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 6 × ★ + 19 = 73, what number does ★ stand for?
6 · 19 · 73 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 3 = 99, what number does ★ stand for?
8 · 3 · 99 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 18 = 109, what number does ★ stand for?
7 · 18 · 109 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 8 = 36, what number does ★ stand for?
4 · 8 · 36 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 8 = 98, what number does ★ stand for?
6 · 8 · 98 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 1 = 89, what number does ★ stand for?
8 · 1 · 89 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 3 = 15, what number does ★ stand for?
4 · 3 · 15 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 22, what number does ★ stand for?
3 · 7 · 22 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 74, what number does ★ stand for?
5 · 4 · 74 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 115, what number does ★ stand for?
8 · 11 · 115 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 11 = 20, what number does ★ stand for?
3 · 11 · 20 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
5 · 19 · 89 · Symbol equation puzzles

12 questions · Seed 74 · 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 × ★ + 19 = 73, what number does ★ stand for?
9
Subtract 19 from 73 to get 54, then divide by 6: ★ = 9.
2. If ★ represents the same whole number each time and 8 × ★ + 3 = 99, what number does ★ stand for?
12
Subtract 3 from 99 to get 96, then divide by 8: ★ = 12.
3. If ★ represents the same whole number each time and 7 × ★ + 18 = 109, what number does ★ stand for?
13
Subtract 18 from 109 to get 91, then divide by 7: ★ = 13.
4. If ★ represents the same whole number each time and 4 × ★ + 8 = 36, what number does ★ stand for?
7
Subtract 8 from 36 to get 28, then divide by 4: ★ = 7.
5. If ★ represents the same whole number each time and 6 × ★ + 8 = 98, what number does ★ stand for?
15
Subtract 8 from 98 to get 90, then divide by 6: ★ = 15.
6. 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.
7. If ★ represents the same whole number each time and 4 × ★ + 3 = 15, what number does ★ stand for?
3
Subtract 3 from 15 to get 12, then divide by 4: ★ = 3.
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 22, what number does ★ stand for?
5
Subtract 7 from 22 to get 15, then divide by 3: ★ = 5.
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 74, what number does ★ stand for?
14
Subtract 4 from 74 to get 70, then divide by 5: ★ = 14.
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 115, what number does ★ stand for?
13
Subtract 11 from 115 to get 104, then divide by 8: ★ = 13.
11. If ★ represents the same whole number each time and 3 × ★ + 11 = 20, what number does ★ stand for?
3
Subtract 11 from 20 to get 9, then divide by 3: ★ = 3.
12. 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.

12 questions · Seed 74 · 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 × ★ + 19 = 73, what number does ★ stand for?
6 · 19 · 73 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 3 = 99, what number does ★ stand for?
8 · 3 · 99 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 18 = 109, what number does ★ stand for?
7 · 18 · 109 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 8 = 36, what number does ★ stand for?
4 · 8 · 36 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 8 = 98, what number does ★ stand for?
6 · 8 · 98 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 1 = 89, what number does ★ stand for?
8 · 1 · 89 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 3 = 15, what number does ★ stand for?
4 · 3 · 15 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 22, what number does ★ stand for?
3 · 7 · 22 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 74, what number does ★ stand for?
5 · 4 · 74 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 115, what number does ★ stand for?
8 · 11 · 115 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 11 = 20, what number does ★ stand for?
3 · 11 · 20 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 19 = 89, what number does ★ stand for?
5 · 19 · 89 · Symbol equation puzzles

12 questions · Seed 74 · 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 × ★ + 19 = 73, what number does ★ stand for?
9
Subtract 19 from 73 to get 54, then divide by 6: ★ = 9.
2. If ★ represents the same whole number each time and 8 × ★ + 3 = 99, what number does ★ stand for?
12
Subtract 3 from 99 to get 96, then divide by 8: ★ = 12.
3. If ★ represents the same whole number each time and 7 × ★ + 18 = 109, what number does ★ stand for?
13
Subtract 18 from 109 to get 91, then divide by 7: ★ = 13.
4. If ★ represents the same whole number each time and 4 × ★ + 8 = 36, what number does ★ stand for?
7
Subtract 8 from 36 to get 28, then divide by 4: ★ = 7.
5. If ★ represents the same whole number each time and 6 × ★ + 8 = 98, what number does ★ stand for?
15
Subtract 8 from 98 to get 90, then divide by 6: ★ = 15.
6. 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.
7. If ★ represents the same whole number each time and 4 × ★ + 3 = 15, what number does ★ stand for?
3
Subtract 3 from 15 to get 12, then divide by 4: ★ = 3.
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 22, what number does ★ stand for?
5
Subtract 7 from 22 to get 15, then divide by 3: ★ = 5.
9. If ★ represents the same whole number each time and 5 × ★ + 4 = 74, what number does ★ stand for?
14
Subtract 4 from 74 to get 70, then divide by 5: ★ = 14.
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 115, what number does ★ stand for?
13
Subtract 11 from 115 to get 104, then divide by 8: ★ = 13.
11. If ★ represents the same whole number each time and 3 × ★ + 11 = 20, what number does ★ stand for?
3
Subtract 11 from 20 to get 9, then divide by 3: ★ = 3.
12. 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.

12 questions · Seed 74 · Age guidance, not curriculum certification