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 2 × ★ + 15 = 21, what number does ★ stand for?
2 · 15 · 21 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 19 = 75, what number does ★ stand for?
8 · 19 · 75 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 17 = 41, what number does ★ stand for?
8 · 17 · 41 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 16 = 31, what number does ★ stand for?
3 · 16 · 31 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 7 = 31, what number does ★ stand for?
3 · 7 · 31 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 11 = 35, what number does ★ stand for?
3 · 11 · 35 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
8 · 20 · 44 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 12 = 48, what number does ★ stand for?
4 · 12 · 48 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 29, what number does ★ stand for?
5 · 19 · 29 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 20 = 50, what number does ★ stand for?
5 · 20 · 50 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 15 = 55, what number does ★ stand for?
8 · 15 · 55 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 8 = 26, what number does ★ stand for?
3 · 8 · 26 · Symbol equation puzzles

12 questions · Seed 76 · 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 2 × ★ + 15 = 21, what number does ★ stand for?
3
Subtract 15 from 21 to get 6, then divide by 2: ★ = 3.
2. If ★ represents the same whole number each time and 8 × ★ + 19 = 75, what number does ★ stand for?
7
Subtract 19 from 75 to get 56, then divide by 8: ★ = 7.
3. If ★ represents the same whole number each time and 8 × ★ + 17 = 41, what number does ★ stand for?
3
Subtract 17 from 41 to get 24, then divide by 8: ★ = 3.
4. If ★ represents the same whole number each time and 3 × ★ + 16 = 31, what number does ★ stand for?
5
Subtract 16 from 31 to get 15, then divide by 3: ★ = 5.
5. If ★ represents the same whole number each time and 3 × ★ + 7 = 31, what number does ★ stand for?
8
Subtract 7 from 31 to get 24, then divide by 3: ★ = 8.
6. If ★ represents the same whole number each time and 3 × ★ + 11 = 35, what number does ★ stand for?
8
Subtract 11 from 35 to get 24, then divide by 3: ★ = 8.
7. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
3
Subtract 20 from 44 to get 24, then divide by 8: ★ = 3.
8. If ★ represents the same whole number each time and 4 × ★ + 12 = 48, what number does ★ stand for?
9
Subtract 12 from 48 to get 36, then divide by 4: ★ = 9.
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 29, what number does ★ stand for?
2
Subtract 19 from 29 to get 10, then divide by 5: ★ = 2.
10. If ★ represents the same whole number each time and 5 × ★ + 20 = 50, what number does ★ stand for?
6
Subtract 20 from 50 to get 30, then divide by 5: ★ = 6.
11. If ★ represents the same whole number each time and 8 × ★ + 15 = 55, what number does ★ stand for?
5
Subtract 15 from 55 to get 40, then divide by 8: ★ = 5.
12. 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.

12 questions · Seed 76 · 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 2 × ★ + 15 = 21, what number does ★ stand for?
2 · 15 · 21 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 19 = 75, what number does ★ stand for?
8 · 19 · 75 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 17 = 41, what number does ★ stand for?
8 · 17 · 41 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 16 = 31, what number does ★ stand for?
3 · 16 · 31 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 7 = 31, what number does ★ stand for?
3 · 7 · 31 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 11 = 35, what number does ★ stand for?
3 · 11 · 35 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
8 · 20 · 44 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 12 = 48, what number does ★ stand for?
4 · 12 · 48 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 29, what number does ★ stand for?
5 · 19 · 29 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 20 = 50, what number does ★ stand for?
5 · 20 · 50 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 15 = 55, what number does ★ stand for?
8 · 15 · 55 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 8 = 26, what number does ★ stand for?
3 · 8 · 26 · Symbol equation puzzles

12 questions · Seed 76 · 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 2 × ★ + 15 = 21, what number does ★ stand for?
3
Subtract 15 from 21 to get 6, then divide by 2: ★ = 3.
2. If ★ represents the same whole number each time and 8 × ★ + 19 = 75, what number does ★ stand for?
7
Subtract 19 from 75 to get 56, then divide by 8: ★ = 7.
3. If ★ represents the same whole number each time and 8 × ★ + 17 = 41, what number does ★ stand for?
3
Subtract 17 from 41 to get 24, then divide by 8: ★ = 3.
4. If ★ represents the same whole number each time and 3 × ★ + 16 = 31, what number does ★ stand for?
5
Subtract 16 from 31 to get 15, then divide by 3: ★ = 5.
5. If ★ represents the same whole number each time and 3 × ★ + 7 = 31, what number does ★ stand for?
8
Subtract 7 from 31 to get 24, then divide by 3: ★ = 8.
6. If ★ represents the same whole number each time and 3 × ★ + 11 = 35, what number does ★ stand for?
8
Subtract 11 from 35 to get 24, then divide by 3: ★ = 8.
7. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
3
Subtract 20 from 44 to get 24, then divide by 8: ★ = 3.
8. If ★ represents the same whole number each time and 4 × ★ + 12 = 48, what number does ★ stand for?
9
Subtract 12 from 48 to get 36, then divide by 4: ★ = 9.
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 29, what number does ★ stand for?
2
Subtract 19 from 29 to get 10, then divide by 5: ★ = 2.
10. If ★ represents the same whole number each time and 5 × ★ + 20 = 50, what number does ★ stand for?
6
Subtract 20 from 50 to get 30, then divide by 5: ★ = 6.
11. If ★ represents the same whole number each time and 8 × ★ + 15 = 55, what number does ★ stand for?
5
Subtract 15 from 55 to get 40, then divide by 8: ★ = 5.
12. 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.

12 questions · Seed 76 · Age guidance, not curriculum certification