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Use a pencil and ruler to draw several different lines all the way across the length or width of a piece of paper. Make lines diagonally at different angles instead of horizontally or vertically.
Make several copies of the paper with lines drawn in this manner. Using a paper cutter, slice the paper into the given pieces and place pieces from one paper into separate envelopes.
Divide students into groups and give each group one envelope. Groups race to discover the longest measurement that they can find of all of the pieces in the envelope. The first group to get the correct answer wins.
You can also download a PDF version of this game to file away for later here on my site or on TeachersPayTeachers.