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 5 × ★ + 11 = 41, what number does ★ stand for?
5 · 11 · 41 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7 · 9 · 58 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 88, what number does ★ stand for?
7 · 4 · 88 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 13 = 93, what number does ★ stand for?
8 · 13 · 93 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 19 = 61, what number does ★ stand for?
3 · 19 · 61 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 8 = 16, what number does ★ stand for?
2 · 8 · 16 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 14 = 42, what number does ★ stand for?
2 · 14 · 42 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 18 = 82, what number does ★ stand for?
8 · 18 · 82 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 15 = 87, what number does ★ stand for?
8 · 15 · 87 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 2 = 14, what number does ★ stand for?
2 · 2 · 14 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 19 = 82, what number does ★ stand for?
7 · 19 · 82 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 17 = 47, what number does ★ stand for?
3 · 17 · 47 · Symbol equation puzzles

12 questions · Seed 54 · 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 × ★ + 11 = 41, what number does ★ stand for?
6
Subtract 11 from 41 to get 30, then divide by 5: ★ = 6.
2. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7
Subtract 9 from 58 to get 49, then divide by 7: ★ = 7.
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 88, what number does ★ stand for?
12
Subtract 4 from 88 to get 84, then divide by 7: ★ = 12.
4. If ★ represents the same whole number each time and 8 × ★ + 13 = 93, what number does ★ stand for?
10
Subtract 13 from 93 to get 80, then divide by 8: ★ = 10.
5. If ★ represents the same whole number each time and 3 × ★ + 19 = 61, what number does ★ stand for?
14
Subtract 19 from 61 to get 42, then divide by 3: ★ = 14.
6. If ★ represents the same whole number each time and 2 × ★ + 8 = 16, what number does ★ stand for?
4
Subtract 8 from 16 to get 8, then divide by 2: ★ = 4.
7. If ★ represents the same whole number each time and 2 × ★ + 14 = 42, what number does ★ stand for?
14
Subtract 14 from 42 to get 28, then divide by 2: ★ = 14.
8. If ★ represents the same whole number each time and 8 × ★ + 18 = 82, what number does ★ stand for?
8
Subtract 18 from 82 to get 64, then divide by 8: ★ = 8.
9. If ★ represents the same whole number each time and 8 × ★ + 15 = 87, what number does ★ stand for?
9
Subtract 15 from 87 to get 72, then divide by 8: ★ = 9.
10. If ★ represents the same whole number each time and 2 × ★ + 2 = 14, what number does ★ stand for?
6
Subtract 2 from 14 to get 12, then divide by 2: ★ = 6.
11. If ★ represents the same whole number each time and 7 × ★ + 19 = 82, what number does ★ stand for?
9
Subtract 19 from 82 to get 63, then divide by 7: ★ = 9.
12. If ★ represents the same whole number each time and 3 × ★ + 17 = 47, what number does ★ stand for?
10
Subtract 17 from 47 to get 30, then divide by 3: ★ = 10.

12 questions · Seed 54 · 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 × ★ + 11 = 41, what number does ★ stand for?
5 · 11 · 41 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7 · 9 · 58 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 88, what number does ★ stand for?
7 · 4 · 88 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 13 = 93, what number does ★ stand for?
8 · 13 · 93 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 19 = 61, what number does ★ stand for?
3 · 19 · 61 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 8 = 16, what number does ★ stand for?
2 · 8 · 16 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 14 = 42, what number does ★ stand for?
2 · 14 · 42 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 18 = 82, what number does ★ stand for?
8 · 18 · 82 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 15 = 87, what number does ★ stand for?
8 · 15 · 87 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 2 = 14, what number does ★ stand for?
2 · 2 · 14 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 19 = 82, what number does ★ stand for?
7 · 19 · 82 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 17 = 47, what number does ★ stand for?
3 · 17 · 47 · Symbol equation puzzles

12 questions · Seed 54 · 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 × ★ + 11 = 41, what number does ★ stand for?
6
Subtract 11 from 41 to get 30, then divide by 5: ★ = 6.
2. If ★ represents the same whole number each time and 7 × ★ + 9 = 58, what number does ★ stand for?
7
Subtract 9 from 58 to get 49, then divide by 7: ★ = 7.
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 88, what number does ★ stand for?
12
Subtract 4 from 88 to get 84, then divide by 7: ★ = 12.
4. If ★ represents the same whole number each time and 8 × ★ + 13 = 93, what number does ★ stand for?
10
Subtract 13 from 93 to get 80, then divide by 8: ★ = 10.
5. If ★ represents the same whole number each time and 3 × ★ + 19 = 61, what number does ★ stand for?
14
Subtract 19 from 61 to get 42, then divide by 3: ★ = 14.
6. If ★ represents the same whole number each time and 2 × ★ + 8 = 16, what number does ★ stand for?
4
Subtract 8 from 16 to get 8, then divide by 2: ★ = 4.
7. If ★ represents the same whole number each time and 2 × ★ + 14 = 42, what number does ★ stand for?
14
Subtract 14 from 42 to get 28, then divide by 2: ★ = 14.
8. If ★ represents the same whole number each time and 8 × ★ + 18 = 82, what number does ★ stand for?
8
Subtract 18 from 82 to get 64, then divide by 8: ★ = 8.
9. If ★ represents the same whole number each time and 8 × ★ + 15 = 87, what number does ★ stand for?
9
Subtract 15 from 87 to get 72, then divide by 8: ★ = 9.
10. If ★ represents the same whole number each time and 2 × ★ + 2 = 14, what number does ★ stand for?
6
Subtract 2 from 14 to get 12, then divide by 2: ★ = 6.
11. If ★ represents the same whole number each time and 7 × ★ + 19 = 82, what number does ★ stand for?
9
Subtract 19 from 82 to get 63, then divide by 7: ★ = 9.
12. If ★ represents the same whole number each time and 3 × ★ + 17 = 47, what number does ★ stand for?
10
Subtract 17 from 47 to get 30, then divide by 3: ★ = 10.

12 questions · Seed 54 · Age guidance, not curriculum certification