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 5 × ★ + 19 = 64, what number does ★ stand for?
5 · 19 · 64 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 14 = 56, what number does ★ stand for?
6 · 14 · 56 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 8 = 120, what number does ★ stand for?
8 · 8 · 120 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2 · 18 · 22 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 8 = 24, what number does ★ stand for?
2 · 8 · 24 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 6 = 45, what number does ★ stand for?
3 · 6 · 45 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 17 = 94, what number does ★ stand for?
7 · 17 · 94 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 3 = 48, what number does ★ stand for?
5 · 3 · 48 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 15 = 99, what number does ★ stand for?
7 · 15 · 99 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 15 = 33, what number does ★ stand for?
3 · 15 · 33 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 1 = 89, what number does ★ stand for?
8 · 1 · 89 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
7 · 17 · 31 · Symbol equation puzzles

12 questions · Seed 83 · 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 5 × ★ + 19 = 64, what number does ★ stand for?
9
Subtract 19 from 64 to get 45, then divide by 5: ★ = 9.
2. If ★ represents the same whole number each time and 6 × ★ + 14 = 56, what number does ★ stand for?
7
Subtract 14 from 56 to get 42, then divide by 6: ★ = 7.
3. If ★ represents the same whole number each time and 8 × ★ + 8 = 120, what number does ★ stand for?
14
Subtract 8 from 120 to get 112, then divide by 8: ★ = 14.
4. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2
Subtract 18 from 22 to get 4, then divide by 2: ★ = 2.
5. If ★ represents the same whole number each time and 2 × ★ + 8 = 24, what number does ★ stand for?
8
Subtract 8 from 24 to get 16, then divide by 2: ★ = 8.
6. If ★ represents the same whole number each time and 3 × ★ + 6 = 45, what number does ★ stand for?
13
Subtract 6 from 45 to get 39, then divide by 3: ★ = 13.
7. If ★ represents the same whole number each time and 7 × ★ + 17 = 94, what number does ★ stand for?
11
Subtract 17 from 94 to get 77, then divide by 7: ★ = 11.
8. If ★ represents the same whole number each time and 5 × ★ + 3 = 48, what number does ★ stand for?
9
Subtract 3 from 48 to get 45, then divide by 5: ★ = 9.
9. If ★ represents the same whole number each time and 7 × ★ + 15 = 99, what number does ★ stand for?
12
Subtract 15 from 99 to get 84, then divide by 7: ★ = 12.
10. If ★ represents the same whole number each time and 3 × ★ + 15 = 33, what number does ★ stand for?
6
Subtract 15 from 33 to get 18, then divide by 3: ★ = 6.
11. If ★ represents the same whole number each time and 8 × ★ + 1 = 89, what number does ★ stand for?
11
Subtract 1 from 89 to get 88, then divide by 8: ★ = 11.
12. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
2
Subtract 17 from 31 to get 14, then divide by 7: ★ = 2.

12 questions · Seed 83 · 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 5 × ★ + 19 = 64, what number does ★ stand for?
5 · 19 · 64 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 14 = 56, what number does ★ stand for?
6 · 14 · 56 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 8 = 120, what number does ★ stand for?
8 · 8 · 120 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2 · 18 · 22 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 8 = 24, what number does ★ stand for?
2 · 8 · 24 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 6 = 45, what number does ★ stand for?
3 · 6 · 45 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 17 = 94, what number does ★ stand for?
7 · 17 · 94 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 3 = 48, what number does ★ stand for?
5 · 3 · 48 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 15 = 99, what number does ★ stand for?
7 · 15 · 99 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 15 = 33, what number does ★ stand for?
3 · 15 · 33 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 1 = 89, what number does ★ stand for?
8 · 1 · 89 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
7 · 17 · 31 · Symbol equation puzzles

12 questions · Seed 83 · 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 5 × ★ + 19 = 64, what number does ★ stand for?
9
Subtract 19 from 64 to get 45, then divide by 5: ★ = 9.
2. If ★ represents the same whole number each time and 6 × ★ + 14 = 56, what number does ★ stand for?
7
Subtract 14 from 56 to get 42, then divide by 6: ★ = 7.
3. If ★ represents the same whole number each time and 8 × ★ + 8 = 120, what number does ★ stand for?
14
Subtract 8 from 120 to get 112, then divide by 8: ★ = 14.
4. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2
Subtract 18 from 22 to get 4, then divide by 2: ★ = 2.
5. If ★ represents the same whole number each time and 2 × ★ + 8 = 24, what number does ★ stand for?
8
Subtract 8 from 24 to get 16, then divide by 2: ★ = 8.
6. If ★ represents the same whole number each time and 3 × ★ + 6 = 45, what number does ★ stand for?
13
Subtract 6 from 45 to get 39, then divide by 3: ★ = 13.
7. If ★ represents the same whole number each time and 7 × ★ + 17 = 94, what number does ★ stand for?
11
Subtract 17 from 94 to get 77, then divide by 7: ★ = 11.
8. If ★ represents the same whole number each time and 5 × ★ + 3 = 48, what number does ★ stand for?
9
Subtract 3 from 48 to get 45, then divide by 5: ★ = 9.
9. If ★ represents the same whole number each time and 7 × ★ + 15 = 99, what number does ★ stand for?
12
Subtract 15 from 99 to get 84, then divide by 7: ★ = 12.
10. If ★ represents the same whole number each time and 3 × ★ + 15 = 33, what number does ★ stand for?
6
Subtract 15 from 33 to get 18, then divide by 3: ★ = 6.
11. If ★ represents the same whole number each time and 8 × ★ + 1 = 89, what number does ★ stand for?
11
Subtract 1 from 89 to get 88, then divide by 8: ★ = 11.
12. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
2
Subtract 17 from 31 to get 14, then divide by 7: ★ = 2.

12 questions · Seed 83 · Age guidance, not curriculum certification