Sunday, February 27, 2011

Animated Video on the Sum of an Arithmetic Series

It's no secret that mathematicians like to play with numbers.  The most basic sequences of numbers is 1, 2, 3, 4, ... , which is called an arithmetic sequence of the counting numbers.  One might wonder if you can add these numbers 1 + 2 + 3 + ... up to say, 100, without having to actually add 100 numbers together.  In fact, you can multiply instead of add, and in this video, "Staircases, Handshakes, and the Sum of an Arithmetic Series" I show a few different ways of thinking about this problem using drawings (visual represenations), real world contexts, and symbolic arithmetic equations to justify my reasoning.  Accordingly, this is also a lesson in using multiple representations for a single mathematical concept.  This video is illustrated an animated with Doceri software.   Please feel free to use it in your math classes.

Tags: arithmetic series gauss trick area rectangle diagonal polygon multiple representations elementary high school doceri hand writing software finite series

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