Squares

Can you find the squares hidden on these coordinate grids?

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

What is the greatest number of squares you can make by overlapping three squares?

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?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

What can you see? What do you notice? What questions can you ask?