Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
Investigate these hexagons drawn from different sized equilateral
Finding the best solution for this
problem depended on thinking very carefully about what was meant by
DIFFERENT ways of arranging the five triangles. For example:
Christine (Malborough School) explained:
As Sophie said:
Leyla (Private IRMAK Primary School, Istanbul,
Turkey) sent in drawings of the four ways:
Merve (Private IRMAK Primary School,
Istanbul, Turkey) agreed with this set of four shapes
Caroline and Rebecca (The Mount School, York)
also realised that some shapes they found were really the same as
others if you turned them around or flipped them over:
Kirstine (Tattingstone School) also saw
how to group some 'variations' of the same shape together.
However, if you decided to think about each position of
the shape as being different, then there would be many shapes in
Ece (Private Irmak Primary School) found $18$
shapes. Do think there are any more?
Christopher (Tattingstone School) found two
more variations of the straight line. Well done to everyone else
who sent in some shapes.