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 7 × ★ + 13 = 90, what number does ★ stand for?
7 · 13 · 90 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 5 = 41, what number does ★ stand for?
6 · 5 · 41 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
5 · 19 · 89 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 9 = 86, what number does ★ stand for?
7 · 9 · 86 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 56, what number does ★ stand for?
8 · 16 · 56 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 13 = 28, what number does ★ stand for?
3 · 13 · 28 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 4 = 20, what number does ★ stand for?
8 · 4 · 20 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 15 = 70, what number does ★ stand for?
5 · 15 · 70 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 12 = 103, what number does ★ stand for?
7 · 12 · 103 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 10 = 82, what number does ★ stand for?
8 · 10 · 82 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 4 = 49, what number does ★ stand for?
5 · 4 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 15 = 43, what number does ★ stand for?
7 · 15 · 43 · Symbol equation puzzles

12 questions · Seed 81 · 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 7 × ★ + 13 = 90, what number does ★ stand for?
11
Subtract 13 from 90 to get 77, then divide by 7: ★ = 11.
2. If ★ represents the same whole number each time and 6 × ★ + 5 = 41, what number does ★ stand for?
6
Subtract 5 from 41 to get 36, then divide by 6: ★ = 6.
3. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
14
Subtract 19 from 89 to get 70, then divide by 5: ★ = 14.
4. If ★ represents the same whole number each time and 7 × ★ + 9 = 86, what number does ★ stand for?
11
Subtract 9 from 86 to get 77, then divide by 7: ★ = 11.
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 56, what number does ★ stand for?
5
Subtract 16 from 56 to get 40, then divide by 8: ★ = 5.
6. If ★ represents the same whole number each time and 3 × ★ + 13 = 28, what number does ★ stand for?
5
Subtract 13 from 28 to get 15, then divide by 3: ★ = 5.
7. If ★ represents the same whole number each time and 8 × ★ + 4 = 20, what number does ★ stand for?
2
Subtract 4 from 20 to get 16, then divide by 8: ★ = 2.
8. If ★ represents the same whole number each time and 5 × ★ + 15 = 70, what number does ★ stand for?
11
Subtract 15 from 70 to get 55, then divide by 5: ★ = 11.
9. If ★ represents the same whole number each time and 7 × ★ + 12 = 103, what number does ★ stand for?
13
Subtract 12 from 103 to get 91, then divide by 7: ★ = 13.
10. If ★ represents the same whole number each time and 8 × ★ + 10 = 82, what number does ★ stand for?
9
Subtract 10 from 82 to get 72, then divide by 8: ★ = 9.
11. If ★ represents the same whole number each time and 5 × ★ + 4 = 49, what number does ★ stand for?
9
Subtract 4 from 49 to get 45, then divide by 5: ★ = 9.
12. If ★ represents the same whole number each time and 7 × ★ + 15 = 43, what number does ★ stand for?
4
Subtract 15 from 43 to get 28, then divide by 7: ★ = 4.

12 questions · Seed 81 · 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 7 × ★ + 13 = 90, what number does ★ stand for?
7 · 13 · 90 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 5 = 41, what number does ★ stand for?
6 · 5 · 41 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
5 · 19 · 89 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 9 = 86, what number does ★ stand for?
7 · 9 · 86 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 56, what number does ★ stand for?
8 · 16 · 56 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 13 = 28, what number does ★ stand for?
3 · 13 · 28 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 4 = 20, what number does ★ stand for?
8 · 4 · 20 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 15 = 70, what number does ★ stand for?
5 · 15 · 70 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 12 = 103, what number does ★ stand for?
7 · 12 · 103 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 10 = 82, what number does ★ stand for?
8 · 10 · 82 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 4 = 49, what number does ★ stand for?
5 · 4 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 15 = 43, what number does ★ stand for?
7 · 15 · 43 · Symbol equation puzzles

12 questions · Seed 81 · 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 7 × ★ + 13 = 90, what number does ★ stand for?
11
Subtract 13 from 90 to get 77, then divide by 7: ★ = 11.
2. If ★ represents the same whole number each time and 6 × ★ + 5 = 41, what number does ★ stand for?
6
Subtract 5 from 41 to get 36, then divide by 6: ★ = 6.
3. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
14
Subtract 19 from 89 to get 70, then divide by 5: ★ = 14.
4. If ★ represents the same whole number each time and 7 × ★ + 9 = 86, what number does ★ stand for?
11
Subtract 9 from 86 to get 77, then divide by 7: ★ = 11.
5. If ★ represents the same whole number each time and 8 × ★ + 16 = 56, what number does ★ stand for?
5
Subtract 16 from 56 to get 40, then divide by 8: ★ = 5.
6. If ★ represents the same whole number each time and 3 × ★ + 13 = 28, what number does ★ stand for?
5
Subtract 13 from 28 to get 15, then divide by 3: ★ = 5.
7. If ★ represents the same whole number each time and 8 × ★ + 4 = 20, what number does ★ stand for?
2
Subtract 4 from 20 to get 16, then divide by 8: ★ = 2.
8. If ★ represents the same whole number each time and 5 × ★ + 15 = 70, what number does ★ stand for?
11
Subtract 15 from 70 to get 55, then divide by 5: ★ = 11.
9. If ★ represents the same whole number each time and 7 × ★ + 12 = 103, what number does ★ stand for?
13
Subtract 12 from 103 to get 91, then divide by 7: ★ = 13.
10. If ★ represents the same whole number each time and 8 × ★ + 10 = 82, what number does ★ stand for?
9
Subtract 10 from 82 to get 72, then divide by 8: ★ = 9.
11. If ★ represents the same whole number each time and 5 × ★ + 4 = 49, what number does ★ stand for?
9
Subtract 4 from 49 to get 45, then divide by 5: ★ = 9.
12. If ★ represents the same whole number each time and 7 × ★ + 15 = 43, what number does ★ stand for?
4
Subtract 15 from 43 to get 28, then divide by 7: ★ = 4.

12 questions · Seed 81 · Age guidance, not curriculum certification