The “Three Doors, One Prize” Probability Puzzle

In the recent movie: “21” a probability puzzle is presented:

A quiz show contestant is lead to a room with three doors. Behind one of them there’s an expensive sports car; behind the other two there’s a goat. The candidate chooses one of the doors. But it is not opened; the host (who knows the location of the sports car) opens one of the other doors instead and shows a goat. The rules of the game, which are known to all participants, require the host to do this irrespective of the candidate’s initial choice. The candidate is now asked if he wants to stick with the door he chose originally or if he prefers to switch to the other remaining closed door. His goal is the sports car, of course!

The question now is:

* Is the candidate better off if he sticks with his original choice, * are his chances better if he switches, or * does it not matter whether he switches or not?

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Interesting Puzzle- how does this work?

1. Take an eight by eight grid (with 64 squares).
2. Fill it randomly with digits 1 through 8.
3. Now start at any number on the left most column.
4. Move that many spaces down your grid (going up to the top of the next column if you run out of space).
5. Whatever number you land on, take that many steps down the grid, moving to the top of the next column if you run out of space, and continue.
6. Continue this procedure, until you run out of room on the whole grid.
7. Mark the last spot you landed on.
8. Start again with a new number on the left most column of your grid. Redo the whole procedure.
9. Try again, starting with yet another number on the left most column of the grid. And again. And again.
10. What happened?

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Building houses of straw, sticks, and bricks – The Three Little Pigs lesson plan

Keeping with the theme of building, my last workshop for the younger elementary students was about building structures of different materials. I first read the kids the classic tale of the Three Little Pigs. This is an amazing little story that can be used as a starting point for a Scientific Method / Building Lesson Plan.

After that we discussed the different materials that were used to build the three houses. I asked the kids to make a hypothesis whether the story is correct. Here are some questions we discussed:

  • Which house is really the best one? Why do you think so?
  • What is the manipulated variable in this story? What is the responding variable? What about the controlled variables?
  • How could we test out the hypothesis? How many times would we have to do the experiment to feel satisfied that the story is correct or incorrect?

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Teaching Hydraulics and Pneumatics Unit to Children

Hydraulics and Pneumatics are great topics to teach children.  First of all both words sound very impressive and when the children learn these words they will sound very important and knowledgeable if they use them.  Also,  hydraulics and pneumatics are used in many machines and in many everyday applications, therefore it is easy to show the importance of understanding these topics.  One can easily show and explain the difference between hydraulics and pneumatics – a great “Compare and Contrast” analysis. Thirdly, there are many fun and impressive experiments that can be done with hydraulics and pneumatics in a very inexpensive way, with very accessible materials.  And finally, since hydraulics and pneumatics is so useful, there can be multiple projects that children can actually build themselves.  Thus weaker students and stronger science students can both do projects, yet with differing complexity. Here are some of the techniques I use in order to teach hydraulics and pneumatics to children:

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Does frequency of light affect the current of the Photoelectric Effect?

This week, one of my students challenged my understanding of the photoelectric effect… Basically, he didn’t think that the current produced by the photoelectric effect should be affected by the frequency of the photons, but only by the intensity of the light. After a while, he convinced me – more photons per second (the intensity) should mean more electrons per second, but why would the speed of the electrons have an effect on the current?

However, from the PHET simulation of the photoelectric effect as well as the experimental results of a photoelectric device we have at school, it was obvious that current should be affected by frequency. I looked on the internet for a possible explanation… I couldn’t find anything reasonable. I even looked at the spectrum of our light used in the experiment, thinking that the intensity of the blue light was larger than the intensity of the red light – but no, that wasn’t the case.

So I asked an expert – Dr. Friesen, the professor responsible for the Modern Physics course at the University of Calgary. He was kind enough to reply with an incredibly clear explanation.

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