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 × ★ + 16 = 51, what number does ★ stand for?
5 · 16 · 51 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 5 × ★ + 11 = 26, what number does ★ stand for?
5 · 11 · 26 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 3 × ★ + 15 = 21, what number does ★ stand for?
3 · 15 · 21 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 7 = 47, what number does ★ stand for?
5 · 7 · 47 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 12 = 20, what number does ★ stand for?
4 · 12 · 20 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 19 = 31, what number does ★ stand for?
6 · 19 · 31 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2 · 18 · 22 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 5 = 35, what number does ★ stand for?
3 · 5 · 35 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 12, what number does ★ stand for?
5 · 2 · 12 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 1 = 26, what number does ★ stand for?
5 · 1 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 12 = 132, what number does ★ stand for?
8 · 12 · 132 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 14 = 28, what number does ★ stand for?
2 · 14 · 28 · Symbol equation puzzles

12 questions · Seed 63 · 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 × ★ + 16 = 51, what number does ★ stand for?
7
Subtract 16 from 51 to get 35, then divide by 5: ★ = 7.
2. If ★ represents the same whole number each time and 5 × ★ + 11 = 26, what number does ★ stand for?
3
Subtract 11 from 26 to get 15, then divide by 5: ★ = 3.
3. If ★ represents the same whole number each time and 3 × ★ + 15 = 21, what number does ★ stand for?
2
Subtract 15 from 21 to get 6, then divide by 3: ★ = 2.
4. If ★ represents the same whole number each time and 5 × ★ + 7 = 47, what number does ★ stand for?
8
Subtract 7 from 47 to get 40, then divide by 5: ★ = 8.
5. If ★ represents the same whole number each time and 4 × ★ + 12 = 20, what number does ★ stand for?
2
Subtract 12 from 20 to get 8, then divide by 4: ★ = 2.
6. If ★ represents the same whole number each time and 6 × ★ + 19 = 31, what number does ★ stand for?
2
Subtract 19 from 31 to get 12, then divide by 6: ★ = 2.
7. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2
Subtract 18 from 22 to get 4, then divide by 2: ★ = 2.
8. If ★ represents the same whole number each time and 3 × ★ + 5 = 35, what number does ★ stand for?
10
Subtract 5 from 35 to get 30, then divide by 3: ★ = 10.
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 12, what number does ★ stand for?
2
Subtract 2 from 12 to get 10, then divide by 5: ★ = 2.
10. If ★ represents the same whole number each time and 5 × ★ + 1 = 26, what number does ★ stand for?
5
Subtract 1 from 26 to get 25, then divide by 5: ★ = 5.
11. If ★ represents the same whole number each time and 8 × ★ + 12 = 132, what number does ★ stand for?
15
Subtract 12 from 132 to get 120, then divide by 8: ★ = 15.
12. If ★ represents the same whole number each time and 2 × ★ + 14 = 28, what number does ★ stand for?
7
Subtract 14 from 28 to get 14, then divide by 2: ★ = 7.

12 questions · Seed 63 · 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 × ★ + 16 = 51, what number does ★ stand for?
5 · 16 · 51 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 5 × ★ + 11 = 26, what number does ★ stand for?
5 · 11 · 26 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 3 × ★ + 15 = 21, what number does ★ stand for?
3 · 15 · 21 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 7 = 47, what number does ★ stand for?
5 · 7 · 47 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 12 = 20, what number does ★ stand for?
4 · 12 · 20 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 19 = 31, what number does ★ stand for?
6 · 19 · 31 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2 · 18 · 22 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 5 = 35, what number does ★ stand for?
3 · 5 · 35 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 12, what number does ★ stand for?
5 · 2 · 12 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 5 × ★ + 1 = 26, what number does ★ stand for?
5 · 1 · 26 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 12 = 132, what number does ★ stand for?
8 · 12 · 132 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 14 = 28, what number does ★ stand for?
2 · 14 · 28 · Symbol equation puzzles

12 questions · Seed 63 · 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 × ★ + 16 = 51, what number does ★ stand for?
7
Subtract 16 from 51 to get 35, then divide by 5: ★ = 7.
2. If ★ represents the same whole number each time and 5 × ★ + 11 = 26, what number does ★ stand for?
3
Subtract 11 from 26 to get 15, then divide by 5: ★ = 3.
3. If ★ represents the same whole number each time and 3 × ★ + 15 = 21, what number does ★ stand for?
2
Subtract 15 from 21 to get 6, then divide by 3: ★ = 2.
4. If ★ represents the same whole number each time and 5 × ★ + 7 = 47, what number does ★ stand for?
8
Subtract 7 from 47 to get 40, then divide by 5: ★ = 8.
5. If ★ represents the same whole number each time and 4 × ★ + 12 = 20, what number does ★ stand for?
2
Subtract 12 from 20 to get 8, then divide by 4: ★ = 2.
6. If ★ represents the same whole number each time and 6 × ★ + 19 = 31, what number does ★ stand for?
2
Subtract 19 from 31 to get 12, then divide by 6: ★ = 2.
7. If ★ represents the same whole number each time and 2 × ★ + 18 = 22, what number does ★ stand for?
2
Subtract 18 from 22 to get 4, then divide by 2: ★ = 2.
8. If ★ represents the same whole number each time and 3 × ★ + 5 = 35, what number does ★ stand for?
10
Subtract 5 from 35 to get 30, then divide by 3: ★ = 10.
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 12, what number does ★ stand for?
2
Subtract 2 from 12 to get 10, then divide by 5: ★ = 2.
10. If ★ represents the same whole number each time and 5 × ★ + 1 = 26, what number does ★ stand for?
5
Subtract 1 from 26 to get 25, then divide by 5: ★ = 5.
11. If ★ represents the same whole number each time and 8 × ★ + 12 = 132, what number does ★ stand for?
15
Subtract 12 from 132 to get 120, then divide by 8: ★ = 15.
12. If ★ represents the same whole number each time and 2 × ★ + 14 = 28, what number does ★ stand for?
7
Subtract 14 from 28 to get 14, then divide by 2: ★ = 7.

12 questions · Seed 63 · Age guidance, not curriculum certification