Right menu

Featured resource

Making number talks matter

Making number talks matter

A number talk is a brief daily practice where students mentally solve computation problems and talk about their strategies. The talks help students to work flexibly with numbers and arithmetic properties, building a solid foundation and confident disposition for future learning.

Members: $ 34.00 inc.GST Others: $ 42.50 inc.GST


Grandi’s series

Consider 1 – 1 + 1 – 1 + ….

Is the answer 0, 1 or ½? Or all three?

Approaches:

[A]    (1 – 1) + (1 – 1) + (1 – 1) + … = 0 + 0 + 0 + … = 0

 

[B]     1 + (– 1 + 1) + (– 1 + 1 ) + (– 1 + 1) + … = 1 + 0 + 0 + 0 + … = 1

 

[C]     S = (1 – 1 + 1 – 1 + 1 – 1 +  …) , so

    1 – S = 1 – (1 – 1 + 1 – 1 + 1 – 1 + …) = 1 – 1 + 1 – 1 + 1 – 1 + 1 … = S

    1 – S = S

          1 = 2S

          S = ½