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 2 × ★ + 3 = 9, what number does ★ stand for?
2 · 3 · 9 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 13 = 33, what number does ★ stand for?
2 · 13 · 33 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 1 = 9, what number does ★ stand for?
2 · 1 · 9 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 11 = 61, what number does ★ stand for?
5 · 11 · 61 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 20 = 42, what number does ★ stand for?
2 · 20 · 42 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 20 = 125, what number does ★ stand for?
7 · 20 · 125 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 11 = 53, what number does ★ stand for?
6 · 11 · 53 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 16 = 46, what number does ★ stand for?
3 · 16 · 46 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 16 = 30, what number does ★ stand for?
2 · 16 · 30 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 10 = 26, what number does ★ stand for?
4 · 10 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 18 = 93, what number does ★ stand for?
5 · 18 · 93 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 14 = 34, what number does ★ stand for?
2 · 14 · 34 · Symbol equation puzzles

12 questions · Seed 104746 · 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 2 × ★ + 3 = 9, what number does ★ stand for?
3
Subtract 3 from 9 to get 6, then divide by 2: ★ = 3.
2. If ★ represents the same whole number each time and 2 × ★ + 13 = 33, what number does ★ stand for?
10
Subtract 13 from 33 to get 20, then divide by 2: ★ = 10.
3. If ★ represents the same whole number each time and 2 × ★ + 1 = 9, what number does ★ stand for?
4
Subtract 1 from 9 to get 8, then divide by 2: ★ = 4.
4. If ★ represents the same whole number each time and 5 × ★ + 11 = 61, what number does ★ stand for?
10
Subtract 11 from 61 to get 50, then divide by 5: ★ = 10.
5. If ★ represents the same whole number each time and 2 × ★ + 20 = 42, what number does ★ stand for?
11
Subtract 20 from 42 to get 22, then divide by 2: ★ = 11.
6. If ★ represents the same whole number each time and 7 × ★ + 20 = 125, what number does ★ stand for?
15
Subtract 20 from 125 to get 105, then divide by 7: ★ = 15.
7. If ★ represents the same whole number each time and 6 × ★ + 11 = 53, what number does ★ stand for?
7
Subtract 11 from 53 to get 42, then divide by 6: ★ = 7.
8. If ★ represents the same whole number each time and 3 × ★ + 16 = 46, what number does ★ stand for?
10
Subtract 16 from 46 to get 30, then divide by 3: ★ = 10.
9. If ★ represents the same whole number each time and 2 × ★ + 16 = 30, what number does ★ stand for?
7
Subtract 16 from 30 to get 14, then divide by 2: ★ = 7.
10. If ★ represents the same whole number each time and 4 × ★ + 10 = 26, what number does ★ stand for?
4
Subtract 10 from 26 to get 16, then divide by 4: ★ = 4.
11. If ★ represents the same whole number each time and 5 × ★ + 18 = 93, what number does ★ stand for?
15
Subtract 18 from 93 to get 75, then divide by 5: ★ = 15.
12. If ★ represents the same whole number each time and 2 × ★ + 14 = 34, what number does ★ stand for?
10
Subtract 14 from 34 to get 20, then divide by 2: ★ = 10.

12 questions · Seed 104746 · 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 2 × ★ + 3 = 9, what number does ★ stand for?
2 · 3 · 9 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 13 = 33, what number does ★ stand for?
2 · 13 · 33 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 1 = 9, what number does ★ stand for?
2 · 1 · 9 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 11 = 61, what number does ★ stand for?
5 · 11 · 61 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 20 = 42, what number does ★ stand for?
2 · 20 · 42 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 20 = 125, what number does ★ stand for?
7 · 20 · 125 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 11 = 53, what number does ★ stand for?
6 · 11 · 53 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 16 = 46, what number does ★ stand for?
3 · 16 · 46 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 16 = 30, what number does ★ stand for?
2 · 16 · 30 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 10 = 26, what number does ★ stand for?
4 · 10 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 18 = 93, what number does ★ stand for?
5 · 18 · 93 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 14 = 34, what number does ★ stand for?
2 · 14 · 34 · Symbol equation puzzles

12 questions · Seed 104746 · 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 2 × ★ + 3 = 9, what number does ★ stand for?
3
Subtract 3 from 9 to get 6, then divide by 2: ★ = 3.
2. If ★ represents the same whole number each time and 2 × ★ + 13 = 33, what number does ★ stand for?
10
Subtract 13 from 33 to get 20, then divide by 2: ★ = 10.
3. If ★ represents the same whole number each time and 2 × ★ + 1 = 9, what number does ★ stand for?
4
Subtract 1 from 9 to get 8, then divide by 2: ★ = 4.
4. If ★ represents the same whole number each time and 5 × ★ + 11 = 61, what number does ★ stand for?
10
Subtract 11 from 61 to get 50, then divide by 5: ★ = 10.
5. If ★ represents the same whole number each time and 2 × ★ + 20 = 42, what number does ★ stand for?
11
Subtract 20 from 42 to get 22, then divide by 2: ★ = 11.
6. If ★ represents the same whole number each time and 7 × ★ + 20 = 125, what number does ★ stand for?
15
Subtract 20 from 125 to get 105, then divide by 7: ★ = 15.
7. If ★ represents the same whole number each time and 6 × ★ + 11 = 53, what number does ★ stand for?
7
Subtract 11 from 53 to get 42, then divide by 6: ★ = 7.
8. If ★ represents the same whole number each time and 3 × ★ + 16 = 46, what number does ★ stand for?
10
Subtract 16 from 46 to get 30, then divide by 3: ★ = 10.
9. If ★ represents the same whole number each time and 2 × ★ + 16 = 30, what number does ★ stand for?
7
Subtract 16 from 30 to get 14, then divide by 2: ★ = 7.
10. If ★ represents the same whole number each time and 4 × ★ + 10 = 26, what number does ★ stand for?
4
Subtract 10 from 26 to get 16, then divide by 4: ★ = 4.
11. If ★ represents the same whole number each time and 5 × ★ + 18 = 93, what number does ★ stand for?
15
Subtract 18 from 93 to get 75, then divide by 5: ★ = 15.
12. If ★ represents the same whole number each time and 2 × ★ + 14 = 34, what number does ★ stand for?
10
Subtract 14 from 34 to get 20, then divide by 2: ★ = 10.

12 questions · Seed 104746 · Age guidance, not curriculum certification