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Q&A #721


Probability

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From: Marielouise (for Teacher2Teacher Service)
Date: Nov 04, 1998 at 16:50:45
Subject: Re: Probability

Hi, Clare,

I was so thrilled to see where you are studying.  I was in Scotland ,
Edinburgh and St. Andrew's, last summer.  You have a beautiful country.  Now
to answering your question.

This first reply is from a teacher named Tracey who participated in a
discussion on probability in elementary school:

"I always "bribe" my students while teaching probability and they love
 it!  I always take the pound bags of M&M's and split them into zipper bags
(one for each student) making sure that there is a variety of colors in each
bag.  Then I ask them questions about probability and odds.  For example,
"What is the probability/odds that you will draw a red M&M out of your bag?"
Even though most of the students answers will be different, they really enjoy
the activity and have a clear understanding of probability and odds.  (The
students only get to eat the M&M's if they participate in the activity.) "

-------

The second is a reply from a teacher named Susan on T2T who has also answered
this type of question before.

"Not knowing exactly what grade level you are teaching will make my answer a
bit general, but first let me suggest an excellent resource: "Math By All
Means: Probability", by Marilyn Burns.

Start by developing the language with children. Ask questions like: "If
someone said it is POSSIBLE that it will snow, what would they mean?" or "Can
you be CERTAIN that everyone will be in school tomorrow?"

Get the kids to develop sentences for words like possible, likely, probably,
impossible, certain, maybe, and so on.

Make a chart of "PROBABILITY WORDS" to post and add to as your lessons
progress. Have three columns on a chart:

CERTAIN     POSSIBLE     IMPOSSIBLE

- brainstorm things that would fit in each column and make the kids prove
them.

I like to limit the younger ones, at first, to things that happen in school,
or you'll get too much information."

---------

I like to include trying to find out all the possible probabilities that can
happen.  Playing cards are one of the standard ways to approach this.

The first reply talked about working with M&M candies.  What is interesting
about the packaging of M&M's that for large quantities the distribution is
quite close to what is expected.

Another approach to probability is to look at it geometrically.  Consider a
circle inscribed inside a square.  What is the probability that is randomly
selected a point will lie inside the square but outside the circle.  This is
done by finding the areas of both the circle and the square.  Therefore, the
probability if (Area of Square - Area of Circle) / (Area of Square).
Students like to make up figures and do this.  A very sophisticated project
to is take a small box, such as one that holds raisins.  Open up the box and
lay it flat on a piece of graph paper.  Outline the box.  The area of the box
is not easy to find since it consists of so many pieces that are not very
regular.  However, you can put the box into a rectangle and count all of the
squares that are covered.  This number covered / total number of squares in
the rectangle approximate the area.  By using smaller size graph paper, you
can better approximate the area.  It is a challenging problem but well worth
the effort to do.

 -Marielouise, for the Teacher2Teacher service

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