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 3 × ★ + 16 = 58, what number does ★ stand for?
3 · 16 · 58 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
7 · 1 · 43 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 102, what number does ★ stand for?
7 · 4 · 102 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 18 = 43, what number does ★ stand for?
5 · 18 · 43 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 17 = 45, what number does ★ stand for?
4 · 17 · 45 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 10 = 40, what number does ★ stand for?
2 · 10 · 40 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 15 = 63, what number does ★ stand for?
6 · 15 · 63 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 19 = 49, what number does ★ stand for?
3 · 19 · 49 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 79, what number does ★ stand for?
5 · 19 · 79 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 17 = 105, what number does ★ stand for?
8 · 17 · 105 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 35, what number does ★ stand for?
3 · 14 · 35 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 16 = 100, what number does ★ stand for?
7 · 16 · 100 · Symbol equation puzzles

12 questions · Seed 64 · 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 3 × ★ + 16 = 58, what number does ★ stand for?
14
Subtract 16 from 58 to get 42, then divide by 3: ★ = 14.
2. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
6
Subtract 1 from 43 to get 42, then divide by 7: ★ = 6.
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 102, what number does ★ stand for?
14
Subtract 4 from 102 to get 98, then divide by 7: ★ = 14.
4. If ★ represents the same whole number each time and 5 × ★ + 18 = 43, what number does ★ stand for?
5
Subtract 18 from 43 to get 25, then divide by 5: ★ = 5.
5. If ★ represents the same whole number each time and 4 × ★ + 17 = 45, what number does ★ stand for?
7
Subtract 17 from 45 to get 28, then divide by 4: ★ = 7.
6. If ★ represents the same whole number each time and 2 × ★ + 10 = 40, what number does ★ stand for?
15
Subtract 10 from 40 to get 30, then divide by 2: ★ = 15.
7. If ★ represents the same whole number each time and 6 × ★ + 15 = 63, what number does ★ stand for?
8
Subtract 15 from 63 to get 48, then divide by 6: ★ = 8.
8. If ★ represents the same whole number each time and 3 × ★ + 19 = 49, what number does ★ stand for?
10
Subtract 19 from 49 to get 30, then divide by 3: ★ = 10.
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 79, what number does ★ stand for?
12
Subtract 19 from 79 to get 60, then divide by 5: ★ = 12.
10. If ★ represents the same whole number each time and 8 × ★ + 17 = 105, what number does ★ stand for?
11
Subtract 17 from 105 to get 88, then divide by 8: ★ = 11.
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 35, what number does ★ stand for?
7
Subtract 14 from 35 to get 21, then divide by 3: ★ = 7.
12. If ★ represents the same whole number each time and 7 × ★ + 16 = 100, what number does ★ stand for?
12
Subtract 16 from 100 to get 84, then divide by 7: ★ = 12.

12 questions · Seed 64 · 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 3 × ★ + 16 = 58, what number does ★ stand for?
3 · 16 · 58 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
7 · 1 · 43 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 102, what number does ★ stand for?
7 · 4 · 102 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 18 = 43, what number does ★ stand for?
5 · 18 · 43 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 17 = 45, what number does ★ stand for?
4 · 17 · 45 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 10 = 40, what number does ★ stand for?
2 · 10 · 40 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 15 = 63, what number does ★ stand for?
6 · 15 · 63 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 19 = 49, what number does ★ stand for?
3 · 19 · 49 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 79, what number does ★ stand for?
5 · 19 · 79 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 17 = 105, what number does ★ stand for?
8 · 17 · 105 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 35, what number does ★ stand for?
3 · 14 · 35 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 16 = 100, what number does ★ stand for?
7 · 16 · 100 · Symbol equation puzzles

12 questions · Seed 64 · 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 3 × ★ + 16 = 58, what number does ★ stand for?
14
Subtract 16 from 58 to get 42, then divide by 3: ★ = 14.
2. If ★ represents the same whole number each time and 7 × ★ + 1 = 43, what number does ★ stand for?
6
Subtract 1 from 43 to get 42, then divide by 7: ★ = 6.
3. If ★ represents the same whole number each time and 7 × ★ + 4 = 102, what number does ★ stand for?
14
Subtract 4 from 102 to get 98, then divide by 7: ★ = 14.
4. If ★ represents the same whole number each time and 5 × ★ + 18 = 43, what number does ★ stand for?
5
Subtract 18 from 43 to get 25, then divide by 5: ★ = 5.
5. If ★ represents the same whole number each time and 4 × ★ + 17 = 45, what number does ★ stand for?
7
Subtract 17 from 45 to get 28, then divide by 4: ★ = 7.
6. If ★ represents the same whole number each time and 2 × ★ + 10 = 40, what number does ★ stand for?
15
Subtract 10 from 40 to get 30, then divide by 2: ★ = 15.
7. If ★ represents the same whole number each time and 6 × ★ + 15 = 63, what number does ★ stand for?
8
Subtract 15 from 63 to get 48, then divide by 6: ★ = 8.
8. If ★ represents the same whole number each time and 3 × ★ + 19 = 49, what number does ★ stand for?
10
Subtract 19 from 49 to get 30, then divide by 3: ★ = 10.
9. If ★ represents the same whole number each time and 5 × ★ + 19 = 79, what number does ★ stand for?
12
Subtract 19 from 79 to get 60, then divide by 5: ★ = 12.
10. If ★ represents the same whole number each time and 8 × ★ + 17 = 105, what number does ★ stand for?
11
Subtract 17 from 105 to get 88, then divide by 8: ★ = 11.
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 35, what number does ★ stand for?
7
Subtract 14 from 35 to get 21, then divide by 3: ★ = 7.
12. If ★ represents the same whole number each time and 7 × ★ + 16 = 100, what number does ★ stand for?
12
Subtract 16 from 100 to get 84, then divide by 7: ★ = 12.

12 questions · Seed 64 · Age guidance, not curriculum certification