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 × ★ + 17 = 65, what number does ★ stand for?
8 · 17 · 65 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 24, what number does ★ stand for?
2 · 12 · 24 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
3 · 9 · 24 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 11 = 35, what number does ★ stand for?
6 · 11 · 35 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 7 = 97, what number does ★ stand for?
6 · 7 · 97 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 106, what number does ★ stand for?
8 · 2 · 106 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 19 = 61, what number does ★ stand for?
7 · 19 · 61 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 12 = 52, what number does ★ stand for?
8 · 12 · 52 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 20 = 26, what number does ★ stand for?
2 · 20 · 26 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 1 = 61, what number does ★ stand for?
4 · 1 · 61 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 1 = 49, what number does ★ stand for?
4 · 1 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 9 = 21, what number does ★ stand for?
2 · 9 · 21 · Symbol equation puzzles

12 questions · Seed 82 · 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 × ★ + 17 = 65, what number does ★ stand for?
6
Subtract 17 from 65 to get 48, then divide by 8: ★ = 6.
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 24, what number does ★ stand for?
6
Subtract 12 from 24 to get 12, then divide by 2: ★ = 6.
3. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
5
Subtract 9 from 24 to get 15, then divide by 3: ★ = 5.
4. If ★ represents the same whole number each time and 6 × ★ + 11 = 35, what number does ★ stand for?
4
Subtract 11 from 35 to get 24, then divide by 6: ★ = 4.
5. If ★ represents the same whole number each time and 6 × ★ + 7 = 97, what number does ★ stand for?
15
Subtract 7 from 97 to get 90, then divide by 6: ★ = 15.
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 106, what number does ★ stand for?
13
Subtract 2 from 106 to get 104, then divide by 8: ★ = 13.
7. If ★ represents the same whole number each time and 7 × ★ + 19 = 61, what number does ★ stand for?
6
Subtract 19 from 61 to get 42, then divide by 7: ★ = 6.
8. If ★ represents the same whole number each time and 8 × ★ + 12 = 52, what number does ★ stand for?
5
Subtract 12 from 52 to get 40, then divide by 8: ★ = 5.
9. If ★ represents the same whole number each time and 2 × ★ + 20 = 26, what number does ★ stand for?
3
Subtract 20 from 26 to get 6, then divide by 2: ★ = 3.
10. If ★ represents the same whole number each time and 4 × ★ + 1 = 61, what number does ★ stand for?
15
Subtract 1 from 61 to get 60, then divide by 4: ★ = 15.
11. If ★ represents the same whole number each time and 4 × ★ + 1 = 49, what number does ★ stand for?
12
Subtract 1 from 49 to get 48, then divide by 4: ★ = 12.
12. If ★ represents the same whole number each time and 2 × ★ + 9 = 21, what number does ★ stand for?
6
Subtract 9 from 21 to get 12, then divide by 2: ★ = 6.

12 questions · Seed 82 · 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 × ★ + 17 = 65, what number does ★ stand for?
8 · 17 · 65 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 24, what number does ★ stand for?
2 · 12 · 24 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
3 · 9 · 24 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 11 = 35, what number does ★ stand for?
6 · 11 · 35 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 7 = 97, what number does ★ stand for?
6 · 7 · 97 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 106, what number does ★ stand for?
8 · 2 · 106 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 19 = 61, what number does ★ stand for?
7 · 19 · 61 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 12 = 52, what number does ★ stand for?
8 · 12 · 52 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 20 = 26, what number does ★ stand for?
2 · 20 · 26 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 1 = 61, what number does ★ stand for?
4 · 1 · 61 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 1 = 49, what number does ★ stand for?
4 · 1 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 9 = 21, what number does ★ stand for?
2 · 9 · 21 · Symbol equation puzzles

12 questions · Seed 82 · 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 × ★ + 17 = 65, what number does ★ stand for?
6
Subtract 17 from 65 to get 48, then divide by 8: ★ = 6.
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 24, what number does ★ stand for?
6
Subtract 12 from 24 to get 12, then divide by 2: ★ = 6.
3. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
5
Subtract 9 from 24 to get 15, then divide by 3: ★ = 5.
4. If ★ represents the same whole number each time and 6 × ★ + 11 = 35, what number does ★ stand for?
4
Subtract 11 from 35 to get 24, then divide by 6: ★ = 4.
5. If ★ represents the same whole number each time and 6 × ★ + 7 = 97, what number does ★ stand for?
15
Subtract 7 from 97 to get 90, then divide by 6: ★ = 15.
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 106, what number does ★ stand for?
13
Subtract 2 from 106 to get 104, then divide by 8: ★ = 13.
7. If ★ represents the same whole number each time and 7 × ★ + 19 = 61, what number does ★ stand for?
6
Subtract 19 from 61 to get 42, then divide by 7: ★ = 6.
8. If ★ represents the same whole number each time and 8 × ★ + 12 = 52, what number does ★ stand for?
5
Subtract 12 from 52 to get 40, then divide by 8: ★ = 5.
9. If ★ represents the same whole number each time and 2 × ★ + 20 = 26, what number does ★ stand for?
3
Subtract 20 from 26 to get 6, then divide by 2: ★ = 3.
10. If ★ represents the same whole number each time and 4 × ★ + 1 = 61, what number does ★ stand for?
15
Subtract 1 from 61 to get 60, then divide by 4: ★ = 15.
11. If ★ represents the same whole number each time and 4 × ★ + 1 = 49, what number does ★ stand for?
12
Subtract 1 from 49 to get 48, then divide by 4: ★ = 12.
12. If ★ represents the same whole number each time and 2 × ★ + 9 = 21, what number does ★ stand for?
6
Subtract 9 from 21 to get 12, then divide by 2: ★ = 6.

12 questions · Seed 82 · Age guidance, not curriculum certification