ stand for?
8
Subtract 10 from 74 to get 64, then divide by 8: ★ = 8.
10. If ★ represents the same whole number each time and 2 × ★ + 2 = 32, what number does ★ stand for?
15
Subtract 2 from 32 to get 30, then divide by 2: ★ = 15.
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 31, what number does ★ stand for?
9
Subtract 4 from 31 to get 27, then divide by 3: ★ = 9.
12. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
5
Subtract 9 from 24 to get 15, then divide by 3: ★ = 5.

12 questions · Seed 55 · 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 8 × ★ + 1 = 81, what number does ★ stand for?
8 · 1 · 81 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 14 = 58, what number does ★ stand for?
4 · 14 · 58 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 20 = 76, what number does ★ stand for?
7 · 20 · 76 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 4 = 95, what number does ★ stand for?
7 · 4 · 95 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 18 = 98, what number does ★ stand for?
8 · 18 · 98 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 12 = 36, what number does ★ stand for?
8 · 12 · 36 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 5 = 50, what number does ★ stand for?
3 · 5 · 50 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 18 = 46, what number does ★ stand for?
7 · 18 · 46 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 10 = 74, what number does ★ stand for?
8 · 10 · 74 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 2 = 32, what number does ★ stand for?
2 · 2 · 32 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 31, what number does ★ stand for?
3 · 4 · 31 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
3 · 9 · 24 · Symbol equation puzzles

12 questions · Seed 55 · 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 8 × ★ + 1 = 81, what number does ★ stand for?
10
Subtract 1 from 81 to get 80, then divide by 8: ★ = 10.
2. If ★ represents the same whole number each time and 4 × ★ + 14 = 58, what number does ★ stand for?
11
Subtract 14 from 58 to get 44, then divide by 4: ★ = 11.
3. If ★ represents the same whole number each time and 7 × ★ + 20 = 76, what number does ★ stand for?
8
Subtract 20 from 76 to get 56, then divide by 7: ★ = 8.
4. If ★ represents the same whole number each time and 7 × ★ + 4 = 95, what number does ★ stand for?
13
Subtract 4 from 95 to get 91, then divide by 7: ★ = 13.
5. If ★ represents the same whole number each time and 8 × ★ + 18 = 98, what number does ★ stand for?
10
Subtract 18 from 98 to get 80, then divide by 8: ★ = 10.
6. If ★ represents the same whole number each time and 8 × ★ + 12 = 36, what number does ★ stand for?
3
Subtract 12 from 36 to get 24, then divide by 8: ★ = 3.
7. If ★ represents the same whole number each time and 3 × ★ + 5 = 50, what number does ★ stand for?
15
Subtract 5 from 50 to get 45, then divide by 3: ★ = 15.
8. If ★ represents the same whole number each time and 7 × ★ + 18 = 46, what number does ★ stand for?
4
Subtract 18 from 46 to get 28, then divide by 7: ★ = 4.
9. If ★ represents the same whole number each time and 8 × ★ + 10 = 74, what number does ★ stand for?
8
Subtract 10 from 74 to get 64, then divide by 8: ★ = 8.
10. If ★ represents the same whole number each time and 2 × ★ + 2 = 32, what number does ★ stand for?
15
Subtract 2 from 32 to get 30, then divide by 2: ★ = 15.
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 31, what number does ★ stand for?
9
Subtract 4 from 31 to get 27, then divide by 3: ★ = 9.
12. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
5
Subtract 9 from 24 to get 15, then divide by 3: ★ = 5.

12 questions · Seed 55 · Age guidance, not curriculum certification