PROGRESSION IN NUMBER AND ALGEBRA. Objectives The objectives vary depending on which attainment target(s) are relative to the learning objectives of your.

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Presentation transcript:

PROGRESSION IN NUMBER AND ALGEBRA

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

Addition Arithmagons = ? = ? = ? The number in the square is equal to the sum of the circles connected to it

Addition Arithmagons Sum of the circles? Sum of the squares? Σ = 2 x Σ 15 30

Addition Arithmagons Can you make 15 another way? Σ = 15 Σ = +

Addition Arithmagons Σ = + Σ = 2 x Σ Σ = Magic Number + = Magic Number

Addition Arithmagons Sum of the squares? Magic number? ? ? ?

12 Addition Arithmagons Sum of the squares? Magic number? ? ? ?

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

Addition Arithmagons Sum of the squares? Magic number? ? ? ?

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

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

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

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

b = 5 2b + 2 b b + 6 Addition Arithmagons 3b+82b+6 3b =

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

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