Edible Fractions
(Suggested by Yarrow Durbin/Shorecrest High School)
1. Each group of four has received three licorice twists.
If the people in your group are to share the licorice equally, how much will each receive. Express your answer as a fraction or mixed number where the unit is one whole twist.
Each twist is 6 inches long. Find a way to make one cut of the twists so that each member will get her/his equal share. Sketch the situation and include the inch markings. ( Note: More than one twist may be cut at a time, but the knife can only make one slice. The ends of the twists need not line up.) Use the strips of paper to test your slice. When you are satisfied that you have a solution, call over an instructor who will bring the licorice for you to cut and share.
2. Now each group of four should use five six-inch twists. Show at least two ways to divide the licorice into equal shares that involves only one cut. In your sketch of each situation, include the inch markings for the location of the cuts.
3. Repeat the process with 6 1/2 six- inch twists. How much should each person receive? What part of a whole twist will each group member receive?
Show several ways that this can be done in only one cut. Draw sketches and label the exact locations of the cuts in inches.
4. So far, each situation involving a given amount of licorice can be divided evenly among a group of four using only one cut. Find an amount of licorice (consisting of 3 or more pieces) that cannot be divided evenly among four people with only one cut. Keep track of the numbers you have tried. After you have tried at least six additional numbers, begin to describe a strategy for finding numbers of pieces that might not work. Also describe your strategies for making the cuts. Are you finding one or two that seem to work in every case?