ReasoningAges 7-9

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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Worksheet StudioPractice pack · Ages 7-9

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
5 · 14 · 29 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 2 = 58, what number does ★ stand for?
7 · 2 · 58 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 9 = 105, what number does ★ stand for?
8 · 9 · 105 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
2 · 17 · 39 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 17 = 107, what number does ★ stand for?
6 · 17 · 107 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 9 = 129, what number does ★ stand for?
8 · 9 · 129 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 11 = 43, what number does ★ stand for?
8 · 11 · 43 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 8 = 50, what number does ★ stand for?
3 · 8 · 50 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 69, what number does ★ stand for?
5 · 4 · 69 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 1 = 65, what number does ★ stand for?
8 · 1 · 65 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 15 = 31, what number does ★ stand for?
4 · 15 · 31 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 1 = 13, what number does ★ stand for?
3 · 1 · 13 · Symbol equation puzzles

12 questions · Seed 53 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 7-9

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
3
Subtract 14 from 29 to get 15, then divide by 5: ★ = 3.
2. If ★ represents the same whole number each time and 7 × ★ + 2 = 58, what number does ★ stand for?
8
Subtract 2 from 58 to get 56, then divide by 7: ★ = 8.
3. If ★ represents the same whole number each time and 8 × ★ + 9 = 105, what number does ★ stand for?
12
Subtract 9 from 105 to get 96, then divide by 8: ★ = 12.
4. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
11
Subtract 17 from 39 to get 22, then divide by 2: ★ = 11.
5. If ★ represents the same whole number each time and 6 × ★ + 17 = 107, what number does ★ stand for?
15
Subtract 17 from 107 to get 90, then divide by 6: ★ = 15.
6. If ★ represents the same whole number each time and 8 × ★ + 9 = 129, what number does ★ stand for?
15
Subtract 9 from 129 to get 120, then divide by 8: ★ = 15.
7. If ★ represents the same whole number each time and 8 × ★ + 11 = 43, what number does ★ stand for?
4
Subtract 11 from 43 to get 32, then divide by 8: ★ = 4.
8. If ★ represents the same whole number each time and 3 × ★ + 8 = 50, what number does ★ stand for?
14
Subtract 8 from 50 to get 42, then divide by 3: ★ = 14.
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 69, what number does ★ stand for?
13
Subtract 4 from 69 to get 65, then divide by 5: ★ = 13.
10. If ★ represents the same whole number each time and 8 × ★ + 1 = 65, what number does ★ stand for?
8
Subtract 1 from 65 to get 64, then divide by 8: ★ = 8.
11. If ★ represents the same whole number each time and 4 × ★ + 15 = 31, what number does ★ stand for?
4
Subtract 15 from 31 to get 16, then divide by 4: ★ = 4.
12. If ★ represents the same whole number each time and 3 × ★ + 1 = 13, what number does ★ stand for?
4
Subtract 1 from 13 to get 12, then divide by 3: ★ = 4.

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 7-9

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
5 · 14 · 29 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 2 = 58, what number does ★ stand for?
7 · 2 · 58 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 9 = 105, what number does ★ stand for?
8 · 9 · 105 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
2 · 17 · 39 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 17 = 107, what number does ★ stand for?
6 · 17 · 107 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 9 = 129, what number does ★ stand for?
8 · 9 · 129 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 11 = 43, what number does ★ stand for?
8 · 11 · 43 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 8 = 50, what number does ★ stand for?
3 · 8 · 50 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 69, what number does ★ stand for?
5 · 4 · 69 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 1 = 65, what number does ★ stand for?
8 · 1 · 65 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 15 = 31, what number does ★ stand for?
4 · 15 · 31 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 1 = 13, what number does ★ stand for?
3 · 1 · 13 · Symbol equation puzzles

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 7-9

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
3
Subtract 14 from 29 to get 15, then divide by 5: ★ = 3.
2. If ★ represents the same whole number each time and 7 × ★ + 2 = 58, what number does ★ stand for?
8
Subtract 2 from 58 to get 56, then divide by 7: ★ = 8.
3. If ★ represents the same whole number each time and 8 × ★ + 9 = 105, what number does ★ stand for?
12
Subtract 9 from 105 to get 96, then divide by 8: ★ = 12.
4. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
11
Subtract 17 from 39 to get 22, then divide by 2: ★ = 11.
5. If ★ represents the same whole number each time and 6 × ★ + 17 = 107, what number does ★ stand for?
15
Subtract 17 from 107 to get 90, then divide by 6: ★ = 15.
6. If ★ represents the same whole number each time and 8 × ★ + 9 = 129, what number does ★ stand for?
15
Subtract 9 from 129 to get 120, then divide by 8: ★ = 15.
7. If ★ represents the same whole number each time and 8 × ★ + 11 = 43, what number does ★ stand for?
4
Subtract 11 from 43 to get 32, then divide by 8: ★ = 4.
8. If ★ represents the same whole number each time and 3 × ★ + 8 = 50, what number does ★ stand for?
14
Subtract 8 from 50 to get 42, then divide by 3: ★ = 14.
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 69, what number does ★ stand for?
13
Subtract 4 from 69 to get 65, then divide by 5: ★ = 13.
10. If ★ represents the same whole number each time and 8 × ★ + 1 = 65, what number does ★ stand for?
8
Subtract 1 from 65 to get 64, then divide by 8: ★ = 8.
11. If ★ represents the same whole number each time and 4 × ★ + 15 = 31, what number does ★ stand for?
4
Subtract 15 from 31 to get 16, then divide by 4: ★ = 4.
12. If ★ represents the same whole number each time and 3 × ★ + 1 = 13, what number does ★ stand for?
4
Subtract 1 from 13 to get 12, then divide by 3: ★ = 4.

12 questions · Seed 53 · Age guidance, not curriculum certification