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 6 × ★ + 8 = 20, what number does ★ stand for?
6 · 8 · 20 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 26, what number does ★ stand for?
2 · 12 · 26 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 19 = 47, what number does ★ stand for?
7 · 19 · 47 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 2 = 79, what number does ★ stand for?
7 · 2 · 79 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 17, what number does ★ stand for?
2 · 11 · 17 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 16 = 72, what number does ★ stand for?
7 · 16 · 72 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 2 = 22, what number does ★ stand for?
5 · 2 · 22 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 20 = 38, what number does ★ stand for?
6 · 20 · 38 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 6 = 62, what number does ★ stand for?
4 · 6 · 62 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 18 = 63, what number does ★ stand for?
5 · 18 · 63 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 29, what number does ★ stand for?
2 · 3 · 29 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 18 = 123, what number does ★ stand for?
7 · 18 · 123 · Symbol equation puzzles

12 questions · Seed 104731 · 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 6 × ★ + 8 = 20, what number does ★ stand for?
2
Subtract 8 from 20 to get 12, then divide by 6: ★ = 2.
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 26, what number does ★ stand for?
7
Subtract 12 from 26 to get 14, then divide by 2: ★ = 7.
3. 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.
4. If ★ represents the same whole number each time and 7 × ★ + 2 = 79, what number does ★ stand for?
11
Subtract 2 from 79 to get 77, then divide by 7: ★ = 11.
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 17, what number does ★ stand for?
3
Subtract 11 from 17 to get 6, then divide by 2: ★ = 3.
6. If ★ represents the same whole number each time and 7 × ★ + 16 = 72, what number does ★ stand for?
8
Subtract 16 from 72 to get 56, then divide by 7: ★ = 8.
7. If ★ represents the same whole number each time and 5 × ★ + 2 = 22, what number does ★ stand for?
4
Subtract 2 from 22 to get 20, then divide by 5: ★ = 4.
8. If ★ represents the same whole number each time and 6 × ★ + 20 = 38, what number does ★ stand for?
3
Subtract 20 from 38 to get 18, then divide by 6: ★ = 3.
9. If ★ represents the same whole number each time and 4 × ★ + 6 = 62, what number does ★ stand for?
14
Subtract 6 from 62 to get 56, then divide by 4: ★ = 14.
10. If ★ represents the same whole number each time and 5 × ★ + 18 = 63, what number does ★ stand for?
9
Subtract 18 from 63 to get 45, then divide by 5: ★ = 9.
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 29, what number does ★ stand for?
13
Subtract 3 from 29 to get 26, then divide by 2: ★ = 13.
12. If ★ represents the same whole number each time and 7 × ★ + 18 = 123, what number does ★ stand for?
15
Subtract 18 from 123 to get 105, then divide by 7: ★ = 15.

12 questions · Seed 104731 · 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 6 × ★ + 8 = 20, what number does ★ stand for?
6 · 8 · 20 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 26, what number does ★ stand for?
2 · 12 · 26 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 19 = 47, what number does ★ stand for?
7 · 19 · 47 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 2 = 79, what number does ★ stand for?
7 · 2 · 79 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 17, what number does ★ stand for?
2 · 11 · 17 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 16 = 72, what number does ★ stand for?
7 · 16 · 72 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 2 = 22, what number does ★ stand for?
5 · 2 · 22 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 20 = 38, what number does ★ stand for?
6 · 20 · 38 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 6 = 62, what number does ★ stand for?
4 · 6 · 62 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 18 = 63, what number does ★ stand for?
5 · 18 · 63 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 29, what number does ★ stand for?
2 · 3 · 29 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 18 = 123, what number does ★ stand for?
7 · 18 · 123 · Symbol equation puzzles

12 questions · Seed 104731 · 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 6 × ★ + 8 = 20, what number does ★ stand for?
2
Subtract 8 from 20 to get 12, then divide by 6: ★ = 2.
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 26, what number does ★ stand for?
7
Subtract 12 from 26 to get 14, then divide by 2: ★ = 7.
3. 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.
4. If ★ represents the same whole number each time and 7 × ★ + 2 = 79, what number does ★ stand for?
11
Subtract 2 from 79 to get 77, then divide by 7: ★ = 11.
5. If ★ represents the same whole number each time and 2 × ★ + 11 = 17, what number does ★ stand for?
3
Subtract 11 from 17 to get 6, then divide by 2: ★ = 3.
6. If ★ represents the same whole number each time and 7 × ★ + 16 = 72, what number does ★ stand for?
8
Subtract 16 from 72 to get 56, then divide by 7: ★ = 8.
7. If ★ represents the same whole number each time and 5 × ★ + 2 = 22, what number does ★ stand for?
4
Subtract 2 from 22 to get 20, then divide by 5: ★ = 4.
8. If ★ represents the same whole number each time and 6 × ★ + 20 = 38, what number does ★ stand for?
3
Subtract 20 from 38 to get 18, then divide by 6: ★ = 3.
9. If ★ represents the same whole number each time and 4 × ★ + 6 = 62, what number does ★ stand for?
14
Subtract 6 from 62 to get 56, then divide by 4: ★ = 14.
10. If ★ represents the same whole number each time and 5 × ★ + 18 = 63, what number does ★ stand for?
9
Subtract 18 from 63 to get 45, then divide by 5: ★ = 9.
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 29, what number does ★ stand for?
13
Subtract 3 from 29 to get 26, then divide by 2: ★ = 13.
12. If ★ represents the same whole number each time and 7 × ★ + 18 = 123, what number does ★ stand for?
15
Subtract 18 from 123 to get 105, then divide by 7: ★ = 15.

12 questions · Seed 104731 · Age guidance, not curriculum certification