Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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.

Challenge Level

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

Challenge Level

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Challenge Level

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

Challenge Level

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

Challenge Level

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?