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 × ★ + 13 = 63, what number does ★ stand for?
5 · 13 · 63 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
8 · 20 · 44 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 3 = 25, what number does ★ stand for?
2 · 3 · 25 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 17 = 21, what number does ★ stand for?
2 · 17 · 21 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 1 = 43, what number does ★ stand for?
3 · 1 · 43 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 4 = 52, what number does ★ stand for?
8 · 4 · 52 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 12 = 52, what number does ★ stand for?
5 · 12 · 52 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 1 = 28, what number does ★ stand for?
3 · 1 · 28 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 5 = 35, what number does ★ stand for?
2 · 5 · 35 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 14 = 26, what number does ★ stand for?
2 · 14 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 26, what number does ★ stand for?
3 · 14 · 26 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 6 = 20, what number does ★ stand for?
2 · 6 · 20 · Symbol equation puzzles

12 questions · Seed 104744 · 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 × ★ + 13 = 63, what number does ★ stand for?
10
Subtract 13 from 63 to get 50, then divide by 5: ★ = 10.
2. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
3
Subtract 20 from 44 to get 24, then divide by 8: ★ = 3.
3. If ★ represents the same whole number each time and 2 × ★ + 3 = 25, what number does ★ stand for?
11
Subtract 3 from 25 to get 22, then divide by 2: ★ = 11.
4. If ★ represents the same whole number each time and 2 × ★ + 17 = 21, what number does ★ stand for?
2
Subtract 17 from 21 to get 4, then divide by 2: ★ = 2.
5. If ★ represents the same whole number each time and 3 × ★ + 1 = 43, what number does ★ stand for?
14
Subtract 1 from 43 to get 42, then divide by 3: ★ = 14.
6. If ★ represents the same whole number each time and 8 × ★ + 4 = 52, what number does ★ stand for?
6
Subtract 4 from 52 to get 48, then divide by 8: ★ = 6.
7. If ★ represents the same whole number each time and 5 × ★ + 12 = 52, what number does ★ stand for?
8
Subtract 12 from 52 to get 40, then divide by 5: ★ = 8.
8. If ★ represents the same whole number each time and 3 × ★ + 1 = 28, what number does ★ stand for?
9
Subtract 1 from 28 to get 27, then divide by 3: ★ = 9.
9. If ★ represents the same whole number each time and 2 × ★ + 5 = 35, what number does ★ stand for?
15
Subtract 5 from 35 to get 30, then divide by 2: ★ = 15.
10. If ★ represents the same whole number each time and 2 × ★ + 14 = 26, what number does ★ stand for?
6
Subtract 14 from 26 to get 12, then divide by 2: ★ = 6.
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 26, what number does ★ stand for?
4
Subtract 14 from 26 to get 12, then divide by 3: ★ = 4.
12. If ★ represents the same whole number each time and 2 × ★ + 6 = 20, what number does ★ stand for?
7
Subtract 6 from 20 to get 14, then divide by 2: ★ = 7.

12 questions · Seed 104744 · 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 × ★ + 13 = 63, what number does ★ stand for?
5 · 13 · 63 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
8 · 20 · 44 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 3 = 25, what number does ★ stand for?
2 · 3 · 25 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 17 = 21, what number does ★ stand for?
2 · 17 · 21 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 1 = 43, what number does ★ stand for?
3 · 1 · 43 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 4 = 52, what number does ★ stand for?
8 · 4 · 52 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 12 = 52, what number does ★ stand for?
5 · 12 · 52 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 1 = 28, what number does ★ stand for?
3 · 1 · 28 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 5 = 35, what number does ★ stand for?
2 · 5 · 35 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 14 = 26, what number does ★ stand for?
2 · 14 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 26, what number does ★ stand for?
3 · 14 · 26 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 6 = 20, what number does ★ stand for?
2 · 6 · 20 · Symbol equation puzzles

12 questions · Seed 104744 · 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 × ★ + 13 = 63, what number does ★ stand for?
10
Subtract 13 from 63 to get 50, then divide by 5: ★ = 10.
2. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
3
Subtract 20 from 44 to get 24, then divide by 8: ★ = 3.
3. If ★ represents the same whole number each time and 2 × ★ + 3 = 25, what number does ★ stand for?
11
Subtract 3 from 25 to get 22, then divide by 2: ★ = 11.
4. If ★ represents the same whole number each time and 2 × ★ + 17 = 21, what number does ★ stand for?
2
Subtract 17 from 21 to get 4, then divide by 2: ★ = 2.
5. If ★ represents the same whole number each time and 3 × ★ + 1 = 43, what number does ★ stand for?
14
Subtract 1 from 43 to get 42, then divide by 3: ★ = 14.
6. If ★ represents the same whole number each time and 8 × ★ + 4 = 52, what number does ★ stand for?
6
Subtract 4 from 52 to get 48, then divide by 8: ★ = 6.
7. If ★ represents the same whole number each time and 5 × ★ + 12 = 52, what number does ★ stand for?
8
Subtract 12 from 52 to get 40, then divide by 5: ★ = 8.
8. If ★ represents the same whole number each time and 3 × ★ + 1 = 28, what number does ★ stand for?
9
Subtract 1 from 28 to get 27, then divide by 3: ★ = 9.
9. If ★ represents the same whole number each time and 2 × ★ + 5 = 35, what number does ★ stand for?
15
Subtract 5 from 35 to get 30, then divide by 2: ★ = 15.
10. If ★ represents the same whole number each time and 2 × ★ + 14 = 26, what number does ★ stand for?
6
Subtract 14 from 26 to get 12, then divide by 2: ★ = 6.
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 26, what number does ★ stand for?
4
Subtract 14 from 26 to get 12, then divide by 3: ★ = 4.
12. If ★ represents the same whole number each time and 2 × ★ + 6 = 20, what number does ★ stand for?
7
Subtract 6 from 20 to get 14, then divide by 2: ★ = 7.

12 questions · Seed 104744 · Age guidance, not curriculum certification