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 3 × ★ + 8 = 20, what number does ★ stand for?
3 · 8 · 20 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 11 = 35, what number does ★ stand for?
4 · 11 · 35 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 13 = 69, what number does ★ stand for?
8 · 13 · 69 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 4 = 16, what number does ★ stand for?
3 · 4 · 16 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 20 = 44, what number does ★ stand for?
6 · 20 · 44 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 8 = 38, what number does ★ stand for?
2 · 8 · 38 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 1 = 27, what number does ★ stand for?
2 · 1 · 27 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 7 = 23, what number does ★ stand for?
8 · 7 · 23 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 12 = 60, what number does ★ stand for?
6 · 12 · 60 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 3 = 18, what number does ★ stand for?
3 · 3 · 18 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 3 = 81, what number does ★ stand for?
6 · 3 · 81 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 8 = 50, what number does ★ stand for?
3 · 8 · 50 · Symbol equation puzzles

12 questions · Seed 49 · 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 3 × ★ + 8 = 20, what number does ★ stand for?
4
Subtract 8 from 20 to get 12, then divide by 3: ★ = 4.
2. If ★ represents the same whole number each time and 4 × ★ + 11 = 35, what number does ★ stand for?
6
Subtract 11 from 35 to get 24, then divide by 4: ★ = 6.
3. If ★ represents the same whole number each time and 8 × ★ + 13 = 69, what number does ★ stand for?
7
Subtract 13 from 69 to get 56, then divide by 8: ★ = 7.
4. If ★ represents the same whole number each time and 3 × ★ + 4 = 16, what number does ★ stand for?
4
Subtract 4 from 16 to get 12, then divide by 3: ★ = 4.
5. If ★ represents the same whole number each time and 6 × ★ + 20 = 44, what number does ★ stand for?
4
Subtract 20 from 44 to get 24, then divide by 6: ★ = 4.
6. If ★ represents the same whole number each time and 2 × ★ + 8 = 38, what number does ★ stand for?
15
Subtract 8 from 38 to get 30, then divide by 2: ★ = 15.
7. If ★ represents the same whole number each time and 2 × ★ + 1 = 27, what number does ★ stand for?
13
Subtract 1 from 27 to get 26, then divide by 2: ★ = 13.
8. If ★ represents the same whole number each time and 8 × ★ + 7 = 23, what number does ★ stand for?
2
Subtract 7 from 23 to get 16, then divide by 8: ★ = 2.
9. If ★ represents the same whole number each time and 6 × ★ + 12 = 60, what number does ★ stand for?
8
Subtract 12 from 60 to get 48, then divide by 6: ★ = 8.
10. If ★ represents the same whole number each time and 3 × ★ + 3 = 18, what number does ★ stand for?
5
Subtract 3 from 18 to get 15, then divide by 3: ★ = 5.
11. If ★ represents the same whole number each time and 6 × ★ + 3 = 81, what number does ★ stand for?
13
Subtract 3 from 81 to get 78, then divide by 6: ★ = 13.
12. 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.

12 questions · Seed 49 · 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 3 × ★ + 8 = 20, what number does ★ stand for?
3 · 8 · 20 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 11 = 35, what number does ★ stand for?
4 · 11 · 35 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 13 = 69, what number does ★ stand for?
8 · 13 · 69 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 4 = 16, what number does ★ stand for?
3 · 4 · 16 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 20 = 44, what number does ★ stand for?
6 · 20 · 44 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 8 = 38, what number does ★ stand for?
2 · 8 · 38 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 1 = 27, what number does ★ stand for?
2 · 1 · 27 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 7 = 23, what number does ★ stand for?
8 · 7 · 23 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 12 = 60, what number does ★ stand for?
6 · 12 · 60 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 3 = 18, what number does ★ stand for?
3 · 3 · 18 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 3 = 81, what number does ★ stand for?
6 · 3 · 81 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 8 = 50, what number does ★ stand for?
3 · 8 · 50 · Symbol equation puzzles

12 questions · Seed 49 · 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 3 × ★ + 8 = 20, what number does ★ stand for?
4
Subtract 8 from 20 to get 12, then divide by 3: ★ = 4.
2. If ★ represents the same whole number each time and 4 × ★ + 11 = 35, what number does ★ stand for?
6
Subtract 11 from 35 to get 24, then divide by 4: ★ = 6.
3. If ★ represents the same whole number each time and 8 × ★ + 13 = 69, what number does ★ stand for?
7
Subtract 13 from 69 to get 56, then divide by 8: ★ = 7.
4. If ★ represents the same whole number each time and 3 × ★ + 4 = 16, what number does ★ stand for?
4
Subtract 4 from 16 to get 12, then divide by 3: ★ = 4.
5. If ★ represents the same whole number each time and 6 × ★ + 20 = 44, what number does ★ stand for?
4
Subtract 20 from 44 to get 24, then divide by 6: ★ = 4.
6. If ★ represents the same whole number each time and 2 × ★ + 8 = 38, what number does ★ stand for?
15
Subtract 8 from 38 to get 30, then divide by 2: ★ = 15.
7. If ★ represents the same whole number each time and 2 × ★ + 1 = 27, what number does ★ stand for?
13
Subtract 1 from 27 to get 26, then divide by 2: ★ = 13.
8. If ★ represents the same whole number each time and 8 × ★ + 7 = 23, what number does ★ stand for?
2
Subtract 7 from 23 to get 16, then divide by 8: ★ = 2.
9. If ★ represents the same whole number each time and 6 × ★ + 12 = 60, what number does ★ stand for?
8
Subtract 12 from 60 to get 48, then divide by 6: ★ = 8.
10. If ★ represents the same whole number each time and 3 × ★ + 3 = 18, what number does ★ stand for?
5
Subtract 3 from 18 to get 15, then divide by 3: ★ = 5.
11. If ★ represents the same whole number each time and 6 × ★ + 3 = 81, what number does ★ stand for?
13
Subtract 3 from 81 to get 78, then divide by 6: ★ = 13.
12. 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.

12 questions · Seed 49 · Age guidance, not curriculum certification