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 7 × ★ + 10 = 45, what number does ★ stand for?
7 · 10 · 45 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 14 = 70, what number does ★ stand for?
7 · 14 · 70 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 11 = 71, what number does ★ stand for?
5 · 11 · 71 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 19 = 43, what number does ★ stand for?
6 · 19 · 43 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 18 = 48, what number does ★ stand for?
5 · 18 · 48 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 8 = 53, what number does ★ stand for?
3 · 8 · 53 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 15 = 64, what number does ★ stand for?
7 · 15 · 64 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 7 = 112, what number does ★ stand for?
7 · 7 · 112 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 4 = 40, what number does ★ stand for?
4 · 4 · 40 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 7 = 47, what number does ★ stand for?
4 · 7 · 47 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 12 = 18, what number does ★ stand for?
3 · 12 · 18 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 7 = 52, what number does ★ stand for?
5 · 7 · 52 · Symbol equation puzzles

12 questions · Seed 104742 · 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 7 × ★ + 10 = 45, what number does ★ stand for?
5
Subtract 10 from 45 to get 35, then divide by 7: ★ = 5.
2. If ★ represents the same whole number each time and 7 × ★ + 14 = 70, what number does ★ stand for?
8
Subtract 14 from 70 to get 56, then divide by 7: ★ = 8.
3. If ★ represents the same whole number each time and 5 × ★ + 11 = 71, what number does ★ stand for?
12
Subtract 11 from 71 to get 60, then divide by 5: ★ = 12.
4. If ★ represents the same whole number each time and 6 × ★ + 19 = 43, what number does ★ stand for?
4
Subtract 19 from 43 to get 24, then divide by 6: ★ = 4.
5. If ★ represents the same whole number each time and 5 × ★ + 18 = 48, what number does ★ stand for?
6
Subtract 18 from 48 to get 30, then divide by 5: ★ = 6.
6. If ★ represents the same whole number each time and 3 × ★ + 8 = 53, what number does ★ stand for?
15
Subtract 8 from 53 to get 45, then divide by 3: ★ = 15.
7. If ★ represents the same whole number each time and 7 × ★ + 15 = 64, what number does ★ stand for?
7
Subtract 15 from 64 to get 49, then divide by 7: ★ = 7.
8. If ★ represents the same whole number each time and 7 × ★ + 7 = 112, what number does ★ stand for?
15
Subtract 7 from 112 to get 105, then divide by 7: ★ = 15.
9. If ★ represents the same whole number each time and 4 × ★ + 4 = 40, what number does ★ stand for?
9
Subtract 4 from 40 to get 36, then divide by 4: ★ = 9.
10. If ★ represents the same whole number each time and 4 × ★ + 7 = 47, what number does ★ stand for?
10
Subtract 7 from 47 to get 40, then divide by 4: ★ = 10.
11. If ★ represents the same whole number each time and 3 × ★ + 12 = 18, what number does ★ stand for?
2
Subtract 12 from 18 to get 6, then divide by 3: ★ = 2.
12. If ★ represents the same whole number each time and 5 × ★ + 7 = 52, what number does ★ stand for?
9
Subtract 7 from 52 to get 45, then divide by 5: ★ = 9.

12 questions · Seed 104742 · 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 7 × ★ + 10 = 45, what number does ★ stand for?
7 · 10 · 45 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 14 = 70, what number does ★ stand for?
7 · 14 · 70 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 11 = 71, what number does ★ stand for?
5 · 11 · 71 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 19 = 43, what number does ★ stand for?
6 · 19 · 43 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 18 = 48, what number does ★ stand for?
5 · 18 · 48 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 8 = 53, what number does ★ stand for?
3 · 8 · 53 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 7 × ★ + 15 = 64, what number does ★ stand for?
7 · 15 · 64 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 7 × ★ + 7 = 112, what number does ★ stand for?
7 · 7 · 112 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 4 = 40, what number does ★ stand for?
4 · 4 · 40 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 7 = 47, what number does ★ stand for?
4 · 7 · 47 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 12 = 18, what number does ★ stand for?
3 · 12 · 18 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 7 = 52, what number does ★ stand for?
5 · 7 · 52 · Symbol equation puzzles

12 questions · Seed 104742 · 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 7 × ★ + 10 = 45, what number does ★ stand for?
5
Subtract 10 from 45 to get 35, then divide by 7: ★ = 5.
2. If ★ represents the same whole number each time and 7 × ★ + 14 = 70, what number does ★ stand for?
8
Subtract 14 from 70 to get 56, then divide by 7: ★ = 8.
3. If ★ represents the same whole number each time and 5 × ★ + 11 = 71, what number does ★ stand for?
12
Subtract 11 from 71 to get 60, then divide by 5: ★ = 12.
4. If ★ represents the same whole number each time and 6 × ★ + 19 = 43, what number does ★ stand for?
4
Subtract 19 from 43 to get 24, then divide by 6: ★ = 4.
5. If ★ represents the same whole number each time and 5 × ★ + 18 = 48, what number does ★ stand for?
6
Subtract 18 from 48 to get 30, then divide by 5: ★ = 6.
6. If ★ represents the same whole number each time and 3 × ★ + 8 = 53, what number does ★ stand for?
15
Subtract 8 from 53 to get 45, then divide by 3: ★ = 15.
7. If ★ represents the same whole number each time and 7 × ★ + 15 = 64, what number does ★ stand for?
7
Subtract 15 from 64 to get 49, then divide by 7: ★ = 7.
8. If ★ represents the same whole number each time and 7 × ★ + 7 = 112, what number does ★ stand for?
15
Subtract 7 from 112 to get 105, then divide by 7: ★ = 15.
9. If ★ represents the same whole number each time and 4 × ★ + 4 = 40, what number does ★ stand for?
9
Subtract 4 from 40 to get 36, then divide by 4: ★ = 9.
10. If ★ represents the same whole number each time and 4 × ★ + 7 = 47, what number does ★ stand for?
10
Subtract 7 from 47 to get 40, then divide by 4: ★ = 10.
11. If ★ represents the same whole number each time and 3 × ★ + 12 = 18, what number does ★ stand for?
2
Subtract 12 from 18 to get 6, then divide by 3: ★ = 2.
12. If ★ represents the same whole number each time and 5 × ★ + 7 = 52, what number does ★ stand for?
9
Subtract 7 from 52 to get 45, then divide by 5: ★ = 9.

12 questions · Seed 104742 · Age guidance, not curriculum certification