sierpinski

how many black triangles at each stage?

how many black triangles?
how can you work this out from the sequence?

Sierpinski triangles are fairly easy to construct on an electronic whiteboard

draw a shape (or a word)
copy this twice and put the three together as an equilateral (or isosceles) triangle
group these three and maybe shrink them

copy two more of these and again fit them together in a triangle

keep going...

this task presents a way of looking at powers:

• if you count the number of black triangles at each stage you get powers of 3
• if you look at the way the base line is divided into equal sections you get powers of 2
• if you look at the fractions of the whole triangles shaded (black), you get powers of 3/4