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 8 × ★ + 16 = 136, what number does ★ stand for?
8 · 16 · 136 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 19 = 75, what number does ★ stand for?
7 · 19 · 75 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 7 = 31, what number does ★ stand for?
2 · 7 · 31 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 18 = 57, what number does ★ stand for?
3 · 18 · 57 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 20 = 125, what number does ★ stand for?
7 · 20 · 125 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 6 = 51, what number does ★ stand for?
3 · 6 · 51 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 19 = 79, what number does ★ stand for?
5 · 19 · 79 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 15 = 50, what number does ★ stand for?
5 · 15 · 50 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 18 = 32, what number does ★ stand for?
7 · 18 · 32 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 8 = 26, what number does ★ stand for?
3 · 8 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
7 · 17 · 31 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 51, what number does ★ stand for?
8 · 19 · 51 · Symbol equation puzzles

12 questions · Seed 57 · 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 8 × ★ + 16 = 136, what number does ★ stand for?
15
Subtract 16 from 136 to get 120, then divide by 8: ★ = 15.
2. If ★ represents the same whole number each time and 7 × ★ + 19 = 75, what number does ★ stand for?
8
Subtract 19 from 75 to get 56, then divide by 7: ★ = 8.
3. If ★ represents the same whole number each time and 2 × ★ + 7 = 31, what number does ★ stand for?
12
Subtract 7 from 31 to get 24, then divide by 2: ★ = 12.
4. If ★ represents the same whole number each time and 3 × ★ + 18 = 57, what number does ★ stand for?
13
Subtract 18 from 57 to get 39, then divide by 3: ★ = 13.
5. If ★ represents the same whole number each time and 7 × ★ + 20 = 125, what number does ★ stand for?
15
Subtract 20 from 125 to get 105, then divide by 7: ★ = 15.
6. If ★ represents the same whole number each time and 3 × ★ + 6 = 51, what number does ★ stand for?
15
Subtract 6 from 51 to get 45, then divide by 3: ★ = 15.
7. If ★ represents the same whole number each time and 5 × ★ + 19 = 79, what number does ★ stand for?
12
Subtract 19 from 79 to get 60, then divide by 5: ★ = 12.
8. If ★ represents the same whole number each time and 5 × ★ + 15 = 50, what number does ★ stand for?
7
Subtract 15 from 50 to get 35, then divide by 5: ★ = 7.
9. If ★ represents the same whole number each time and 7 × ★ + 18 = 32, what number does ★ stand for?
2
Subtract 18 from 32 to get 14, then divide by 7: ★ = 2.
10. If ★ represents the same whole number each time and 3 × ★ + 8 = 26, what number does ★ stand for?
6
Subtract 8 from 26 to get 18, then divide by 3: ★ = 6.
11. 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. If ★ represents the same whole number each time and 8 × ★ + 19 = 51, what number does ★ stand for?
4
Subtract 19 from 51 to get 32, then divide by 8: ★ = 4.

12 questions · Seed 57 · 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 8 × ★ + 16 = 136, what number does ★ stand for?
8 · 16 · 136 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 19 = 75, what number does ★ stand for?
7 · 19 · 75 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 7 = 31, what number does ★ stand for?
2 · 7 · 31 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 18 = 57, what number does ★ stand for?
3 · 18 · 57 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 20 = 125, what number does ★ stand for?
7 · 20 · 125 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 6 = 51, what number does ★ stand for?
3 · 6 · 51 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 19 = 79, what number does ★ stand for?
5 · 19 · 79 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 15 = 50, what number does ★ stand for?
5 · 15 · 50 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 18 = 32, what number does ★ stand for?
7 · 18 · 32 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 8 = 26, what number does ★ stand for?
3 · 8 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
7 · 17 · 31 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 51, what number does ★ stand for?
8 · 19 · 51 · Symbol equation puzzles

12 questions · Seed 57 · 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 8 × ★ + 16 = 136, what number does ★ stand for?
15
Subtract 16 from 136 to get 120, then divide by 8: ★ = 15.
2. If ★ represents the same whole number each time and 7 × ★ + 19 = 75, what number does ★ stand for?
8
Subtract 19 from 75 to get 56, then divide by 7: ★ = 8.
3. If ★ represents the same whole number each time and 2 × ★ + 7 = 31, what number does ★ stand for?
12
Subtract 7 from 31 to get 24, then divide by 2: ★ = 12.
4. If ★ represents the same whole number each time and 3 × ★ + 18 = 57, what number does ★ stand for?
13
Subtract 18 from 57 to get 39, then divide by 3: ★ = 13.
5. If ★ represents the same whole number each time and 7 × ★ + 20 = 125, what number does ★ stand for?
15
Subtract 20 from 125 to get 105, then divide by 7: ★ = 15.
6. If ★ represents the same whole number each time and 3 × ★ + 6 = 51, what number does ★ stand for?
15
Subtract 6 from 51 to get 45, then divide by 3: ★ = 15.
7. If ★ represents the same whole number each time and 5 × ★ + 19 = 79, what number does ★ stand for?
12
Subtract 19 from 79 to get 60, then divide by 5: ★ = 12.
8. If ★ represents the same whole number each time and 5 × ★ + 15 = 50, what number does ★ stand for?
7
Subtract 15 from 50 to get 35, then divide by 5: ★ = 7.
9. If ★ represents the same whole number each time and 7 × ★ + 18 = 32, what number does ★ stand for?
2
Subtract 18 from 32 to get 14, then divide by 7: ★ = 2.
10. If ★ represents the same whole number each time and 3 × ★ + 8 = 26, what number does ★ stand for?
6
Subtract 8 from 26 to get 18, then divide by 3: ★ = 6.
11. 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. If ★ represents the same whole number each time and 8 × ★ + 19 = 51, what number does ★ stand for?
4
Subtract 19 from 51 to get 32, then divide by 8: ★ = 4.

12 questions · Seed 57 · Age guidance, not curriculum certification