# Punk Rock Operations Research

## a seven year old science fair project

Posted by Laura McLay on April 2, 2012

My seven year-old daughter worked on a science fair project this year. She decided to do a Yahtzee-like science fair project, where she rolled five fair dice and recorded how many unique numbers she rolled. Her hypothesis was that dice with fewer sides would have more matching numbers. She recorded 20 trials for 4, 6, 8, 10, 12, and 20-sided dice (6-sided dice were the control group). This was a great project that she could do on her own. She even made the bar charts herself.

My daughter’s project was the only project in the “math” category that didn’t involve M&Ms. That is probably worth a discussion of its own, but I’ll discuss the scientific findings here. Her poster is below. To the right, you can see one of the M&M projects.

Interestingly, 20 trials were not enough for the rolls to “average out” to the analytical solution. The results obtained from rolling the dice are below, with 20 trials in each column. She never rolled a full house, four-of-a-kind, or five-of-a-kind. The table here shows what she rolled, not what she expected. I compare expectations with reality in the figures below.

 # of sides on dice–> 4 6 8 10 12 20 All different 0 6 2 6 7 10 One pair 6 8 10 8 8 10 Two pairs 10 2 5 3 3 0 Three of a kind 4 4 3 3 2 0

I compared the actual results to the analytical solution for each type of dice. The results are shown below. I performed a goodness-of-fit test and did not obtain significant p-values (at the 0.05 level) for any of the scenarios, presumably because I had a small sample size. (I also had to combine bins to have at least 5 observations in each bin). The 6-sided dice seem to deviate the most from expectations. Here, my daughter expected 1.85 (of 20) rolls to result in all 5 dice being different, but she observed this outcome 6 times.

4-sided dice

6-sided dice

8-sided dice

10-sided dice

12-sided dice

20-sided dice

I love doing science fair projects. Math science fair projects are perfect for little ones. The advantages are:

• they are learning a lot of math in school, so it reinforces what they are learning in school,
• they can get started with their project before they lose interest, and
• they can do many trials very easily to draw a reasonable conclusion.

I also recommend making as many bar charts as possible, regardless of the topic. I have learned that bar charts are really intuitive for little minds. My kids started to learn about bar charts at about three years old in day care. Bar charts are part of the curriculum in kindergarten. To make a bar chart in a science fair project, you need to do more than 2-3 trials.

For more reading, check out my daughter’s science fair project in first grade, where she solved the subset sum problem or read about these science fair suggestions.

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1. ### Dr Nicsaid

Nice. Has your 7-year old seen Rogo? http://www.rogopuzzle.co.nz/mathematics-teaching/children/ It has great potential for a science fair project for next year. It is based on a prize-collecting subset selection tsp.
I have some teaching hints on the rogopuzzle blog. She could time people doing different puzzles, and make bar charts by person and by puzzle!
http://www.rogopuzzle.co.nz/rogo-news/teaching-rogo-math/

I’d love to hear how she goes.