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 × ★ + 16 = 44, what number does ★ stand for?
4 · 16 · 44 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 4 = 70, what number does ★ stand for?
6 · 4 · 70 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 7 = 25, what number does ★ stand for?
2 · 7 · 25 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 18 = 108, what number does ★ stand for?
6 · 18 · 108 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 9 = 19, what number does ★ stand for?
2 · 9 · 19 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 1 = 57, what number does ★ stand for?
7 · 1 · 57 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 9 = 17, what number does ★ stand for?
4 · 9 · 17 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 16 = 55, what number does ★ stand for?
3 · 16 · 55 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 1 = 40, what number does ★ stand for?
3 · 1 · 40 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 12 = 34, what number does ★ stand for?
2 · 12 · 34 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 15 = 27, what number does ★ stand for?
2 · 15 · 27 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 10 = 30, what number does ★ stand for?
5 · 10 · 30 · Symbol equation puzzles

12 questions · Seed 69 · 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 × ★ + 16 = 44, what number does ★ stand for?
7
Subtract 16 from 44 to get 28, then divide by 4: ★ = 7.
2. If ★ represents the same whole number each time and 6 × ★ + 4 = 70, what number does ★ stand for?
11
Subtract 4 from 70 to get 66, then divide by 6: ★ = 11.
3. If ★ represents the same whole number each time and 2 × ★ + 7 = 25, what number does ★ stand for?
9
Subtract 7 from 25 to get 18, then divide by 2: ★ = 9.
4. If ★ represents the same whole number each time and 6 × ★ + 18 = 108, what number does ★ stand for?
15
Subtract 18 from 108 to get 90, then divide by 6: ★ = 15.
5. If ★ represents the same whole number each time and 2 × ★ + 9 = 19, what number does ★ stand for?
5
Subtract 9 from 19 to get 10, then divide by 2: ★ = 5.
6. If ★ represents the same whole number each time and 7 × ★ + 1 = 57, what number does ★ stand for?
8
Subtract 1 from 57 to get 56, then divide by 7: ★ = 8.
7. If ★ represents the same whole number each time and 4 × ★ + 9 = 17, what number does ★ stand for?
2
Subtract 9 from 17 to get 8, then divide by 4: ★ = 2.
8. If ★ represents the same whole number each time and 3 × ★ + 16 = 55, what number does ★ stand for?
13
Subtract 16 from 55 to get 39, then divide by 3: ★ = 13.
9. If ★ represents the same whole number each time and 3 × ★ + 1 = 40, what number does ★ stand for?
13
Subtract 1 from 40 to get 39, then divide by 3: ★ = 13.
10. If ★ represents the same whole number each time and 2 × ★ + 12 = 34, what number does ★ stand for?
11
Subtract 12 from 34 to get 22, then divide by 2: ★ = 11.
11. If ★ represents the same whole number each time and 2 × ★ + 15 = 27, what number does ★ stand for?
6
Subtract 15 from 27 to get 12, then divide by 2: ★ = 6.
12. 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.

12 questions · Seed 69 · 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 × ★ + 16 = 44, what number does ★ stand for?
4 · 16 · 44 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 4 = 70, what number does ★ stand for?
6 · 4 · 70 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 7 = 25, what number does ★ stand for?
2 · 7 · 25 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 18 = 108, what number does ★ stand for?
6 · 18 · 108 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 9 = 19, what number does ★ stand for?
2 · 9 · 19 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 1 = 57, what number does ★ stand for?
7 · 1 · 57 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 9 = 17, what number does ★ stand for?
4 · 9 · 17 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 16 = 55, what number does ★ stand for?
3 · 16 · 55 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 1 = 40, what number does ★ stand for?
3 · 1 · 40 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 12 = 34, what number does ★ stand for?
2 · 12 · 34 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 15 = 27, what number does ★ stand for?
2 · 15 · 27 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 10 = 30, what number does ★ stand for?
5 · 10 · 30 · Symbol equation puzzles

12 questions · Seed 69 · 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 × ★ + 16 = 44, what number does ★ stand for?
7
Subtract 16 from 44 to get 28, then divide by 4: ★ = 7.
2. If ★ represents the same whole number each time and 6 × ★ + 4 = 70, what number does ★ stand for?
11
Subtract 4 from 70 to get 66, then divide by 6: ★ = 11.
3. If ★ represents the same whole number each time and 2 × ★ + 7 = 25, what number does ★ stand for?
9
Subtract 7 from 25 to get 18, then divide by 2: ★ = 9.
4. If ★ represents the same whole number each time and 6 × ★ + 18 = 108, what number does ★ stand for?
15
Subtract 18 from 108 to get 90, then divide by 6: ★ = 15.
5. If ★ represents the same whole number each time and 2 × ★ + 9 = 19, what number does ★ stand for?
5
Subtract 9 from 19 to get 10, then divide by 2: ★ = 5.
6. If ★ represents the same whole number each time and 7 × ★ + 1 = 57, what number does ★ stand for?
8
Subtract 1 from 57 to get 56, then divide by 7: ★ = 8.
7. If ★ represents the same whole number each time and 4 × ★ + 9 = 17, what number does ★ stand for?
2
Subtract 9 from 17 to get 8, then divide by 4: ★ = 2.
8. If ★ represents the same whole number each time and 3 × ★ + 16 = 55, what number does ★ stand for?
13
Subtract 16 from 55 to get 39, then divide by 3: ★ = 13.
9. If ★ represents the same whole number each time and 3 × ★ + 1 = 40, what number does ★ stand for?
13
Subtract 1 from 40 to get 39, then divide by 3: ★ = 13.
10. If ★ represents the same whole number each time and 2 × ★ + 12 = 34, what number does ★ stand for?
11
Subtract 12 from 34 to get 22, then divide by 2: ★ = 11.
11. If ★ represents the same whole number each time and 2 × ★ + 15 = 27, what number does ★ stand for?
6
Subtract 15 from 27 to get 12, then divide by 2: ★ = 6.
12. 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.

12 questions · Seed 69 · Age guidance, not curriculum certification