ReasoningAges 7-9

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 7-9

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 2 × ★ + 9 = 27, what number does ★ stand for?
2 · 9 · 27 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 16 = 38, what number does ★ stand for?
2 · 16 · 38 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 3 = 18, what number does ★ stand for?
5 · 3 · 18 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 9 = 129, what number does ★ stand for?
8 · 9 · 129 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 13 = 85, what number does ★ stand for?
8 · 13 · 85 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 8 = 26, what number does ★ stand for?
6 · 8 · 26 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 13 = 53, what number does ★ stand for?
5 · 13 · 53 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 10 = 28, what number does ★ stand for?
2 · 10 · 28 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 18 = 44, what number does ★ stand for?
2 · 18 · 44 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
2 · 4 · 32 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 5 = 61, what number does ★ stand for?
7 · 5 · 61 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 13 = 90, what number does ★ stand for?
7 · 13 · 90 · Symbol equation puzzles

12 questions · Seed 42 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 7-9

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 2 × ★ + 9 = 27, what number does ★ stand for?
9
Subtract 9 from 27 to get 18, then divide by 2: ★ = 9.
2. If ★ represents the same whole number each time and 2 × ★ + 16 = 38, what number does ★ stand for?
11
Subtract 16 from 38 to get 22, then divide by 2: ★ = 11.
3. If ★ represents the same whole number each time and 5 × ★ + 3 = 18, what number does ★ stand for?
3
Subtract 3 from 18 to get 15, then divide by 5: ★ = 3.
4. If ★ represents the same whole number each time and 8 × ★ + 9 = 129, what number does ★ stand for?
15
Subtract 9 from 129 to get 120, then divide by 8: ★ = 15.
5. If ★ represents the same whole number each time and 8 × ★ + 13 = 85, what number does ★ stand for?
9
Subtract 13 from 85 to get 72, then divide by 8: ★ = 9.
6. If ★ represents the same whole number each time and 6 × ★ + 8 = 26, what number does ★ stand for?
3
Subtract 8 from 26 to get 18, then divide by 6: ★ = 3.
7. If ★ represents the same whole number each time and 5 × ★ + 13 = 53, what number does ★ stand for?
8
Subtract 13 from 53 to get 40, then divide by 5: ★ = 8.
8. If ★ represents the same whole number each time and 2 × ★ + 10 = 28, what number does ★ stand for?
9
Subtract 10 from 28 to get 18, then divide by 2: ★ = 9.
9. If ★ represents the same whole number each time and 2 × ★ + 18 = 44, what number does ★ stand for?
13
Subtract 18 from 44 to get 26, then divide by 2: ★ = 13.
10. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
14
Subtract 4 from 32 to get 28, then divide by 2: ★ = 14.
11. If ★ represents the same whole number each time and 7 × ★ + 5 = 61, what number does ★ stand for?
8
Subtract 5 from 61 to get 56, then divide by 7: ★ = 8.
12. If ★ represents the same whole number each time and 7 × ★ + 13 = 90, what number does ★ stand for?
11
Subtract 13 from 90 to get 77, then divide by 7: ★ = 11.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 7-9

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 2 × ★ + 9 = 27, what number does ★ stand for?
2 · 9 · 27 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 16 = 38, what number does ★ stand for?
2 · 16 · 38 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 3 = 18, what number does ★ stand for?
5 · 3 · 18 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 9 = 129, what number does ★ stand for?
8 · 9 · 129 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 13 = 85, what number does ★ stand for?
8 · 13 · 85 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 8 = 26, what number does ★ stand for?
6 · 8 · 26 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 13 = 53, what number does ★ stand for?
5 · 13 · 53 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 10 = 28, what number does ★ stand for?
2 · 10 · 28 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 18 = 44, what number does ★ stand for?
2 · 18 · 44 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
2 · 4 · 32 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 5 = 61, what number does ★ stand for?
7 · 5 · 61 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 13 = 90, what number does ★ stand for?
7 · 13 · 90 · Symbol equation puzzles

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 7-9

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 2 × ★ + 9 = 27, what number does ★ stand for?
9
Subtract 9 from 27 to get 18, then divide by 2: ★ = 9.
2. If ★ represents the same whole number each time and 2 × ★ + 16 = 38, what number does ★ stand for?
11
Subtract 16 from 38 to get 22, then divide by 2: ★ = 11.
3. If ★ represents the same whole number each time and 5 × ★ + 3 = 18, what number does ★ stand for?
3
Subtract 3 from 18 to get 15, then divide by 5: ★ = 3.
4. If ★ represents the same whole number each time and 8 × ★ + 9 = 129, what number does ★ stand for?
15
Subtract 9 from 129 to get 120, then divide by 8: ★ = 15.
5. If ★ represents the same whole number each time and 8 × ★ + 13 = 85, what number does ★ stand for?
9
Subtract 13 from 85 to get 72, then divide by 8: ★ = 9.
6. If ★ represents the same whole number each time and 6 × ★ + 8 = 26, what number does ★ stand for?
3
Subtract 8 from 26 to get 18, then divide by 6: ★ = 3.
7. If ★ represents the same whole number each time and 5 × ★ + 13 = 53, what number does ★ stand for?
8
Subtract 13 from 53 to get 40, then divide by 5: ★ = 8.
8. If ★ represents the same whole number each time and 2 × ★ + 10 = 28, what number does ★ stand for?
9
Subtract 10 from 28 to get 18, then divide by 2: ★ = 9.
9. If ★ represents the same whole number each time and 2 × ★ + 18 = 44, what number does ★ stand for?
13
Subtract 18 from 44 to get 26, then divide by 2: ★ = 13.
10. If ★ represents the same whole number each time and 2 × ★ + 4 = 32, what number does ★ stand for?
14
Subtract 4 from 32 to get 28, then divide by 2: ★ = 14.
11. If ★ represents the same whole number each time and 7 × ★ + 5 = 61, what number does ★ stand for?
8
Subtract 5 from 61 to get 56, then divide by 7: ★ = 8.
12. If ★ represents the same whole number each time and 7 × ★ + 13 = 90, what number does ★ stand for?
11
Subtract 13 from 90 to get 77, then divide by 7: ★ = 11.

12 questions · Seed 42 · Age guidance, not curriculum certification