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 7 × ★ + 2 = 93, what number does ★ stand for?
7 · 2 · 93 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 15 = 81, what number does ★ stand for?
6 · 15 · 81 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 8 = 23, what number does ★ stand for?
5 · 8 · 23 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 20 = 55, what number does ★ stand for?
5 · 20 · 55 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 19 = 49, what number does ★ stand for?
5 · 19 · 49 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 11 = 59, what number does ★ stand for?
6 · 11 · 59 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 3 = 69, what number does ★ stand for?
6 · 3 · 69 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 20 = 36, what number does ★ stand for?
8 · 20 · 36 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 4 = 102, what number does ★ stand for?
7 · 4 · 102 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 15 = 71, what number does ★ stand for?
7 · 15 · 71 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 5 = 65, what number does ★ stand for?
6 · 5 · 65 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 13 = 21, what number does ★ stand for?
4 · 13 · 21 · Symbol equation puzzles

12 questions · Seed 84 · 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 × ★ + 2 = 93, what number does ★ stand for?
13
Subtract 2 from 93 to get 91, then divide by 7: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 15 = 81, what number does ★ stand for?
11
Subtract 15 from 81 to get 66, then divide by 6: ★ = 11.
3. If ★ represents the same whole number each time and 5 × ★ + 8 = 23, what number does ★ stand for?
3
Subtract 8 from 23 to get 15, then divide by 5: ★ = 3.
4. If ★ represents the same whole number each time and 5 × ★ + 20 = 55, what number does ★ stand for?
7
Subtract 20 from 55 to get 35, then divide by 5: ★ = 7.
5. If ★ represents the same whole number each time and 5 × ★ + 19 = 49, what number does ★ stand for?
6
Subtract 19 from 49 to get 30, then divide by 5: ★ = 6.
6. If ★ represents the same whole number each time and 6 × ★ + 11 = 59, what number does ★ stand for?
8
Subtract 11 from 59 to get 48, then divide by 6: ★ = 8.
7. If ★ represents the same whole number each time and 6 × ★ + 3 = 69, what number does ★ stand for?
11
Subtract 3 from 69 to get 66, then divide by 6: ★ = 11.
8. If ★ represents the same whole number each time and 8 × ★ + 20 = 36, what number does ★ stand for?
2
Subtract 20 from 36 to get 16, then divide by 8: ★ = 2.
9. 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.
10. If ★ represents the same whole number each time and 7 × ★ + 15 = 71, what number does ★ stand for?
8
Subtract 15 from 71 to get 56, then divide by 7: ★ = 8.
11. If ★ represents the same whole number each time and 6 × ★ + 5 = 65, what number does ★ stand for?
10
Subtract 5 from 65 to get 60, then divide by 6: ★ = 10.
12. If ★ represents the same whole number each time and 4 × ★ + 13 = 21, what number does ★ stand for?
2
Subtract 13 from 21 to get 8, then divide by 4: ★ = 2.

12 questions · Seed 84 · 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 × ★ + 2 = 93, what number does ★ stand for?
7 · 2 · 93 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 15 = 81, what number does ★ stand for?
6 · 15 · 81 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 8 = 23, what number does ★ stand for?
5 · 8 · 23 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 20 = 55, what number does ★ stand for?
5 · 20 · 55 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 5 × ★ + 19 = 49, what number does ★ stand for?
5 · 19 · 49 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 6 × ★ + 11 = 59, what number does ★ stand for?
6 · 11 · 59 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 3 = 69, what number does ★ stand for?
6 · 3 · 69 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 20 = 36, what number does ★ stand for?
8 · 20 · 36 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 4 = 102, what number does ★ stand for?
7 · 4 · 102 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 7 × ★ + 15 = 71, what number does ★ stand for?
7 · 15 · 71 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 6 × ★ + 5 = 65, what number does ★ stand for?
6 · 5 · 65 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 13 = 21, what number does ★ stand for?
4 · 13 · 21 · Symbol equation puzzles

12 questions · Seed 84 · 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 × ★ + 2 = 93, what number does ★ stand for?
13
Subtract 2 from 93 to get 91, then divide by 7: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 15 = 81, what number does ★ stand for?
11
Subtract 15 from 81 to get 66, then divide by 6: ★ = 11.
3. If ★ represents the same whole number each time and 5 × ★ + 8 = 23, what number does ★ stand for?
3
Subtract 8 from 23 to get 15, then divide by 5: ★ = 3.
4. If ★ represents the same whole number each time and 5 × ★ + 20 = 55, what number does ★ stand for?
7
Subtract 20 from 55 to get 35, then divide by 5: ★ = 7.
5. If ★ represents the same whole number each time and 5 × ★ + 19 = 49, what number does ★ stand for?
6
Subtract 19 from 49 to get 30, then divide by 5: ★ = 6.
6. If ★ represents the same whole number each time and 6 × ★ + 11 = 59, what number does ★ stand for?
8
Subtract 11 from 59 to get 48, then divide by 6: ★ = 8.
7. If ★ represents the same whole number each time and 6 × ★ + 3 = 69, what number does ★ stand for?
11
Subtract 3 from 69 to get 66, then divide by 6: ★ = 11.
8. If ★ represents the same whole number each time and 8 × ★ + 20 = 36, what number does ★ stand for?
2
Subtract 20 from 36 to get 16, then divide by 8: ★ = 2.
9. 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.
10. If ★ represents the same whole number each time and 7 × ★ + 15 = 71, what number does ★ stand for?
8
Subtract 15 from 71 to get 56, then divide by 7: ★ = 8.
11. If ★ represents the same whole number each time and 6 × ★ + 5 = 65, what number does ★ stand for?
10
Subtract 5 from 65 to get 60, then divide by 6: ★ = 10.
12. If ★ represents the same whole number each time and 4 × ★ + 13 = 21, what number does ★ stand for?
2
Subtract 13 from 21 to get 8, then divide by 4: ★ = 2.

12 questions · Seed 84 · Age guidance, not curriculum certification