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 Discussion: All Topics Topic: Pascal's Triangle Related Item: http://mathforum.org/mathtools/tool/424/

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 Subject: Pascal's Triangle Author: jon Date: Feb 20 2004
I'm a big fan of number theory.  Especially in incorporating it into middle and
high school level math classes.  Stuff like this Pascal's Triangle applet can be
a fun way to introduce very abstract and beautiful patterns.  Students can
appreciate it on a couple different levels.  There's the aesthetically pleasing
level of seeing patterns of where multiples of certain numbers are placed.
There's the more geometrical and mathematical level of perhaps asking students
to predict how the pattern continues.

It seems like you could use this applet in a number of grade levels and for a
variety of purposes.  Take for example a class of more mathematically inclined
students.  You, as a teacher, could ask harder questions like PROVE such and
such.  You could ask something like prove why this pattern exists, or maybe if
you can infer what the pattern for multiples of 12 will be from say multiples of
6 and 2 or 3 and 4?  It doesn't matter that they don't get a formal proof.
Heck, I don't know the answer too these, but they're cool questions
nonetheless.

The applet itself is nice because it extends the triangle for a good number of
rows, and students can better see the pattern in that. The ability to zoom in
and out is nice as well, giving the students the chance to see the pattern from
afar, but also the numbers that make up the pattern closer in.

This is a good applet, but it lacks (individually) some good questions.
However, this site does happen to have a handful of good questions.

http://www.shodor.org/interactivate/activities/pascal1/index.html #

All in all this is a nice tool to get kids thinking slightly more
abstractly.