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 2 × ★ + 18 = 32, what number does ★ stand for?
2 · 18 · 32 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 8 = 50, what number does ★ stand for?
6 · 8 · 50 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 12 = 22, what number does ★ stand for?
2 · 12 · 22 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 3 = 68, what number does ★ stand for?
5 · 3 · 68 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 64, what number does ★ stand for?
8 · 16 · 64 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 20 = 104, what number does ★ stand for?
6 · 20 · 104 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 5 = 23, what number does ★ stand for?
2 · 5 · 23 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 7 = 35, what number does ★ stand for?
4 · 7 · 35 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 5 = 68, what number does ★ stand for?
7 · 5 · 68 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 3 = 66, what number does ★ stand for?
7 · 3 · 66 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 8 = 23, what number does ★ stand for?
5 · 8 · 23 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 3 = 28, what number does ★ stand for?
5 · 3 · 28 · Symbol equation puzzles

12 questions · Seed 50 · 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 2 × ★ + 18 = 32, what number does ★ stand for?
7
Subtract 18 from 32 to get 14, then divide by 2: ★ = 7.
2. 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.
3. If ★ represents the same whole number each time and 2 × ★ + 12 = 22, what number does ★ stand for?
5
Subtract 12 from 22 to get 10, then divide by 2: ★ = 5.
4. If ★ represents the same whole number each time and 5 × ★ + 3 = 68, what number does ★ stand for?
13
Subtract 3 from 68 to get 65, then divide by 5: ★ = 13.
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 64, what number does ★ stand for?
6
Subtract 16 from 64 to get 48, then divide by 8: ★ = 6.
6. If ★ represents the same whole number each time and 6 × ★ + 20 = 104, what number does ★ stand for?
14
Subtract 20 from 104 to get 84, then divide by 6: ★ = 14.
7. If ★ represents the same whole number each time and 2 × ★ + 5 = 23, what number does ★ stand for?
9
Subtract 5 from 23 to get 18, then divide by 2: ★ = 9.
8. If ★ represents the same whole number each time and 4 × ★ + 7 = 35, what number does ★ stand for?
7
Subtract 7 from 35 to get 28, then divide by 4: ★ = 7.
9. If ★ represents the same whole number each time and 7 × ★ + 5 = 68, what number does ★ stand for?
9
Subtract 5 from 68 to get 63, then divide by 7: ★ = 9.
10. If ★ represents the same whole number each time and 7 × ★ + 3 = 66, what number does ★ stand for?
9
Subtract 3 from 66 to get 63, then divide by 7: ★ = 9.
11. If ★ represents the same whole number each time and 5 × ★ + 8 = 23, what number does ★ stand for?
3
Subtract 8 from 23 to get 15, then divide by 5: ★ = 3.
12. If ★ represents the same whole number each time and 5 × ★ + 3 = 28, what number does ★ stand for?
5
Subtract 3 from 28 to get 25, then divide by 5: ★ = 5.

12 questions · Seed 50 · 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 2 × ★ + 18 = 32, what number does ★ stand for?
2 · 18 · 32 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 8 = 50, what number does ★ stand for?
6 · 8 · 50 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 12 = 22, what number does ★ stand for?
2 · 12 · 22 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 3 = 68, what number does ★ stand for?
5 · 3 · 68 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 64, what number does ★ stand for?
8 · 16 · 64 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 20 = 104, what number does ★ stand for?
6 · 20 · 104 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 5 = 23, what number does ★ stand for?
2 · 5 · 23 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 7 = 35, what number does ★ stand for?
4 · 7 · 35 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 5 = 68, what number does ★ stand for?
7 · 5 · 68 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 3 = 66, what number does ★ stand for?
7 · 3 · 66 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 8 = 23, what number does ★ stand for?
5 · 8 · 23 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 3 = 28, what number does ★ stand for?
5 · 3 · 28 · Symbol equation puzzles

12 questions · Seed 50 · 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 2 × ★ + 18 = 32, what number does ★ stand for?
7
Subtract 18 from 32 to get 14, then divide by 2: ★ = 7.
2. 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.
3. If ★ represents the same whole number each time and 2 × ★ + 12 = 22, what number does ★ stand for?
5
Subtract 12 from 22 to get 10, then divide by 2: ★ = 5.
4. If ★ represents the same whole number each time and 5 × ★ + 3 = 68, what number does ★ stand for?
13
Subtract 3 from 68 to get 65, then divide by 5: ★ = 13.
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 64, what number does ★ stand for?
6
Subtract 16 from 64 to get 48, then divide by 8: ★ = 6.
6. If ★ represents the same whole number each time and 6 × ★ + 20 = 104, what number does ★ stand for?
14
Subtract 20 from 104 to get 84, then divide by 6: ★ = 14.
7. If ★ represents the same whole number each time and 2 × ★ + 5 = 23, what number does ★ stand for?
9
Subtract 5 from 23 to get 18, then divide by 2: ★ = 9.
8. If ★ represents the same whole number each time and 4 × ★ + 7 = 35, what number does ★ stand for?
7
Subtract 7 from 35 to get 28, then divide by 4: ★ = 7.
9. If ★ represents the same whole number each time and 7 × ★ + 5 = 68, what number does ★ stand for?
9
Subtract 5 from 68 to get 63, then divide by 7: ★ = 9.
10. If ★ represents the same whole number each time and 7 × ★ + 3 = 66, what number does ★ stand for?
9
Subtract 3 from 66 to get 63, then divide by 7: ★ = 9.
11. If ★ represents the same whole number each time and 5 × ★ + 8 = 23, what number does ★ stand for?
3
Subtract 8 from 23 to get 15, then divide by 5: ★ = 3.
12. If ★ represents the same whole number each time and 5 × ★ + 3 = 28, what number does ★ stand for?
5
Subtract 3 from 28 to get 25, then divide by 5: ★ = 5.

12 questions · Seed 50 · Age guidance, not curriculum certification