Tuesday, October 16, 2012
Classic Algebra Problems
Here are some videos I've made covering those Perennial Algebra Problems...the ones you'll find in every Algebra Text Book or course.
These "exercises" are supposed to teach you about fog, substitution/evaluation and how to express one thing in terms of another. Instead of f(x) for the function they want f(h)...in order to do that you have to put x in terms of h.
In this case you have to figure out that x = h/2 and you have to know how to find the area of a triangle...
It helps to understand rectangles and that all it is is A = (1/2)LW but instead of Length and Width we are talking about Base and Height so we get A = (1/2)bh and all we have is a special triangle that is 30-60-90 so the base is h/2 and the (√3)(h/2) or vise versa depending on how you look at your triangle. So then all you do is substitute terms and you're done. Somehow they usually don't make it that easy.
Express The Area Of A 30-60-90 Triangle In terms Of Hypotenuse:
Crewton Ramone Express Hypotenuse In Terms Of Perimeter of a Triangle.
Explaining via Mortensen Math...this is basically the same as this vid except I explain it with the emphasis for teachers and trainers who are using the Mortensen method...here is regular explanation: http://youtu.be/7NvnLPwkZVw
In this vid I talk about the concepts of Hero Zero and No Fun Get Back To One as well as the rectangle and SAME.
I left out the concept of the rectangle and squares...and that
(a+b)² = a² + 2ab + b² which should be familiar. (x+1)² = x² + 2x + 1 or x² + 2x + 1²...
Here are little boys playing with the concept of (a+b)² or (x+1)² or (x+y)²:
Important concepts to understand here. They stumble in exactly the same places high school and college kids do...but by the time they are teens these concepts will be second nature.
It got cut off at the end, but basically I was explaining that I give him a hard time because he's my son...but that I was very pleased with his work today. And then they did their usual Crewton Ramone's house of math sign off...but the camera died. Happily the lesson was over so we didn't really lose anything...less than 30 seconds got cut off.
Also we talked about it afterwards and the reason he said 14 when adding 6 + 5 is that he was looking at it upside down and the 6 does indeed look like a 9 when you are looking at it upside down so he automatically decoded the symbols as 9 + 5 and got 14 even though he heard 6 + 5..."I know what 6 + 5 is dad...I've been doing it my whole life!"
A note to those with dyslexic kids...what they "see" and the decoding going on there is usually more "powerful" than what they hear.
More videos and sample lessons you won't find anywhere else with these two are here:
http://www.crewtonramoneshouseofmath.com/Dboyz.html There are several hours worth of video there now. You need a password.
Here is some more typical high school algebra:
These are screencasts.
And last but not leaste a problem where we put Pythagoras to the test:
Here a blogpost on using Pythagorean theorem.
All of these problems can be fun if presented properly and if the students have a firm foundation in mathematical concepts. If not they tend to strike fear and cause confusion and delay to quote Thomas and Friends. Just remember rectangles are easy to count and triangles can be a bitch to count so we turn them into rectangles. We also do this with circles and areas under curves.
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