ReasoningAges 10-12

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 10-12

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 2 × ★ + 6 = 14, what number does ★ stand for?
2 · 6 · 14 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 5 = 9, what number does ★ stand for?
2 · 5 · 9 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 10 = 74, what number does ★ stand for?
8 · 10 · 74 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 33, what number does ★ stand for?
4 · 13 · 33 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 39, what number does ★ stand for?
2 · 11 · 39 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 5 = 29, what number does ★ stand for?
6 · 5 · 29 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
4 · 20 · 48 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 20 = 34, what number does ★ stand for?
2 · 20 · 34 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 11 = 46, what number does ★ stand for?
5 · 11 · 46 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 75, what number does ★ stand for?
7 · 5 · 75 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 19 = 47, what number does ★ stand for?
7 · 19 · 47 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 7 = 19, what number does ★ stand for?
3 · 7 · 19 · Symbol equation puzzles

12 questions · Seed 104735 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 2 × ★ + 6 = 14, what number does ★ stand for?
4
Subtract 6 from 14 to get 8, then divide by 2: ★ = 4.
2. If ★ represents the same whole number each time and 2 × ★ + 5 = 9, what number does ★ stand for?
2
Subtract 5 from 9 to get 4, then divide by 2: ★ = 2.
3. If ★ represents the same whole number each time and 8 × ★ + 10 = 74, what number does ★ stand for?
8
Subtract 10 from 74 to get 64, then divide by 8: ★ = 8.
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 33, what number does ★ stand for?
5
Subtract 13 from 33 to get 20, then divide by 4: ★ = 5.
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 39, what number does ★ stand for?
14
Subtract 11 from 39 to get 28, then divide by 2: ★ = 14.
6. If ★ represents the same whole number each time and 6 × ★ + 5 = 29, what number does ★ stand for?
4
Subtract 5 from 29 to get 24, then divide by 6: ★ = 4.
7. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
7
Subtract 20 from 48 to get 28, then divide by 4: ★ = 7.
8. If ★ represents the same whole number each time and 2 × ★ + 20 = 34, what number does ★ stand for?
7
Subtract 20 from 34 to get 14, then divide by 2: ★ = 7.
9. If ★ represents the same whole number each time and 5 × ★ + 11 = 46, what number does ★ stand for?
7
Subtract 11 from 46 to get 35, then divide by 5: ★ = 7.
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 75, what number does ★ stand for?
10
Subtract 5 from 75 to get 70, then divide by 7: ★ = 10.
11. If ★ represents the same whole number each time and 7 × ★ + 19 = 47, what number does ★ stand for?
4
Subtract 19 from 47 to get 28, then divide by 7: ★ = 4.
12. If ★ represents the same whole number each time and 3 × ★ + 7 = 19, what number does ★ stand for?
4
Subtract 7 from 19 to get 12, then divide by 3: ★ = 4.

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 2 × ★ + 6 = 14, what number does ★ stand for?
2 · 6 · 14 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 5 = 9, what number does ★ stand for?
2 · 5 · 9 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 10 = 74, what number does ★ stand for?
8 · 10 · 74 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 33, what number does ★ stand for?
4 · 13 · 33 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 39, what number does ★ stand for?
2 · 11 · 39 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 5 = 29, what number does ★ stand for?
6 · 5 · 29 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
4 · 20 · 48 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 20 = 34, what number does ★ stand for?
2 · 20 · 34 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 11 = 46, what number does ★ stand for?
5 · 11 · 46 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 75, what number does ★ stand for?
7 · 5 · 75 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 19 = 47, what number does ★ stand for?
7 · 19 · 47 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 7 = 19, what number does ★ stand for?
3 · 7 · 19 · Symbol equation puzzles

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 2 × ★ + 6 = 14, what number does ★ stand for?
4
Subtract 6 from 14 to get 8, then divide by 2: ★ = 4.
2. If ★ represents the same whole number each time and 2 × ★ + 5 = 9, what number does ★ stand for?
2
Subtract 5 from 9 to get 4, then divide by 2: ★ = 2.
3. If ★ represents the same whole number each time and 8 × ★ + 10 = 74, what number does ★ stand for?
8
Subtract 10 from 74 to get 64, then divide by 8: ★ = 8.
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 33, what number does ★ stand for?
5
Subtract 13 from 33 to get 20, then divide by 4: ★ = 5.
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 39, what number does ★ stand for?
14
Subtract 11 from 39 to get 28, then divide by 2: ★ = 14.
6. If ★ represents the same whole number each time and 6 × ★ + 5 = 29, what number does ★ stand for?
4
Subtract 5 from 29 to get 24, then divide by 6: ★ = 4.
7. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
7
Subtract 20 from 48 to get 28, then divide by 4: ★ = 7.
8. If ★ represents the same whole number each time and 2 × ★ + 20 = 34, what number does ★ stand for?
7
Subtract 20 from 34 to get 14, then divide by 2: ★ = 7.
9. If ★ represents the same whole number each time and 5 × ★ + 11 = 46, what number does ★ stand for?
7
Subtract 11 from 46 to get 35, then divide by 5: ★ = 7.
10. If ★ represents the same whole number each time and 7 × ★ + 5 = 75, what number does ★ stand for?
10
Subtract 5 from 75 to get 70, then divide by 7: ★ = 10.
11. If ★ represents the same whole number each time and 7 × ★ + 19 = 47, what number does ★ stand for?
4
Subtract 19 from 47 to get 28, then divide by 7: ★ = 4.
12. If ★ represents the same whole number each time and 3 × ★ + 7 = 19, what number does ★ stand for?
4
Subtract 7 from 19 to get 12, then divide by 3: ★ = 4.

12 questions · Seed 104735 · Age guidance, not curriculum certification