What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Can you draw a square in which the perimeter is numerically equal to the area?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
How many faces can you see when you arrange these three cubes in different ways?