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 × ★ + 19 = 55, what number does ★ stand for?
4 · 19 · 55 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 21, what number does ★ stand for?
7 · 7 · 21 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 20 = 62, what number does ★ stand for?
7 · 20 · 62 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 9 = 36, what number does ★ stand for?
3 · 9 · 36 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 5 = 93, what number does ★ stand for?
8 · 5 · 93 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 28, what number does ★ stand for?
5 · 8 · 28 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 8 = 32, what number does ★ stand for?
2 · 8 · 32 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 14 = 74, what number does ★ stand for?
5 · 14 · 74 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 15 = 65, what number does ★ stand for?
5 · 15 · 65 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 6 = 97, what number does ★ stand for?
7 · 6 · 97 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 7, what number does ★ stand for?
2 · 3 · 7 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 13 = 55, what number does ★ stand for?
3 · 13 · 55 · Symbol equation puzzles

12 questions · Seed 89 · 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 × ★ + 19 = 55, what number does ★ stand for?
9
Subtract 19 from 55 to get 36, then divide by 4: ★ = 9.
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 21, what number does ★ stand for?
2
Subtract 7 from 21 to get 14, then divide by 7: ★ = 2.
3. If ★ represents the same whole number each time and 7 × ★ + 20 = 62, what number does ★ stand for?
6
Subtract 20 from 62 to get 42, then divide by 7: ★ = 6.
4. If ★ represents the same whole number each time and 3 × ★ + 9 = 36, what number does ★ stand for?
9
Subtract 9 from 36 to get 27, then divide by 3: ★ = 9.
5. If ★ represents the same whole number each time and 8 × ★ + 5 = 93, what number does ★ stand for?
11
Subtract 5 from 93 to get 88, then divide by 8: ★ = 11.
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 28, what number does ★ stand for?
4
Subtract 8 from 28 to get 20, then divide by 5: ★ = 4.
7. If ★ represents the same whole number each time and 2 × ★ + 8 = 32, what number does ★ stand for?
12
Subtract 8 from 32 to get 24, then divide by 2: ★ = 12.
8. If ★ represents the same whole number each time and 5 × ★ + 14 = 74, what number does ★ stand for?
12
Subtract 14 from 74 to get 60, then divide by 5: ★ = 12.
9. If ★ represents the same whole number each time and 5 × ★ + 15 = 65, what number does ★ stand for?
10
Subtract 15 from 65 to get 50, then divide by 5: ★ = 10.
10. If ★ represents the same whole number each time and 7 × ★ + 6 = 97, what number does ★ stand for?
13
Subtract 6 from 97 to get 91, then divide by 7: ★ = 13.
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 7, what number does ★ stand for?
2
Subtract 3 from 7 to get 4, then divide by 2: ★ = 2.
12. If ★ represents the same whole number each time and 3 × ★ + 13 = 55, what number does ★ stand for?
14
Subtract 13 from 55 to get 42, then divide by 3: ★ = 14.

12 questions · Seed 89 · 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 × ★ + 19 = 55, what number does ★ stand for?
4 · 19 · 55 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 21, what number does ★ stand for?
7 · 7 · 21 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 20 = 62, what number does ★ stand for?
7 · 20 · 62 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 3 × ★ + 9 = 36, what number does ★ stand for?
3 · 9 · 36 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 5 = 93, what number does ★ stand for?
8 · 5 · 93 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 28, what number does ★ stand for?
5 · 8 · 28 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 8 = 32, what number does ★ stand for?
2 · 8 · 32 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 14 = 74, what number does ★ stand for?
5 · 14 · 74 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 15 = 65, what number does ★ stand for?
5 · 15 · 65 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 6 = 97, what number does ★ stand for?
7 · 6 · 97 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 7, what number does ★ stand for?
2 · 3 · 7 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 13 = 55, what number does ★ stand for?
3 · 13 · 55 · Symbol equation puzzles

12 questions · Seed 89 · 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 × ★ + 19 = 55, what number does ★ stand for?
9
Subtract 19 from 55 to get 36, then divide by 4: ★ = 9.
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 21, what number does ★ stand for?
2
Subtract 7 from 21 to get 14, then divide by 7: ★ = 2.
3. If ★ represents the same whole number each time and 7 × ★ + 20 = 62, what number does ★ stand for?
6
Subtract 20 from 62 to get 42, then divide by 7: ★ = 6.
4. If ★ represents the same whole number each time and 3 × ★ + 9 = 36, what number does ★ stand for?
9
Subtract 9 from 36 to get 27, then divide by 3: ★ = 9.
5. If ★ represents the same whole number each time and 8 × ★ + 5 = 93, what number does ★ stand for?
11
Subtract 5 from 93 to get 88, then divide by 8: ★ = 11.
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 28, what number does ★ stand for?
4
Subtract 8 from 28 to get 20, then divide by 5: ★ = 4.
7. If ★ represents the same whole number each time and 2 × ★ + 8 = 32, what number does ★ stand for?
12
Subtract 8 from 32 to get 24, then divide by 2: ★ = 12.
8. If ★ represents the same whole number each time and 5 × ★ + 14 = 74, what number does ★ stand for?
12
Subtract 14 from 74 to get 60, then divide by 5: ★ = 12.
9. If ★ represents the same whole number each time and 5 × ★ + 15 = 65, what number does ★ stand for?
10
Subtract 15 from 65 to get 50, then divide by 5: ★ = 10.
10. If ★ represents the same whole number each time and 7 × ★ + 6 = 97, what number does ★ stand for?
13
Subtract 6 from 97 to get 91, then divide by 7: ★ = 13.
11. If ★ represents the same whole number each time and 2 × ★ + 3 = 7, what number does ★ stand for?
2
Subtract 3 from 7 to get 4, then divide by 2: ★ = 2.
12. If ★ represents the same whole number each time and 3 × ★ + 13 = 55, what number does ★ stand for?
14
Subtract 13 from 55 to get 42, then divide by 3: ★ = 14.

12 questions · Seed 89 · Age guidance, not curriculum certification