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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