3rd Power Algebra? It's Just Complex Counting.

Here is an excerpt from a lesson where we played around with some third degree algebra made rectangles and counted the sides.

You can see from the vid we are in the drawing stage, but we still get out manipulatives so we can get a solid handle on what we are doing which is counting. We start off with all positive expressions and basically factor them. Then we move on to expressions with negative coefficients and do division too. When you are first starting out just doing one problem can take up 15 minutes or more...but then as the understanding increases it will go faster and faster.

The way to increase understanding is not to do the same thing over and over again just using symbols and changing the problems, the way to get them to "get it" is to start in the concrete move to drawings and increase the degree of difficulty gradually as concepts are understood and mastered. This also shows how important neat writing is...lol...sloppy symbols can make the difference between an A and a B, or worse a C and an F. Also, for those with a password you will see on the follow up vids on the Advanced Algebra Page. Password costs all of 3 bucks or $12 for a year pass. Buck a month is hard to beat.

You will note sometimes I say one thing and mean another in these vids when I read the problems and say "x-squared" instead of "x to the third" and so on. I watched one vid where I did it over and over again...but eventually I say it right. Painful for me to watch.

Problems like x³-4x²+x+6/x-2 take a long time just to say but they are quite instructive. They are also intimidating to some students who find them confusing and scary just because of all the symbols, but once we get into it and it becomes familiar, they see that actually it's pretty easy...just have to count and keep track. Here we are going over the positive ones:



As usual I forget to turn the camera on until we've done a lot of them. Remember always start in the concrete, use three period lessons and make sure drawing is part of the lesson too, don't just use symbols.

Here we see that base x also has place value and answer the question "why do they go where they go?"...you'll see this on the next video look for "P2 Crewton Ramone and Syd Play with the 3rd Powers" on the Advanced Algebra page. Scroll down to the part that covers 3rd and 4th power.

My friends in Africa have shown that the passwords are valuable enough to steal, and enjoy putting jibberish in the email list box to let me know they have gotten into the password pages without paying. So far the ISP's trace back to Ghana and Nigeria. It's good to know they have enough value to some that they are worth stealing. Passwords will change soon so put your name in when you get in, that way you can be kept up to date on the new password and the new stuff that's being added so you can get the most out of your password while it works. Also Next year prices will go up a little again as more and more people find out about how cool this is. Those who have passwords or have bought passwords will get special discounts on renewals. If you buy kits or products from me or take tutoring you automatically get a password gratis.

Be sure to find me on Facebook or follow along on Twitter. There's only one Crewton Ramone so searching out vids and pages should be pretty easy.

Happy Tau Day

This is fun especially since it's the 28th. Of course it's even more fun when you look at the symbols, π and τ, Tau looks like half a Pie to me and Pie looks like 2τ, stuck together but that besides the point.



When we talk about radians tau really does simplify things. And math is about simplicity and beauty although you would be hard pressed to get the average high school algebra student to agree.

The boys have π memorized out to 3.14 lol, but they beginning to understand what it means...c/d. I will slowly increase this week by week...until they get out well past 20...JFSAG. 3.14159625...1971.

And while I posting other people's Youtube vids might as well put this one up. Note how he tries to make it clear that mathematics is just the language we use to describe the philosophy, math in and of itself cannot BE the philosophy of economics. And way back when, when I used to study economic theory as an aside when I was teaching people to pass the standardized tests to get securities licenses I too though these freaking formulas don't mean anything!! Turns out I wasn't the only one.

More Autistic Intergers Plus Algebra Too

This is a pretty good lesson for beginners on integers. I believe in introducing integers EARLY. The one thing missing in this lesson is the time consuming task of drawing the problems. This step should not be left out especially for the younger students.

Again you don't want to draw every single problem (or build every single problem with the blocks) but you don't want to skip drawing them either. This vid is a lesson AFTER lessons where we drew quite a few of them. I did not get vid of the preivious sessions where she drew them. On the internet that means it didn't happen...lol..but I assure you it did. DRAWING IS A MUST. It's not optional. Why? Because it works. It bridges the gap between the symbols and the blocks. For some students this gap is wider than others, so more drawing may need to be done.

The drawing and symbols can go together and they can be very simple. In fact the better understood the concepts are, the less complex the drawings need to be, so some kids may start off with complex drawing of whatever it is, in this case integers and you will encourage them to move to simpler drawing and finally symbols only.

Drawings of integers usually involve holes in the ground, not a number line. Or up in Washinton and Idaho and a few other places a log standing on end can be put in holes and then figure out how much is sticking out...make up stories that the kids can relate to in their own situations. In the city that might be telephone poles or whatever. You can also combine drawings and blocks on a white board quite easily...draw a hole 3 deep, and then put a nine block in it. Show the various ways we can write this. -3+9, 9-3, 9+(-3), -3-(-9), etc...



Got to The House Of Math and find Sarah's page, the tab says Sarah SL for the complete vid P1 and P2 and also P3 which is another 6 minutes on algebra with negative factors. These vids might create greater understanding for students and teachers who are NOT autistic or working with SPED students too.

11 Year Old Math Enrichment

Here is an 11 year old who is just getting started at the house of math. His primary assignment is to work on multiplication.

While he is doing that, I expose him to various basic math concepts. He has played in algebra and fractions, and he is seeing that multiplication helps because it allows you count quickly. This gives some motivation to work on his multiplication. I specifically tell him (and his parents) not to just drill on multiplication tables but to play games, listen to music, and generally mix it up so it doesn't become tedious and boring.

We also work on addends...addition and multiplication are just ways of counting quickly. We need to be able to count quickly in order to math but math IS NOT computation in and of itself.



In just three lessons he has already come a long way.



The third lesson is a lesson on fractions if you'd like to see it you need a password and you can find it here (currently at the bottom of the page) called Fractions with Koa. My fractions page needs work, but there is a lot of stuff there and I have a few fractions worksheets for beginners up too. You can download the pdfs and see more vids with a password.

Find us on Facebook. And you can find me on twitter too...

Algebra Is Child's Play

Here we see a six year old knocking out factoring problems with ease. He doesn't know factoring polynomials is supposed to be hard and that I've had to work with kids 10 years his senior on these exact same problems...only they were frustrated and confused.

We just did a few problems for fun first thing in the morning. His brother chose not to play, opting for cars instead which I am told is equally fun not really MORE fun. Algebra doesn't have to be painful. The basic concepts can be mastered at an early age thus freeing up the teen age years for other things, more math if they want or whatever topic catches their interest. This child will have ALL the math currently taught in public schools through sophomore year MASTERED by the time his is about 9 or 10. Notice I use the word mastered. This is completely different from "memorized to be forgotten", which is what is currently the norm in classrooms through out the country, including our universities...

Here is a very short vid showing him developing his problem solving skills, along with a host of other math skills used for factoring polynomials.



Here you can see his progress. Algebra gets easier and easier as he gets better at counting and making symbols.


Learn more at The House Of Math.

Math Erichment For Two (Twin) Girls

These two are bright and energetic...their math experience is limited so it's more fun and exciting for them than a lot of kids their age...each lesson is full of discoveries. Makes it fun for me two. Now the trick will be trying to capture some of the ah-ha moments on video.

Here is a snippet of my first meeting with them. They informed me that they don't do multiplication.



We played and had fun and the hour went quickly. Their mother and little sister stayed for the first one. A good time was had by all.

The next lesson was just the two of them and we covered a lot of ground...their homework was and will be "do multiplication."

Normally you need a password to see vids like this but just for fun and because it's basically a compilation of a bunch of other stuff with other students you can already get for free on Youtube or my Screencast channel, I put it here for you for FREE. Lets other parents see how to run a lesson for beginners too.



As you can see we cover lots of ground and lots of concepts just to expose them to the mathematics, not expecting them to retain it all for a test later. They are being exposed to math. We will focus on the basics of counting and then get to more complex counting as we move along but they are seeing first hand is that all math is, is counting. Multiplication allows you to count very quickly and therefore MUST be mastered.

There are many half hour and longer sample lessons on the password protected pages at Crewton Ramones's House of Math along with pdf's and detailed explanations of how to teach various topics of math using manipulatives...there are also tutorials for parents and teachers as well as links to an hour over-view of Mortensen Math.

Math Erichment For Any Age

Look at these problems. They would pose a challenge for most high school kids and even college students...but actually they are child's play:

Here you can see both the symbols and the drawings if you know what you are looking for...the skill required to solve these is quite simply the ability to count.

Here is a simple video:




Find out more:

http://www.crewtonramoneshouseofmath.com

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