1. PROGRESSION IN NUMBER AND ALGEBRA

2. Objectives The objectives vary depending on which attainment target(s) are relative to the learning objectives of your lesson

3. Addition Arithmagons 3 8 4 1211 7 8 + 4 = ? 8 + 3 = ? 4 + 3 = ? The number in the square is equal to the sum of the circles connected to it

4. Addition Arithmagons 3 8 4 1211 7 Sum of the circles? Sum of the squares? Σ = 2 x Σ 15 30

5. Addition Arithmagons 3 8 4 1211 7 Can you make 15 another way? Σ = 15 Σ = +

6. Addition Arithmagons 3 8 4 1211 7 Σ = + Σ = 2 x Σ Σ = Magic Number + = Magic Number

7. Addition Arithmagons 10 4 7 1114 17 Sum of the squares? Magic number? 42 21 ? ? ?

8. 12 Addition Arithmagons 15 1114 27 Sum of the squares? Magic number? 52 26 ? ? ?

9. 12 Addition Arithmagons 15 1114 27 So, if the numbers in the squares do not satisfy the triangle inequality then you get zero or negative numbers?

10. 6.59.5 4.5 Addition Arithmagons 1114 16 Sum of the squares? Magic number? 41 20.5 ? ? ?

11. 4½4½7½7½ 6½6½ Addition Arithmagons 1114 12 So, if the sum of the squares is odd then you get fractions and/or decimals numbers!

12. 6aa 3a Addition Arithmagons 9a4a 7a Sum of the squares? Magic number? 20a 10a ? ? ?

13. 2b + 2 b b + 6 Addition Arithmagons 3b+82b+6 3b+2 Sum of the squares? Magic number? 8b + 16 4b + 8 ? ? ?

14. 2b + 2 b b + 6 Arithmagons and equations 3b+82b+6 3b+2 Sum of the squares? 8b + 16 So 4b + 8 = 28 and b = 5 We are told that the sum of the circles = 28

15. b = 5 2b + 2 b b + 6 Addition Arithmagons 3b+82b+6 3b+2 12 5 11 2316 17 =

16. Arithmagon: Generalisation Sum of the squares = a + b + b + c + a +c = 2a + 2b + 2c = 2(a + b + c) So, sum of squares = 2 x sum of circles What do we notice? a c b a +bb + c a + c

17. Arithmagon: Generalisation That the sum of a circle and a square opposite each other = a + b + c What do we notice? a c b a +bb + c a + c The End