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 = 89, what number does ★ stand for?
8 · 1 · 89 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 8 = 47, what number does ★ stand for?
3 · 8 · 47 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 3 = 24, what number does ★ stand for?
7 · 3 · 24 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 1 = 9, what number does ★ stand for?
4 · 1 · 9 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 7 = 19, what number does ★ stand for?
2 · 7 · 19 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 10 = 22, what number does ★ stand for?
6 · 10 · 22 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 13 = 28, what number does ★ stand for?
5 · 13 · 28 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 13 = 37, what number does ★ stand for?
4 · 13 · 37 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 11 = 56, what number does ★ stand for?
3 · 11 · 56 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
3 · 12 · 54 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 11 = 19, what number does ★ stand for?
4 · 11 · 19 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 7 = 31, what number does ★ stand for?
8 · 7 · 31 · Symbol equation puzzles

12 questions · Seed 45 · 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 = 89, what number does ★ stand for?
11
Subtract 1 from 89 to get 88, then divide by 8: ★ = 11.
2. If ★ represents the same whole number each time and 3 × ★ + 8 = 47, what number does ★ stand for?
13
Subtract 8 from 47 to get 39, then divide by 3: ★ = 13.
3. If ★ represents the same whole number each time and 7 × ★ + 3 = 24, what number does ★ stand for?
3
Subtract 3 from 24 to get 21, then divide by 7: ★ = 3.
4. If ★ represents the same whole number each time and 4 × ★ + 1 = 9, what number does ★ stand for?
2
Subtract 1 from 9 to get 8, then divide by 4: ★ = 2.
5. If ★ represents the same whole number each time and 2 × ★ + 7 = 19, what number does ★ stand for?
6
Subtract 7 from 19 to get 12, then divide by 2: ★ = 6.
6. If ★ represents the same whole number each time and 6 × ★ + 10 = 22, what number does ★ stand for?
2
Subtract 10 from 22 to get 12, then divide by 6: ★ = 2.
7. If ★ represents the same whole number each time and 5 × ★ + 13 = 28, what number does ★ stand for?
3
Subtract 13 from 28 to get 15, then divide by 5: ★ = 3.
8. If ★ represents the same whole number each time and 4 × ★ + 13 = 37, what number does ★ stand for?
6
Subtract 13 from 37 to get 24, then divide by 4: ★ = 6.
9. If ★ represents the same whole number each time and 3 × ★ + 11 = 56, what number does ★ stand for?
15
Subtract 11 from 56 to get 45, then divide by 3: ★ = 15.
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
14
Subtract 12 from 54 to get 42, then divide by 3: ★ = 14.
11. If ★ represents the same whole number each time and 4 × ★ + 11 = 19, what number does ★ stand for?
2
Subtract 11 from 19 to get 8, then divide by 4: ★ = 2.
12. If ★ represents the same whole number each time and 8 × ★ + 7 = 31, what number does ★ stand for?
3
Subtract 7 from 31 to get 24, then divide by 8: ★ = 3.

12 questions · Seed 45 · 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 = 89, what number does ★ stand for?
8 · 1 · 89 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 8 = 47, what number does ★ stand for?
3 · 8 · 47 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 3 = 24, what number does ★ stand for?
7 · 3 · 24 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 1 = 9, what number does ★ stand for?
4 · 1 · 9 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 7 = 19, what number does ★ stand for?
2 · 7 · 19 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 10 = 22, what number does ★ stand for?
6 · 10 · 22 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 13 = 28, what number does ★ stand for?
5 · 13 · 28 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 13 = 37, what number does ★ stand for?
4 · 13 · 37 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 11 = 56, what number does ★ stand for?
3 · 11 · 56 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
3 · 12 · 54 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 11 = 19, what number does ★ stand for?
4 · 11 · 19 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 7 = 31, what number does ★ stand for?
8 · 7 · 31 · Symbol equation puzzles

12 questions · Seed 45 · 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 = 89, what number does ★ stand for?
11
Subtract 1 from 89 to get 88, then divide by 8: ★ = 11.
2. If ★ represents the same whole number each time and 3 × ★ + 8 = 47, what number does ★ stand for?
13
Subtract 8 from 47 to get 39, then divide by 3: ★ = 13.
3. If ★ represents the same whole number each time and 7 × ★ + 3 = 24, what number does ★ stand for?
3
Subtract 3 from 24 to get 21, then divide by 7: ★ = 3.
4. If ★ represents the same whole number each time and 4 × ★ + 1 = 9, what number does ★ stand for?
2
Subtract 1 from 9 to get 8, then divide by 4: ★ = 2.
5. If ★ represents the same whole number each time and 2 × ★ + 7 = 19, what number does ★ stand for?
6
Subtract 7 from 19 to get 12, then divide by 2: ★ = 6.
6. If ★ represents the same whole number each time and 6 × ★ + 10 = 22, what number does ★ stand for?
2
Subtract 10 from 22 to get 12, then divide by 6: ★ = 2.
7. If ★ represents the same whole number each time and 5 × ★ + 13 = 28, what number does ★ stand for?
3
Subtract 13 from 28 to get 15, then divide by 5: ★ = 3.
8. If ★ represents the same whole number each time and 4 × ★ + 13 = 37, what number does ★ stand for?
6
Subtract 13 from 37 to get 24, then divide by 4: ★ = 6.
9. If ★ represents the same whole number each time and 3 × ★ + 11 = 56, what number does ★ stand for?
15
Subtract 11 from 56 to get 45, then divide by 3: ★ = 15.
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
14
Subtract 12 from 54 to get 42, then divide by 3: ★ = 14.
11. If ★ represents the same whole number each time and 4 × ★ + 11 = 19, what number does ★ stand for?
2
Subtract 11 from 19 to get 8, then divide by 4: ★ = 2.
12. If ★ represents the same whole number each time and 8 × ★ + 7 = 31, what number does ★ stand for?
3
Subtract 7 from 31 to get 24, then divide by 8: ★ = 3.

12 questions · Seed 45 · Age guidance, not curriculum certification