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 2 × ★ + 13 = 35, what number does ★ stand for?
2 · 13 · 35 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 19 = 25, what number does ★ stand for?
3 · 19 · 25 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 3 × ★ + 16 = 58, what number does ★ stand for?
3 · 16 · 58 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 19 = 64, what number does ★ stand for?
5 · 19 · 64 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 10 = 100, what number does ★ stand for?
6 · 10 · 100 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 16 = 55, what number does ★ stand for?
3 · 16 · 55 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 11 = 17, what number does ★ stand for?
2 · 11 · 17 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 8 = 48, what number does ★ stand for?
5 · 8 · 48 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 11 = 51, what number does ★ stand for?
4 · 11 · 51 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 19 = 124, what number does ★ stand for?
7 · 19 · 124 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 14 = 35, what number does ★ stand for?
7 · 14 · 35 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 16 = 46, what number does ★ stand for?
5 · 16 · 46 · Symbol equation puzzles

12 questions · Seed 62 · 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 2 × ★ + 13 = 35, what number does ★ stand for?
11
Subtract 13 from 35 to get 22, then divide by 2: ★ = 11.
2. If ★ represents the same whole number each time and 3 × ★ + 19 = 25, what number does ★ stand for?
2
Subtract 19 from 25 to get 6, then divide by 3: ★ = 2.
3. If ★ represents the same whole number each time and 3 × ★ + 16 = 58, what number does ★ stand for?
14
Subtract 16 from 58 to get 42, then divide by 3: ★ = 14.
4. If ★ represents the same whole number each time and 5 × ★ + 19 = 64, what number does ★ stand for?
9
Subtract 19 from 64 to get 45, then divide by 5: ★ = 9.
5. If ★ represents the same whole number each time and 6 × ★ + 10 = 100, what number does ★ stand for?
15
Subtract 10 from 100 to get 90, then divide by 6: ★ = 15.
6. If ★ represents the same whole number each time and 3 × ★ + 16 = 55, what number does ★ stand for?
13
Subtract 16 from 55 to get 39, then divide by 3: ★ = 13.
7. 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.
8. If ★ represents the same whole number each time and 5 × ★ + 8 = 48, what number does ★ stand for?
8
Subtract 8 from 48 to get 40, then divide by 5: ★ = 8.
9. If ★ represents the same whole number each time and 4 × ★ + 11 = 51, what number does ★ stand for?
10
Subtract 11 from 51 to get 40, then divide by 4: ★ = 10.
10. If ★ represents the same whole number each time and 7 × ★ + 19 = 124, what number does ★ stand for?
15
Subtract 19 from 124 to get 105, then divide by 7: ★ = 15.
11. If ★ represents the same whole number each time and 7 × ★ + 14 = 35, what number does ★ stand for?
3
Subtract 14 from 35 to get 21, then divide by 7: ★ = 3.
12. If ★ represents the same whole number each time and 5 × ★ + 16 = 46, what number does ★ stand for?
6
Subtract 16 from 46 to get 30, then divide by 5: ★ = 6.

12 questions · Seed 62 · 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 2 × ★ + 13 = 35, what number does ★ stand for?
2 · 13 · 35 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 19 = 25, what number does ★ stand for?
3 · 19 · 25 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 3 × ★ + 16 = 58, what number does ★ stand for?
3 · 16 · 58 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 19 = 64, what number does ★ stand for?
5 · 19 · 64 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 10 = 100, what number does ★ stand for?
6 · 10 · 100 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 16 = 55, what number does ★ stand for?
3 · 16 · 55 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 11 = 17, what number does ★ stand for?
2 · 11 · 17 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 8 = 48, what number does ★ stand for?
5 · 8 · 48 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 11 = 51, what number does ★ stand for?
4 · 11 · 51 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 19 = 124, what number does ★ stand for?
7 · 19 · 124 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 7 × ★ + 14 = 35, what number does ★ stand for?
7 · 14 · 35 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 16 = 46, what number does ★ stand for?
5 · 16 · 46 · Symbol equation puzzles

12 questions · Seed 62 · 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 2 × ★ + 13 = 35, what number does ★ stand for?
11
Subtract 13 from 35 to get 22, then divide by 2: ★ = 11.
2. If ★ represents the same whole number each time and 3 × ★ + 19 = 25, what number does ★ stand for?
2
Subtract 19 from 25 to get 6, then divide by 3: ★ = 2.
3. If ★ represents the same whole number each time and 3 × ★ + 16 = 58, what number does ★ stand for?
14
Subtract 16 from 58 to get 42, then divide by 3: ★ = 14.
4. If ★ represents the same whole number each time and 5 × ★ + 19 = 64, what number does ★ stand for?
9
Subtract 19 from 64 to get 45, then divide by 5: ★ = 9.
5. If ★ represents the same whole number each time and 6 × ★ + 10 = 100, what number does ★ stand for?
15
Subtract 10 from 100 to get 90, then divide by 6: ★ = 15.
6. If ★ represents the same whole number each time and 3 × ★ + 16 = 55, what number does ★ stand for?
13
Subtract 16 from 55 to get 39, then divide by 3: ★ = 13.
7. 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.
8. If ★ represents the same whole number each time and 5 × ★ + 8 = 48, what number does ★ stand for?
8
Subtract 8 from 48 to get 40, then divide by 5: ★ = 8.
9. If ★ represents the same whole number each time and 4 × ★ + 11 = 51, what number does ★ stand for?
10
Subtract 11 from 51 to get 40, then divide by 4: ★ = 10.
10. If ★ represents the same whole number each time and 7 × ★ + 19 = 124, what number does ★ stand for?
15
Subtract 19 from 124 to get 105, then divide by 7: ★ = 15.
11. If ★ represents the same whole number each time and 7 × ★ + 14 = 35, what number does ★ stand for?
3
Subtract 14 from 35 to get 21, then divide by 7: ★ = 3.
12. If ★ represents the same whole number each time and 5 × ★ + 16 = 46, what number does ★ stand for?
6
Subtract 16 from 46 to get 30, then divide by 5: ★ = 6.

12 questions · Seed 62 · Age guidance, not curriculum certification