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 4 × ★ + 9 = 33, what number does ★ stand for?
4 · 9 · 33 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 17 = 37, what number does ★ stand for?
4 · 17 · 37 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 4 = 52, what number does ★ stand for?
6 · 4 · 52 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 20 = 90, what number does ★ stand for?
5 · 20 · 90 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 18 = 53, what number does ★ stand for?
7 · 18 · 53 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 4 × ★ + 4 = 24, what number does ★ stand for?
4 · 4 · 24 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 1 = 61, what number does ★ stand for?
6 · 1 · 61 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 7 = 112, what number does ★ stand for?
7 · 7 · 112 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 15 = 60, what number does ★ stand for?
3 · 15 · 60 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 16 = 86, what number does ★ stand for?
7 · 16 · 86 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 19, what number does ★ stand for?
2 · 3 · 19 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 14 = 98, what number does ★ stand for?
7 · 14 · 98 · Symbol equation puzzles

12 questions · Seed 104730 · 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 4 × ★ + 9 = 33, what number does ★ stand for?
6
Subtract 9 from 33 to get 24, then divide by 4: ★ = 6.
2. If ★ represents the same whole number each time and 4 × ★ + 17 = 37, what number does ★ stand for?
5
Subtract 17 from 37 to get 20, then divide by 4: ★ = 5.
3. If ★ represents the same whole number each time and 6 × ★ + 4 = 52, what number does ★ stand for?
8
Subtract 4 from 52 to get 48, then divide by 6: ★ = 8.
4. If ★ represents the same whole number each time and 5 × ★ + 20 = 90, what number does ★ stand for?
14
Subtract 20 from 90 to get 70, then divide by 5: ★ = 14.
5. If ★ represents the same whole number each time and 7 × ★ + 18 = 53, what number does ★ stand for?
5
Subtract 18 from 53 to get 35, then divide by 7: ★ = 5.
6. If ★ represents the same whole number each time and 4 × ★ + 4 = 24, what number does ★ stand for?
5
Subtract 4 from 24 to get 20, then divide by 4: ★ = 5.
7. If ★ represents the same whole number each time and 6 × ★ + 1 = 61, what number does ★ stand for?
10
Subtract 1 from 61 to get 60, then divide by 6: ★ = 10.
8. If ★ represents the same whole number each time and 7 × ★ + 7 = 112, what number does ★ stand for?
15
Subtract 7 from 112 to get 105, then divide by 7: ★ = 15.
9. If ★ represents the same whole number each time and 3 × ★ + 15 = 60, what number does ★ stand for?
15
Subtract 15 from 60 to get 45, then divide by 3: ★ = 15.
10. If ★ represents the same whole number each time and 7 × ★ + 16 = 86, what number does ★ stand for?
10
Subtract 16 from 86 to get 70, then divide by 7: ★ = 10.
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 19, what number does ★ stand for?
8
Subtract 3 from 19 to get 16, then divide by 2: ★ = 8.
12. If ★ represents the same whole number each time and 7 × ★ + 14 = 98, what number does ★ stand for?
12
Subtract 14 from 98 to get 84, then divide by 7: ★ = 12.

12 questions · Seed 104730 · 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 4 × ★ + 9 = 33, what number does ★ stand for?
4 · 9 · 33 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 17 = 37, what number does ★ stand for?
4 · 17 · 37 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 4 = 52, what number does ★ stand for?
6 · 4 · 52 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 20 = 90, what number does ★ stand for?
5 · 20 · 90 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 18 = 53, what number does ★ stand for?
7 · 18 · 53 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 4 × ★ + 4 = 24, what number does ★ stand for?
4 · 4 · 24 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 1 = 61, what number does ★ stand for?
6 · 1 · 61 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 7 = 112, what number does ★ stand for?
7 · 7 · 112 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 15 = 60, what number does ★ stand for?
3 · 15 · 60 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 16 = 86, what number does ★ stand for?
7 · 16 · 86 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 19, what number does ★ stand for?
2 · 3 · 19 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 14 = 98, what number does ★ stand for?
7 · 14 · 98 · Symbol equation puzzles

12 questions · Seed 104730 · 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 4 × ★ + 9 = 33, what number does ★ stand for?
6
Subtract 9 from 33 to get 24, then divide by 4: ★ = 6.
2. If ★ represents the same whole number each time and 4 × ★ + 17 = 37, what number does ★ stand for?
5
Subtract 17 from 37 to get 20, then divide by 4: ★ = 5.
3. If ★ represents the same whole number each time and 6 × ★ + 4 = 52, what number does ★ stand for?
8
Subtract 4 from 52 to get 48, then divide by 6: ★ = 8.
4. If ★ represents the same whole number each time and 5 × ★ + 20 = 90, what number does ★ stand for?
14
Subtract 20 from 90 to get 70, then divide by 5: ★ = 14.
5. If ★ represents the same whole number each time and 7 × ★ + 18 = 53, what number does ★ stand for?
5
Subtract 18 from 53 to get 35, then divide by 7: ★ = 5.
6. If ★ represents the same whole number each time and 4 × ★ + 4 = 24, what number does ★ stand for?
5
Subtract 4 from 24 to get 20, then divide by 4: ★ = 5.
7. If ★ represents the same whole number each time and 6 × ★ + 1 = 61, what number does ★ stand for?
10
Subtract 1 from 61 to get 60, then divide by 6: ★ = 10.
8. If ★ represents the same whole number each time and 7 × ★ + 7 = 112, what number does ★ stand for?
15
Subtract 7 from 112 to get 105, then divide by 7: ★ = 15.
9. If ★ represents the same whole number each time and 3 × ★ + 15 = 60, what number does ★ stand for?
15
Subtract 15 from 60 to get 45, then divide by 3: ★ = 15.
10. If ★ represents the same whole number each time and 7 × ★ + 16 = 86, what number does ★ stand for?
10
Subtract 16 from 86 to get 70, then divide by 7: ★ = 10.
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 19, what number does ★ stand for?
8
Subtract 3 from 19 to get 16, then divide by 2: ★ = 8.
12. If ★ represents the same whole number each time and 7 × ★ + 14 = 98, what number does ★ stand for?
12
Subtract 14 from 98 to get 84, then divide by 7: ★ = 12.

12 questions · Seed 104730 · Age guidance, not curriculum certification