We have been going through the Living Math History lesson plans very, very slowly. Don't let our pace fool you, though. I love these plans. Julie, at Living Math, did an awesome job with these ideas. We are having so much fun. My kids are being introduced to the Masters of thought, as well as to higher math. We are also discovering wonderful math books.
I wanted to post about what we did on Tuesday with the Pythagorean Theorum. Mia has already done square numbers but it has been awhile and she is a bit rusty in this area. Rocky is just beginning multiplication so we haven't reached squares yet so this lesson was an introduction for him. We have been reading about Pythagorus of the famed Theorum. Did you know that Pythagorus is also responsible for coming up with even and odd numbers. He also discovered square and triangle numbers. ( I have to admit that I didn't know about triangle numbers--never heard of them before. If I was taught this in school, I must have been daydreaming that day, which is very possible. 
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To teach the concept of square numbers, the living math history plans have a few great ideas. The idea that I used was to draw a right angle triangle on the white board. I, then, placed 1 in. tiles around the perimeter of the triangle. One leg of the triangle had 3 tiles on it, so then I proceeded to make that 3 into a square with the tiles to show the the square of 3 is 9. The second leg of the triangle was 4 in. I did the same thing with that. The hypotenuse was 5 in. long and I made that into a square as well with 25 tiles. I, then, wrote out the Pythagoreum Theorum and had the kids figure out the formula with our triangle and its tiles. This was cool.
We, then, read Sea Squares by Joyce Hulme. This is a cute story that does a great job of introducing square numbers to the younger set.
I love learning how to introduce higher math concepts to my kids using simple, hands-on methods. This is what living math is all about. This is why I am enjoying this so much.