1. Objective:
Today we will investigate the ‘magic’ in magic squares

2. 4 14 3 6 7 8 11 10 This is a ‘magic’ square.
Can you see what properties it has? 6 7 8 11 10

3. Magic square rules
All row totals
all column totals
two diagonal totals
are all the same
no number should be repeated

4. Complete the magic square using the remaining digits from 1 to 92
Complete the magic square using the remaining digits from 1 to 9 3 5 1 6

5. 5 2 4 4 9 8 4 6 8 5 11 10 6 5 6 12 9 11 21 10 15 19 13 23 12 19 7 16 25 22 29 10

6. 5 10 3 2 9 4 8 9 4 9 8 13 4 6 8 7 5 3 3 7 11 14 10 6 9 2 7 6 1 8 10 5 6 7 12 11
solutions 12 21 9 11 21 10 18 27 15 19 30 11 11 14 17 13 14 15 17 20 23 12 20 28 19 7 16 18 7 17 25 13 22 29 10 21

7. 3 6
3.9 4 2
0.5
2.5
5.5
5.9
5.1 3 4
complete the magic squares so they have the same row, column and diagonal totals
1.4
0.6 1
0.5 2
0.6
1.3
1.3 1 2 3 1

8. solutions
1.5 1 2 3 4
3.5
0.5
2.5
5.5 6 5
4.9
6.1
4.1
5.9
3.9
5.1
1.8
0.8
0.4
1.2
1.6
0.6
1.4
1.7
3.7
2.3
1.3
0.3
2.7
1.1
0.1

9. – 0.8
2.4
0.41
0.6
1.6
1.8
2.2
1.2
2.1
1.4
0.8
0.2
– 0.06
0.34
0.12
– 0.43
1.63 1
complete the magic squares so they have the same row, column and diagonal totals
– 0.23

10. solutions
– 1.2 1 2
0.6
– 0.8
2.4
0.23
0.41
0.05
2.03
1.8
0.2
1.2
1.4
1.6
0.8
2.8
2.2
2.1
0.7
0.5
1.3
1.9
– 0.4
0.3
– 0.06
0.34
0.16
0.52
0.12
– 0.03
1.83
– 0.43
1.63
– 0.23