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.

New variation Try interactive challenge Browse templates

Age band:Ages 7-9 Ages 10-12

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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 × ★ + 12 = 67, what number does ★ stand for?
5 · 12 · 67 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 19 = 47, what number does ★ stand for?
2 · 19 · 47 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 5 = 61, what number does ★ stand for?
7 · 5 · 61 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 8 = 92, what number does ★ stand for?
7 · 8 · 92 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 10 = 43, what number does ★ stand for?
3 · 10 · 43 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 5 = 110, what number does ★ stand for?
7 · 5 · 110 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 6 = 54, what number does ★ stand for?
4 · 6 · 54 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 14 = 24, what number does ★ stand for?
2 · 14 · 24 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 3 = 35, what number does ★ stand for?
4 · 3 · 35 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 18 = 34, what number does ★ stand for?
8 · 18 · 34 · 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 × ★ + 19 = 58, what number does ★ stand for?
3 · 19 · 58 · Symbol equation puzzles

12 questions · Seed 60 · 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 × ★ + 12 = 67, what number does ★ stand for?
11
Subtract 12 from 67 to get 55, then divide by 5: ★ = 11.
2. If ★ represents the same whole number each time and 2 × ★ + 19 = 47, what number does ★ stand for?
14
Subtract 19 from 47 to get 28, then divide by 2: ★ = 14.
3. If ★ represents the same whole number each time and 7 × ★ + 5 = 61, what number does ★ stand for?
8
Subtract 5 from 61 to get 56, then divide by 7: ★ = 8.
4. If ★ represents the same whole number each time and 7 × ★ + 8 = 92, what number does ★ stand for?
12
Subtract 8 from 92 to get 84, then divide by 7: ★ = 12.
5. If ★ represents the same whole number each time and 3 × ★ + 10 = 43, what number does ★ stand for?
11
Subtract 10 from 43 to get 33, then divide by 3: ★ = 11.
6. If ★ represents the same whole number each time and 7 × ★ + 5 = 110, what number does ★ stand for?
15
Subtract 5 from 110 to get 105, then divide by 7: ★ = 15.
7. If ★ represents the same whole number each time and 4 × ★ + 6 = 54, what number does ★ stand for?
12
Subtract 6 from 54 to get 48, then divide by 4: ★ = 12.
8. If ★ represents the same whole number each time and 2 × ★ + 14 = 24, what number does ★ stand for?
5
Subtract 14 from 24 to get 10, then divide by 2: ★ = 5.
9. If ★ represents the same whole number each time and 4 × ★ + 3 = 35, what number does ★ stand for?
8
Subtract 3 from 35 to get 32, then divide by 4: ★ = 8.
10. If ★ represents the same whole number each time and 8 × ★ + 18 = 34, what number does ★ stand for?
2
Subtract 18 from 34 to get 16, then divide by 8: ★ = 2.
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 × ★ + 19 = 58, what number does ★ stand for?
13
Subtract 19 from 58 to get 39, then divide by 3: ★ = 13.

12 questions · Seed 60 · 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 × ★ + 12 = 67, what number does ★ stand for?
5 · 12 · 67 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 19 = 47, what number does ★ stand for?
2 · 19 · 47 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 5 = 61, what number does ★ stand for?
7 · 5 · 61 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 8 = 92, what number does ★ stand for?
7 · 8 · 92 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 10 = 43, what number does ★ stand for?
3 · 10 · 43 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 5 = 110, what number does ★ stand for?
7 · 5 · 110 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 6 = 54, what number does ★ stand for?
4 · 6 · 54 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 14 = 24, what number does ★ stand for?
2 · 14 · 24 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 3 = 35, what number does ★ stand for?
4 · 3 · 35 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 18 = 34, what number does ★ stand for?
8 · 18 · 34 · 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 × ★ + 19 = 58, what number does ★ stand for?
3 · 19 · 58 · Symbol equation puzzles

12 questions · Seed 60 · 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 × ★ + 12 = 67, what number does ★ stand for?
11
Subtract 12 from 67 to get 55, then divide by 5: ★ = 11.
2. If ★ represents the same whole number each time and 2 × ★ + 19 = 47, what number does ★ stand for?
14
Subtract 19 from 47 to get 28, then divide by 2: ★ = 14.
3. If ★ represents the same whole number each time and 7 × ★ + 5 = 61, what number does ★ stand for?
8
Subtract 5 from 61 to get 56, then divide by 7: ★ = 8.
4. If ★ represents the same whole number each time and 7 × ★ + 8 = 92, what number does ★ stand for?
12
Subtract 8 from 92 to get 84, then divide by 7: ★ = 12.
5. If ★ represents the same whole number each time and 3 × ★ + 10 = 43, what number does ★ stand for?
11
Subtract 10 from 43 to get 33, then divide by 3: ★ = 11.
6. If ★ represents the same whole number each time and 7 × ★ + 5 = 110, what number does ★ stand for?
15
Subtract 5 from 110 to get 105, then divide by 7: ★ = 15.
7. If ★ represents the same whole number each time and 4 × ★ + 6 = 54, what number does ★ stand for?
12
Subtract 6 from 54 to get 48, then divide by 4: ★ = 12.
8. If ★ represents the same whole number each time and 2 × ★ + 14 = 24, what number does ★ stand for?
5
Subtract 14 from 24 to get 10, then divide by 2: ★ = 5.
9. If ★ represents the same whole number each time and 4 × ★ + 3 = 35, what number does ★ stand for?
8
Subtract 3 from 35 to get 32, then divide by 4: ★ = 8.
10. If ★ represents the same whole number each time and 8 × ★ + 18 = 34, what number does ★ stand for?
2
Subtract 18 from 34 to get 16, then divide by 8: ★ = 2.
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 × ★ + 19 = 58, what number does ★ stand for?
13
Subtract 19 from 58 to get 39, then divide by 3: ★ = 13.

12 questions · Seed 60 · Age guidance, not curriculum certification