This document discusses magic squares, which are grids of numbers where the sums of each row, column and diagonal are equal. It provides examples of magic squares and asks the reader to determine which are magic squares and their magic totals. It also explains that a quick way to find the magic total is to multiply the center number by 3. The document covers identifying magic squares, completing magic squares, and using number sequences to make magic squares.

1. Unit 1: Magic squares Lesson 1: It’s magic 7.1.1

3. Make it magic 12 7 8 13 9 5 10 11 6 What is the total of these three numbers? 27 27 27 27 27 27 27 27 7.1.1

4. More magic 7 13 9 5 10 11 6 12 8 If all the straight lines of numbers add up to the same total then the square is called a ‘ magic square ’. The total is called the ‘ magic total ’. 27 27 27 27 27 27 27 27 7.1.1

5. Which of these squares are magic squares? What are their magic totals? 60 84 More magic 7.1.1 26 34 20 6 30 14 16 24 10 3 12 9 5 8 15 4 14 10 31 29 28 27 30 25 29 27 26

6. 13 How can the middle square be made magic? Change 12 … 3 9 5 8 15 4 14 10 60 84 12 12 to 13 7.1.1 More magic 26 34 20 6 30 14 16 24 10 31 29 28 27 30 25 29 27 26

7. It’s magic! 7.1.1 More magic

8. 13 Find the missing numbers in each square. What are the magic totals? 5 11 14 17 8 23 11 17 20 2 9 12 4 16 7 11 14 5 11 10 9 8 15 7 13 12 42 30 12 6 27 7.1.1 More magic

9. 13 What is a quick way of finding the magic total? 5 11 17 8 23 11 17 20 2 12 4 16 7 11 14 5 11 9 8 15 7 13 12 42 30 12 6 27 Multiply the centre number by 3 14 9 10 14 9 10 7.1.1 More magic

10. The magic square that uses each of the numbers 1–9 is attributed to Emperor Yu. He reigned in China in about 2200BC. The study of magic squares has continued since then using squares of different sizes. 7.1.1 More magic