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Five Ideas for Preparing Kids for Public Speaking

Eight year-old No. One stood in front of a room of 50 people at the junior track of engineering conference with a mic and a laser pointer.  She was describing a two-bit binary adder she’d built, and she nailed it! She and her sibs pretty routinely speak in public—although not with that big of an audience—in one form or another.  To them, it’s not a big deal.  It’s something everyone else around them does, so why wouldn’t they?  They never got the memo telling them that public speaking was something to be feared. Part of their comfort—I think—has to do with the fact that they inadvertently grew up speaking in public; thanks in part to me being lazy.  Here are five things we did together that I think got them used to the idea of public speaking. Paying the ticket at the restaurant:  It’s always been the job of the youngest kid to take our money for the restaurant bill to our server.  The three to four year-old kid wanders around, finds the pers...

Combinatorics and LCMs

Working through the problems in Niven's book on combinatorics, I came across the following one that cleverly introduces least-common-multiples without saying any of those words.  The book asks the following question: How many numbers that are evenly divisible by 11 exist between 1 and 2000?  How many that aren't also evenly divisible by 3?  How many numbers that are evenly divisible by 6, but not by 4 exist between 1 and 2000? The hastily scribbled answer can be seen below, with each of the answers boxed in succession down the screen. By simply dividing 2000 by 11, we find out how many integers between 1 and 2000 are evenly divisible by 11.  In other words, we ask how many multiples of 11 can fit between 1 and 2000.  When we want to eliminate the multiples of 3, that's when the least common multiple comes in.  We already have the answer for all numbers divisible by 11, but how to eliminate those also divisible by 3?  By first asking what number...