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 × ★ + 13 = 117, what number does ★ stand for?
8 · 13 · 117 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 2 = 62, what number does ★ stand for?
6 · 2 · 62 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 16 = 106, what number does ★ stand for?
6 · 16 · 106 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 5 = 11, what number does ★ stand for?
2 · 5 · 11 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 3 = 17, what number does ★ stand for?
7 · 3 · 17 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
7 · 1 · 43 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 17 = 72, what number does ★ stand for?
5 · 17 · 72 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 34, what number does ★ stand for?
3 · 7 · 34 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 1 = 13, what number does ★ stand for?
6 · 1 · 13 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7 · 9 · 58 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 14 = 86, what number does ★ stand for?
6 · 14 · 86 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 18 = 42, what number does ★ stand for?
3 · 18 · 42 · Symbol equation puzzles

12 questions · Seed 66 · 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 × ★ + 13 = 117, what number does ★ stand for?
13
Subtract 13 from 117 to get 104, then divide by 8: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 2 = 62, what number does ★ stand for?
10
Subtract 2 from 62 to get 60, then divide by 6: ★ = 10.
3. If ★ represents the same whole number each time and 6 × ★ + 16 = 106, what number does ★ stand for?
15
Subtract 16 from 106 to get 90, then divide by 6: ★ = 15.
4. If ★ represents the same whole number each time and 2 × ★ + 5 = 11, what number does ★ stand for?
3
Subtract 5 from 11 to get 6, then divide by 2: ★ = 3.
5. If ★ represents the same whole number each time and 7 × ★ + 3 = 17, what number does ★ stand for?
2
Subtract 3 from 17 to get 14, then divide by 7: ★ = 2.
6. 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.
7. If ★ represents the same whole number each time and 5 × ★ + 17 = 72, what number does ★ stand for?
11
Subtract 17 from 72 to get 55, then divide by 5: ★ = 11.
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 34, what number does ★ stand for?
9
Subtract 7 from 34 to get 27, then divide by 3: ★ = 9.
9. If ★ represents the same whole number each time and 6 × ★ + 1 = 13, what number does ★ stand for?
2
Subtract 1 from 13 to get 12, then divide by 6: ★ = 2.
10. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7
Subtract 9 from 58 to get 49, then divide by 7: ★ = 7.
11. If ★ represents the same whole number each time and 6 × ★ + 14 = 86, what number does ★ stand for?
12
Subtract 14 from 86 to get 72, then divide by 6: ★ = 12.
12. If ★ represents the same whole number each time and 3 × ★ + 18 = 42, what number does ★ stand for?
8
Subtract 18 from 42 to get 24, then divide by 3: ★ = 8.

12 questions · Seed 66 · 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 × ★ + 13 = 117, what number does ★ stand for?
8 · 13 · 117 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 2 = 62, what number does ★ stand for?
6 · 2 · 62 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 16 = 106, what number does ★ stand for?
6 · 16 · 106 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 5 = 11, what number does ★ stand for?
2 · 5 · 11 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 3 = 17, what number does ★ stand for?
7 · 3 · 17 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
7 · 1 · 43 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 17 = 72, what number does ★ stand for?
5 · 17 · 72 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 34, what number does ★ stand for?
3 · 7 · 34 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 1 = 13, what number does ★ stand for?
6 · 1 · 13 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7 · 9 · 58 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 14 = 86, what number does ★ stand for?
6 · 14 · 86 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 18 = 42, what number does ★ stand for?
3 · 18 · 42 · Symbol equation puzzles

12 questions · Seed 66 · 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 × ★ + 13 = 117, what number does ★ stand for?
13
Subtract 13 from 117 to get 104, then divide by 8: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 2 = 62, what number does ★ stand for?
10
Subtract 2 from 62 to get 60, then divide by 6: ★ = 10.
3. If ★ represents the same whole number each time and 6 × ★ + 16 = 106, what number does ★ stand for?
15
Subtract 16 from 106 to get 90, then divide by 6: ★ = 15.
4. If ★ represents the same whole number each time and 2 × ★ + 5 = 11, what number does ★ stand for?
3
Subtract 5 from 11 to get 6, then divide by 2: ★ = 3.
5. If ★ represents the same whole number each time and 7 × ★ + 3 = 17, what number does ★ stand for?
2
Subtract 3 from 17 to get 14, then divide by 7: ★ = 2.
6. 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.
7. If ★ represents the same whole number each time and 5 × ★ + 17 = 72, what number does ★ stand for?
11
Subtract 17 from 72 to get 55, then divide by 5: ★ = 11.
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 34, what number does ★ stand for?
9
Subtract 7 from 34 to get 27, then divide by 3: ★ = 9.
9. If ★ represents the same whole number each time and 6 × ★ + 1 = 13, what number does ★ stand for?
2
Subtract 1 from 13 to get 12, then divide by 6: ★ = 2.
10. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7
Subtract 9 from 58 to get 49, then divide by 7: ★ = 7.
11. If ★ represents the same whole number each time and 6 × ★ + 14 = 86, what number does ★ stand for?
12
Subtract 14 from 86 to get 72, then divide by 6: ★ = 12.
12. If ★ represents the same whole number each time and 3 × ★ + 18 = 42, what number does ★ stand for?
8
Subtract 18 from 42 to get 24, then divide by 3: ★ = 8.

12 questions · Seed 66 · Age guidance, not curriculum certification