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

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

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

Complete the magic square using the remaining digits from 1 to 9 2 Complete the magic square using the remaining digits from 1 to 9 3 5 1 6

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

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

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

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

– 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

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