In the first applet, explore how the shape and volume of a box changes as you cut squares from the corner of a 20cm square and fold up the sides. The slider a controls the size of the squares you cut off.
The second applet explores where the maximum volume occurs, for different sizes of square paper. This allows students to conjecture about the relationship between the maximum volume and the side length.
The third applet allows us to control both the length and the width of paper, to explore the maximum volume of rectangular boxes.