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.

New variation Try interactive challenge Browse templates

Age band:Ages 7-9 Ages 10-12

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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 8 × ★ + 14 = 46, what number does ★ stand for?
8 · 14 · 46 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 13 = 61, what number does ★ stand for?
6 · 13 · 61 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 15 = 81, what number does ★ stand for?
6 · 15 · 81 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 16 = 20, what number does ★ stand for?
2 · 16 · 20 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 13 = 58, what number does ★ stand for?
5 · 13 · 58 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 3 = 48, what number does ★ stand for?
3 · 3 · 48 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 3 = 75, what number does ★ stand for?
6 · 3 · 75 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 19 = 55, what number does ★ stand for?
3 · 19 · 55 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 1 = 13, what number does ★ stand for?
3 · 1 · 13 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2 · 18 · 22 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 12 = 42, what number does ★ stand for?
2 · 12 · 42 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
4 · 3 · 47 · Symbol equation puzzles

12 questions · Seed 47 · 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 8 × ★ + 14 = 46, what number does ★ stand for?
4
Subtract 14 from 46 to get 32, then divide by 8: ★ = 4.
2. If ★ represents the same whole number each time and 6 × ★ + 13 = 61, what number does ★ stand for?
8
Subtract 13 from 61 to get 48, then divide by 6: ★ = 8.
3. If ★ represents the same whole number each time and 6 × ★ + 15 = 81, what number does ★ stand for?
11
Subtract 15 from 81 to get 66, then divide by 6: ★ = 11.
4. If ★ represents the same whole number each time and 2 × ★ + 16 = 20, what number does ★ stand for?
2
Subtract 16 from 20 to get 4, then divide by 2: ★ = 2.
5. If ★ represents the same whole number each time and 5 × ★ + 13 = 58, what number does ★ stand for?
9
Subtract 13 from 58 to get 45, then divide by 5: ★ = 9.
6. If ★ represents the same whole number each time and 3 × ★ + 3 = 48, what number does ★ stand for?
15
Subtract 3 from 48 to get 45, then divide by 3: ★ = 15.
7. If ★ represents the same whole number each time and 6 × ★ + 3 = 75, what number does ★ stand for?
12
Subtract 3 from 75 to get 72, then divide by 6: ★ = 12.
8. If ★ represents the same whole number each time and 3 × ★ + 19 = 55, what number does ★ stand for?
12
Subtract 19 from 55 to get 36, then divide by 3: ★ = 12.
9. If ★ represents the same whole number each time and 3 × ★ + 1 = 13, what number does ★ stand for?
4
Subtract 1 from 13 to get 12, then divide by 3: ★ = 4.
10. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2
Subtract 18 from 22 to get 4, then divide by 2: ★ = 2.
11. If ★ represents the same whole number each time and 2 × ★ + 12 = 42, what number does ★ stand for?
15
Subtract 12 from 42 to get 30, then divide by 2: ★ = 15.
12. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
11
Subtract 3 from 47 to get 44, then divide by 4: ★ = 11.

12 questions · Seed 47 · 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 8 × ★ + 14 = 46, what number does ★ stand for?
8 · 14 · 46 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 13 = 61, what number does ★ stand for?
6 · 13 · 61 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 15 = 81, what number does ★ stand for?
6 · 15 · 81 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 16 = 20, what number does ★ stand for?
2 · 16 · 20 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 13 = 58, what number does ★ stand for?
5 · 13 · 58 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 3 = 48, what number does ★ stand for?
3 · 3 · 48 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 3 = 75, what number does ★ stand for?
6 · 3 · 75 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 19 = 55, what number does ★ stand for?
3 · 19 · 55 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 1 = 13, what number does ★ stand for?
3 · 1 · 13 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2 · 18 · 22 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 12 = 42, what number does ★ stand for?
2 · 12 · 42 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
4 · 3 · 47 · Symbol equation puzzles

12 questions · Seed 47 · 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 8 × ★ + 14 = 46, what number does ★ stand for?
4
Subtract 14 from 46 to get 32, then divide by 8: ★ = 4.
2. If ★ represents the same whole number each time and 6 × ★ + 13 = 61, what number does ★ stand for?
8
Subtract 13 from 61 to get 48, then divide by 6: ★ = 8.
3. If ★ represents the same whole number each time and 6 × ★ + 15 = 81, what number does ★ stand for?
11
Subtract 15 from 81 to get 66, then divide by 6: ★ = 11.
4. If ★ represents the same whole number each time and 2 × ★ + 16 = 20, what number does ★ stand for?
2
Subtract 16 from 20 to get 4, then divide by 2: ★ = 2.
5. If ★ represents the same whole number each time and 5 × ★ + 13 = 58, what number does ★ stand for?
9
Subtract 13 from 58 to get 45, then divide by 5: ★ = 9.
6. If ★ represents the same whole number each time and 3 × ★ + 3 = 48, what number does ★ stand for?
15
Subtract 3 from 48 to get 45, then divide by 3: ★ = 15.
7. If ★ represents the same whole number each time and 6 × ★ + 3 = 75, what number does ★ stand for?
12
Subtract 3 from 75 to get 72, then divide by 6: ★ = 12.
8. If ★ represents the same whole number each time and 3 × ★ + 19 = 55, what number does ★ stand for?
12
Subtract 19 from 55 to get 36, then divide by 3: ★ = 12.
9. If ★ represents the same whole number each time and 3 × ★ + 1 = 13, what number does ★ stand for?
4
Subtract 1 from 13 to get 12, then divide by 3: ★ = 4.
10. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2
Subtract 18 from 22 to get 4, then divide by 2: ★ = 2.
11. If ★ represents the same whole number each time and 2 × ★ + 12 = 42, what number does ★ stand for?
15
Subtract 12 from 42 to get 30, then divide by 2: ★ = 15.
12. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
11
Subtract 3 from 47 to get 44, then divide by 4: ★ = 11.

12 questions · Seed 47 · Age guidance, not curriculum certification