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 4 × ★ + 9 = 45, what number does ★ stand for?
4 · 9 · 45 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 12 = 52, what number does ★ stand for?
4 · 12 · 52 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 16 = 32, what number does ★ stand for?
4 · 16 · 32 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 18 = 102, what number does ★ stand for?
7 · 18 · 102 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 5 = 80, what number does ★ stand for?
5 · 5 · 80 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 10 = 37, what number does ★ stand for?
3 · 10 · 37 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 6 = 70, what number does ★ stand for?
8 · 6 · 70 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7 · 9 · 58 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 15 = 69, what number does ★ stand for?
6 · 15 · 69 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 16 = 40, what number does ★ stand for?
4 · 16 · 40 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 4 = 36, what number does ★ stand for?
8 · 4 · 36 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 1 = 5, what number does ★ stand for?
2 · 1 · 5 · Symbol equation puzzles

12 questions · Seed 104733 · 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 4 × ★ + 9 = 45, what number does ★ stand for?
9
Subtract 9 from 45 to get 36, then divide by 4: ★ = 9.
2. If ★ represents the same whole number each time and 4 × ★ + 12 = 52, what number does ★ stand for?
10
Subtract 12 from 52 to get 40, then divide by 4: ★ = 10.
3. If ★ represents the same whole number each time and 4 × ★ + 16 = 32, what number does ★ stand for?
4
Subtract 16 from 32 to get 16, then divide by 4: ★ = 4.
4. If ★ represents the same whole number each time and 7 × ★ + 18 = 102, what number does ★ stand for?
12
Subtract 18 from 102 to get 84, then divide by 7: ★ = 12.
5. If ★ represents the same whole number each time and 5 × ★ + 5 = 80, what number does ★ stand for?
15
Subtract 5 from 80 to get 75, then divide by 5: ★ = 15.
6. If ★ represents the same whole number each time and 3 × ★ + 10 = 37, what number does ★ stand for?
9
Subtract 10 from 37 to get 27, then divide by 3: ★ = 9.
7. If ★ represents the same whole number each time and 8 × ★ + 6 = 70, what number does ★ stand for?
8
Subtract 6 from 70 to get 64, then divide by 8: ★ = 8.
8. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7
Subtract 9 from 58 to get 49, then divide by 7: ★ = 7.
9. If ★ represents the same whole number each time and 6 × ★ + 15 = 69, what number does ★ stand for?
9
Subtract 15 from 69 to get 54, then divide by 6: ★ = 9.
10. If ★ represents the same whole number each time and 4 × ★ + 16 = 40, what number does ★ stand for?
6
Subtract 16 from 40 to get 24, then divide by 4: ★ = 6.
11. If ★ represents the same whole number each time and 8 × ★ + 4 = 36, what number does ★ stand for?
4
Subtract 4 from 36 to get 32, then divide by 8: ★ = 4.
12. If ★ represents the same whole number each time and 2 × ★ + 1 = 5, what number does ★ stand for?
2
Subtract 1 from 5 to get 4, then divide by 2: ★ = 2.

12 questions · Seed 104733 · 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 4 × ★ + 9 = 45, what number does ★ stand for?
4 · 9 · 45 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 12 = 52, what number does ★ stand for?
4 · 12 · 52 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 16 = 32, what number does ★ stand for?
4 · 16 · 32 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 18 = 102, what number does ★ stand for?
7 · 18 · 102 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 5 = 80, what number does ★ stand for?
5 · 5 · 80 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 10 = 37, what number does ★ stand for?
3 · 10 · 37 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 6 = 70, what number does ★ stand for?
8 · 6 · 70 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7 · 9 · 58 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 15 = 69, what number does ★ stand for?
6 · 15 · 69 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 16 = 40, what number does ★ stand for?
4 · 16 · 40 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 4 = 36, what number does ★ stand for?
8 · 4 · 36 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 1 = 5, what number does ★ stand for?
2 · 1 · 5 · Symbol equation puzzles

12 questions · Seed 104733 · 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 4 × ★ + 9 = 45, what number does ★ stand for?
9
Subtract 9 from 45 to get 36, then divide by 4: ★ = 9.
2. If ★ represents the same whole number each time and 4 × ★ + 12 = 52, what number does ★ stand for?
10
Subtract 12 from 52 to get 40, then divide by 4: ★ = 10.
3. If ★ represents the same whole number each time and 4 × ★ + 16 = 32, what number does ★ stand for?
4
Subtract 16 from 32 to get 16, then divide by 4: ★ = 4.
4. If ★ represents the same whole number each time and 7 × ★ + 18 = 102, what number does ★ stand for?
12
Subtract 18 from 102 to get 84, then divide by 7: ★ = 12.
5. If ★ represents the same whole number each time and 5 × ★ + 5 = 80, what number does ★ stand for?
15
Subtract 5 from 80 to get 75, then divide by 5: ★ = 15.
6. If ★ represents the same whole number each time and 3 × ★ + 10 = 37, what number does ★ stand for?
9
Subtract 10 from 37 to get 27, then divide by 3: ★ = 9.
7. If ★ represents the same whole number each time and 8 × ★ + 6 = 70, what number does ★ stand for?
8
Subtract 6 from 70 to get 64, then divide by 8: ★ = 8.
8. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7
Subtract 9 from 58 to get 49, then divide by 7: ★ = 7.
9. If ★ represents the same whole number each time and 6 × ★ + 15 = 69, what number does ★ stand for?
9
Subtract 15 from 69 to get 54, then divide by 6: ★ = 9.
10. If ★ represents the same whole number each time and 4 × ★ + 16 = 40, what number does ★ stand for?
6
Subtract 16 from 40 to get 24, then divide by 4: ★ = 6.
11. If ★ represents the same whole number each time and 8 × ★ + 4 = 36, what number does ★ stand for?
4
Subtract 4 from 36 to get 32, then divide by 8: ★ = 4.
12. If ★ represents the same whole number each time and 2 × ★ + 1 = 5, what number does ★ stand for?
2
Subtract 1 from 5 to get 4, then divide by 2: ★ = 2.

12 questions · Seed 104733 · Age guidance, not curriculum certification