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 7 × ★ + 1 = 106, what number does ★ stand for?
7 · 1 · 106 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 1 = 71, what number does ★ stand for?
7 · 1 · 71 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 57, what number does ★ stand for?
4 · 9 · 57 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 2 = 30, what number does ★ stand for?
2 · 2 · 30 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 8 = 48, what number does ★ stand for?
5 · 8 · 48 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 20 = 48, what number does ★ stand for?
2 · 20 · 48 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 15 = 79, what number does ★ stand for?
8 · 15 · 79 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 3 = 67, what number does ★ stand for?
8 · 3 · 67 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 15 = 19, what number does ★ stand for?
2 · 15 · 19 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
5 · 19 · 89 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 8 = 22, what number does ★ stand for?
7 · 8 · 22 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 12 = 82, what number does ★ stand for?
5 · 12 · 82 · Symbol equation puzzles

12 questions · Seed 68 · 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 7 × ★ + 1 = 106, what number does ★ stand for?
15
Subtract 1 from 106 to get 105, then divide by 7: ★ = 15.
2. If ★ represents the same whole number each time and 7 × ★ + 1 = 71, what number does ★ stand for?
10
Subtract 1 from 71 to get 70, then divide by 7: ★ = 10.
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 57, what number does ★ stand for?
12
Subtract 9 from 57 to get 48, then divide by 4: ★ = 12.
4. If ★ represents the same whole number each time and 2 × ★ + 2 = 30, what number does ★ stand for?
14
Subtract 2 from 30 to get 28, then divide by 2: ★ = 14.
5. If ★ represents the same whole number each time and 5 × ★ + 8 = 48, what number does ★ stand for?
8
Subtract 8 from 48 to get 40, then divide by 5: ★ = 8.
6. If ★ represents the same whole number each time and 2 × ★ + 20 = 48, what number does ★ stand for?
14
Subtract 20 from 48 to get 28, then divide by 2: ★ = 14.
7. If ★ represents the same whole number each time and 8 × ★ + 15 = 79, what number does ★ stand for?
8
Subtract 15 from 79 to get 64, then divide by 8: ★ = 8.
8. If ★ represents the same whole number each time and 8 × ★ + 3 = 67, what number does ★ stand for?
8
Subtract 3 from 67 to get 64, then divide by 8: ★ = 8.
9. If ★ represents the same whole number each time and 2 × ★ + 15 = 19, what number does ★ stand for?
2
Subtract 15 from 19 to get 4, then divide by 2: ★ = 2.
10. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
14
Subtract 19 from 89 to get 70, then divide by 5: ★ = 14.
11. If ★ represents the same whole number each time and 7 × ★ + 8 = 22, what number does ★ stand for?
2
Subtract 8 from 22 to get 14, then divide by 7: ★ = 2.
12. If ★ represents the same whole number each time and 5 × ★ + 12 = 82, what number does ★ stand for?
14
Subtract 12 from 82 to get 70, then divide by 5: ★ = 14.

12 questions · Seed 68 · 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 7 × ★ + 1 = 106, what number does ★ stand for?
7 · 1 · 106 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 1 = 71, what number does ★ stand for?
7 · 1 · 71 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 57, what number does ★ stand for?
4 · 9 · 57 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 2 = 30, what number does ★ stand for?
2 · 2 · 30 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 8 = 48, what number does ★ stand for?
5 · 8 · 48 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 20 = 48, what number does ★ stand for?
2 · 20 · 48 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 15 = 79, what number does ★ stand for?
8 · 15 · 79 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 3 = 67, what number does ★ stand for?
8 · 3 · 67 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 15 = 19, what number does ★ stand for?
2 · 15 · 19 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
5 · 19 · 89 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 8 = 22, what number does ★ stand for?
7 · 8 · 22 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 12 = 82, what number does ★ stand for?
5 · 12 · 82 · Symbol equation puzzles

12 questions · Seed 68 · 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 7 × ★ + 1 = 106, what number does ★ stand for?
15
Subtract 1 from 106 to get 105, then divide by 7: ★ = 15.
2. If ★ represents the same whole number each time and 7 × ★ + 1 = 71, what number does ★ stand for?
10
Subtract 1 from 71 to get 70, then divide by 7: ★ = 10.
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 57, what number does ★ stand for?
12
Subtract 9 from 57 to get 48, then divide by 4: ★ = 12.
4. If ★ represents the same whole number each time and 2 × ★ + 2 = 30, what number does ★ stand for?
14
Subtract 2 from 30 to get 28, then divide by 2: ★ = 14.
5. If ★ represents the same whole number each time and 5 × ★ + 8 = 48, what number does ★ stand for?
8
Subtract 8 from 48 to get 40, then divide by 5: ★ = 8.
6. If ★ represents the same whole number each time and 2 × ★ + 20 = 48, what number does ★ stand for?
14
Subtract 20 from 48 to get 28, then divide by 2: ★ = 14.
7. If ★ represents the same whole number each time and 8 × ★ + 15 = 79, what number does ★ stand for?
8
Subtract 15 from 79 to get 64, then divide by 8: ★ = 8.
8. If ★ represents the same whole number each time and 8 × ★ + 3 = 67, what number does ★ stand for?
8
Subtract 3 from 67 to get 64, then divide by 8: ★ = 8.
9. If ★ represents the same whole number each time and 2 × ★ + 15 = 19, what number does ★ stand for?
2
Subtract 15 from 19 to get 4, then divide by 2: ★ = 2.
10. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
14
Subtract 19 from 89 to get 70, then divide by 5: ★ = 14.
11. If ★ represents the same whole number each time and 7 × ★ + 8 = 22, what number does ★ stand for?
2
Subtract 8 from 22 to get 14, then divide by 7: ★ = 2.
12. If ★ represents the same whole number each time and 5 × ★ + 12 = 82, what number does ★ stand for?
14
Subtract 12 from 82 to get 70, then divide by 5: ★ = 14.

12 questions · Seed 68 · Age guidance, not curriculum certification