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 2 × ★ + 20 = 40, what number does ★ stand for?
2 · 20 · 40 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
2 · 4 · 32 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 8 = 32, what number does ★ stand for?
4 · 8 · 32 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 16 = 40, what number does ★ stand for?
3 · 16 · 40 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 7 = 13, what number does ★ stand for?
2 · 7 · 13 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 15 = 127, what number does ★ stand for?
8 · 15 · 127 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 31, what number does ★ stand for?
3 · 13 · 31 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 13 = 23, what number does ★ stand for?
2 · 13 · 23 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 17 = 92, what number does ★ stand for?
5 · 17 · 92 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 16 = 66, what number does ★ stand for?
5 · 16 · 66 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 14 = 26, what number does ★ stand for?
3 · 14 · 26 · Symbol equation puzzles

12 questions · Seed 48 · 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 2 × ★ + 20 = 40, what number does ★ stand for?
10
Subtract 20 from 40 to get 20, then divide by 2: ★ = 10.
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
14
Subtract 4 from 32 to get 28, then divide by 2: ★ = 14.
4. If ★ represents the same whole number each time and 4 × ★ + 8 = 32, what number does ★ stand for?
6
Subtract 8 from 32 to get 24, then divide by 4: ★ = 6.
5. If ★ represents the same whole number each time and 3 × ★ + 16 = 40, what number does ★ stand for?
8
Subtract 16 from 40 to get 24, then divide by 3: ★ = 8.
6. If ★ represents the same whole number each time and 2 × ★ + 7 = 13, what number does ★ stand for?
3
Subtract 7 from 13 to get 6, then divide by 2: ★ = 3.
7. If ★ represents the same whole number each time and 8 × ★ + 15 = 127, what number does ★ stand for?
14
Subtract 15 from 127 to get 112, then divide by 8: ★ = 14.
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 31, what number does ★ stand for?
6
Subtract 13 from 31 to get 18, then divide by 3: ★ = 6.
9. If ★ represents the same whole number each time and 2 × ★ + 13 = 23, what number does ★ stand for?
5
Subtract 13 from 23 to get 10, then divide by 2: ★ = 5.
10. If ★ represents the same whole number each time and 5 × ★ + 17 = 92, what number does ★ stand for?
15
Subtract 17 from 92 to get 75, then divide by 5: ★ = 15.
11. If ★ represents the same whole number each time and 5 × ★ + 16 = 66, what number does ★ stand for?
10
Subtract 16 from 66 to get 50, then divide by 5: ★ = 10.
12. If ★ represents the same whole number each time and 3 × ★ + 14 = 26, what number does ★ stand for?
4
Subtract 14 from 26 to get 12, then divide by 3: ★ = 4.

12 questions · Seed 48 · 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 2 × ★ + 20 = 40, what number does ★ stand for?
2 · 20 · 40 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
2 · 4 · 32 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 8 = 32, what number does ★ stand for?
4 · 8 · 32 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 16 = 40, what number does ★ stand for?
3 · 16 · 40 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 7 = 13, what number does ★ stand for?
2 · 7 · 13 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 15 = 127, what number does ★ stand for?
8 · 15 · 127 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 31, what number does ★ stand for?
3 · 13 · 31 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 13 = 23, what number does ★ stand for?
2 · 13 · 23 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 17 = 92, what number does ★ stand for?
5 · 17 · 92 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 16 = 66, what number does ★ stand for?
5 · 16 · 66 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 14 = 26, what number does ★ stand for?
3 · 14 · 26 · Symbol equation puzzles

12 questions · Seed 48 · 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 2 × ★ + 20 = 40, what number does ★ stand for?
10
Subtract 20 from 40 to get 20, then divide by 2: ★ = 10.
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
14
Subtract 4 from 32 to get 28, then divide by 2: ★ = 14.
4. If ★ represents the same whole number each time and 4 × ★ + 8 = 32, what number does ★ stand for?
6
Subtract 8 from 32 to get 24, then divide by 4: ★ = 6.
5. If ★ represents the same whole number each time and 3 × ★ + 16 = 40, what number does ★ stand for?
8
Subtract 16 from 40 to get 24, then divide by 3: ★ = 8.
6. If ★ represents the same whole number each time and 2 × ★ + 7 = 13, what number does ★ stand for?
3
Subtract 7 from 13 to get 6, then divide by 2: ★ = 3.
7. If ★ represents the same whole number each time and 8 × ★ + 15 = 127, what number does ★ stand for?
14
Subtract 15 from 127 to get 112, then divide by 8: ★ = 14.
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 31, what number does ★ stand for?
6
Subtract 13 from 31 to get 18, then divide by 3: ★ = 6.
9. If ★ represents the same whole number each time and 2 × ★ + 13 = 23, what number does ★ stand for?
5
Subtract 13 from 23 to get 10, then divide by 2: ★ = 5.
10. If ★ represents the same whole number each time and 5 × ★ + 17 = 92, what number does ★ stand for?
15
Subtract 17 from 92 to get 75, then divide by 5: ★ = 15.
11. If ★ represents the same whole number each time and 5 × ★ + 16 = 66, what number does ★ stand for?
10
Subtract 16 from 66 to get 50, then divide by 5: ★ = 10.
12. If ★ represents the same whole number each time and 3 × ★ + 14 = 26, what number does ★ stand for?
4
Subtract 14 from 26 to get 12, then divide by 3: ★ = 4.

12 questions · Seed 48 · Age guidance, not curriculum certification