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 6 × ★ + 13 = 37, what number does ★ stand for?
6 · 13 · 37 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 19 = 43, what number does ★ stand for?
8 · 19 · 43 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 16 = 40, what number does ★ stand for?
4 · 16 · 40 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 4 = 49, what number does ★ stand for?
5 · 4 · 49 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 20 = 100, what number does ★ stand for?
8 · 20 · 100 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 3 = 25, what number does ★ stand for?
2 · 3 · 25 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 19 = 34, what number does ★ stand for?
5 · 19 · 34 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 5 = 38, what number does ★ stand for?
3 · 5 · 38 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 52, what number does ★ stand for?
4 · 16 · 52 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 10 = 70, what number does ★ stand for?
4 · 10 · 70 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 17 = 33, what number does ★ stand for?
2 · 17 · 33 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 2 = 67, what number does ★ stand for?
5 · 2 · 67 · Symbol equation puzzles

12 questions · Seed 87 · 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 6 × ★ + 13 = 37, what number does ★ stand for?
4
Subtract 13 from 37 to get 24, then divide by 6: ★ = 4.
2. If ★ represents the same whole number each time and 8 × ★ + 19 = 43, what number does ★ stand for?
3
Subtract 19 from 43 to get 24, then divide by 8: ★ = 3.
3. If ★ represents the same whole number each time and 4 × ★ + 16 = 40, what number does ★ stand for?
6
Subtract 16 from 40 to get 24, then divide by 4: ★ = 6.
4. If ★ represents the same whole number each time and 5 × ★ + 4 = 49, what number does ★ stand for?
9
Subtract 4 from 49 to get 45, then divide by 5: ★ = 9.
5. If ★ represents the same whole number each time and 8 × ★ + 20 = 100, what number does ★ stand for?
10
Subtract 20 from 100 to get 80, then divide by 8: ★ = 10.
6. If ★ represents the same whole number each time and 2 × ★ + 3 = 25, what number does ★ stand for?
11
Subtract 3 from 25 to get 22, then divide by 2: ★ = 11.
7. If ★ represents the same whole number each time and 5 × ★ + 19 = 34, what number does ★ stand for?
3
Subtract 19 from 34 to get 15, then divide by 5: ★ = 3.
8. If ★ represents the same whole number each time and 3 × ★ + 5 = 38, what number does ★ stand for?
11
Subtract 5 from 38 to get 33, then divide by 3: ★ = 11.
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 52, what number does ★ stand for?
9
Subtract 16 from 52 to get 36, then divide by 4: ★ = 9.
10. If ★ represents the same whole number each time and 4 × ★ + 10 = 70, what number does ★ stand for?
15
Subtract 10 from 70 to get 60, then divide by 4: ★ = 15.
11. If ★ represents the same whole number each time and 2 × ★ + 17 = 33, what number does ★ stand for?
8
Subtract 17 from 33 to get 16, then divide by 2: ★ = 8.
12. If ★ represents the same whole number each time and 5 × ★ + 2 = 67, what number does ★ stand for?
13
Subtract 2 from 67 to get 65, then divide by 5: ★ = 13.

12 questions · Seed 87 · 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 6 × ★ + 13 = 37, what number does ★ stand for?
6 · 13 · 37 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 19 = 43, what number does ★ stand for?
8 · 19 · 43 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 16 = 40, what number does ★ stand for?
4 · 16 · 40 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 4 = 49, what number does ★ stand for?
5 · 4 · 49 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 20 = 100, what number does ★ stand for?
8 · 20 · 100 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 3 = 25, what number does ★ stand for?
2 · 3 · 25 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 19 = 34, what number does ★ stand for?
5 · 19 · 34 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 5 = 38, what number does ★ stand for?
3 · 5 · 38 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 52, what number does ★ stand for?
4 · 16 · 52 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 10 = 70, what number does ★ stand for?
4 · 10 · 70 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 17 = 33, what number does ★ stand for?
2 · 17 · 33 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 2 = 67, what number does ★ stand for?
5 · 2 · 67 · Symbol equation puzzles

12 questions · Seed 87 · 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 6 × ★ + 13 = 37, what number does ★ stand for?
4
Subtract 13 from 37 to get 24, then divide by 6: ★ = 4.
2. If ★ represents the same whole number each time and 8 × ★ + 19 = 43, what number does ★ stand for?
3
Subtract 19 from 43 to get 24, then divide by 8: ★ = 3.
3. If ★ represents the same whole number each time and 4 × ★ + 16 = 40, what number does ★ stand for?
6
Subtract 16 from 40 to get 24, then divide by 4: ★ = 6.
4. If ★ represents the same whole number each time and 5 × ★ + 4 = 49, what number does ★ stand for?
9
Subtract 4 from 49 to get 45, then divide by 5: ★ = 9.
5. If ★ represents the same whole number each time and 8 × ★ + 20 = 100, what number does ★ stand for?
10
Subtract 20 from 100 to get 80, then divide by 8: ★ = 10.
6. If ★ represents the same whole number each time and 2 × ★ + 3 = 25, what number does ★ stand for?
11
Subtract 3 from 25 to get 22, then divide by 2: ★ = 11.
7. If ★ represents the same whole number each time and 5 × ★ + 19 = 34, what number does ★ stand for?
3
Subtract 19 from 34 to get 15, then divide by 5: ★ = 3.
8. If ★ represents the same whole number each time and 3 × ★ + 5 = 38, what number does ★ stand for?
11
Subtract 5 from 38 to get 33, then divide by 3: ★ = 11.
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 52, what number does ★ stand for?
9
Subtract 16 from 52 to get 36, then divide by 4: ★ = 9.
10. If ★ represents the same whole number each time and 4 × ★ + 10 = 70, what number does ★ stand for?
15
Subtract 10 from 70 to get 60, then divide by 4: ★ = 15.
11. If ★ represents the same whole number each time and 2 × ★ + 17 = 33, what number does ★ stand for?
8
Subtract 17 from 33 to get 16, then divide by 2: ★ = 8.
12. If ★ represents the same whole number each time and 5 × ★ + 2 = 67, what number does ★ stand for?
13
Subtract 2 from 67 to get 65, then divide by 5: ★ = 13.

12 questions · Seed 87 · Age guidance, not curriculum certification