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 × ★ + 18 = 33, what number does ★ stand for?
3 · 18 · 33 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
3 · 9 · 24 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 6 = 71, what number does ★ stand for?
5 · 6 · 71 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 15 = 45, what number does ★ stand for?
6 · 15 · 45 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 5 = 20, what number does ★ stand for?
3 · 5 · 20 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 4 × ★ + 15 = 27, what number does ★ stand for?
4 · 15 · 27 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 14 = 74, what number does ★ stand for?
6 · 14 · 74 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 12 = 87, what number does ★ stand for?
5 · 12 · 87 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 11 = 91, what number does ★ stand for?
8 · 11 · 91 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 11 = 56, what number does ★ stand for?
5 · 11 · 56 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 13 = 45, what number does ★ stand for?
4 · 13 · 45 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 16 = 26, what number does ★ stand for?
5 · 16 · 26 · Symbol equation puzzles

12 questions · Seed 104737 · 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 × ★ + 18 = 33, what number does ★ stand for?
5
Subtract 18 from 33 to get 15, then divide by 3: ★ = 5.
2. 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.
3. If ★ represents the same whole number each time and 5 × ★ + 6 = 71, what number does ★ stand for?
13
Subtract 6 from 71 to get 65, then divide by 5: ★ = 13.
4. If ★ represents the same whole number each time and 6 × ★ + 15 = 45, what number does ★ stand for?
5
Subtract 15 from 45 to get 30, then divide by 6: ★ = 5.
5. If ★ represents the same whole number each time and 3 × ★ + 5 = 20, what number does ★ stand for?
5
Subtract 5 from 20 to get 15, then divide by 3: ★ = 5.
6. If ★ represents the same whole number each time and 4 × ★ + 15 = 27, what number does ★ stand for?
3
Subtract 15 from 27 to get 12, then divide by 4: ★ = 3.
7. If ★ represents the same whole number each time and 6 × ★ + 14 = 74, what number does ★ stand for?
10
Subtract 14 from 74 to get 60, then divide by 6: ★ = 10.
8. If ★ represents the same whole number each time and 5 × ★ + 12 = 87, what number does ★ stand for?
15
Subtract 12 from 87 to get 75, then divide by 5: ★ = 15.
9. If ★ represents the same whole number each time and 8 × ★ + 11 = 91, what number does ★ stand for?
10
Subtract 11 from 91 to get 80, then divide by 8: ★ = 10.
10. If ★ represents the same whole number each time and 5 × ★ + 11 = 56, what number does ★ stand for?
9
Subtract 11 from 56 to get 45, then divide by 5: ★ = 9.
11. If ★ represents the same whole number each time and 4 × ★ + 13 = 45, what number does ★ stand for?
8
Subtract 13 from 45 to get 32, then divide by 4: ★ = 8.
12. If ★ represents the same whole number each time and 5 × ★ + 16 = 26, what number does ★ stand for?
2
Subtract 16 from 26 to get 10, then divide by 5: ★ = 2.

12 questions · Seed 104737 · 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 × ★ + 18 = 33, what number does ★ stand for?
3 · 18 · 33 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
3 · 9 · 24 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 6 = 71, what number does ★ stand for?
5 · 6 · 71 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 15 = 45, what number does ★ stand for?
6 · 15 · 45 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 5 = 20, what number does ★ stand for?
3 · 5 · 20 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 4 × ★ + 15 = 27, what number does ★ stand for?
4 · 15 · 27 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 14 = 74, what number does ★ stand for?
6 · 14 · 74 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 12 = 87, what number does ★ stand for?
5 · 12 · 87 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 11 = 91, what number does ★ stand for?
8 · 11 · 91 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 11 = 56, what number does ★ stand for?
5 · 11 · 56 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 13 = 45, what number does ★ stand for?
4 · 13 · 45 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 16 = 26, what number does ★ stand for?
5 · 16 · 26 · Symbol equation puzzles

12 questions · Seed 104737 · 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 × ★ + 18 = 33, what number does ★ stand for?
5
Subtract 18 from 33 to get 15, then divide by 3: ★ = 5.
2. 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.
3. If ★ represents the same whole number each time and 5 × ★ + 6 = 71, what number does ★ stand for?
13
Subtract 6 from 71 to get 65, then divide by 5: ★ = 13.
4. If ★ represents the same whole number each time and 6 × ★ + 15 = 45, what number does ★ stand for?
5
Subtract 15 from 45 to get 30, then divide by 6: ★ = 5.
5. If ★ represents the same whole number each time and 3 × ★ + 5 = 20, what number does ★ stand for?
5
Subtract 5 from 20 to get 15, then divide by 3: ★ = 5.
6. If ★ represents the same whole number each time and 4 × ★ + 15 = 27, what number does ★ stand for?
3
Subtract 15 from 27 to get 12, then divide by 4: ★ = 3.
7. If ★ represents the same whole number each time and 6 × ★ + 14 = 74, what number does ★ stand for?
10
Subtract 14 from 74 to get 60, then divide by 6: ★ = 10.
8. If ★ represents the same whole number each time and 5 × ★ + 12 = 87, what number does ★ stand for?
15
Subtract 12 from 87 to get 75, then divide by 5: ★ = 15.
9. If ★ represents the same whole number each time and 8 × ★ + 11 = 91, what number does ★ stand for?
10
Subtract 11 from 91 to get 80, then divide by 8: ★ = 10.
10. If ★ represents the same whole number each time and 5 × ★ + 11 = 56, what number does ★ stand for?
9
Subtract 11 from 56 to get 45, then divide by 5: ★ = 9.
11. If ★ represents the same whole number each time and 4 × ★ + 13 = 45, what number does ★ stand for?
8
Subtract 13 from 45 to get 32, then divide by 4: ★ = 8.
12. If ★ represents the same whole number each time and 5 × ★ + 16 = 26, what number does ★ stand for?
2
Subtract 16 from 26 to get 10, then divide by 5: ★ = 2.

12 questions · Seed 104737 · Age guidance, not curriculum certification