Wrapping presents on the diagonal

Dr. Sara Santos is a popular mathematician and speaker on mathematics.  She has worked out a method for wrapping boxes (rectangular prisms) as efficiently as possible. (Watch the video above)  Her method was written up in this article in Mental Floss and she was interviewed about her wrapping paper method in this video clip from The One Show.

In this activity students determine if this method for minimizing wrapping paper is actually more efficient then the traditional method.   For a hands on learning experiment, have students actually wrap a small rectangular prism using any available paper in both the traditional and diagonal methods. Then let them compare the two quantities of wrapping paper and decide which method uses less paper and by what percent.

This a good opportunity to work with surface area and the Pythagorean Theorem.  If students are too young to have worked with the Pythagorean Theorem you can use this representation of each rectangular prism which gives a scale drawing on a grid of the 6 by 6 and 6 by 8 faces.  Students can figure out the diagonal length by doing a little scale conversion work.  How much wrapping paper does this method save?  Should you just use a gift bag?

Finally ask students to try to explain why this diagonal method works (Extension).