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Probability Pi Day Carnival, Part II!

07 Mar

Here’s how the Pi Day preparations are going and what the students are up to.  There is some great math going on, and every year I enjoy this project more and more.  I always finish the unit wondering why I don’t do more project-based learning.

First:  Students need to create a game, and write the rules for it.  They have to determine how much you pay to play, and include how much you win for various levels of prizes.  The math has to contain multiple probabilities or multiple events to get an advanced grade.  This group of students has a game where you pick a card, which has a fraction on it from 1/5 to 4/5.  You turn around, and they put pigs under the buckets such that the fraction represents your probability of revealing a pig.  When you choose a bucket, you win a prize if you find a pig.

Sort of a Monty Hall idea?

Sort of a Monty Hall idea?

Second: Students need to calculate the theoretical probability of winning.  They need to show how they arrived at the probability.

This group used a counting tree to determine the probability of drawing two matching puzzle pieces.

This group used a counting tree to determine the probability of drawing two matching puzzle pieces.

This student uses Area = pi x r^2 to figure out the probability of throwing a ball through a precisely measured circular hole.

This student uses Area = pi x r^2 to figure out the probability of throwing a ball through a precisely measured circular hole.

Third: Students have to test their game 100 times to determine the experimental probability, and discuss differences between experimental and theoretical probability.  Games of skill often have a big difference between experimental and theoretical, while pure chance games are very close!

A student intern tries to put these 5 jars of candy in the right order, blindfolded.

A student intern tries to put these 5 jars of candy in the right order, blindfolded.

 

These students roll marbles onto their target area.

These students roll marbles onto their target area.

Fourth: Students have to make predictions based on their probabilities, to help the carnival organizers determine how many prizes they’ll need to buy – and to make sure their project will make a profit!

These students say the buckets will be full of prizes for their duck game. How full though?

These students say the buckets will be full of prizes for their duck game. How full though?

 

Lastly, the students make a presentation pitching their game to the carnival committee, and the committee determines which games make the cut.  We pick about a third of the games to represent the school in the big Pi Day carnival after school.  The rest of the games will be played in the class mini-carnival on the day before Spring Break.

This young man couldn't decide on a name for this spinner game, but thought "The Wheel of Awesomeness" would help in his sales pitch.

This young man couldn’t decide on a name for this spinner game, but thought “The Wheel of Awesomeness” would help in his sales pitch.

These students collaborate on their presentation using Google Docs.  Their game is called "Flash Dice".

These students collaborate on their presentation using Google Docs. Their game is called “Flash Dice”.

 

On March 14, after school, we reserve the gym.  We set up a table for each group and allow them to come set up their project.  We sell tickets for ten cents each, and provide each group with some tickets and a small bag of candy to give away.  If tickets are given as prizes, they can be entered in a big raffle drawing.  We also have food, drinks, and a silent auction.  It ends up being one of the biggest events of the year, and it’s a celebration of math!

 

Photos of the big day coming soon.  I will also post a grading rubric for the projects!

 

 

 

 

 

 

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Posted by on March 7, 2013 in Uncategorized

 

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