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Magic Square: Fill In the Numbers

In this worksheet, students use a simple rule to work out the missing numbers in a magic square.

'Magic Square: Fill In the Numbers' worksheet

Key stage:  KS 2

Curriculum topic:  Number: Addition and Subtraction

Curriculum subtopic:  Use Correct Methods to Problem Solve

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In this worksheet you will learn how to fill missing numbers in magic squares.

 

Example

Fill in the missing numbers in this magic square.

  3
 
  7  

 

Answer 

Each row, column and diagonal will add to the same amount (the magic total).

The clue here is that we have 3, 5 and 7 in a column, which means that the magic total is 3 + 5 + 7 = 15

Use this fact to complete the square using addition and subtraction.

 

8 3
9 
6 7 2 

Fill in the missing numbers in this magic square.

The magic total is 33.

 

 

 A 4  B
 C 20
 D 18 3

Column A

Column B

A
11
B
10
C
19
D
12

Fill in the missing numbers in this magic square.

The magic total is 21.

 

 

8 A 5
B 7 C
D 6 6

Column A

Column B

A
8
B
10
C
4
D
9

Fill in the missing numbers in this magic square.

The magic total is 30.

 

 

A 3 B
C D 19
11 17 2

Column A

Column B

A
1
B
18
C
10
D
9

Fill in the missing numbers in this magic square.

The magic total is 20 + 3 + 10.

 

 

20 3 10
 1 A  B
C 19 D

Column A

Column B

A
11
B
12
C
21
D
2

Fill in the missing numbers in this magic square.

The magic total is 9.

 

 

4 3 A
B C 5
4 3 D

Column A

Column B

A
2
B
2
C
3
D
1

Fill in the missing numbers in this magic square.

The magic total is 4 + 6 + 8.

 

 

9 A 4
1 6 B
8 C D

Column A

Column B

A
3
B
5
C
7
D
11

Fill in the missing numbers in this magic square.

Work out the magical total first.

 

 

A 3 10
B 11 C
12 19 D

Column A

Column B

A
1
B
20
C
21
D
2

Fill in the missing numbers in this magic square.

The magic total is 2 + 7 + 3.

 

  

5 A 2
1 B 7
C D 3

Column A

Column B

A
3
B
4
C
5
D
6

Fill in the missing numbers in this magic square.

The magic total is 18.

 

 

A 6 B
4 C 8
7 D 5

Column A

Column B

A
6
B
7
C
5
D
6

Fill in the missing numbers in this magic square.

Work out the magic total first.

 

 

 A B 6
1 C 13
D 11 2

Column A

Column B

A
3
B
7
C
12
D
8
  • Question 1

Fill in the missing numbers in this magic square.

The magic total is 33.

 

 

 A 4  B
 C 20
 D 18 3
CORRECT ANSWER

Column A

Column B

A
19
B
10
C
11
D
12
EDDIE SAYS
We can work out D first, as we are given the two other numbers on that row. So, we can work out 33 - 18 - 3, which is 12, so we know that D = 12.
Next, we can work out A, as we have the two other numbers in that column. 33 - 12 - 2 = 19, so A = 19.
Next we can work out B. 33 - 4 - 19 = 10.
This means that C must be 11. To check, we can to 33 - 4 - 18, which = 11.
  • Question 2

Fill in the missing numbers in this magic square.

The magic total is 21.

 

 

8 A 5
B 7 C
D 6 6
CORRECT ANSWER

Column A

Column B

A
8
B
4
C
10
D
9
EDDIE SAYS
This time, we can work out A first. 21 - 7 - 7 = 8, so A = 8.
Next, we can work out C. 21 - 5 - 6 = 10, so C = 10.
We can then work out B. 21 - 7 - 10 = 4.
Finally, we can work out D. 21 - 6 - 6 = 9.
  • Question 3

Fill in the missing numbers in this magic square.

The magic total is 30.

 

 

A 3 B
C D 19
11 17 2
CORRECT ANSWER

Column A

Column B

A
18
B
9
C
1
D
10
EDDIE SAYS
Let's work out B first. 30 - 19 - 2 = 9, so B = 9.
We can then work out A. 30 - 3 - 9 = 18, so A = 19.
To work out C, we do 30 - 11 - 18 = 1, so C = 1.
Finally, we can work out D. 30 - 19 - 1 = 10, so D = 10.
  • Question 4

Fill in the missing numbers in this magic square.

The magic total is 20 + 3 + 10.

 

 

20 3 10
 1 A  B
C 19 D
CORRECT ANSWER

Column A

Column B

A
11
B
21
C
12
D
2
EDDIE SAYS
In this question, we must work out the magic total first. 20 + 3 + 10 = 33. Then, we can work out the missing numbers:
A = 33 - 3 - 19 = 11, so A = 11
B = 33 - 1 - 11 = 21, so B = 21
C = 33 - 20 - 1 = 12, so C = 12
Finally, D = 33 - 19 - 12 = 2, so D = 2.
  • Question 5

Fill in the missing numbers in this magic square.

The magic total is 9.

 

 

4 3 A
B C 5
4 3 D
CORRECT ANSWER

Column A

Column B

A
2
B
1
C
3
D
2
EDDIE SAYS
First, we can work out A. 9 - 3 - 4 = 2
B = 9 - 4 - 4 = 1
C = 9 - 5 - 1 = 3
C = 9 - 5 - 2 = 2
  • Question 6

Fill in the missing numbers in this magic square.

The magic total is 4 + 6 + 8.

 

 

9 A 4
1 6 B
8 C D
CORRECT ANSWER

Column A

Column B

A
5
B
11
C
7
D
3
EDDIE SAYS
First, we must work out the magic total. 4 + 6 + 8 = 18. Now, we can work out the missing numbers:
A = 18 - 9 - 4 = 5
B = 18 - 6 - 1 = 11
C = 18 - 6 - 5 = 7
D = 18 - 8 - 7 = 3
  • Question 7

Fill in the missing numbers in this magic square.

Work out the magical total first.

 

 

A 3 10
B 11 C
12 19 D
CORRECT ANSWER

Column A

Column B

A
20
B
1
C
21
D
2
EDDIE SAYS
In this question, we have to work out the magic total first. In the middle column, all three numbers are provided, so we can add them up to work out the total. 3 + 11 + 19 = 33.
Now, we can work out the missing numbers:
A = 33 - 3 - 10 = 20
B = 33 - 12 - 20 = 1
C = 33 - 11 - 1 = 21
D = 33 - 19 - 12 = 2
  • Question 8

Fill in the missing numbers in this magic square.

The magic total is 2 + 7 + 3.

 

  

5 A 2
1 B 7
C D 3
CORRECT ANSWER

Column A

Column B

A
5
B
4
C
6
D
3
EDDIE SAYS
Again, we must first work out the magic total. 2 + 7 + 3 = 12. Now we can work out the missing numbers:
A = 12 - 5 - 2 = 5
B = 12 - 1 - 7 = 4
C = 12 - 5 - 1 = 6
D = 12 - 3 - 6 = 3
  • Question 9

Fill in the missing numbers in this magic square.

The magic total is 18.

 

 

A 6 B
4 C 8
7 D 5
CORRECT ANSWER

Column A

Column B

A
7
B
5
C
6
D
6
EDDIE SAYS
A = 18 - 4 - 7 = 7
B = 18 - 8 - 5 = 5
C = 18 - 4 - 8 = 6
D = 18 - 7 - 5 = 6
  • Question 10

Fill in the missing numbers in this magic square.

Work out the magic total first.

 

 

 A B 6
1 C 13
D 11 2
CORRECT ANSWER

Column A

Column B

A
12
B
3
C
7
D
8
EDDIE SAYS
Again, we have to work out the magic total first. In the right hand column, all three numbers are provided, so we can add them up to work out the total. 6 + 13 + 2 = 21.
Now, we can work out the missing numbers:
C = 21 - 13 - 1 = 7
A = 21 - 2 - 7 = 12
B = 21 - 6 - 12 = 3
D = 21 - 11 - 2 = 8
---- OR ----

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