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 × ★ + 18 = 36, what number does ★ stand for?
3 · 18 · 36 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 30, what number does ★ stand for?
2 · 12 · 30 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 6 = 14, what number does ★ stand for?
4 · 6 · 14 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 5 = 54, what number does ★ stand for?
7 · 5 · 54 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 21, what number does ★ stand for?
2 · 11 · 21 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 4 × ★ + 3 = 19, what number does ★ stand for?
4 · 3 · 19 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 16 = 81, what number does ★ stand for?
5 · 16 · 81 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 11 = 26, what number does ★ stand for?
3 · 11 · 26 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 29, what number does ★ stand for?
5 · 4 · 29 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 18 = 42, what number does ★ stand for?
8 · 18 · 42 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 8 = 41, what number does ★ stand for?
3 · 8 · 41 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 12 = 40, what number does ★ stand for?
4 · 12 · 40 · Symbol equation puzzles

12 questions · Seed 52 · 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 × ★ + 18 = 36, what number does ★ stand for?
6
Subtract 18 from 36 to get 18, then divide by 3: ★ = 6.
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 30, what number does ★ stand for?
9
Subtract 12 from 30 to get 18, then divide by 2: ★ = 9.
3. If ★ represents the same whole number each time and 4 × ★ + 6 = 14, what number does ★ stand for?
2
Subtract 6 from 14 to get 8, then divide by 4: ★ = 2.
4. If ★ represents the same whole number each time and 7 × ★ + 5 = 54, what number does ★ stand for?
7
Subtract 5 from 54 to get 49, then divide by 7: ★ = 7.
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 21, what number does ★ stand for?
5
Subtract 11 from 21 to get 10, then divide by 2: ★ = 5.
6. If ★ represents the same whole number each time and 4 × ★ + 3 = 19, what number does ★ stand for?
4
Subtract 3 from 19 to get 16, then divide by 4: ★ = 4.
7. If ★ represents the same whole number each time and 5 × ★ + 16 = 81, what number does ★ stand for?
13
Subtract 16 from 81 to get 65, then divide by 5: ★ = 13.
8. If ★ represents the same whole number each time and 3 × ★ + 11 = 26, what number does ★ stand for?
5
Subtract 11 from 26 to get 15, then divide by 3: ★ = 5.
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 29, what number does ★ stand for?
5
Subtract 4 from 29 to get 25, then divide by 5: ★ = 5.
10. If ★ represents the same whole number each time and 8 × ★ + 18 = 42, what number does ★ stand for?
3
Subtract 18 from 42 to get 24, then divide by 8: ★ = 3.
11. If ★ represents the same whole number each time and 3 × ★ + 8 = 41, what number does ★ stand for?
11
Subtract 8 from 41 to get 33, then divide by 3: ★ = 11.
12. If ★ represents the same whole number each time and 4 × ★ + 12 = 40, what number does ★ stand for?
7
Subtract 12 from 40 to get 28, then divide by 4: ★ = 7.

12 questions · Seed 52 · 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 × ★ + 18 = 36, what number does ★ stand for?
3 · 18 · 36 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 30, what number does ★ stand for?
2 · 12 · 30 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 6 = 14, what number does ★ stand for?
4 · 6 · 14 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 5 = 54, what number does ★ stand for?
7 · 5 · 54 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 21, what number does ★ stand for?
2 · 11 · 21 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 4 × ★ + 3 = 19, what number does ★ stand for?
4 · 3 · 19 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 16 = 81, what number does ★ stand for?
5 · 16 · 81 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 11 = 26, what number does ★ stand for?
3 · 11 · 26 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 29, what number does ★ stand for?
5 · 4 · 29 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 18 = 42, what number does ★ stand for?
8 · 18 · 42 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 8 = 41, what number does ★ stand for?
3 · 8 · 41 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 12 = 40, what number does ★ stand for?
4 · 12 · 40 · Symbol equation puzzles

12 questions · Seed 52 · 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 × ★ + 18 = 36, what number does ★ stand for?
6
Subtract 18 from 36 to get 18, then divide by 3: ★ = 6.
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 30, what number does ★ stand for?
9
Subtract 12 from 30 to get 18, then divide by 2: ★ = 9.
3. If ★ represents the same whole number each time and 4 × ★ + 6 = 14, what number does ★ stand for?
2
Subtract 6 from 14 to get 8, then divide by 4: ★ = 2.
4. If ★ represents the same whole number each time and 7 × ★ + 5 = 54, what number does ★ stand for?
7
Subtract 5 from 54 to get 49, then divide by 7: ★ = 7.
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 21, what number does ★ stand for?
5
Subtract 11 from 21 to get 10, then divide by 2: ★ = 5.
6. If ★ represents the same whole number each time and 4 × ★ + 3 = 19, what number does ★ stand for?
4
Subtract 3 from 19 to get 16, then divide by 4: ★ = 4.
7. If ★ represents the same whole number each time and 5 × ★ + 16 = 81, what number does ★ stand for?
13
Subtract 16 from 81 to get 65, then divide by 5: ★ = 13.
8. If ★ represents the same whole number each time and 3 × ★ + 11 = 26, what number does ★ stand for?
5
Subtract 11 from 26 to get 15, then divide by 3: ★ = 5.
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 29, what number does ★ stand for?
5
Subtract 4 from 29 to get 25, then divide by 5: ★ = 5.
10. If ★ represents the same whole number each time and 8 × ★ + 18 = 42, what number does ★ stand for?
3
Subtract 18 from 42 to get 24, then divide by 8: ★ = 3.
11. If ★ represents the same whole number each time and 3 × ★ + 8 = 41, what number does ★ stand for?
11
Subtract 8 from 41 to get 33, then divide by 3: ★ = 11.
12. If ★ represents the same whole number each time and 4 × ★ + 12 = 40, what number does ★ stand for?
7
Subtract 12 from 40 to get 28, then divide by 4: ★ = 7.

12 questions · Seed 52 · Age guidance, not curriculum certification