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 5 × ★ + 5 = 15, what number does ★ stand for?
5 · 5 · 15 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 12 = 68, what number does ★ stand for?
7 · 12 · 68 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 3 = 11, what number does ★ stand for?
2 · 3 · 11 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 19 = 52, what number does ★ stand for?
3 · 19 · 52 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 3 = 51, what number does ★ stand for?
6 · 3 · 51 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 11 = 27, what number does ★ stand for?
8 · 11 · 27 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 6 = 83, what number does ★ stand for?
7 · 6 · 83 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 7 = 57, what number does ★ stand for?
5 · 7 · 57 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
4 · 3 · 47 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 16 = 68, what number does ★ stand for?
4 · 16 · 68 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 16 = 46, what number does ★ stand for?
2 · 16 · 46 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 1 = 57, what number does ★ stand for?
8 · 1 · 57 · Symbol equation puzzles

12 questions · Seed 73 · 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 5 × ★ + 5 = 15, what number does ★ stand for?
2
Subtract 5 from 15 to get 10, then divide by 5: ★ = 2.
2. If ★ represents the same whole number each time and 7 × ★ + 12 = 68, what number does ★ stand for?
8
Subtract 12 from 68 to get 56, then divide by 7: ★ = 8.
3. If ★ represents the same whole number each time and 2 × ★ + 3 = 11, what number does ★ stand for?
4
Subtract 3 from 11 to get 8, then divide by 2: ★ = 4.
4. If ★ represents the same whole number each time and 3 × ★ + 19 = 52, what number does ★ stand for?
11
Subtract 19 from 52 to get 33, then divide by 3: ★ = 11.
5. If ★ represents the same whole number each time and 6 × ★ + 3 = 51, what number does ★ stand for?
8
Subtract 3 from 51 to get 48, then divide by 6: ★ = 8.
6. If ★ represents the same whole number each time and 8 × ★ + 11 = 27, what number does ★ stand for?
2
Subtract 11 from 27 to get 16, then divide by 8: ★ = 2.
7. If ★ represents the same whole number each time and 7 × ★ + 6 = 83, what number does ★ stand for?
11
Subtract 6 from 83 to get 77, then divide by 7: ★ = 11.
8. If ★ represents the same whole number each time and 5 × ★ + 7 = 57, what number does ★ stand for?
10
Subtract 7 from 57 to get 50, then divide by 5: ★ = 10.
9. 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.
10. If ★ represents the same whole number each time and 4 × ★ + 16 = 68, what number does ★ stand for?
13
Subtract 16 from 68 to get 52, then divide by 4: ★ = 13.
11. If ★ represents the same whole number each time and 2 × ★ + 16 = 46, what number does ★ stand for?
15
Subtract 16 from 46 to get 30, then divide by 2: ★ = 15.
12. If ★ represents the same whole number each time and 8 × ★ + 1 = 57, what number does ★ stand for?
7
Subtract 1 from 57 to get 56, then divide by 8: ★ = 7.

12 questions · Seed 73 · 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 5 × ★ + 5 = 15, what number does ★ stand for?
5 · 5 · 15 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 12 = 68, what number does ★ stand for?
7 · 12 · 68 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 3 = 11, what number does ★ stand for?
2 · 3 · 11 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 19 = 52, what number does ★ stand for?
3 · 19 · 52 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 3 = 51, what number does ★ stand for?
6 · 3 · 51 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 11 = 27, what number does ★ stand for?
8 · 11 · 27 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 6 = 83, what number does ★ stand for?
7 · 6 · 83 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 7 = 57, what number does ★ stand for?
5 · 7 · 57 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
4 · 3 · 47 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 16 = 68, what number does ★ stand for?
4 · 16 · 68 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 16 = 46, what number does ★ stand for?
2 · 16 · 46 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 1 = 57, what number does ★ stand for?
8 · 1 · 57 · Symbol equation puzzles

12 questions · Seed 73 · 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 5 × ★ + 5 = 15, what number does ★ stand for?
2
Subtract 5 from 15 to get 10, then divide by 5: ★ = 2.
2. If ★ represents the same whole number each time and 7 × ★ + 12 = 68, what number does ★ stand for?
8
Subtract 12 from 68 to get 56, then divide by 7: ★ = 8.
3. If ★ represents the same whole number each time and 2 × ★ + 3 = 11, what number does ★ stand for?
4
Subtract 3 from 11 to get 8, then divide by 2: ★ = 4.
4. If ★ represents the same whole number each time and 3 × ★ + 19 = 52, what number does ★ stand for?
11
Subtract 19 from 52 to get 33, then divide by 3: ★ = 11.
5. If ★ represents the same whole number each time and 6 × ★ + 3 = 51, what number does ★ stand for?
8
Subtract 3 from 51 to get 48, then divide by 6: ★ = 8.
6. If ★ represents the same whole number each time and 8 × ★ + 11 = 27, what number does ★ stand for?
2
Subtract 11 from 27 to get 16, then divide by 8: ★ = 2.
7. If ★ represents the same whole number each time and 7 × ★ + 6 = 83, what number does ★ stand for?
11
Subtract 6 from 83 to get 77, then divide by 7: ★ = 11.
8. If ★ represents the same whole number each time and 5 × ★ + 7 = 57, what number does ★ stand for?
10
Subtract 7 from 57 to get 50, then divide by 5: ★ = 10.
9. 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.
10. If ★ represents the same whole number each time and 4 × ★ + 16 = 68, what number does ★ stand for?
13
Subtract 16 from 68 to get 52, then divide by 4: ★ = 13.
11. If ★ represents the same whole number each time and 2 × ★ + 16 = 46, what number does ★ stand for?
15
Subtract 16 from 46 to get 30, then divide by 2: ★ = 15.
12. If ★ represents the same whole number each time and 8 × ★ + 1 = 57, what number does ★ stand for?
7
Subtract 1 from 57 to get 56, then divide by 8: ★ = 7.

12 questions · Seed 73 · Age guidance, not curriculum certification