In December, I asked for suggestions for my six year old daughter’s science fair project. After getting many excellent suggestions, my daughter ended up picking her own project. I promised to blog about her project, so here goes.

The science fair project began on a snowy day in December when I took my daughter to my office when her school closed. To keep her occupied, I printed out math worksheets and let her poke around on educational websites on my laptop. During a lull in the day’s activities, I wrote an instance of the subset sum problem with four items on my chalkboard just for kicks. I drew bars with lengths equal to the item sizes and then drew a number line of length ten to serve as the capacity. She then fit three of the items along the number line to exactly fit within the capacity of ten. She had so much fun with this, that we decided to do a subset sum science fair project. Could she always find numbers that would add up to ten?

Her experimental setup was to randomly generate sets of five items using five six-sided dice. She considered capacities of ten and twelve. We chose these capacities since (a) her class has done a lot of math involving the number 10 recently, and (b) 30 randomly generated Excel instances gave sizes that summed to fourteen or more, so twelve seemed like a reasonable capacity that wasn’t too big.

The goal of the project was to solve the subset sum problem visually and to then turn it into an addition problem. If she couldn’t find numbers that would exactly equal ten or twelve, she would find the closest number without going over the capacity. To solve the problems visually, we cut out bars of length 1″ to 6″ using grid paper and then made two number lines of length 10″ and 12″. We stuck Velcro to the numbers to make them stick.

When we set up the experiment and ran through a test case, my daughter figured out which numbers added to ten and how to write it down as an addition problem. She immediately said “This is fun!” and the rest is history. Soon, she was able to record the results in her log herself in addition to running the experiments.

We made a bar graph of the results together (the one thing I know about early math education is to use bar graphs! hers is below) and discussed whether the hypothesis was correct. She practiced explaining the experiment to me, and it was amazing how much she had learned during the process.

When I brought her poster to school, I noticed that she was the only kid to do a project in the “Math/Computer Science” category in grades K-2, the “junior” division (Chemistry, Life Sciences, and Physics were the popular categories). They K-2 projects were not judged, but as someone with science fair judging experience, I think she did a fantastic job. Regardless, I was happy with increasing my six year old’s enthusiasm for operations research.