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 × ★ + 7 = 13, what number does ★ stand for?
2 · 7 · 13 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 11 = 83, what number does ★ stand for?
6 · 11 · 83 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 3 × ★ + 6 = 45, what number does ★ stand for?
3 · 6 · 45 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 18 = 84, what number does ★ stand for?
6 · 18 · 84 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 6 = 16, what number does ★ stand for?
5 · 6 · 16 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 13 = 63, what number does ★ stand for?
5 · 13 · 63 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 2 = 22, what number does ★ stand for?
4 · 2 · 22 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 2 = 14, what number does ★ stand for?
6 · 2 · 14 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 8 = 74, what number does ★ stand for?
6 · 8 · 74 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 19 = 94, what number does ★ stand for?
5 · 19 · 94 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 18 = 68, what number does ★ stand for?
5 · 18 · 68 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 16 = 88, what number does ★ stand for?
6 · 16 · 88 · Symbol equation puzzles

12 questions · Seed 70 · 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 × ★ + 7 = 13, what number does ★ stand for?
3
Subtract 7 from 13 to get 6, then divide by 2: ★ = 3.
2. If ★ represents the same whole number each time and 6 × ★ + 11 = 83, what number does ★ stand for?
12
Subtract 11 from 83 to get 72, then divide by 6: ★ = 12.
3. If ★ represents the same whole number each time and 3 × ★ + 6 = 45, what number does ★ stand for?
13
Subtract 6 from 45 to get 39, then divide by 3: ★ = 13.
4. If ★ represents the same whole number each time and 6 × ★ + 18 = 84, what number does ★ stand for?
11
Subtract 18 from 84 to get 66, then divide by 6: ★ = 11.
5. If ★ represents the same whole number each time and 5 × ★ + 6 = 16, what number does ★ stand for?
2
Subtract 6 from 16 to get 10, then divide by 5: ★ = 2.
6. If ★ represents the same whole number each time and 5 × ★ + 13 = 63, what number does ★ stand for?
10
Subtract 13 from 63 to get 50, then divide by 5: ★ = 10.
7. If ★ represents the same whole number each time and 4 × ★ + 2 = 22, what number does ★ stand for?
5
Subtract 2 from 22 to get 20, then divide by 4: ★ = 5.
8. If ★ represents the same whole number each time and 6 × ★ + 2 = 14, what number does ★ stand for?
2
Subtract 2 from 14 to get 12, then divide by 6: ★ = 2.
9. If ★ represents the same whole number each time and 6 × ★ + 8 = 74, what number does ★ stand for?
11
Subtract 8 from 74 to get 66, then divide by 6: ★ = 11.
10. If ★ represents the same whole number each time and 5 × ★ + 19 = 94, what number does ★ stand for?
15
Subtract 19 from 94 to get 75, then divide by 5: ★ = 15.
11. If ★ represents the same whole number each time and 5 × ★ + 18 = 68, what number does ★ stand for?
10
Subtract 18 from 68 to get 50, then divide by 5: ★ = 10.
12. If ★ represents the same whole number each time and 6 × ★ + 16 = 88, what number does ★ stand for?
12
Subtract 16 from 88 to get 72, then divide by 6: ★ = 12.

12 questions · Seed 70 · 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 × ★ + 7 = 13, what number does ★ stand for?
2 · 7 · 13 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 11 = 83, what number does ★ stand for?
6 · 11 · 83 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 3 × ★ + 6 = 45, what number does ★ stand for?
3 · 6 · 45 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 18 = 84, what number does ★ stand for?
6 · 18 · 84 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 6 = 16, what number does ★ stand for?
5 · 6 · 16 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 13 = 63, what number does ★ stand for?
5 · 13 · 63 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 2 = 22, what number does ★ stand for?
4 · 2 · 22 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 2 = 14, what number does ★ stand for?
6 · 2 · 14 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 6 × ★ + 8 = 74, what number does ★ stand for?
6 · 8 · 74 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 19 = 94, what number does ★ stand for?
5 · 19 · 94 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 18 = 68, what number does ★ stand for?
5 · 18 · 68 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 16 = 88, what number does ★ stand for?
6 · 16 · 88 · Symbol equation puzzles

12 questions · Seed 70 · 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 × ★ + 7 = 13, what number does ★ stand for?
3
Subtract 7 from 13 to get 6, then divide by 2: ★ = 3.
2. If ★ represents the same whole number each time and 6 × ★ + 11 = 83, what number does ★ stand for?
12
Subtract 11 from 83 to get 72, then divide by 6: ★ = 12.
3. If ★ represents the same whole number each time and 3 × ★ + 6 = 45, what number does ★ stand for?
13
Subtract 6 from 45 to get 39, then divide by 3: ★ = 13.
4. If ★ represents the same whole number each time and 6 × ★ + 18 = 84, what number does ★ stand for?
11
Subtract 18 from 84 to get 66, then divide by 6: ★ = 11.
5. If ★ represents the same whole number each time and 5 × ★ + 6 = 16, what number does ★ stand for?
2
Subtract 6 from 16 to get 10, then divide by 5: ★ = 2.
6. If ★ represents the same whole number each time and 5 × ★ + 13 = 63, what number does ★ stand for?
10
Subtract 13 from 63 to get 50, then divide by 5: ★ = 10.
7. If ★ represents the same whole number each time and 4 × ★ + 2 = 22, what number does ★ stand for?
5
Subtract 2 from 22 to get 20, then divide by 4: ★ = 5.
8. If ★ represents the same whole number each time and 6 × ★ + 2 = 14, what number does ★ stand for?
2
Subtract 2 from 14 to get 12, then divide by 6: ★ = 2.
9. If ★ represents the same whole number each time and 6 × ★ + 8 = 74, what number does ★ stand for?
11
Subtract 8 from 74 to get 66, then divide by 6: ★ = 11.
10. If ★ represents the same whole number each time and 5 × ★ + 19 = 94, what number does ★ stand for?
15
Subtract 19 from 94 to get 75, then divide by 5: ★ = 15.
11. If ★ represents the same whole number each time and 5 × ★ + 18 = 68, what number does ★ stand for?
10
Subtract 18 from 68 to get 50, then divide by 5: ★ = 10.
12. If ★ represents the same whole number each time and 6 × ★ + 16 = 88, what number does ★ stand for?
12
Subtract 16 from 88 to get 72, then divide by 6: ★ = 12.

12 questions · Seed 70 · Age guidance, not curriculum certification