What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
How would you move the bands on the pegboard to alter these shapes?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?
