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 3 × ★ + 7 = 28, what number does ★ stand for?
3 · 7 · 28 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 4 = 64, what number does ★ stand for?
4 · 4 · 64 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 13 = 45, what number does ★ stand for?
4 · 13 · 45 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 5 = 29, what number does ★ stand for?
8 · 5 · 29 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 11 = 23, what number does ★ stand for?
6 · 11 · 23 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 2 = 72, what number does ★ stand for?
7 · 2 · 72 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 18 = 98, what number does ★ stand for?
8 · 18 · 98 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 1 = 85, what number does ★ stand for?
7 · 1 · 85 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 37, what number does ★ stand for?
5 · 2 · 37 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 8 = 83, what number does ★ stand for?
5 · 8 · 83 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 16 = 49, what number does ★ stand for?
3 · 16 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 20 = 83, what number does ★ stand for?
7 · 20 · 83 · Symbol equation puzzles

12 questions · Seed 88 · 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 3 × ★ + 7 = 28, what number does ★ stand for?
7
Subtract 7 from 28 to get 21, then divide by 3: ★ = 7.
2. If ★ represents the same whole number each time and 4 × ★ + 4 = 64, what number does ★ stand for?
15
Subtract 4 from 64 to get 60, then divide by 4: ★ = 15.
3. If ★ represents the same whole number each time and 4 × ★ + 13 = 45, what number does ★ stand for?
8
Subtract 13 from 45 to get 32, then divide by 4: ★ = 8.
4. If ★ represents the same whole number each time and 8 × ★ + 5 = 29, what number does ★ stand for?
3
Subtract 5 from 29 to get 24, then divide by 8: ★ = 3.
5. If ★ represents the same whole number each time and 6 × ★ + 11 = 23, what number does ★ stand for?
2
Subtract 11 from 23 to get 12, then divide by 6: ★ = 2.
6. If ★ represents the same whole number each time and 7 × ★ + 2 = 72, what number does ★ stand for?
10
Subtract 2 from 72 to get 70, then divide by 7: ★ = 10.
7. If ★ represents the same whole number each time and 8 × ★ + 18 = 98, what number does ★ stand for?
10
Subtract 18 from 98 to get 80, then divide by 8: ★ = 10.
8. If ★ represents the same whole number each time and 7 × ★ + 1 = 85, what number does ★ stand for?
12
Subtract 1 from 85 to get 84, then divide by 7: ★ = 12.
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 37, what number does ★ stand for?
7
Subtract 2 from 37 to get 35, then divide by 5: ★ = 7.
10. If ★ represents the same whole number each time and 5 × ★ + 8 = 83, what number does ★ stand for?
15
Subtract 8 from 83 to get 75, then divide by 5: ★ = 15.
11. If ★ represents the same whole number each time and 3 × ★ + 16 = 49, what number does ★ stand for?
11
Subtract 16 from 49 to get 33, then divide by 3: ★ = 11.
12. If ★ represents the same whole number each time and 7 × ★ + 20 = 83, what number does ★ stand for?
9
Subtract 20 from 83 to get 63, then divide by 7: ★ = 9.

12 questions · Seed 88 · 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 3 × ★ + 7 = 28, what number does ★ stand for?
3 · 7 · 28 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 4 = 64, what number does ★ stand for?
4 · 4 · 64 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 13 = 45, what number does ★ stand for?
4 · 13 · 45 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 5 = 29, what number does ★ stand for?
8 · 5 · 29 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 11 = 23, what number does ★ stand for?
6 · 11 · 23 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 2 = 72, what number does ★ stand for?
7 · 2 · 72 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 18 = 98, what number does ★ stand for?
8 · 18 · 98 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 1 = 85, what number does ★ stand for?
7 · 1 · 85 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 37, what number does ★ stand for?
5 · 2 · 37 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 8 = 83, what number does ★ stand for?
5 · 8 · 83 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 16 = 49, what number does ★ stand for?
3 · 16 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 20 = 83, what number does ★ stand for?
7 · 20 · 83 · Symbol equation puzzles

12 questions · Seed 88 · 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 3 × ★ + 7 = 28, what number does ★ stand for?
7
Subtract 7 from 28 to get 21, then divide by 3: ★ = 7.
2. If ★ represents the same whole number each time and 4 × ★ + 4 = 64, what number does ★ stand for?
15
Subtract 4 from 64 to get 60, then divide by 4: ★ = 15.
3. If ★ represents the same whole number each time and 4 × ★ + 13 = 45, what number does ★ stand for?
8
Subtract 13 from 45 to get 32, then divide by 4: ★ = 8.
4. If ★ represents the same whole number each time and 8 × ★ + 5 = 29, what number does ★ stand for?
3
Subtract 5 from 29 to get 24, then divide by 8: ★ = 3.
5. If ★ represents the same whole number each time and 6 × ★ + 11 = 23, what number does ★ stand for?
2
Subtract 11 from 23 to get 12, then divide by 6: ★ = 2.
6. If ★ represents the same whole number each time and 7 × ★ + 2 = 72, what number does ★ stand for?
10
Subtract 2 from 72 to get 70, then divide by 7: ★ = 10.
7. If ★ represents the same whole number each time and 8 × ★ + 18 = 98, what number does ★ stand for?
10
Subtract 18 from 98 to get 80, then divide by 8: ★ = 10.
8. If ★ represents the same whole number each time and 7 × ★ + 1 = 85, what number does ★ stand for?
12
Subtract 1 from 85 to get 84, then divide by 7: ★ = 12.
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 37, what number does ★ stand for?
7
Subtract 2 from 37 to get 35, then divide by 5: ★ = 7.
10. If ★ represents the same whole number each time and 5 × ★ + 8 = 83, what number does ★ stand for?
15
Subtract 8 from 83 to get 75, then divide by 5: ★ = 15.
11. If ★ represents the same whole number each time and 3 × ★ + 16 = 49, what number does ★ stand for?
11
Subtract 16 from 49 to get 33, then divide by 3: ★ = 11.
12. If ★ represents the same whole number each time and 7 × ★ + 20 = 83, what number does ★ stand for?
9
Subtract 20 from 83 to get 63, then divide by 7: ★ = 9.

12 questions · Seed 88 · Age guidance, not curriculum certification