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 5 × ★ + 10 = 30, what number does ★ stand for?
5 · 10 · 30 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 18 = 40, what number does ★ stand for?
2 · 18 · 40 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 12 = 24, what number does ★ stand for?
2 · 12 · 24 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 6 = 104, what number does ★ stand for?
7 · 6 · 104 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 12 = 132, what number does ★ stand for?
8 · 12 · 132 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 10 = 59, what number does ★ stand for?
7 · 10 · 59 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 13 = 61, what number does ★ stand for?
8 · 13 · 61 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
7 · 1 · 43 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 56, what number does ★ stand for?
4 · 16 · 56 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 75, what number does ★ stand for?
7 · 5 · 75 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 6 = 110, what number does ★ stand for?
8 · 6 · 110 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 3 = 123, what number does ★ stand for?
8 · 3 · 123 · Symbol equation puzzles

12 questions · Seed 104740 · 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 5 × ★ + 10 = 30, what number does ★ stand for?
4
Subtract 10 from 30 to get 20, then divide by 5: ★ = 4.
2. If ★ represents the same whole number each time and 2 × ★ + 18 = 40, what number does ★ stand for?
11
Subtract 18 from 40 to get 22, then divide by 2: ★ = 11.
3. 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.
4. If ★ represents the same whole number each time and 7 × ★ + 6 = 104, what number does ★ stand for?
14
Subtract 6 from 104 to get 98, then divide by 7: ★ = 14.
5. If ★ represents the same whole number each time and 8 × ★ + 12 = 132, what number does ★ stand for?
15
Subtract 12 from 132 to get 120, then divide by 8: ★ = 15.
6. If ★ represents the same whole number each time and 7 × ★ + 10 = 59, what number does ★ stand for?
7
Subtract 10 from 59 to get 49, then divide by 7: ★ = 7.
7. If ★ represents the same whole number each time and 8 × ★ + 13 = 61, what number does ★ stand for?
6
Subtract 13 from 61 to get 48, then divide by 8: ★ = 6.
8. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
6
Subtract 1 from 43 to get 42, then divide by 7: ★ = 6.
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 56, what number does ★ stand for?
10
Subtract 16 from 56 to get 40, then divide by 4: ★ = 10.
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 75, what number does ★ stand for?
10
Subtract 5 from 75 to get 70, then divide by 7: ★ = 10.
11. If ★ represents the same whole number each time and 8 × ★ + 6 = 110, what number does ★ stand for?
13
Subtract 6 from 110 to get 104, then divide by 8: ★ = 13.
12. If ★ represents the same whole number each time and 8 × ★ + 3 = 123, what number does ★ stand for?
15
Subtract 3 from 123 to get 120, then divide by 8: ★ = 15.

12 questions · Seed 104740 · 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 5 × ★ + 10 = 30, what number does ★ stand for?
5 · 10 · 30 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 18 = 40, what number does ★ stand for?
2 · 18 · 40 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 12 = 24, what number does ★ stand for?
2 · 12 · 24 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 6 = 104, what number does ★ stand for?
7 · 6 · 104 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 12 = 132, what number does ★ stand for?
8 · 12 · 132 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 10 = 59, what number does ★ stand for?
7 · 10 · 59 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 13 = 61, what number does ★ stand for?
8 · 13 · 61 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
7 · 1 · 43 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 56, what number does ★ stand for?
4 · 16 · 56 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 75, what number does ★ stand for?
7 · 5 · 75 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 6 = 110, what number does ★ stand for?
8 · 6 · 110 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 3 = 123, what number does ★ stand for?
8 · 3 · 123 · Symbol equation puzzles

12 questions · Seed 104740 · 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 5 × ★ + 10 = 30, what number does ★ stand for?
4
Subtract 10 from 30 to get 20, then divide by 5: ★ = 4.
2. If ★ represents the same whole number each time and 2 × ★ + 18 = 40, what number does ★ stand for?
11
Subtract 18 from 40 to get 22, then divide by 2: ★ = 11.
3. 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.
4. If ★ represents the same whole number each time and 7 × ★ + 6 = 104, what number does ★ stand for?
14
Subtract 6 from 104 to get 98, then divide by 7: ★ = 14.
5. If ★ represents the same whole number each time and 8 × ★ + 12 = 132, what number does ★ stand for?
15
Subtract 12 from 132 to get 120, then divide by 8: ★ = 15.
6. If ★ represents the same whole number each time and 7 × ★ + 10 = 59, what number does ★ stand for?
7
Subtract 10 from 59 to get 49, then divide by 7: ★ = 7.
7. If ★ represents the same whole number each time and 8 × ★ + 13 = 61, what number does ★ stand for?
6
Subtract 13 from 61 to get 48, then divide by 8: ★ = 6.
8. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
6
Subtract 1 from 43 to get 42, then divide by 7: ★ = 6.
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 56, what number does ★ stand for?
10
Subtract 16 from 56 to get 40, then divide by 4: ★ = 10.
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 75, what number does ★ stand for?
10
Subtract 5 from 75 to get 70, then divide by 7: ★ = 10.
11. If ★ represents the same whole number each time and 8 × ★ + 6 = 110, what number does ★ stand for?
13
Subtract 6 from 110 to get 104, then divide by 8: ★ = 13.
12. If ★ represents the same whole number each time and 8 × ★ + 3 = 123, what number does ★ stand for?
15
Subtract 3 from 123 to get 120, then divide by 8: ★ = 15.

12 questions · Seed 104740 · Age guidance, not curriculum certification