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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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 × ★ + 11 = 23, what number does ★ stand for?
2 · 11 · 23 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 15 = 78, what number does ★ stand for?
7 · 15 · 78 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 8 = 44, what number does ★ stand for?
4 · 8 · 44 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 20 = 92, what number does ★ stand for?
8 · 20 · 92 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 4 = 13, what number does ★ stand for?
3 · 4 · 13 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 11 = 32, what number does ★ stand for?
3 · 11 · 32 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 7 = 29, what number does ★ stand for?
2 · 7 · 29 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 19 = 123, what number does ★ stand for?
8 · 19 · 123 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 36, what number does ★ stand for?
4 · 16 · 36 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 3 = 75, what number does ★ stand for?
8 · 3 · 75 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 20 = 28, what number does ★ stand for?
4 · 20 · 28 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 10 = 85, what number does ★ stand for?
5 · 10 · 85 · Symbol equation puzzles

12 questions · Seed 80 · 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 × ★ + 11 = 23, what number does ★ stand for?
6
Subtract 11 from 23 to get 12, then divide by 2: ★ = 6.
2. If ★ represents the same whole number each time and 7 × ★ + 15 = 78, what number does ★ stand for?
9
Subtract 15 from 78 to get 63, then divide by 7: ★ = 9.
3. If ★ represents the same whole number each time and 4 × ★ + 8 = 44, what number does ★ stand for?
9
Subtract 8 from 44 to get 36, then divide by 4: ★ = 9.
4. If ★ represents the same whole number each time and 8 × ★ + 20 = 92, what number does ★ stand for?
9
Subtract 20 from 92 to get 72, then divide by 8: ★ = 9.
5. If ★ represents the same whole number each time and 3 × ★ + 4 = 13, what number does ★ stand for?
3
Subtract 4 from 13 to get 9, then divide by 3: ★ = 3.
6. If ★ represents the same whole number each time and 3 × ★ + 11 = 32, what number does ★ stand for?
7
Subtract 11 from 32 to get 21, then divide by 3: ★ = 7.
7. If ★ represents the same whole number each time and 2 × ★ + 7 = 29, what number does ★ stand for?
11
Subtract 7 from 29 to get 22, then divide by 2: ★ = 11.
8. If ★ represents the same whole number each time and 8 × ★ + 19 = 123, what number does ★ stand for?
13
Subtract 19 from 123 to get 104, then divide by 8: ★ = 13.
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 36, what number does ★ stand for?
5
Subtract 16 from 36 to get 20, then divide by 4: ★ = 5.
10. If ★ represents the same whole number each time and 8 × ★ + 3 = 75, what number does ★ stand for?
9
Subtract 3 from 75 to get 72, then divide by 8: ★ = 9.
11. If ★ represents the same whole number each time and 4 × ★ + 20 = 28, what number does ★ stand for?
2
Subtract 20 from 28 to get 8, then divide by 4: ★ = 2.
12. If ★ represents the same whole number each time and 5 × ★ + 10 = 85, what number does ★ stand for?
15
Subtract 10 from 85 to get 75, then divide by 5: ★ = 15.

12 questions · Seed 80 · 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 × ★ + 11 = 23, what number does ★ stand for?
2 · 11 · 23 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 15 = 78, what number does ★ stand for?
7 · 15 · 78 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 8 = 44, what number does ★ stand for?
4 · 8 · 44 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 20 = 92, what number does ★ stand for?
8 · 20 · 92 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 4 = 13, what number does ★ stand for?
3 · 4 · 13 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 11 = 32, what number does ★ stand for?
3 · 11 · 32 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 7 = 29, what number does ★ stand for?
2 · 7 · 29 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 19 = 123, what number does ★ stand for?
8 · 19 · 123 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 36, what number does ★ stand for?
4 · 16 · 36 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 3 = 75, what number does ★ stand for?
8 · 3 · 75 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 20 = 28, what number does ★ stand for?
4 · 20 · 28 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 10 = 85, what number does ★ stand for?
5 · 10 · 85 · Symbol equation puzzles

12 questions · Seed 80 · 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 × ★ + 11 = 23, what number does ★ stand for?
6
Subtract 11 from 23 to get 12, then divide by 2: ★ = 6.
2. If ★ represents the same whole number each time and 7 × ★ + 15 = 78, what number does ★ stand for?
9
Subtract 15 from 78 to get 63, then divide by 7: ★ = 9.
3. If ★ represents the same whole number each time and 4 × ★ + 8 = 44, what number does ★ stand for?
9
Subtract 8 from 44 to get 36, then divide by 4: ★ = 9.
4. If ★ represents the same whole number each time and 8 × ★ + 20 = 92, what number does ★ stand for?
9
Subtract 20 from 92 to get 72, then divide by 8: ★ = 9.
5. If ★ represents the same whole number each time and 3 × ★ + 4 = 13, what number does ★ stand for?
3
Subtract 4 from 13 to get 9, then divide by 3: ★ = 3.
6. If ★ represents the same whole number each time and 3 × ★ + 11 = 32, what number does ★ stand for?
7
Subtract 11 from 32 to get 21, then divide by 3: ★ = 7.
7. If ★ represents the same whole number each time and 2 × ★ + 7 = 29, what number does ★ stand for?
11
Subtract 7 from 29 to get 22, then divide by 2: ★ = 11.
8. If ★ represents the same whole number each time and 8 × ★ + 19 = 123, what number does ★ stand for?
13
Subtract 19 from 123 to get 104, then divide by 8: ★ = 13.
9. If ★ represents the same whole number each time and 4 × ★ + 16 = 36, what number does ★ stand for?
5
Subtract 16 from 36 to get 20, then divide by 4: ★ = 5.
10. If ★ represents the same whole number each time and 8 × ★ + 3 = 75, what number does ★ stand for?
9
Subtract 3 from 75 to get 72, then divide by 8: ★ = 9.
11. If ★ represents the same whole number each time and 4 × ★ + 20 = 28, what number does ★ stand for?
2
Subtract 20 from 28 to get 8, then divide by 4: ★ = 2.
12. If ★ represents the same whole number each time and 5 × ★ + 10 = 85, what number does ★ stand for?
15
Subtract 10 from 85 to get 75, then divide by 5: ★ = 15.

12 questions · Seed 80 · Age guidance, not curriculum certification