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 8 × ★ + 10 = 66, what number does ★ stand for?
8 · 10 · 66 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 11 = 23, what number does ★ stand for?
3 · 11 · 23 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
2 · 17 · 39 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 17 = 73, what number does ★ stand for?
4 · 17 · 73 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 16 = 28, what number does ★ stand for?
6 · 16 · 28 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 3 = 63, what number does ★ stand for?
5 · 3 · 63 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 10 = 101, what number does ★ stand for?
7 · 10 · 101 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 8 = 98, what number does ★ stand for?
6 · 8 · 98 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 14 = 20, what number does ★ stand for?
2 · 14 · 20 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 9 = 57, what number does ★ stand for?
8 · 9 · 57 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 1 = 46, what number does ★ stand for?
5 · 1 · 46 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 99, what number does ★ stand for?
8 · 19 · 99 · Symbol equation puzzles

12 questions · Seed 65 · 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 8 × ★ + 10 = 66, what number does ★ stand for?
7
Subtract 10 from 66 to get 56, then divide by 8: ★ = 7.
2. If ★ represents the same whole number each time and 3 × ★ + 11 = 23, what number does ★ stand for?
4
Subtract 11 from 23 to get 12, then divide by 3: ★ = 4.
3. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
11
Subtract 17 from 39 to get 22, then divide by 2: ★ = 11.
4. If ★ represents the same whole number each time and 4 × ★ + 17 = 73, what number does ★ stand for?
14
Subtract 17 from 73 to get 56, then divide by 4: ★ = 14.
5. If ★ represents the same whole number each time and 6 × ★ + 16 = 28, what number does ★ stand for?
2
Subtract 16 from 28 to get 12, then divide by 6: ★ = 2.
6. If ★ represents the same whole number each time and 5 × ★ + 3 = 63, what number does ★ stand for?
12
Subtract 3 from 63 to get 60, then divide by 5: ★ = 12.
7. If ★ represents the same whole number each time and 7 × ★ + 10 = 101, what number does ★ stand for?
13
Subtract 10 from 101 to get 91, then divide by 7: ★ = 13.
8. If ★ represents the same whole number each time and 6 × ★ + 8 = 98, what number does ★ stand for?
15
Subtract 8 from 98 to get 90, then divide by 6: ★ = 15.
9. If ★ represents the same whole number each time and 2 × ★ + 14 = 20, what number does ★ stand for?
3
Subtract 14 from 20 to get 6, then divide by 2: ★ = 3.
10. If ★ represents the same whole number each time and 8 × ★ + 9 = 57, what number does ★ stand for?
6
Subtract 9 from 57 to get 48, then divide by 8: ★ = 6.
11. If ★ represents the same whole number each time and 5 × ★ + 1 = 46, what number does ★ stand for?
9
Subtract 1 from 46 to get 45, then divide by 5: ★ = 9.
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 99, what number does ★ stand for?
10
Subtract 19 from 99 to get 80, then divide by 8: ★ = 10.

12 questions · Seed 65 · 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 8 × ★ + 10 = 66, what number does ★ stand for?
8 · 10 · 66 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 11 = 23, what number does ★ stand for?
3 · 11 · 23 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
2 · 17 · 39 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 17 = 73, what number does ★ stand for?
4 · 17 · 73 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 16 = 28, what number does ★ stand for?
6 · 16 · 28 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 3 = 63, what number does ★ stand for?
5 · 3 · 63 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 10 = 101, what number does ★ stand for?
7 · 10 · 101 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 8 = 98, what number does ★ stand for?
6 · 8 · 98 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 14 = 20, what number does ★ stand for?
2 · 14 · 20 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 9 = 57, what number does ★ stand for?
8 · 9 · 57 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 1 = 46, what number does ★ stand for?
5 · 1 · 46 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 99, what number does ★ stand for?
8 · 19 · 99 · Symbol equation puzzles

12 questions · Seed 65 · 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 8 × ★ + 10 = 66, what number does ★ stand for?
7
Subtract 10 from 66 to get 56, then divide by 8: ★ = 7.
2. If ★ represents the same whole number each time and 3 × ★ + 11 = 23, what number does ★ stand for?
4
Subtract 11 from 23 to get 12, then divide by 3: ★ = 4.
3. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
11
Subtract 17 from 39 to get 22, then divide by 2: ★ = 11.
4. If ★ represents the same whole number each time and 4 × ★ + 17 = 73, what number does ★ stand for?
14
Subtract 17 from 73 to get 56, then divide by 4: ★ = 14.
5. If ★ represents the same whole number each time and 6 × ★ + 16 = 28, what number does ★ stand for?
2
Subtract 16 from 28 to get 12, then divide by 6: ★ = 2.
6. If ★ represents the same whole number each time and 5 × ★ + 3 = 63, what number does ★ stand for?
12
Subtract 3 from 63 to get 60, then divide by 5: ★ = 12.
7. If ★ represents the same whole number each time and 7 × ★ + 10 = 101, what number does ★ stand for?
13
Subtract 10 from 101 to get 91, then divide by 7: ★ = 13.
8. If ★ represents the same whole number each time and 6 × ★ + 8 = 98, what number does ★ stand for?
15
Subtract 8 from 98 to get 90, then divide by 6: ★ = 15.
9. If ★ represents the same whole number each time and 2 × ★ + 14 = 20, what number does ★ stand for?
3
Subtract 14 from 20 to get 6, then divide by 2: ★ = 3.
10. If ★ represents the same whole number each time and 8 × ★ + 9 = 57, what number does ★ stand for?
6
Subtract 9 from 57 to get 48, then divide by 8: ★ = 6.
11. If ★ represents the same whole number each time and 5 × ★ + 1 = 46, what number does ★ stand for?
9
Subtract 1 from 46 to get 45, then divide by 5: ★ = 9.
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 99, what number does ★ stand for?
10
Subtract 19 from 99 to get 80, then divide by 8: ★ = 10.

12 questions · Seed 65 · Age guidance, not curriculum certification