More Pythagorean Theorem

Here is a screencast for you adults talking about Pythagorian Theorem in general terms. We haven't really gotten down to the nittey gritty of solving for "C" by square rooting but it becomes visually obvious that if I know two sides of the rectangle I know the third side.

Search Pythagorean Triples and use those to start off don't just pull funky numbers out of your butt. Make sure the student can easily find the square roots without a calculator to start. AFTER they understand the simple concept then you can start showing them that if we know ANY two sides we know the third side; at last we can put in any two numbers and find the third side, BUT START WITH PYTHAGOREAN TRIPLES.

Again the student can see that "C" isn't 25, it's the SQUARE ROOT of 25...they can also SEE that the two little squares have the same area as the big square...

And then we can start figuring out how to find the other side if we know any two sides by using simple subtraction.

If I take out one of the squares what is left is the other square either "a" or "b"...

Once you get 9 + 16 = 25 down and have played with it you can get out another one and in fact this one is a good one to start with when you have younger students...but it might be hard for them to count that high so you could just use the bigger squares for the concept that the two small squares add up to the big one...note you can but 36 in the middle and the eights around the outside just like with 9 and 16...also you might play with concepts around squaring and exponents...try and get them to tell you that although we doubled the side the area is FOUR TIMES as big...

Here is a screen cast talking about the above graphics...



Now go to the pre-calc page at the house of math and watch the screencasts so that we can apply this knowledge to find the distance between two points...and it should be simple to find the sides of triangles too...allow a few seconds for those screncasts to load...the page goes white for a few seconds and it seems like nothing is happening.


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Pythagorean Theorem at the House of Math.


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