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 3 × ★ + 11 = 50, what number does ★ stand for?
3 · 11 · 50 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 18 = 108, what number does ★ stand for?
6 · 18 · 108 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 10 = 34, what number does ★ stand for?
6 · 10 · 34 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 1 = 16, what number does ★ stand for?
3 · 1 · 16 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 136, what number does ★ stand for?
8 · 16 · 136 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 3 = 123, what number does ★ stand for?
8 · 3 · 123 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 2 = 37, what number does ★ stand for?
7 · 2 · 37 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 18 = 32, what number does ★ stand for?
2 · 18 · 32 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 18 = 38, what number does ★ stand for?
2 · 18 · 38 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 20 = 62, what number does ★ stand for?
3 · 20 · 62 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 25, what number does ★ stand for?
3 · 4 · 25 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 5 = 60, what number does ★ stand for?
5 · 5 · 60 · Symbol equation puzzles

12 questions · Seed 85 · 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 3 × ★ + 11 = 50, what number does ★ stand for?
13
Subtract 11 from 50 to get 39, then divide by 3: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 18 = 108, what number does ★ stand for?
15
Subtract 18 from 108 to get 90, then divide by 6: ★ = 15.
3. If ★ represents the same whole number each time and 6 × ★ + 10 = 34, what number does ★ stand for?
4
Subtract 10 from 34 to get 24, then divide by 6: ★ = 4.
4. If ★ represents the same whole number each time and 3 × ★ + 1 = 16, what number does ★ stand for?
5
Subtract 1 from 16 to get 15, then divide by 3: ★ = 5.
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 136, what number does ★ stand for?
15
Subtract 16 from 136 to get 120, then divide by 8: ★ = 15.
6. If ★ represents the same whole number each time and 8 × ★ + 3 = 123, what number does ★ stand for?
15
Subtract 3 from 123 to get 120, then divide by 8: ★ = 15.
7. If ★ represents the same whole number each time and 7 × ★ + 2 = 37, what number does ★ stand for?
5
Subtract 2 from 37 to get 35, then divide by 7: ★ = 5.
8. If ★ represents the same whole number each time and 2 × ★ + 18 = 32, what number does ★ stand for?
7
Subtract 18 from 32 to get 14, then divide by 2: ★ = 7.
9. If ★ represents the same whole number each time and 2 × ★ + 18 = 38, what number does ★ stand for?
10
Subtract 18 from 38 to get 20, then divide by 2: ★ = 10.
10. If ★ represents the same whole number each time and 3 × ★ + 20 = 62, what number does ★ stand for?
14
Subtract 20 from 62 to get 42, then divide by 3: ★ = 14.
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 25, what number does ★ stand for?
7
Subtract 4 from 25 to get 21, then divide by 3: ★ = 7.
12. If ★ represents the same whole number each time and 5 × ★ + 5 = 60, what number does ★ stand for?
11
Subtract 5 from 60 to get 55, then divide by 5: ★ = 11.

12 questions · Seed 85 · 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 3 × ★ + 11 = 50, what number does ★ stand for?
3 · 11 · 50 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 18 = 108, what number does ★ stand for?
6 · 18 · 108 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 10 = 34, what number does ★ stand for?
6 · 10 · 34 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 1 = 16, what number does ★ stand for?
3 · 1 · 16 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 136, what number does ★ stand for?
8 · 16 · 136 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 3 = 123, what number does ★ stand for?
8 · 3 · 123 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 2 = 37, what number does ★ stand for?
7 · 2 · 37 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 18 = 32, what number does ★ stand for?
2 · 18 · 32 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 18 = 38, what number does ★ stand for?
2 · 18 · 38 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 20 = 62, what number does ★ stand for?
3 · 20 · 62 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 25, what number does ★ stand for?
3 · 4 · 25 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 5 = 60, what number does ★ stand for?
5 · 5 · 60 · Symbol equation puzzles

12 questions · Seed 85 · 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 3 × ★ + 11 = 50, what number does ★ stand for?
13
Subtract 11 from 50 to get 39, then divide by 3: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 18 = 108, what number does ★ stand for?
15
Subtract 18 from 108 to get 90, then divide by 6: ★ = 15.
3. If ★ represents the same whole number each time and 6 × ★ + 10 = 34, what number does ★ stand for?
4
Subtract 10 from 34 to get 24, then divide by 6: ★ = 4.
4. If ★ represents the same whole number each time and 3 × ★ + 1 = 16, what number does ★ stand for?
5
Subtract 1 from 16 to get 15, then divide by 3: ★ = 5.
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 136, what number does ★ stand for?
15
Subtract 16 from 136 to get 120, then divide by 8: ★ = 15.
6. If ★ represents the same whole number each time and 8 × ★ + 3 = 123, what number does ★ stand for?
15
Subtract 3 from 123 to get 120, then divide by 8: ★ = 15.
7. If ★ represents the same whole number each time and 7 × ★ + 2 = 37, what number does ★ stand for?
5
Subtract 2 from 37 to get 35, then divide by 7: ★ = 5.
8. If ★ represents the same whole number each time and 2 × ★ + 18 = 32, what number does ★ stand for?
7
Subtract 18 from 32 to get 14, then divide by 2: ★ = 7.
9. If ★ represents the same whole number each time and 2 × ★ + 18 = 38, what number does ★ stand for?
10
Subtract 18 from 38 to get 20, then divide by 2: ★ = 10.
10. If ★ represents the same whole number each time and 3 × ★ + 20 = 62, what number does ★ stand for?
14
Subtract 20 from 62 to get 42, then divide by 3: ★ = 14.
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 25, what number does ★ stand for?
7
Subtract 4 from 25 to get 21, then divide by 3: ★ = 7.
12. If ★ represents the same whole number each time and 5 × ★ + 5 = 60, what number does ★ stand for?
11
Subtract 5 from 60 to get 55, then divide by 5: ★ = 11.

12 questions · Seed 85 · Age guidance, not curriculum certification