ReasoningAges 10-12

Magic square missing values

Use the constant row sum of a 3 × 3 magic square to deduce the missing cell value. 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 10-12

Magic square missing values

Take your time. Show your thinking.

1. In a magic square, every row adds up to 28. One row has 13, 8, and ____. What is the missing number?
28 · 13 · 8 · Magic square missing values
2. In a magic square, every row adds up to 39. One row has 13, 6, and ____. What is the missing number?
39 · 13 · 6 · Magic square missing values
3. In a magic square, every row adds up to 35. One row has 6, 12, and ____. What is the missing number?
35 · 6 · 12 · Magic square missing values
4. In a magic square, every row adds up to 40. One row has 12, 20, and ____. What is the missing number?
40 · 12 · 20 · Magic square missing values
5. In a magic square, every row adds up to 26. One row has 7, 11, and ____. What is the missing number?
26 · 7 · 11 · Magic square missing values
6. In a magic square, every row adds up to 28. One row has 13, 5, and ____. What is the missing number?
28 · 13 · 5 · Magic square missing values
7. In a magic square, every row adds up to 35. One row has 11, 11, and ____. What is the missing number?
35 · 11 · 11 · Magic square missing values
8. In a magic square, every row adds up to 31. One row has 8, 17, and ____. What is the missing number?
31 · 8 · 17 · Magic square missing values
9. In a magic square, every row adds up to 39. One row has 15, 7, and ____. What is the missing number?
39 · 15 · 7 · Magic square missing values
10. In a magic square, every row adds up to 31. One row has 6, 16, and ____. What is the missing number?
31 · 6 · 16 · Magic square missing values
11. In a magic square, every row adds up to 28. One row has 9, 11, and ____. What is the missing number?
28 · 9 · 11 · Magic square missing values
12. In a magic square, every row adds up to 18. One row has 4, 3, and ____. What is the missing number?
18 · 4 · 3 · Magic square missing values

12 questions · Seed 45 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Magic square missing values

Answers and reasoning. Review before teaching.

1. In a magic square, every row adds up to 28. One row has 13, 8, and ____. What is the missing number?
7
Subtract 13 + 8 = 21 from 28: 28 − 21 = 7.
2. In a magic square, every row adds up to 39. One row has 13, 6, and ____. What is the missing number?
20
Subtract 13 + 6 = 19 from 39: 39 − 19 = 20.
3. In a magic square, every row adds up to 35. One row has 6, 12, and ____. What is the missing number?
17
Subtract 6 + 12 = 18 from 35: 35 − 18 = 17.
4. In a magic square, every row adds up to 40. One row has 12, 20, and ____. What is the missing number?
8
Subtract 12 + 20 = 32 from 40: 40 − 32 = 8.
5. In a magic square, every row adds up to 26. One row has 7, 11, and ____. What is the missing number?
8
Subtract 7 + 11 = 18 from 26: 26 − 18 = 8.
6. In a magic square, every row adds up to 28. One row has 13, 5, and ____. What is the missing number?
10
Subtract 13 + 5 = 18 from 28: 28 − 18 = 10.
7. In a magic square, every row adds up to 35. One row has 11, 11, and ____. What is the missing number?
13
Subtract 11 + 11 = 22 from 35: 35 − 22 = 13.
8. In a magic square, every row adds up to 31. One row has 8, 17, and ____. What is the missing number?
6
Subtract 8 + 17 = 25 from 31: 31 − 25 = 6.
9. In a magic square, every row adds up to 39. One row has 15, 7, and ____. What is the missing number?
17
Subtract 15 + 7 = 22 from 39: 39 − 22 = 17.
10. In a magic square, every row adds up to 31. One row has 6, 16, and ____. What is the missing number?
9
Subtract 6 + 16 = 22 from 31: 31 − 22 = 9.
11. In a magic square, every row adds up to 28. One row has 9, 11, and ____. What is the missing number?
8
Subtract 9 + 11 = 20 from 28: 28 − 20 = 8.
12. In a magic square, every row adds up to 18. One row has 4, 3, and ____. What is the missing number?
11
Subtract 4 + 3 = 7 from 18: 18 − 7 = 11.

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Magic square missing values

Take your time. Show your thinking.

1. In a magic square, every row adds up to 28. One row has 13, 8, and ____. What is the missing number?
28 · 13 · 8 · Magic square missing values
2. In a magic square, every row adds up to 39. One row has 13, 6, and ____. What is the missing number?
39 · 13 · 6 · Magic square missing values
3. In a magic square, every row adds up to 35. One row has 6, 12, and ____. What is the missing number?
35 · 6 · 12 · Magic square missing values
4. In a magic square, every row adds up to 40. One row has 12, 20, and ____. What is the missing number?
40 · 12 · 20 · Magic square missing values
5. In a magic square, every row adds up to 26. One row has 7, 11, and ____. What is the missing number?
26 · 7 · 11 · Magic square missing values
6. In a magic square, every row adds up to 28. One row has 13, 5, and ____. What is the missing number?
28 · 13 · 5 · Magic square missing values
7. In a magic square, every row adds up to 35. One row has 11, 11, and ____. What is the missing number?
35 · 11 · 11 · Magic square missing values
8. In a magic square, every row adds up to 31. One row has 8, 17, and ____. What is the missing number?
31 · 8 · 17 · Magic square missing values
9. In a magic square, every row adds up to 39. One row has 15, 7, and ____. What is the missing number?
39 · 15 · 7 · Magic square missing values
10. In a magic square, every row adds up to 31. One row has 6, 16, and ____. What is the missing number?
31 · 6 · 16 · Magic square missing values
11. In a magic square, every row adds up to 28. One row has 9, 11, and ____. What is the missing number?
28 · 9 · 11 · Magic square missing values
12. In a magic square, every row adds up to 18. One row has 4, 3, and ____. What is the missing number?
18 · 4 · 3 · Magic square missing values

12 questions · Seed 45 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Magic square missing values

Answers and reasoning. Review before teaching.

1. In a magic square, every row adds up to 28. One row has 13, 8, and ____. What is the missing number?
7
Subtract 13 + 8 = 21 from 28: 28 − 21 = 7.
2. In a magic square, every row adds up to 39. One row has 13, 6, and ____. What is the missing number?
20
Subtract 13 + 6 = 19 from 39: 39 − 19 = 20.
3. In a magic square, every row adds up to 35. One row has 6, 12, and ____. What is the missing number?
17
Subtract 6 + 12 = 18 from 35: 35 − 18 = 17.
4. In a magic square, every row adds up to 40. One row has 12, 20, and ____. What is the missing number?
8
Subtract 12 + 20 = 32 from 40: 40 − 32 = 8.
5. In a magic square, every row adds up to 26. One row has 7, 11, and ____. What is the missing number?
8
Subtract 7 + 11 = 18 from 26: 26 − 18 = 8.
6. In a magic square, every row adds up to 28. One row has 13, 5, and ____. What is the missing number?
10
Subtract 13 + 5 = 18 from 28: 28 − 18 = 10.
7. In a magic square, every row adds up to 35. One row has 11, 11, and ____. What is the missing number?
13
Subtract 11 + 11 = 22 from 35: 35 − 22 = 13.
8. In a magic square, every row adds up to 31. One row has 8, 17, and ____. What is the missing number?
6
Subtract 8 + 17 = 25 from 31: 31 − 25 = 6.
9. In a magic square, every row adds up to 39. One row has 15, 7, and ____. What is the missing number?
17
Subtract 15 + 7 = 22 from 39: 39 − 22 = 17.
10. In a magic square, every row adds up to 31. One row has 6, 16, and ____. What is the missing number?
9
Subtract 6 + 16 = 22 from 31: 31 − 22 = 9.
11. In a magic square, every row adds up to 28. One row has 9, 11, and ____. What is the missing number?
8
Subtract 9 + 11 = 20 from 28: 28 − 20 = 8.
12. In a magic square, every row adds up to 18. One row has 4, 3, and ____. What is the missing number?
11
Subtract 4 + 3 = 7 from 18: 18 − 7 = 11.

12 questions · Seed 45 · Age guidance, not curriculum certification