Pre-calc or Precal as some college kids like to refer to it, isn't quite as hard as it seems.
The first time I took it in High School I got C's and struggled to get them...now distance formula is so easy it hurts my feelings when kids tell me they "just don't get it".
The student I was tutoring here for example failed to make the connection between Pythagoras' Theorem and distance formula. But them after some protest about how he already got that and he needed help with this he made the tell tale sounds" Ohhhhh" and "Ahhhhh"..."Okay, I get it."
This page one day will have much more and many links but for now here is some simple stuff. Distance formula...and finding the center point of a line, as well as a little "advanced" problem solving...which is basically "No fun get back to one," Hero Zero and "No fun get back to one" again. Makes me laugh.
What follows are screencasts taken from my BLOG. Which is why you hear Crewton Ramone's House of Math so many times, because the idea of the blog is to send people here for more detailed explanation. Since I have yet to make pages with more detailed information regarding Pythagoras and Pythagorean Theorem as it applies to Pre-Calculus this page will have to suffice for now...
I spend so much time with the little kids people think we don't do "higher math" here...
Here is a pre-calc problem at random that we worked on:
I am inhibited by the fact that I only have 5 minutes to screencast, or 10 minutes on Youtube...here is a problem solving page that shows the exact same CONCEPTS we used to do this "advanced" Pre-calc problem.
Here is a page to go along with square numbers about Pythagorean Theorem, you might click that link go there and study a bit and understand it because this student did not do so well when it came to "Distance Formula" (and finding the mid-point of a line) because no one ever drew the connection for him between the two. Be reminded you may watch this as many times as you need.
Once you understand Pythagorean Theorem you can do Distance Formula in 5 minutes or less...
Now once you have watched that, finding the midpoint of the line problems are also EASY:
You may want to watch those two Screencasts a couple of times. Note how I try to get you to do some thinking rather than just spoon feed you answers.
Here is another problem from the session, my job is making it easy and understandable:
One thing I left out of the screencast was the drawing of the graph, which is kind of crucial for understanding...otherwise it's just some symbols. Those symbols describe a graph...and I made him draw it out so the answer makes MORE sense. He had a picture of two lines that were perpendicular to each other and went through the points mentioned.
One more very easy problem solving question and that's it for this page. I want to do webinars to teach homeschoolers and teachers how to get from the so called "simple math" to the more "complex math" or "harder higher math" Math is math folks. Five concepts. Counting. Period.
With reading, watching vids and screencasts this page should take you about half an hour to 45 min...(especially if you follow all the links) but it should show you where it is we are going with the foundations set up here at Crewton Ramone's House of Math for preschoolers and kindergartners with concept based manipulative teaching. By the time they are ten these problems are EASY. It's just more of the same with more and more complex numbers.
The concept is the same for solving each of these:
3x = 9
3(x+1) = 9
3(x2+5x+9) = 9
No fun get back to 1. (Divide by whatever the coefficient is.)
Hero Zero. (Remove "SAME" from both sides.)
In the last case you have to factor it and then you'll get two answers...by using HERO ZERO again.
Same goes for
x/3 = 9
Instead of dividing we multiply...any little kid can do these once they understand the concepts.
I will come back and add more later so you may want to come back and see if I've added updates.
Many of the students that were taught with this method as youngsters go on to ace the "higher math" (like pre-calc)...and understand it. This post should help you see why.
Get it? "See Y"!!! OMG I'm the funniest MF* you know.
*MF = Math Fanatic
Here is a 11 year old finding the equation (y = mx + b) from a set of ordered pairs:
Check out Functions And Relationships, this page has one of the Series A Manuals along with a video showing some of the material contained therein on it. This is basically simple Pre-calc. Very important for understanding basic CONCEPTS. Password required.
“Nine tenths of education is encouragement.” ~Anatole France
“The aim of education should be to teach us rather how to think, than what to think - rather to improve our minds, so as to enable us to think for ourselves, than to load the memory with thoughts of other men.” ~Bill Beattie
“Knowledge will forever govern ignorance; and a people who mean to be their own governors must arm themselves with the power which knowledge gives.” ~James Madison
“Education is a better safeguard of liberty than a standing army.” ~Edward Everett
"A teacher affects eternity; he can never tell where his influence stops." ~Henry Brooks Adams
"Much learning does not teach understanding." ~Heraclitus