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 4 × ★ + 8 = 16, what number does ★ stand for?
4 · 8 · 16 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 11 = 47, what number does ★ stand for?
3 · 11 · 47 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 20 = 44, what number does ★ stand for?
4 · 20 · 44 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 10 = 40, what number does ★ stand for?
6 · 10 · 40 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 14 = 112, what number does ★ stand for?
7 · 14 · 112 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
5 · 14 · 29 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 13 = 49, what number does ★ stand for?
4 · 13 · 49 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 1 = 57, what number does ★ stand for?
8 · 1 · 57 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 13 = 34, what number does ★ stand for?
7 · 13 · 34 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 11 = 27, what number does ★ stand for?
4 · 11 · 27 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 7 = 31, what number does ★ stand for?
6 · 7 · 31 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 17 = 29, what number does ★ stand for?
4 · 17 · 29 · Symbol equation puzzles

12 questions · Seed 59 · 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 4 × ★ + 8 = 16, what number does ★ stand for?
2
Subtract 8 from 16 to get 8, then divide by 4: ★ = 2.
2. If ★ represents the same whole number each time and 3 × ★ + 11 = 47, what number does ★ stand for?
12
Subtract 11 from 47 to get 36, then divide by 3: ★ = 12.
3. If ★ represents the same whole number each time and 4 × ★ + 20 = 44, what number does ★ stand for?
6
Subtract 20 from 44 to get 24, then divide by 4: ★ = 6.
4. If ★ represents the same whole number each time and 6 × ★ + 10 = 40, what number does ★ stand for?
5
Subtract 10 from 40 to get 30, then divide by 6: ★ = 5.
5. If ★ represents the same whole number each time and 7 × ★ + 14 = 112, what number does ★ stand for?
14
Subtract 14 from 112 to get 98, then divide by 7: ★ = 14.
6. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
3
Subtract 14 from 29 to get 15, then divide by 5: ★ = 3.
7. If ★ represents the same whole number each time and 4 × ★ + 13 = 49, what number does ★ stand for?
9
Subtract 13 from 49 to get 36, then divide by 4: ★ = 9.
8. If ★ represents the same whole number each time and 8 × ★ + 1 = 57, what number does ★ stand for?
7
Subtract 1 from 57 to get 56, then divide by 8: ★ = 7.
9. If ★ represents the same whole number each time and 7 × ★ + 13 = 34, what number does ★ stand for?
3
Subtract 13 from 34 to get 21, then divide by 7: ★ = 3.
10. If ★ represents the same whole number each time and 4 × ★ + 11 = 27, what number does ★ stand for?
4
Subtract 11 from 27 to get 16, then divide by 4: ★ = 4.
11. If ★ represents the same whole number each time and 6 × ★ + 7 = 31, what number does ★ stand for?
4
Subtract 7 from 31 to get 24, then divide by 6: ★ = 4.
12. If ★ represents the same whole number each time and 4 × ★ + 17 = 29, what number does ★ stand for?
3
Subtract 17 from 29 to get 12, then divide by 4: ★ = 3.

12 questions · Seed 59 · 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 4 × ★ + 8 = 16, what number does ★ stand for?
4 · 8 · 16 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 11 = 47, what number does ★ stand for?
3 · 11 · 47 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 20 = 44, what number does ★ stand for?
4 · 20 · 44 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 10 = 40, what number does ★ stand for?
6 · 10 · 40 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 14 = 112, what number does ★ stand for?
7 · 14 · 112 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
5 · 14 · 29 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 13 = 49, what number does ★ stand for?
4 · 13 · 49 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 1 = 57, what number does ★ stand for?
8 · 1 · 57 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 13 = 34, what number does ★ stand for?
7 · 13 · 34 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 11 = 27, what number does ★ stand for?
4 · 11 · 27 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 7 = 31, what number does ★ stand for?
6 · 7 · 31 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 17 = 29, what number does ★ stand for?
4 · 17 · 29 · Symbol equation puzzles

12 questions · Seed 59 · 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 4 × ★ + 8 = 16, what number does ★ stand for?
2
Subtract 8 from 16 to get 8, then divide by 4: ★ = 2.
2. If ★ represents the same whole number each time and 3 × ★ + 11 = 47, what number does ★ stand for?
12
Subtract 11 from 47 to get 36, then divide by 3: ★ = 12.
3. If ★ represents the same whole number each time and 4 × ★ + 20 = 44, what number does ★ stand for?
6
Subtract 20 from 44 to get 24, then divide by 4: ★ = 6.
4. If ★ represents the same whole number each time and 6 × ★ + 10 = 40, what number does ★ stand for?
5
Subtract 10 from 40 to get 30, then divide by 6: ★ = 5.
5. If ★ represents the same whole number each time and 7 × ★ + 14 = 112, what number does ★ stand for?
14
Subtract 14 from 112 to get 98, then divide by 7: ★ = 14.
6. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
3
Subtract 14 from 29 to get 15, then divide by 5: ★ = 3.
7. If ★ represents the same whole number each time and 4 × ★ + 13 = 49, what number does ★ stand for?
9
Subtract 13 from 49 to get 36, then divide by 4: ★ = 9.
8. If ★ represents the same whole number each time and 8 × ★ + 1 = 57, what number does ★ stand for?
7
Subtract 1 from 57 to get 56, then divide by 8: ★ = 7.
9. If ★ represents the same whole number each time and 7 × ★ + 13 = 34, what number does ★ stand for?
3
Subtract 13 from 34 to get 21, then divide by 7: ★ = 3.
10. If ★ represents the same whole number each time and 4 × ★ + 11 = 27, what number does ★ stand for?
4
Subtract 11 from 27 to get 16, then divide by 4: ★ = 4.
11. If ★ represents the same whole number each time and 6 × ★ + 7 = 31, what number does ★ stand for?
4
Subtract 7 from 31 to get 24, then divide by 6: ★ = 4.
12. If ★ represents the same whole number each time and 4 × ★ + 17 = 29, what number does ★ stand for?
3
Subtract 17 from 29 to get 12, then divide by 4: ★ = 3.

12 questions · Seed 59 · Age guidance, not curriculum certification