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 7 × ★ + 16 = 30, what number does ★ stand for?
7 · 16 · 30 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 2 = 8, what number does ★ stand for?
3 · 2 · 8 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 7 = 59, what number does ★ stand for?
4 · 7 · 59 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 4 = 60, what number does ★ stand for?
8 · 4 · 60 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 13 = 29, what number does ★ stand for?
8 · 13 · 29 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 12 = 75, what number does ★ stand for?
7 · 12 · 75 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 5 = 53, what number does ★ stand for?
8 · 5 · 53 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 37, what number does ★ stand for?
3 · 13 · 37 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 8 = 24, what number does ★ stand for?
2 · 8 · 24 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 18 = 57, what number does ★ stand for?
3 · 18 · 57 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 17 = 67, what number does ★ stand for?
5 · 17 · 67 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 1 = 31, what number does ★ stand for?
5 · 1 · 31 · Symbol equation puzzles

12 questions · Seed 61 · 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 7 × ★ + 16 = 30, what number does ★ stand for?
2
Subtract 16 from 30 to get 14, then divide by 7: ★ = 2.
2. If ★ represents the same whole number each time and 3 × ★ + 2 = 8, what number does ★ stand for?
2
Subtract 2 from 8 to get 6, then divide by 3: ★ = 2.
3. If ★ represents the same whole number each time and 4 × ★ + 7 = 59, what number does ★ stand for?
13
Subtract 7 from 59 to get 52, then divide by 4: ★ = 13.
4. If ★ represents the same whole number each time and 8 × ★ + 4 = 60, what number does ★ stand for?
7
Subtract 4 from 60 to get 56, then divide by 8: ★ = 7.
5. If ★ represents the same whole number each time and 8 × ★ + 13 = 29, what number does ★ stand for?
2
Subtract 13 from 29 to get 16, then divide by 8: ★ = 2.
6. If ★ represents the same whole number each time and 7 × ★ + 12 = 75, what number does ★ stand for?
9
Subtract 12 from 75 to get 63, then divide by 7: ★ = 9.
7. If ★ represents the same whole number each time and 8 × ★ + 5 = 53, what number does ★ stand for?
6
Subtract 5 from 53 to get 48, then divide by 8: ★ = 6.
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 37, what number does ★ stand for?
8
Subtract 13 from 37 to get 24, then divide by 3: ★ = 8.
9. If ★ represents the same whole number each time and 2 × ★ + 8 = 24, what number does ★ stand for?
8
Subtract 8 from 24 to get 16, then divide by 2: ★ = 8.
10. If ★ represents the same whole number each time and 3 × ★ + 18 = 57, what number does ★ stand for?
13
Subtract 18 from 57 to get 39, then divide by 3: ★ = 13.
11. If ★ represents the same whole number each time and 5 × ★ + 17 = 67, what number does ★ stand for?
10
Subtract 17 from 67 to get 50, then divide by 5: ★ = 10.
12. If ★ represents the same whole number each time and 5 × ★ + 1 = 31, what number does ★ stand for?
6
Subtract 1 from 31 to get 30, then divide by 5: ★ = 6.

12 questions · Seed 61 · 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 7 × ★ + 16 = 30, what number does ★ stand for?
7 · 16 · 30 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 2 = 8, what number does ★ stand for?
3 · 2 · 8 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 7 = 59, what number does ★ stand for?
4 · 7 · 59 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 4 = 60, what number does ★ stand for?
8 · 4 · 60 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 13 = 29, what number does ★ stand for?
8 · 13 · 29 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 12 = 75, what number does ★ stand for?
7 · 12 · 75 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 5 = 53, what number does ★ stand for?
8 · 5 · 53 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 37, what number does ★ stand for?
3 · 13 · 37 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 8 = 24, what number does ★ stand for?
2 · 8 · 24 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 18 = 57, what number does ★ stand for?
3 · 18 · 57 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 17 = 67, what number does ★ stand for?
5 · 17 · 67 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 1 = 31, what number does ★ stand for?
5 · 1 · 31 · Symbol equation puzzles

12 questions · Seed 61 · 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 7 × ★ + 16 = 30, what number does ★ stand for?
2
Subtract 16 from 30 to get 14, then divide by 7: ★ = 2.
2. If ★ represents the same whole number each time and 3 × ★ + 2 = 8, what number does ★ stand for?
2
Subtract 2 from 8 to get 6, then divide by 3: ★ = 2.
3. If ★ represents the same whole number each time and 4 × ★ + 7 = 59, what number does ★ stand for?
13
Subtract 7 from 59 to get 52, then divide by 4: ★ = 13.
4. If ★ represents the same whole number each time and 8 × ★ + 4 = 60, what number does ★ stand for?
7
Subtract 4 from 60 to get 56, then divide by 8: ★ = 7.
5. If ★ represents the same whole number each time and 8 × ★ + 13 = 29, what number does ★ stand for?
2
Subtract 13 from 29 to get 16, then divide by 8: ★ = 2.
6. If ★ represents the same whole number each time and 7 × ★ + 12 = 75, what number does ★ stand for?
9
Subtract 12 from 75 to get 63, then divide by 7: ★ = 9.
7. If ★ represents the same whole number each time and 8 × ★ + 5 = 53, what number does ★ stand for?
6
Subtract 5 from 53 to get 48, then divide by 8: ★ = 6.
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 37, what number does ★ stand for?
8
Subtract 13 from 37 to get 24, then divide by 3: ★ = 8.
9. If ★ represents the same whole number each time and 2 × ★ + 8 = 24, what number does ★ stand for?
8
Subtract 8 from 24 to get 16, then divide by 2: ★ = 8.
10. If ★ represents the same whole number each time and 3 × ★ + 18 = 57, what number does ★ stand for?
13
Subtract 18 from 57 to get 39, then divide by 3: ★ = 13.
11. If ★ represents the same whole number each time and 5 × ★ + 17 = 67, what number does ★ stand for?
10
Subtract 17 from 67 to get 50, then divide by 5: ★ = 10.
12. If ★ represents the same whole number each time and 5 × ★ + 1 = 31, what number does ★ stand for?
6
Subtract 1 from 31 to get 30, then divide by 5: ★ = 6.

12 questions · Seed 61 · Age guidance, not curriculum certification