{{:2018:mathematics:mathematical-thinking-banner-790x50.jpg|Mathematical Thinking Banner}}
=== THESE ACTIVITIES DID NOT FORM PART OF THE ORIGINAL 'MATHEMATICAL THINKING' PROJECT ===

=== GETTING STARTED ===
  * If you are sharing or not using your own journal, Write your name at the top of the page
  * In your journal or at the top of your page, write the date and the title

====== Tower of Hanoi On-line ======
Hanoier is a Tower of Hanoi implementation in JavaScript using jQuery. Read more in the related [[http://www.stoyanr.com/2012/10/hanoier-tower-of-hanoi-in-javascript.html|blog post]].

  * https://github.com/stoyanr/Hanoier

====== CARS AND GOATS ======

=== Date: __.__.__ ===

=== Title: CARS AND GOATS ===

----

Each student takes a turn as a guest/player in an imaginary TV game show.
  * The TV host (teacher or student experimenter/scientist) shows each guest three doors
  * The guest/player is told that behind one of the doors there is a car.
  * Behind the other two doors, there are goats.

The guest/player must try to win the car. To win the car:
  * The TV host/experimenter asks the guest/player to choose a door.
  * After the guest/player makes a choice, the TV host/experimenter opens a different door, revealing a goat. 
  * The TV host/experimenter then says something like "We're down to two pots now, and I'm going to give you the chance to change your mind": To stay with the initial choice, or change their mind and switch to the remaining closed door.

THE PROBLEM
  * If you were the guest/player, do you think it makes any difference which door you choose?
  * If you played this game 30 times, how many times do you think a player would win a car?

Write down how many times you predict a player would win if they played 30 games and draw a circle around your prediction.

Write down your justifications/proof, so that you can share and explain it to other students.

Design an experiment that would test your prediction.

Perform your experiment and record the data (for example, in a table of results in your journal)

  * Write down the number of games and draw a triangle around that number
  * Write down the number of cars that were won in your experiment and draw a square around it.

Do the experimental results (data) support your prediction?

REMEMBER 
  * The game show host/experimenter knows in advance which of the three doors hides the car.
  * Whatever door the guest/player initially chooses, the host/experimenter knows which of the remaining doors to open to reveal a goat.
  * More certain still, the guest/player knows that the host/experimenter will certainly not open the door that hides the car. 

====== A Reminder About How We Do An Experiment: ======
{{ :scientific-method-steps_v6.png |The scientific process}}

----