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 × ★ + 6 = 18, what number does ★ stand for?
4 · 6 · 18 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 1 = 31, what number does ★ stand for?
6 · 1 · 31 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 17 = 108, what number does ★ stand for?
7 · 17 · 108 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 12 = 57, what number does ★ stand for?
5 · 12 · 57 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 10 = 108, what number does ★ stand for?
7 · 10 · 108 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
4 · 10 · 62 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 14 = 38, what number does ★ stand for?
6 · 14 · 38 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 20 = 44, what number does ★ stand for?
3 · 20 · 44 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 20 = 32, what number does ★ stand for?
6 · 20 · 32 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 17 = 53, what number does ★ stand for?
4 · 17 · 53 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 9 = 105, what number does ★ stand for?
8 · 9 · 105 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 35, what number does ★ stand for?
8 · 19 · 35 · Symbol equation puzzles

12 questions · Seed 104747 · 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 × ★ + 6 = 18, what number does ★ stand for?
3
Subtract 6 from 18 to get 12, then divide by 4: ★ = 3.
2. If ★ represents the same whole number each time and 6 × ★ + 1 = 31, what number does ★ stand for?
5
Subtract 1 from 31 to get 30, then divide by 6: ★ = 5.
3. If ★ represents the same whole number each time and 7 × ★ + 17 = 108, what number does ★ stand for?
13
Subtract 17 from 108 to get 91, then divide by 7: ★ = 13.
4. If ★ represents the same whole number each time and 5 × ★ + 12 = 57, what number does ★ stand for?
9
Subtract 12 from 57 to get 45, then divide by 5: ★ = 9.
5. If ★ represents the same whole number each time and 7 × ★ + 10 = 108, what number does ★ stand for?
14
Subtract 10 from 108 to get 98, then divide by 7: ★ = 14.
6. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
13
Subtract 10 from 62 to get 52, then divide by 4: ★ = 13.
7. If ★ represents the same whole number each time and 6 × ★ + 14 = 38, what number does ★ stand for?
4
Subtract 14 from 38 to get 24, then divide by 6: ★ = 4.
8. If ★ represents the same whole number each time and 3 × ★ + 20 = 44, what number does ★ stand for?
8
Subtract 20 from 44 to get 24, then divide by 3: ★ = 8.
9. If ★ represents the same whole number each time and 6 × ★ + 20 = 32, what number does ★ stand for?
2
Subtract 20 from 32 to get 12, then divide by 6: ★ = 2.
10. If ★ represents the same whole number each time and 4 × ★ + 17 = 53, what number does ★ stand for?
9
Subtract 17 from 53 to get 36, then divide by 4: ★ = 9.
11. If ★ represents the same whole number each time and 8 × ★ + 9 = 105, what number does ★ stand for?
12
Subtract 9 from 105 to get 96, then divide by 8: ★ = 12.
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 35, what number does ★ stand for?
2
Subtract 19 from 35 to get 16, then divide by 8: ★ = 2.

12 questions · Seed 104747 · 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 × ★ + 6 = 18, what number does ★ stand for?
4 · 6 · 18 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 1 = 31, what number does ★ stand for?
6 · 1 · 31 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 17 = 108, what number does ★ stand for?
7 · 17 · 108 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 12 = 57, what number does ★ stand for?
5 · 12 · 57 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 10 = 108, what number does ★ stand for?
7 · 10 · 108 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
4 · 10 · 62 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 14 = 38, what number does ★ stand for?
6 · 14 · 38 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 20 = 44, what number does ★ stand for?
3 · 20 · 44 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 20 = 32, what number does ★ stand for?
6 · 20 · 32 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 17 = 53, what number does ★ stand for?
4 · 17 · 53 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 9 = 105, what number does ★ stand for?
8 · 9 · 105 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 35, what number does ★ stand for?
8 · 19 · 35 · Symbol equation puzzles

12 questions · Seed 104747 · 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 × ★ + 6 = 18, what number does ★ stand for?
3
Subtract 6 from 18 to get 12, then divide by 4: ★ = 3.
2. If ★ represents the same whole number each time and 6 × ★ + 1 = 31, what number does ★ stand for?
5
Subtract 1 from 31 to get 30, then divide by 6: ★ = 5.
3. If ★ represents the same whole number each time and 7 × ★ + 17 = 108, what number does ★ stand for?
13
Subtract 17 from 108 to get 91, then divide by 7: ★ = 13.
4. If ★ represents the same whole number each time and 5 × ★ + 12 = 57, what number does ★ stand for?
9
Subtract 12 from 57 to get 45, then divide by 5: ★ = 9.
5. If ★ represents the same whole number each time and 7 × ★ + 10 = 108, what number does ★ stand for?
14
Subtract 10 from 108 to get 98, then divide by 7: ★ = 14.
6. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
13
Subtract 10 from 62 to get 52, then divide by 4: ★ = 13.
7. If ★ represents the same whole number each time and 6 × ★ + 14 = 38, what number does ★ stand for?
4
Subtract 14 from 38 to get 24, then divide by 6: ★ = 4.
8. If ★ represents the same whole number each time and 3 × ★ + 20 = 44, what number does ★ stand for?
8
Subtract 20 from 44 to get 24, then divide by 3: ★ = 8.
9. If ★ represents the same whole number each time and 6 × ★ + 20 = 32, what number does ★ stand for?
2
Subtract 20 from 32 to get 12, then divide by 6: ★ = 2.
10. If ★ represents the same whole number each time and 4 × ★ + 17 = 53, what number does ★ stand for?
9
Subtract 17 from 53 to get 36, then divide by 4: ★ = 9.
11. If ★ represents the same whole number each time and 8 × ★ + 9 = 105, what number does ★ stand for?
12
Subtract 9 from 105 to get 96, then divide by 8: ★ = 12.
12. If ★ represents the same whole number each time and 8 × ★ + 19 = 35, what number does ★ stand for?
2
Subtract 19 from 35 to get 16, then divide by 8: ★ = 2.

12 questions · Seed 104747 · Age guidance, not curriculum certification