Friday, January 14, 2011

Science Fair

It's that time of year again! Time for our homeschool group science fair. We had fun working on our projects and presenting them to the group. What amazes me is the transformation in my younger children, how they have become confident speakers, proud of their work! We presented 4 projects: Is Inside or Outside Air Cleaner (Sophia), Catapults (William), the Birthday Paradox (Jacob and Cade) and Dice Roll (Grant).

The Birthday Paradox: This project shows how mathematical probability sometimes contradicts our intuition. Despite the fact that there are 365 days in a year, if you survey a random group of just 23 people there is a 50% chance that two of them will have the same birthday. It further states that if the sample is expanded to just
57 people, the probability rises to over 99%.

First we ran the study using our homeschool group directory from 2009. There were enough child member birth dates to run an additional 12 group samples. In 6 sample
groups (groups 1, 4, 5, 6, 10, 11) there were shared birthdays and in 6 sample groups (groups 2, 3, 6, 7, 9, 12) there were no shared birthdays, but group #12
did have 3 sets of twins. We had previously decided to exclude twins from our sample since we felt they could impact the data. We then went on to run the study using additional groups (family, 2 online groups and a Moms group).

CONCLUSION: Our sampling of 26 groups of 23 people provided us with results that 15 groups had shared birthdays and 11 groups did not have shared birthdays, which exceeded the probability predicted by the birthday paradox. In 5 of our samples there were even 2 sets of matching birthdays and in 1 sample there were 3 sets of matching birthdays! Each time we merged groups we ended up with at least one matching birthday in the newly created group of 57 (two groups plus an additional person). Our one sample group of 57 (our dad's family) provided us with 3 shared birthdays.

Grant's project was a probability project as well. He wanted to see what number was most likely to appear when you rolled a pair of dice. He ran his trial 155 times and found that 7 and 8 appeared the most often. He had originally thought it would be 7, but after getting the results he did, he understood why he got both number an almost identical number of times.

Sophia decided she wanted to see if outside air or inside air was cleaner. To test this she used 1 1/2 inch squares of white paper covered with Vaseline. She placed on square inside in our dining room and one outside on the porch. Every 24 hours she would replace the square with a new square. She then counted up how many dust and dirt particles were on each square. She ran her trial for 1 week. She decided that outside air was cleaner than inside air.

William enjoyed making and playing with the catapults so much from our science club (see post from last Friday below) that he decided to make some other catapults and show them to everyone. He made 3 additional catapults. His favorite is the mousetrap catapult!

Here are the other designs we made:
Simple catapult using newspaper, tape, rubber band and a spoon:

Catapult using popsicle sticks, tape and rubber band:

And William's favorite, the mousetrap catapult:

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