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 5 × ★ + 17 = 32, what number does ★ stand for?
5 · 17 · 32 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 28, what number does ★ stand for?
7 · 7 · 28 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 10, what number does ★ stand for?
2 · 4 · 10 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 25, what number does ★ stand for?
4 · 13 · 25 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 12 = 40, what number does ★ stand for?
7 · 12 · 40 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 42, what number does ★ stand for?
8 · 2 · 42 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 70, what number does ★ stand for?
4 · 18 · 70 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
4 · 20 · 48 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 17, what number does ★ stand for?
5 · 2 · 17 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 24, what number does ★ stand for?
3 · 12 · 24 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 20, what number does ★ stand for?
3 · 14 · 20 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 19 = 68, what number does ★ stand for?
7 · 19 · 68 · Symbol equation puzzles

12 questions · Seed 51 · 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 5 × ★ + 17 = 32, what number does ★ stand for?
3
Subtract 17 from 32 to get 15, then divide by 5: ★ = 3.
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 28, what number does ★ stand for?
3
Subtract 7 from 28 to get 21, then divide by 7: ★ = 3.
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 10, what number does ★ stand for?
3
Subtract 4 from 10 to get 6, then divide by 2: ★ = 3.
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 25, what number does ★ stand for?
3
Subtract 13 from 25 to get 12, then divide by 4: ★ = 3.
5. If ★ represents the same whole number each time and 7 × ★ + 12 = 40, what number does ★ stand for?
4
Subtract 12 from 40 to get 28, then divide by 7: ★ = 4.
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 42, what number does ★ stand for?
5
Subtract 2 from 42 to get 40, then divide by 8: ★ = 5.
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 70, what number does ★ stand for?
13
Subtract 18 from 70 to get 52, then divide by 4: ★ = 13.
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
7
Subtract 20 from 48 to get 28, then divide by 4: ★ = 7.
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 17, what number does ★ stand for?
3
Subtract 2 from 17 to get 15, then divide by 5: ★ = 3.
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 24, what number does ★ stand for?
4
Subtract 12 from 24 to get 12, then divide by 3: ★ = 4.
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 20, what number does ★ stand for?
2
Subtract 14 from 20 to get 6, then divide by 3: ★ = 2.
12. If ★ represents the same whole number each time and 7 × ★ + 19 = 68, what number does ★ stand for?
7
Subtract 19 from 68 to get 49, then divide by 7: ★ = 7.

12 questions · Seed 51 · 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 5 × ★ + 17 = 32, what number does ★ stand for?
5 · 17 · 32 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 28, what number does ★ stand for?
7 · 7 · 28 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 10, what number does ★ stand for?
2 · 4 · 10 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 25, what number does ★ stand for?
4 · 13 · 25 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 12 = 40, what number does ★ stand for?
7 · 12 · 40 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 42, what number does ★ stand for?
8 · 2 · 42 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 70, what number does ★ stand for?
4 · 18 · 70 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
4 · 20 · 48 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 17, what number does ★ stand for?
5 · 2 · 17 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 24, what number does ★ stand for?
3 · 12 · 24 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 20, what number does ★ stand for?
3 · 14 · 20 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 19 = 68, what number does ★ stand for?
7 · 19 · 68 · Symbol equation puzzles

12 questions · Seed 51 · 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 5 × ★ + 17 = 32, what number does ★ stand for?
3
Subtract 17 from 32 to get 15, then divide by 5: ★ = 3.
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 28, what number does ★ stand for?
3
Subtract 7 from 28 to get 21, then divide by 7: ★ = 3.
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 10, what number does ★ stand for?
3
Subtract 4 from 10 to get 6, then divide by 2: ★ = 3.
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 25, what number does ★ stand for?
3
Subtract 13 from 25 to get 12, then divide by 4: ★ = 3.
5. If ★ represents the same whole number each time and 7 × ★ + 12 = 40, what number does ★ stand for?
4
Subtract 12 from 40 to get 28, then divide by 7: ★ = 4.
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 42, what number does ★ stand for?
5
Subtract 2 from 42 to get 40, then divide by 8: ★ = 5.
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 70, what number does ★ stand for?
13
Subtract 18 from 70 to get 52, then divide by 4: ★ = 13.
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
7
Subtract 20 from 48 to get 28, then divide by 4: ★ = 7.
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 17, what number does ★ stand for?
3
Subtract 2 from 17 to get 15, then divide by 5: ★ = 3.
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 24, what number does ★ stand for?
4
Subtract 12 from 24 to get 12, then divide by 3: ★ = 4.
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 20, what number does ★ stand for?
2
Subtract 14 from 20 to get 6, then divide by 3: ★ = 2.
12. If ★ represents the same whole number each time and 7 × ★ + 19 = 68, what number does ★ stand for?
7
Subtract 19 from 68 to get 49, then divide by 7: ★ = 7.

12 questions · Seed 51 · Age guidance, not curriculum certification