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.

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

The challenge for you is to make a string of six (or more!) graded cubes.

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Can you draw a square in which the perimeter is numerically equal to the area?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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?

These practical challenges are all about making a 'tray' and covering it with paper.