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 5 × ★ + 10 = 40, what number does ★ stand for?
5 · 10 · 40 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 18, what number does ★ stand for?
2 · 12 · 18 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 25, what number does ★ stand for?
7 · 4 · 25 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 4 = 28, what number does ★ stand for?
2 · 4 · 28 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 19 = 79, what number does ★ stand for?
6 · 19 · 79 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 17 = 83, what number does ★ stand for?
6 · 17 · 83 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 18 = 33, what number does ★ stand for?
3 · 18 · 33 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 3 = 87, what number does ★ stand for?
7 · 3 · 87 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 16 = 37, what number does ★ stand for?
7 · 16 · 37 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 4 = 29, what number does ★ stand for?
5 · 4 · 29 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 8 = 80, what number does ★ stand for?
8 · 8 · 80 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 10 = 25, what number does ★ stand for?
3 · 10 · 25 · Symbol equation puzzles

12 questions · Seed 104743 · 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 5 × ★ + 10 = 40, what number does ★ stand for?
6
Subtract 10 from 40 to get 30, then divide by 5: ★ = 6.
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 18, what number does ★ stand for?
3
Subtract 12 from 18 to get 6, then divide by 2: ★ = 3.
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 25, what number does ★ stand for?
3
Subtract 4 from 25 to get 21, then divide by 7: ★ = 3.
4. If ★ represents the same whole number each time and 2 × ★ + 4 = 28, what number does ★ stand for?
12
Subtract 4 from 28 to get 24, then divide by 2: ★ = 12.
5. If ★ represents the same whole number each time and 6 × ★ + 19 = 79, what number does ★ stand for?
10
Subtract 19 from 79 to get 60, then divide by 6: ★ = 10.
6. If ★ represents the same whole number each time and 6 × ★ + 17 = 83, what number does ★ stand for?
11
Subtract 17 from 83 to get 66, then divide by 6: ★ = 11.
7. If ★ represents the same whole number each time and 3 × ★ + 18 = 33, what number does ★ stand for?
5
Subtract 18 from 33 to get 15, then divide by 3: ★ = 5.
8. If ★ represents the same whole number each time and 7 × ★ + 3 = 87, what number does ★ stand for?
12
Subtract 3 from 87 to get 84, then divide by 7: ★ = 12.
9. If ★ represents the same whole number each time and 7 × ★ + 16 = 37, what number does ★ stand for?
3
Subtract 16 from 37 to get 21, then divide by 7: ★ = 3.
10. If ★ represents the same whole number each time and 5 × ★ + 4 = 29, what number does ★ stand for?
5
Subtract 4 from 29 to get 25, then divide by 5: ★ = 5.
11. If ★ represents the same whole number each time and 8 × ★ + 8 = 80, what number does ★ stand for?
9
Subtract 8 from 80 to get 72, then divide by 8: ★ = 9.
12. If ★ represents the same whole number each time and 3 × ★ + 10 = 25, what number does ★ stand for?
5
Subtract 10 from 25 to get 15, then divide by 3: ★ = 5.

12 questions · Seed 104743 · 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 5 × ★ + 10 = 40, what number does ★ stand for?
5 · 10 · 40 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 18, what number does ★ stand for?
2 · 12 · 18 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 25, what number does ★ stand for?
7 · 4 · 25 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 4 = 28, what number does ★ stand for?
2 · 4 · 28 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 19 = 79, what number does ★ stand for?
6 · 19 · 79 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 17 = 83, what number does ★ stand for?
6 · 17 · 83 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 18 = 33, what number does ★ stand for?
3 · 18 · 33 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 3 = 87, what number does ★ stand for?
7 · 3 · 87 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 16 = 37, what number does ★ stand for?
7 · 16 · 37 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 4 = 29, what number does ★ stand for?
5 · 4 · 29 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 8 = 80, what number does ★ stand for?
8 · 8 · 80 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 3 × ★ + 10 = 25, what number does ★ stand for?
3 · 10 · 25 · Symbol equation puzzles

12 questions · Seed 104743 · 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 5 × ★ + 10 = 40, what number does ★ stand for?
6
Subtract 10 from 40 to get 30, then divide by 5: ★ = 6.
2. If ★ represents the same whole number each time and 2 × ★ + 12 = 18, what number does ★ stand for?
3
Subtract 12 from 18 to get 6, then divide by 2: ★ = 3.
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 25, what number does ★ stand for?
3
Subtract 4 from 25 to get 21, then divide by 7: ★ = 3.
4. If ★ represents the same whole number each time and 2 × ★ + 4 = 28, what number does ★ stand for?
12
Subtract 4 from 28 to get 24, then divide by 2: ★ = 12.
5. If ★ represents the same whole number each time and 6 × ★ + 19 = 79, what number does ★ stand for?
10
Subtract 19 from 79 to get 60, then divide by 6: ★ = 10.
6. If ★ represents the same whole number each time and 6 × ★ + 17 = 83, what number does ★ stand for?
11
Subtract 17 from 83 to get 66, then divide by 6: ★ = 11.
7. If ★ represents the same whole number each time and 3 × ★ + 18 = 33, what number does ★ stand for?
5
Subtract 18 from 33 to get 15, then divide by 3: ★ = 5.
8. If ★ represents the same whole number each time and 7 × ★ + 3 = 87, what number does ★ stand for?
12
Subtract 3 from 87 to get 84, then divide by 7: ★ = 12.
9. If ★ represents the same whole number each time and 7 × ★ + 16 = 37, what number does ★ stand for?
3
Subtract 16 from 37 to get 21, then divide by 7: ★ = 3.
10. If ★ represents the same whole number each time and 5 × ★ + 4 = 29, what number does ★ stand for?
5
Subtract 4 from 29 to get 25, then divide by 5: ★ = 5.
11. If ★ represents the same whole number each time and 8 × ★ + 8 = 80, what number does ★ stand for?
9
Subtract 8 from 80 to get 72, then divide by 8: ★ = 9.
12. If ★ represents the same whole number each time and 3 × ★ + 10 = 25, what number does ★ stand for?
5
Subtract 10 from 25 to get 15, then divide by 3: ★ = 5.

12 questions · Seed 104743 · Age guidance, not curriculum certification