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 6 × ★ + 10 = 58, what number does ★ stand for?
6 · 10 · 58 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 18 = 63, what number does ★ stand for?
3 · 18 · 63 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 1 = 29, what number does ★ stand for?
7 · 1 · 29 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 14 = 26, what number does ★ stand for?
6 · 14 · 26 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 14 = 56, what number does ★ stand for?
3 · 14 · 56 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 10 = 22, what number does ★ stand for?
3 · 10 · 22 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 17 = 89, what number does ★ stand for?
6 · 17 · 89 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 13 = 37, what number does ★ stand for?
4 · 13 · 37 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 1 = 105, what number does ★ stand for?
8 · 1 · 105 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
3 · 12 · 54 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 5 = 23, what number does ★ stand for?
3 · 5 · 23 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 8 = 20, what number does ★ stand for?
4 · 8 · 20 · Symbol equation puzzles

12 questions · Seed 44 · 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 6 × ★ + 10 = 58, what number does ★ stand for?
8
Subtract 10 from 58 to get 48, then divide by 6: ★ = 8.
2. If ★ represents the same whole number each time and 3 × ★ + 18 = 63, what number does ★ stand for?
15
Subtract 18 from 63 to get 45, then divide by 3: ★ = 15.
3. If ★ represents the same whole number each time and 7 × ★ + 1 = 29, what number does ★ stand for?
4
Subtract 1 from 29 to get 28, then divide by 7: ★ = 4.
4. If ★ represents the same whole number each time and 6 × ★ + 14 = 26, what number does ★ stand for?
2
Subtract 14 from 26 to get 12, then divide by 6: ★ = 2.
5. If ★ represents the same whole number each time and 3 × ★ + 14 = 56, what number does ★ stand for?
14
Subtract 14 from 56 to get 42, then divide by 3: ★ = 14.
6. If ★ represents the same whole number each time and 3 × ★ + 10 = 22, what number does ★ stand for?
4
Subtract 10 from 22 to get 12, then divide by 3: ★ = 4.
7. If ★ represents the same whole number each time and 6 × ★ + 17 = 89, what number does ★ stand for?
12
Subtract 17 from 89 to get 72, then divide by 6: ★ = 12.
8. If ★ represents the same whole number each time and 4 × ★ + 13 = 37, what number does ★ stand for?
6
Subtract 13 from 37 to get 24, then divide by 4: ★ = 6.
9. If ★ represents the same whole number each time and 8 × ★ + 1 = 105, what number does ★ stand for?
13
Subtract 1 from 105 to get 104, then divide by 8: ★ = 13.
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
14
Subtract 12 from 54 to get 42, then divide by 3: ★ = 14.
11. If ★ represents the same whole number each time and 3 × ★ + 5 = 23, what number does ★ stand for?
6
Subtract 5 from 23 to get 18, then divide by 3: ★ = 6.
12. If ★ represents the same whole number each time and 4 × ★ + 8 = 20, what number does ★ stand for?
3
Subtract 8 from 20 to get 12, then divide by 4: ★ = 3.

12 questions · Seed 44 · 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 6 × ★ + 10 = 58, what number does ★ stand for?
6 · 10 · 58 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 18 = 63, what number does ★ stand for?
3 · 18 · 63 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 1 = 29, what number does ★ stand for?
7 · 1 · 29 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 14 = 26, what number does ★ stand for?
6 · 14 · 26 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 14 = 56, what number does ★ stand for?
3 · 14 · 56 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 10 = 22, what number does ★ stand for?
3 · 10 · 22 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 17 = 89, what number does ★ stand for?
6 · 17 · 89 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 13 = 37, what number does ★ stand for?
4 · 13 · 37 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 1 = 105, what number does ★ stand for?
8 · 1 · 105 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
3 · 12 · 54 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 5 = 23, what number does ★ stand for?
3 · 5 · 23 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 8 = 20, what number does ★ stand for?
4 · 8 · 20 · Symbol equation puzzles

12 questions · Seed 44 · 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 6 × ★ + 10 = 58, what number does ★ stand for?
8
Subtract 10 from 58 to get 48, then divide by 6: ★ = 8.
2. If ★ represents the same whole number each time and 3 × ★ + 18 = 63, what number does ★ stand for?
15
Subtract 18 from 63 to get 45, then divide by 3: ★ = 15.
3. If ★ represents the same whole number each time and 7 × ★ + 1 = 29, what number does ★ stand for?
4
Subtract 1 from 29 to get 28, then divide by 7: ★ = 4.
4. If ★ represents the same whole number each time and 6 × ★ + 14 = 26, what number does ★ stand for?
2
Subtract 14 from 26 to get 12, then divide by 6: ★ = 2.
5. If ★ represents the same whole number each time and 3 × ★ + 14 = 56, what number does ★ stand for?
14
Subtract 14 from 56 to get 42, then divide by 3: ★ = 14.
6. If ★ represents the same whole number each time and 3 × ★ + 10 = 22, what number does ★ stand for?
4
Subtract 10 from 22 to get 12, then divide by 3: ★ = 4.
7. If ★ represents the same whole number each time and 6 × ★ + 17 = 89, what number does ★ stand for?
12
Subtract 17 from 89 to get 72, then divide by 6: ★ = 12.
8. If ★ represents the same whole number each time and 4 × ★ + 13 = 37, what number does ★ stand for?
6
Subtract 13 from 37 to get 24, then divide by 4: ★ = 6.
9. If ★ represents the same whole number each time and 8 × ★ + 1 = 105, what number does ★ stand for?
13
Subtract 1 from 105 to get 104, then divide by 8: ★ = 13.
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 54, what number does ★ stand for?
14
Subtract 12 from 54 to get 42, then divide by 3: ★ = 14.
11. If ★ represents the same whole number each time and 3 × ★ + 5 = 23, what number does ★ stand for?
6
Subtract 5 from 23 to get 18, then divide by 3: ★ = 6.
12. If ★ represents the same whole number each time and 4 × ★ + 8 = 20, what number does ★ stand for?
3
Subtract 8 from 20 to get 12, then divide by 4: ★ = 3.

12 questions · Seed 44 · Age guidance, not curriculum certification