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 × ★ + 2 = 20, what number does ★ stand for?
2 · 2 · 20 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 5 × ★ + 11 = 46, what number does ★ stand for?
5 · 11 · 46 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 14 = 54, what number does ★ stand for?
5 · 14 · 54 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
3 · 9 · 24 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 18 = 34, what number does ★ stand for?
4 · 18 · 34 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 11 = 56, what number does ★ stand for?
5 · 11 · 56 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 6 = 48, what number does ★ stand for?
3 · 6 · 48 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 12 = 18, what number does ★ stand for?
2 · 12 · 18 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 8 = 35, what number does ★ stand for?
3 · 8 · 35 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 18 = 26, what number does ★ stand for?
2 · 18 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 1 = 79, what number does ★ stand for?
6 · 1 · 79 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 4 = 28, what number does ★ stand for?
4 · 4 · 28 · Symbol equation puzzles

12 questions · Seed 75 · 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 × ★ + 2 = 20, what number does ★ stand for?
9
Subtract 2 from 20 to get 18, then divide by 2: ★ = 9.
2. If ★ represents the same whole number each time and 5 × ★ + 11 = 46, what number does ★ stand for?
7
Subtract 11 from 46 to get 35, then divide by 5: ★ = 7.
3. If ★ represents the same whole number each time and 5 × ★ + 14 = 54, what number does ★ stand for?
8
Subtract 14 from 54 to get 40, then divide by 5: ★ = 8.
4. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
5
Subtract 9 from 24 to get 15, then divide by 3: ★ = 5.
5. If ★ represents the same whole number each time and 4 × ★ + 18 = 34, what number does ★ stand for?
4
Subtract 18 from 34 to get 16, then divide by 4: ★ = 4.
6. If ★ represents the same whole number each time and 5 × ★ + 11 = 56, what number does ★ stand for?
9
Subtract 11 from 56 to get 45, then divide by 5: ★ = 9.
7. If ★ represents the same whole number each time and 3 × ★ + 6 = 48, what number does ★ stand for?
14
Subtract 6 from 48 to get 42, then divide by 3: ★ = 14.
8. If ★ represents the same whole number each time and 2 × ★ + 12 = 18, what number does ★ stand for?
3
Subtract 12 from 18 to get 6, then divide by 2: ★ = 3.
9. If ★ represents the same whole number each time and 3 × ★ + 8 = 35, what number does ★ stand for?
9
Subtract 8 from 35 to get 27, then divide by 3: ★ = 9.
10. If ★ represents the same whole number each time and 2 × ★ + 18 = 26, what number does ★ stand for?
4
Subtract 18 from 26 to get 8, then divide by 2: ★ = 4.
11. If ★ represents the same whole number each time and 6 × ★ + 1 = 79, what number does ★ stand for?
13
Subtract 1 from 79 to get 78, then divide by 6: ★ = 13.
12. If ★ represents the same whole number each time and 4 × ★ + 4 = 28, what number does ★ stand for?
6
Subtract 4 from 28 to get 24, then divide by 4: ★ = 6.

12 questions · Seed 75 · 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 × ★ + 2 = 20, what number does ★ stand for?
2 · 2 · 20 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 5 × ★ + 11 = 46, what number does ★ stand for?
5 · 11 · 46 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 14 = 54, what number does ★ stand for?
5 · 14 · 54 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
3 · 9 · 24 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 18 = 34, what number does ★ stand for?
4 · 18 · 34 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 11 = 56, what number does ★ stand for?
5 · 11 · 56 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 6 = 48, what number does ★ stand for?
3 · 6 · 48 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 12 = 18, what number does ★ stand for?
2 · 12 · 18 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 8 = 35, what number does ★ stand for?
3 · 8 · 35 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 18 = 26, what number does ★ stand for?
2 · 18 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 1 = 79, what number does ★ stand for?
6 · 1 · 79 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 4 = 28, what number does ★ stand for?
4 · 4 · 28 · Symbol equation puzzles

12 questions · Seed 75 · 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 × ★ + 2 = 20, what number does ★ stand for?
9
Subtract 2 from 20 to get 18, then divide by 2: ★ = 9.
2. If ★ represents the same whole number each time and 5 × ★ + 11 = 46, what number does ★ stand for?
7
Subtract 11 from 46 to get 35, then divide by 5: ★ = 7.
3. If ★ represents the same whole number each time and 5 × ★ + 14 = 54, what number does ★ stand for?
8
Subtract 14 from 54 to get 40, then divide by 5: ★ = 8.
4. If ★ represents the same whole number each time and 3 × ★ + 9 = 24, what number does ★ stand for?
5
Subtract 9 from 24 to get 15, then divide by 3: ★ = 5.
5. If ★ represents the same whole number each time and 4 × ★ + 18 = 34, what number does ★ stand for?
4
Subtract 18 from 34 to get 16, then divide by 4: ★ = 4.
6. If ★ represents the same whole number each time and 5 × ★ + 11 = 56, what number does ★ stand for?
9
Subtract 11 from 56 to get 45, then divide by 5: ★ = 9.
7. If ★ represents the same whole number each time and 3 × ★ + 6 = 48, what number does ★ stand for?
14
Subtract 6 from 48 to get 42, then divide by 3: ★ = 14.
8. If ★ represents the same whole number each time and 2 × ★ + 12 = 18, what number does ★ stand for?
3
Subtract 12 from 18 to get 6, then divide by 2: ★ = 3.
9. If ★ represents the same whole number each time and 3 × ★ + 8 = 35, what number does ★ stand for?
9
Subtract 8 from 35 to get 27, then divide by 3: ★ = 9.
10. If ★ represents the same whole number each time and 2 × ★ + 18 = 26, what number does ★ stand for?
4
Subtract 18 from 26 to get 8, then divide by 2: ★ = 4.
11. If ★ represents the same whole number each time and 6 × ★ + 1 = 79, what number does ★ stand for?
13
Subtract 1 from 79 to get 78, then divide by 6: ★ = 13.
12. If ★ represents the same whole number each time and 4 × ★ + 4 = 28, what number does ★ stand for?
6
Subtract 4 from 28 to get 24, then divide by 4: ★ = 6.

12 questions · Seed 75 · Age guidance, not curriculum certification