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 7 × ★ + 9 = 72, what number does ★ stand for?
7 · 9 · 72 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 6 = 32, what number does ★ stand for?
2 · 6 · 32 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 3 = 78, what number does ★ stand for?
5 · 3 · 78 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
3 · 12 · 54 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 3 = 75, what number does ★ stand for?
8 · 3 · 75 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 17 = 72, what number does ★ stand for?
5 · 17 · 72 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 11 = 123, what number does ★ stand for?
8 · 11 · 123 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 2 = 100, what number does ★ stand for?
7 · 2 · 100 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 8 = 20, what number does ★ stand for?
6 · 8 · 20 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 8 = 113, what number does ★ stand for?
7 · 8 · 113 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 10 = 80, what number does ★ stand for?
5 · 10 · 80 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 9 = 113, what number does ★ stand for?
8 · 9 · 113 · Symbol equation puzzles

12 questions · Seed 67 · 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 7 × ★ + 9 = 72, what number does ★ stand for?
9
Subtract 9 from 72 to get 63, then divide by 7: ★ = 9.
2. If ★ represents the same whole number each time and 2 × ★ + 6 = 32, what number does ★ stand for?
13
Subtract 6 from 32 to get 26, then divide by 2: ★ = 13.
3. If ★ represents the same whole number each time and 5 × ★ + 3 = 78, what number does ★ stand for?
15
Subtract 3 from 78 to get 75, then divide by 5: ★ = 15.
4. 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.
5. If ★ represents the same whole number each time and 8 × ★ + 3 = 75, what number does ★ stand for?
9
Subtract 3 from 75 to get 72, then divide by 8: ★ = 9.
6. If ★ represents the same whole number each time and 5 × ★ + 17 = 72, what number does ★ stand for?
11
Subtract 17 from 72 to get 55, then divide by 5: ★ = 11.
7. If ★ represents the same whole number each time and 8 × ★ + 11 = 123, what number does ★ stand for?
14
Subtract 11 from 123 to get 112, then divide by 8: ★ = 14.
8. If ★ represents the same whole number each time and 7 × ★ + 2 = 100, what number does ★ stand for?
14
Subtract 2 from 100 to get 98, then divide by 7: ★ = 14.
9. If ★ represents the same whole number each time and 6 × ★ + 8 = 20, what number does ★ stand for?
2
Subtract 8 from 20 to get 12, then divide by 6: ★ = 2.
10. If ★ represents the same whole number each time and 7 × ★ + 8 = 113, what number does ★ stand for?
15
Subtract 8 from 113 to get 105, then divide by 7: ★ = 15.
11. If ★ represents the same whole number each time and 5 × ★ + 10 = 80, what number does ★ stand for?
14
Subtract 10 from 80 to get 70, then divide by 5: ★ = 14.
12. If ★ represents the same whole number each time and 8 × ★ + 9 = 113, what number does ★ stand for?
13
Subtract 9 from 113 to get 104, then divide by 8: ★ = 13.

12 questions · Seed 67 · 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 7 × ★ + 9 = 72, what number does ★ stand for?
7 · 9 · 72 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 6 = 32, what number does ★ stand for?
2 · 6 · 32 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 3 = 78, what number does ★ stand for?
5 · 3 · 78 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
3 · 12 · 54 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 3 = 75, what number does ★ stand for?
8 · 3 · 75 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 17 = 72, what number does ★ stand for?
5 · 17 · 72 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 11 = 123, what number does ★ stand for?
8 · 11 · 123 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 2 = 100, what number does ★ stand for?
7 · 2 · 100 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 8 = 20, what number does ★ stand for?
6 · 8 · 20 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 8 = 113, what number does ★ stand for?
7 · 8 · 113 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 10 = 80, what number does ★ stand for?
5 · 10 · 80 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 9 = 113, what number does ★ stand for?
8 · 9 · 113 · Symbol equation puzzles

12 questions · Seed 67 · 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 7 × ★ + 9 = 72, what number does ★ stand for?
9
Subtract 9 from 72 to get 63, then divide by 7: ★ = 9.
2. If ★ represents the same whole number each time and 2 × ★ + 6 = 32, what number does ★ stand for?
13
Subtract 6 from 32 to get 26, then divide by 2: ★ = 13.
3. If ★ represents the same whole number each time and 5 × ★ + 3 = 78, what number does ★ stand for?
15
Subtract 3 from 78 to get 75, then divide by 5: ★ = 15.
4. 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.
5. If ★ represents the same whole number each time and 8 × ★ + 3 = 75, what number does ★ stand for?
9
Subtract 3 from 75 to get 72, then divide by 8: ★ = 9.
6. If ★ represents the same whole number each time and 5 × ★ + 17 = 72, what number does ★ stand for?
11
Subtract 17 from 72 to get 55, then divide by 5: ★ = 11.
7. If ★ represents the same whole number each time and 8 × ★ + 11 = 123, what number does ★ stand for?
14
Subtract 11 from 123 to get 112, then divide by 8: ★ = 14.
8. If ★ represents the same whole number each time and 7 × ★ + 2 = 100, what number does ★ stand for?
14
Subtract 2 from 100 to get 98, then divide by 7: ★ = 14.
9. If ★ represents the same whole number each time and 6 × ★ + 8 = 20, what number does ★ stand for?
2
Subtract 8 from 20 to get 12, then divide by 6: ★ = 2.
10. If ★ represents the same whole number each time and 7 × ★ + 8 = 113, what number does ★ stand for?
15
Subtract 8 from 113 to get 105, then divide by 7: ★ = 15.
11. If ★ represents the same whole number each time and 5 × ★ + 10 = 80, what number does ★ stand for?
14
Subtract 10 from 80 to get 70, then divide by 5: ★ = 14.
12. If ★ represents the same whole number each time and 8 × ★ + 9 = 113, what number does ★ stand for?
13
Subtract 9 from 113 to get 104, then divide by 8: ★ = 13.

12 questions · Seed 67 · Age guidance, not curriculum certification