October 15, 2017 - Math Circle 2.0

Warm Up

Find the solutions to the following algebraic equations.

5 + x = 8

8 - y = 1

4 + 5 = z + 6

Game Theory

Play the nickel and penny game that we introduced last session with a partner.  Does any player have an advantage?

Remember the game:
A penny is worth one cent and a nickel is worth 5 cents.

There are two players to the game, player one and player two.  Both players will pick a coin in secret to play.  If both coins that are played match, player one wins both coins.  If both coins that are played do not match, player two wins both coins.  

Create payoff matrix for the nickel and penny game that we discussed in the previous math circle.  

What would happen if we added a dime to the mix to create a dime, nickel and penny game?  Let's answer next class.

October 8. 2017 - Math Circle 2.0

Warm Up

Perimeters of squares and circumferences of circles.  

Game Theory

Last class, we learned how to express a the game paper, rock, scissors in a pay-off matrix.  We found that the game was very balanced in which no player really had an advantage over another player.  Let's try another game....  Pennies and nickels.

A penny is worth one cent and a nickel is worth 5 cents.

There are two players to the game, player one and player two.  Both players will pick a coin in secret to play.  If both coins that are played match, player one wins both coins.  If both coins that are played do not match, player two wins both coins.  Play the game at home and see if you can find a winning strategy to win the most money.

Counting

There are three dogs:  Charlotte, Ozzy, and Rosie.  Each dog has a choice of one of four types of snacks:  Bone, Cupcake, Food, and Treats.  There is only one of each snack so two of the dogs cannot receive cupcake, for example.  Using your counting skills, map out the possible combinations of dogs and snacks.  There are 4 x 3 x 2, or 24 combinations.

Here are some combinations to get started:

               Ozzy        Rosie        Charlotte

1.            Bone        Cupcake   Food

2.            Bone        Cupcake   Treats

3.            Bone        Food         Cupcake

4.            Bone        Food         Treats

 

Map the rest of the combinations for homework.

October 1, 2017 - Math Circle 2.0

Homework Review

Using the supplied cup, measure the circumference of the cup.  Next, draw a square that inscribes the circle.  Is the perimeter of the square greater than the circumference of the circle?

Circumference of the circle

Use a string to mesasure the circumference of a set of circles.  Compare the diameter of the circles to the circumference.  In all cases, the circumference of the circle is a little over 3 times the diameter of the circle.  The number that expresses the ratio of diameter to circumference is represented by the greek letter pi.


Rock Paper Scissors

Learn how to play Rock, Paper, Scissors.  

Can you win at Rock Paper Scissors with a strategy?  Create a payoff matrix.

From:  http://shack.typepad.com/shack_in_japan/2012/05/game-theory-for-middle-school-day-1-payoff-matrices-and-rock-paper-scissors.html