Move four sticks so there are exactly four triangles.
Explore the triangles that can be made with seven sticks of the
Reasoning about the number of matches needed to build squares that
share their sides.
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?