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.

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Age band:Ages 7-9 Ages 10-12

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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 × ★ + 15 = 30, what number does ★ stand for?
3 · 15 · 30 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 5 × ★ + 3 = 13, what number does ★ stand for?
5 · 3 · 13 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 17 = 77, what number does ★ stand for?
6 · 17 · 77 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 3 = 63, what number does ★ stand for?
6 · 3 · 63 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 17 = 32, what number does ★ stand for?
5 · 17 · 32 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 5 = 17, what number does ★ stand for?
3 · 5 · 17 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 9 = 45, what number does ★ stand for?
4 · 9 · 45 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 18 = 30, what number does ★ stand for?
2 · 18 · 30 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 10 = 58, what number does ★ stand for?
4 · 10 · 58 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 89, what number does ★ stand for?
7 · 5 · 89 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 11 = 88, what number does ★ stand for?
7 · 11 · 88 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 15 = 27, what number does ★ stand for?
6 · 15 · 27 · Symbol equation puzzles

12 questions · Seed 104741 · 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 × ★ + 15 = 30, what number does ★ stand for?
5
Subtract 15 from 30 to get 15, then divide by 3: ★ = 5.
2. If ★ represents the same whole number each time and 5 × ★ + 3 = 13, what number does ★ stand for?
2
Subtract 3 from 13 to get 10, then divide by 5: ★ = 2.
3. If ★ represents the same whole number each time and 6 × ★ + 17 = 77, what number does ★ stand for?
10
Subtract 17 from 77 to get 60, then divide by 6: ★ = 10.
4. If ★ represents the same whole number each time and 6 × ★ + 3 = 63, what number does ★ stand for?
10
Subtract 3 from 63 to get 60, then divide by 6: ★ = 10.
5. 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.
6. If ★ represents the same whole number each time and 3 × ★ + 5 = 17, what number does ★ stand for?
4
Subtract 5 from 17 to get 12, then divide by 3: ★ = 4.
7. If ★ represents the same whole number each time and 4 × ★ + 9 = 45, what number does ★ stand for?
9
Subtract 9 from 45 to get 36, then divide by 4: ★ = 9.
8. If ★ represents the same whole number each time and 2 × ★ + 18 = 30, what number does ★ stand for?
6
Subtract 18 from 30 to get 12, then divide by 2: ★ = 6.
9. If ★ represents the same whole number each time and 4 × ★ + 10 = 58, what number does ★ stand for?
12
Subtract 10 from 58 to get 48, then divide by 4: ★ = 12.
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 89, what number does ★ stand for?
12
Subtract 5 from 89 to get 84, then divide by 7: ★ = 12.
11. If ★ represents the same whole number each time and 7 × ★ + 11 = 88, what number does ★ stand for?
11
Subtract 11 from 88 to get 77, then divide by 7: ★ = 11.
12. If ★ represents the same whole number each time and 6 × ★ + 15 = 27, what number does ★ stand for?
2
Subtract 15 from 27 to get 12, then divide by 6: ★ = 2.

12 questions · Seed 104741 · 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 × ★ + 15 = 30, what number does ★ stand for?
3 · 15 · 30 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 5 × ★ + 3 = 13, what number does ★ stand for?
5 · 3 · 13 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 17 = 77, what number does ★ stand for?
6 · 17 · 77 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 3 = 63, what number does ★ stand for?
6 · 3 · 63 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 17 = 32, what number does ★ stand for?
5 · 17 · 32 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 5 = 17, what number does ★ stand for?
3 · 5 · 17 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 9 = 45, what number does ★ stand for?
4 · 9 · 45 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 18 = 30, what number does ★ stand for?
2 · 18 · 30 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 10 = 58, what number does ★ stand for?
4 · 10 · 58 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 89, what number does ★ stand for?
7 · 5 · 89 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 11 = 88, what number does ★ stand for?
7 · 11 · 88 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 15 = 27, what number does ★ stand for?
6 · 15 · 27 · Symbol equation puzzles

12 questions · Seed 104741 · 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 × ★ + 15 = 30, what number does ★ stand for?
5
Subtract 15 from 30 to get 15, then divide by 3: ★ = 5.
2. If ★ represents the same whole number each time and 5 × ★ + 3 = 13, what number does ★ stand for?
2
Subtract 3 from 13 to get 10, then divide by 5: ★ = 2.
3. If ★ represents the same whole number each time and 6 × ★ + 17 = 77, what number does ★ stand for?
10
Subtract 17 from 77 to get 60, then divide by 6: ★ = 10.
4. If ★ represents the same whole number each time and 6 × ★ + 3 = 63, what number does ★ stand for?
10
Subtract 3 from 63 to get 60, then divide by 6: ★ = 10.
5. 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.
6. If ★ represents the same whole number each time and 3 × ★ + 5 = 17, what number does ★ stand for?
4
Subtract 5 from 17 to get 12, then divide by 3: ★ = 4.
7. If ★ represents the same whole number each time and 4 × ★ + 9 = 45, what number does ★ stand for?
9
Subtract 9 from 45 to get 36, then divide by 4: ★ = 9.
8. If ★ represents the same whole number each time and 2 × ★ + 18 = 30, what number does ★ stand for?
6
Subtract 18 from 30 to get 12, then divide by 2: ★ = 6.
9. If ★ represents the same whole number each time and 4 × ★ + 10 = 58, what number does ★ stand for?
12
Subtract 10 from 58 to get 48, then divide by 4: ★ = 12.
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 89, what number does ★ stand for?
12
Subtract 5 from 89 to get 84, then divide by 7: ★ = 12.
11. If ★ represents the same whole number each time and 7 × ★ + 11 = 88, what number does ★ stand for?
11
Subtract 11 from 88 to get 77, then divide by 7: ★ = 11.
12. If ★ represents the same whole number each time and 6 × ★ + 15 = 27, what number does ★ stand for?
2
Subtract 15 from 27 to get 12, then divide by 6: ★ = 2.

12 questions · Seed 104741 · Age guidance, not curriculum certification