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 7 × ★ + 2 = 86, what number does ★ stand for?
7 · 2 · 86 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 6 = 86, what number does ★ stand for?
8 · 6 · 86 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 2 = 93, what number does ★ stand for?
7 · 2 · 93 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 4 = 37, what number does ★ stand for?
3 · 4 · 37 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 15 = 106, what number does ★ stand for?
7 · 15 · 106 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 5 = 33, what number does ★ stand for?
2 · 5 · 33 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 17 = 137, what number does ★ stand for?
8 · 17 · 137 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 10 = 19, what number does ★ stand for?
3 · 10 · 19 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 49, what number does ★ stand for?
5 · 19 · 49 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 6 = 24, what number does ★ stand for?
3 · 6 · 24 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 49, what number does ★ stand for?
3 · 4 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 4 = 44, what number does ★ stand for?
4 · 4 · 44 · Symbol equation puzzles

12 questions · Seed 78 · 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 7 × ★ + 2 = 86, what number does ★ stand for?
12
Subtract 2 from 86 to get 84, then divide by 7: ★ = 12.
2. If ★ represents the same whole number each time and 8 × ★ + 6 = 86, what number does ★ stand for?
10
Subtract 6 from 86 to get 80, then divide by 8: ★ = 10.
3. If ★ represents the same whole number each time and 7 × ★ + 2 = 93, what number does ★ stand for?
13
Subtract 2 from 93 to get 91, then divide by 7: ★ = 13.
4. If ★ represents the same whole number each time and 3 × ★ + 4 = 37, what number does ★ stand for?
11
Subtract 4 from 37 to get 33, then divide by 3: ★ = 11.
5. If ★ represents the same whole number each time and 7 × ★ + 15 = 106, what number does ★ stand for?
13
Subtract 15 from 106 to get 91, then divide by 7: ★ = 13.
6. If ★ represents the same whole number each time and 2 × ★ + 5 = 33, what number does ★ stand for?
14
Subtract 5 from 33 to get 28, then divide by 2: ★ = 14.
7. If ★ represents the same whole number each time and 8 × ★ + 17 = 137, what number does ★ stand for?
15
Subtract 17 from 137 to get 120, then divide by 8: ★ = 15.
8. If ★ represents the same whole number each time and 3 × ★ + 10 = 19, what number does ★ stand for?
3
Subtract 10 from 19 to get 9, then divide by 3: ★ = 3.
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 49, what number does ★ stand for?
6
Subtract 19 from 49 to get 30, then divide by 5: ★ = 6.
10. If ★ represents the same whole number each time and 3 × ★ + 6 = 24, what number does ★ stand for?
6
Subtract 6 from 24 to get 18, then divide by 3: ★ = 6.
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 49, what number does ★ stand for?
15
Subtract 4 from 49 to get 45, then divide by 3: ★ = 15.
12. If ★ represents the same whole number each time and 4 × ★ + 4 = 44, what number does ★ stand for?
10
Subtract 4 from 44 to get 40, then divide by 4: ★ = 10.

12 questions · Seed 78 · 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 7 × ★ + 2 = 86, what number does ★ stand for?
7 · 2 · 86 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 6 = 86, what number does ★ stand for?
8 · 6 · 86 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 2 = 93, what number does ★ stand for?
7 · 2 · 93 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 4 = 37, what number does ★ stand for?
3 · 4 · 37 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 15 = 106, what number does ★ stand for?
7 · 15 · 106 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 5 = 33, what number does ★ stand for?
2 · 5 · 33 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 17 = 137, what number does ★ stand for?
8 · 17 · 137 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 10 = 19, what number does ★ stand for?
3 · 10 · 19 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 49, what number does ★ stand for?
5 · 19 · 49 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 6 = 24, what number does ★ stand for?
3 · 6 · 24 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 49, what number does ★ stand for?
3 · 4 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 4 = 44, what number does ★ stand for?
4 · 4 · 44 · Symbol equation puzzles

12 questions · Seed 78 · 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 7 × ★ + 2 = 86, what number does ★ stand for?
12
Subtract 2 from 86 to get 84, then divide by 7: ★ = 12.
2. If ★ represents the same whole number each time and 8 × ★ + 6 = 86, what number does ★ stand for?
10
Subtract 6 from 86 to get 80, then divide by 8: ★ = 10.
3. If ★ represents the same whole number each time and 7 × ★ + 2 = 93, what number does ★ stand for?
13
Subtract 2 from 93 to get 91, then divide by 7: ★ = 13.
4. If ★ represents the same whole number each time and 3 × ★ + 4 = 37, what number does ★ stand for?
11
Subtract 4 from 37 to get 33, then divide by 3: ★ = 11.
5. If ★ represents the same whole number each time and 7 × ★ + 15 = 106, what number does ★ stand for?
13
Subtract 15 from 106 to get 91, then divide by 7: ★ = 13.
6. If ★ represents the same whole number each time and 2 × ★ + 5 = 33, what number does ★ stand for?
14
Subtract 5 from 33 to get 28, then divide by 2: ★ = 14.
7. If ★ represents the same whole number each time and 8 × ★ + 17 = 137, what number does ★ stand for?
15
Subtract 17 from 137 to get 120, then divide by 8: ★ = 15.
8. If ★ represents the same whole number each time and 3 × ★ + 10 = 19, what number does ★ stand for?
3
Subtract 10 from 19 to get 9, then divide by 3: ★ = 3.
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 49, what number does ★ stand for?
6
Subtract 19 from 49 to get 30, then divide by 5: ★ = 6.
10. If ★ represents the same whole number each time and 3 × ★ + 6 = 24, what number does ★ stand for?
6
Subtract 6 from 24 to get 18, then divide by 3: ★ = 6.
11. If ★ represents the same whole number each time and 3 × ★ + 4 = 49, what number does ★ stand for?
15
Subtract 4 from 49 to get 45, then divide by 3: ★ = 15.
12. If ★ represents the same whole number each time and 4 × ★ + 4 = 44, what number does ★ stand for?
10
Subtract 4 from 44 to get 40, then divide by 4: ★ = 10.

12 questions · Seed 78 · Age guidance, not curriculum certification