a² + b² = c² Is easy to understand when you can see it. I need a new white board this one has gotten quite a bit of use...anyhow the vid at the bottom of the page shows how to find the height of a triangle when you only know the sides.
Here is a young bright Honor student who has all "A's" in everything but math. All students (and a lot parents) blame the teacher first when they fail or don't understand. Sometimes this is true and sometimes the teacher is doing the best they can with the tools they have. Other times the student is a little brat and it wouldn't matter who the teacher was the kid would be failing or getting "C's" or what have you on their own account, not because of the teacher. There is also the personality factor, I don't get along with everybody, I don't know about you but I figured out a long time ago you can't please everybody and you will be unhappy if you try.
I always spend a little time getting to know the student first before I take them on, sometimes it's better to refer them elsewhere or say no than yes. It's pretty rare, but it happens. But I digress.
This student is smart, quick minded and when whatever it is, is explained she usually gets it right away or takes meticulous notes so she can study it later if it's iffy. This way we cover the most ground possible. This student does; however, have huge gaps in her math skill sets that need to be addressed but we usually spend all our time studying for the tests instead of increasing her conceptual knowledge base and brushing up on her computation. As with most students I meet, multiplication tables are not mastered, nor are fractions or the basics of algebra specifically hero zero and no fun get back to one.
Happily Pythagorean Theorem (⇐ click that to go to go to CRHOM's page on it) made sense to her because it is pretty straight forward and my explanation using blocks is visually obvious as the Montessori folk like to say.
Here she is being introduced to Pythagorean Theorem the Crewton Ramone House Of Math way. Note this student is advanced and we are pressed for time so this isn't the best presentation for little kids, go to the house of math for that.
I want to stress this is a sharp high school student. (A little freaked out by math but still very quick minded.) This is NOT how you would present it to a young student or a 6th grader or even a not so sharp junior. More examples and don't jump to subtraction after just one problem. You cab see the confusion this causes, happily I am there to clear things up, but I am not always there. And most often things don't get cleared up. Note how I use easy problems that have answers that are whole numbers that don't require a calculator. She can easily see 10 as an answer as compared to a problem with a long decimal for the answer. This also adds to the confusion. Once you understand the concepts all they can do is change the numbers...
After a very short time she is getting it. But three passes do not a quarterback make. PRACTICE is required. Also note how for the most part she told me the formulas, when I told her the formulas she had already got them she just had a little trouble verbalizing them. Contrast this with just telling them to memorize the formula.
Not the best lesson but a good lesson overall. In my defense we were rushing because we had a lot of ground to cover, she had an upcoming test, and she was flustered. Now, this would normally only be on a password protected page, but in the spirit of Christmas, the Flying Spaghetti Monster appeared to me in a dream while driving a fast car, and told me specifically to make this video available to anyone who could find it. In a few weeks this post will be buried on this blog like many other great posts I've made over the years and you will have to search to find it. I have 100's of videos on youtube now. Finding the one you want is made easier with a password because on my website they are grouped by subject. Also many of the vids are unlisted so like the one below you have to know where it is to find it, it won't show up on a search.
It is also on a couple of the password protected pages like advanced algebra, because the problems shown are classic algebra problems that appear in every textbook ever written about algebra...or just about. Now you might have to be in Algebra II but it's basic algebra application as far as I'm concerned. Very few kids figure out how to do this on their own and over the years many kids have come to me failing to understand how to do these kinds of problems...
Students and teachers who have spent time at the house of math have very little trouble understanding this problem because they understand the basic concepts behind each step and the computation doesn't pose a problem. (Get it? I crack myself up.)
You can also see for sure that the drawing on her paper is "not to scale."
I have been told by more than one person the vid above is actually fun to watch because they "get it." A lot of that goes on at the house of math.
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