Third Power Algebra With Little Kids

Base ten blocks make math easy and fun, even third power algebra. Left off an equals sign but you get the point. He factored it two ways and then realized that factoring it down to (3x-2)(x+1)(x+2) would cover all of them…he knew without thinking very hard that x² + 3x + 2 = (x+1)(x+2) and that 3x² + 4x + 4 was just (3x-2)(x+2) so the “last way” was just going to be (3x-2)(x+1) and the other factor of (x+2). So basically he discovered on his own why "we factor it down as far as we can go."

Take 18 for example, 3x3x2 covers all the bases. 2x9, 3x6 same thing, 18.  Just depends on how you multiply the factors.  I use algebra to teach all manner of math concepts. Not only that, you teach more faster because you can compound the lessons.

What you aren’t seeing is the base ten blocks and drawings we used to make this EASY.  So here they are.  My notes for the days class. This was just over an hour's worth of work. But these two are aces. This was FUN for them. Might take you more or less time depending on all manner of factors. (Get it? I crack myself up.)

Started off with the difference of two cubes and they very quickly saw some patterns there...
I leave x³ - 64 for you the reader to do on your own time...might want to start at x³ - 1 with basic ops pieces and work your way up...drawing as you go. Click here for more third power algebra.

We did a few more problems not shown here but they were variations on the drawings you do see.  If these drawings make no sense to you or you are new here go explore over at my house of math. 

The other student was 11. But as he says, "once you get to 10, nobody is impressed you can do algebra."  I'm pretty sure there are still plenty of people who are impressed when all you see is symbols...but what these kids do is see the symbols and translate them into geometric figures that can be easily counted and manipulated in their heads or if need be with the aid of sketches on paper.

They have been factoring polynomials since they were little, just like these two.



Algebra is important. It is the greatest labor saving device ever devised by the mind of man and yet it is currently the most failed subject out there. If you work in retail or fast food, you won't need the algebra much unless you get into top management.  But if you are in the sciences or engineering or architecture you will use algebra EVERYDAY. How do I know? Because when ever I am around engineers or scientists or architects I ask them, "how often do you use the algebra?" And the answer is always: "EVERYDAY."

Little girls can do this just as easily as little boys by the way:


Third (and 4th) power algebra, negative expressions, integers and more are covered in depth on the advanced algebra page. You'll need a password though.

The lessons go like this...I give them the symbols for example x³ - 27 and they have to give me the drawings or just give me the factors...this is exceptionally effective for teaching much more than just factoring polynomials, it can also be used to teach remedial math.

Concept based teaching with base ten blocks works. I can show you how, Find me on facebook, twitter, tumblr, instagram etc.

If "advanced algebra" for your 8 year old is too much for you maybe you could start with subtraction...here is a FREE SUBTRACTION BOOK to get you started, soon stuff like you see here will be child's play.

Algebra and Base Ten Blocks, What's under the cup?

Introduce Algebra right away.

 Just playing with blocks as I have said many times teaches a lot of math. This child likes playing with my boys much more than she likes playing with me alone. Wouldn't you rather play in your sandbox with friends, it's much more fun...

Here we introduce algebra concepts without even trying. We are just playing. The idea here is simple PLAY! You can play with anybody anywhere...all you need is a set of blocks for each participant, and away you go!


At this point with the student they rarely even need to see the symbols and we say 6 plus what is 14...or we can tell a story, we have 14 people but only six cookies how many more cookies do we need? When they do see the symbols the symbols make sense.

Basically it's controlled chaos...but playing math doesn't have to be orderly and silent. I'd argue more learning takes place at this age playing and being rambunctious than sitting with a worksheet in silence...MUCH MORE.



Then here is a quick video with a variation on the theme...which instead of teaching addends and algebra, will teach multiplication and division...



A very simple variation on the theme. Here we can learn addends, multiplication and some algebra too. And we learn how to ask and answer questions mathematically, soon we will relate them to the symbols.

3x = 15 for example, We could skip count the 3's. The sound effects just make it that much more FUN.

These kids are separated by half an ocean and half a continent...video tutoring can give you child an actual head start, or give you as a parent an idea of how easy it is to get started...get a few lessons and then do it on your own...so many parents tell me they don't know how to play math or make it fun because they have absolutely no experience with math being fun. I can show you how and give you a few tips and pointers. Or you could just get a password and you can watch the vids on Rayond's Page and others...there are tons of sample lessons (that page has over 10 hours of video on it) and that's just for starters. The idea is GET STARTED.  Don't be overwhelmed, just take a bite at a time. Here is another bite basically the same thing just a slight bit more emphasis on introducing a 4 year old to problem solving. Rarely too early to start, but often too late.

People are amusing because a few years ago before I got all this together the excuse was, "now that I have blocks there's nothing to show me what to do", or "not enough material to get going with" that excuse has been removed...parent/teacher training is also coming soon. there was a time when the sum total of training was 5 VHS tapes with about 10 hours total of instruction on 5 topics. Very rudimentary. Other than that you had to fly to a training in Idaho...people are actually asking for that kind of live training again. Eventually it could happen. Meantime...

Base Ten Block Parent Teacher Training

The way to Abstraction.

People are demanding that I spoon feed them math even though I have a huge semi-organized website, hundreds of youtube videos and this blog with hundreds of entries. I haven't covered everything but I've covered a lot of stuff in 5 years. With Crewton Ramone plus a search engine you should be able to find lots of stuff on division or algebra or whatever it is...

Now people are wanting actual training...so I am going to make a video series that you can actually buy (down load or eventually buy physically and have shipped). I will have an actual product on DVD in a case and everything..."soon." To start though I'll just stick it on a password protected page with it's own password (have to do this with my book too) and for the fist 50 people who get it I'll sell you a that password for 15 bucks  AND I'll give you a couple months free to the rest of the password protected pages if you don't already have that password. (That will be two passwords.)

Anybody with a Lifetime Password gets the password to this and a download automatically. (Told you a life time password would pay dividends down the road and there's plenty more to come).

FOR 15 bucks you'll get over 2 hours of training like you see here and some more pages and videos that I think are especially pertinent that are out there lurking on the web for FREE that you just might not have seen or found yet but the training you see here won't be available anywhere else...except for maybe Pirate Bay after I make the DVDs. Further if you want physical product after that you can get that too just pay "shipping and handling".

THEN for the next 50 the price is 19.99...but no second password but if you want the physical product just say so and I'll ship that to you no extra charge.

After that the price will be 19.99 for the download/single use password and 24.99 for the download and the physical DVD. Then maybe I'll do a subscription where once a month or so you get another DVD...also eventually I will get an outline and edited transcript done, and that will be part of the package.

Also I plan to "gussy up" the video with some editing and captioning before it goes to the physical DVD stage...and hopefully before it goes up on my site for download too, but a lot of people want it NOW never mind the polish...of course you can have both if you in the first 100. Also a lot of people are going to get the download for FREE, like I said those who are in the early adopters club and any parents who have paid for tutoring...I think with the DVD and transcript plus notes (eBook and physical) it'll be well worth the money.  If you disagree say so in the comments.



If you are new around here, here is an Hour Long Intro and a bunch of other vids. This is good "training" in and of itself. FREE.

Then here is a Getting Started Page. It's for the Deluxe Curriculum Starter Kit but it certainly applies if all you have is a combo kit or just some blocks you got off ebay or whatever.  Be sure to download and read the pdf's there. Still FREE.

People are amazed at my site and all the stuff they get for free...there's even free worksheets (which you are to use SPARINGLY) then they are even more amazed when they cough up a few bucks for a password and see all the stuff they get there. 25 bucks is damh near free when you consider the thousands (and thousands) of bucks I spent traveling to Idaho and bringing Jerry to Maui and and and to get trained because there is very little good training on base ten blocks out there for free or for money. If you find some let me know...put links in the comments box. I aim to be the best. I'm not there yet but I'm going to be.

Here is a lady I liked a lot who was trying to show you didn't have to buy expensive blocks and kits and such; just use what you already have over on Vimeo. She re-made some of my videos except she used her (exceptionally cute) daughters which may be better for those of you with little girls so your daughters can relate...you'll notice I made a few comments on some of her vids.

More updates and math stuff as it happens on my facebook page.  I scour ebay for blocks and Mortensen Math stuff...so you might want to follow me there for that if nothing else...often good deals to be had but they get snapped up quick...


UPDATE: The page has been built and here is the link: http://www.crewtonramoneshouseofmath.com/parents-teachers.html

3rd Power In His Head

Here is a gem. Don't tell me they have to have base 10 blocks or they will become block dependent using this method. Watch the older boy picture this problem

x³ + 9x² + 23x + 16 =

in his head...counting out the parts as he goes and then give it to me to solve.

This is a lesson on factoring and counting and multiplication...and how to be cool and have fun when you do math. The reason they don't need base 10 blocks is because they have been using base ten blocks...and we are learning by drawing and visualizing. Here is a post on 3rd power algebra where you can get an idea of what it is he is "looking at" in his head. We baby stepped our way here but now you begin to see the POWERFUL results of using this method.




More algebra at CRHOM. If you want to see more "advanced" algebra click on the "advanced algebra" tab.

We watched this together. The youngest boy pointed out that he drew 6x² + 10x + 4 and didn't get very much attention for it. He also told me the factors (you can see the drawing in black in front of him) (3x + 2)(2x + 2). "Come on, that was pretty cool dad." So we are going to make a new vid where he gets as much attention as his brother...

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Crewton Ramone's Completely Cool Curious Counters' Kindergarten Compendium

My book has been taking up quite a bit of my time lately but I am happy to report it is just about complete. You are no able to download a PDF off my website...you will of course need a password to do so and you will note it is officially Copyrighted so take it easy with the file sharing...and don't let me catch you trying to sell it for money unless you are an affiliate. I actually sent it in the the US Copyright Office. Now that doesn't mean I don't want you to share it. I do. And I have seen quite a bit about various artists who have gone the creative commons route and basically given their work away for free or for a donation and have forgone DRM of any kind. That's my plan. I'm not even going to attempt it. I know plenty of people will be willing to pay for it once they see it...and I know people will copy it. If you want to see more books like this some of you have better pay for it. It cost me quite a bit in time and money to get this thing done they way I wanted it done. I expect you will be pleased with the result. If you have comments I'd love to hear them.

I added an apostrophe after the S in "Counters" Crewton Ramone's Completely Cool Curious Counters' Kindergarten Compendium hopefully I catch a few other details like that before it hits the presses...

I expect people will share it. I also expect some people will get the PDF and really want to get a book or pay for a version that can go on their favorite E-reader. Like Kindle, iPad, Sony's E-Reader or Nook or what have you. It seems to me if you have an iPad or other tablet the PDF should be good enough.

The plan is to have it available on Smashwords which will push it to several formats, plain ol' regular PDF, a PDF with lots of hyperlinks to vids and web pages and of course an actual Hardcover Children's book. Right now the PDF is done.

I really want the hardcover book to stay around 10 bucks but that may or may not be realistic. As you can see it's full color and full color and lots of graphics adds to the cost of printing. I have a couple ideas for "pre-editions" that will hopefully pay for a run of hard cover books.

So I have quite a ways to go. I will probably start off with a soft cover pamphlet type where you take a 8 1/2 x 11 and fold it in half hit it with a stapler and there you are.

There is nothing like taking a book to bed, and although the concept is on it's way to being obsolete we are not there yet and I think kids will enjoy the rhymes and bright colors this book contains.

Here you see where I take a short digression into the concept of square roots, but mostly it is a book on addends and addition at the very end I introduce the concept of multiplication by two. It really is a book for 5 year olds (and under) and the idea is to have it be a bedtime story book that gets read over and over again like "Cat In The Hat" or your favorite Richard Scary book...my sons ask for the same books over and over again, why not teach them math while you are at it?

In this case you are just teaching them to count...by using addends. I also throw in some simple problem solving along the way and by the end of it we are ready for a problem where we add into the thousands.

This page uses symbols but most of the pages have the blocks on them in full color as you can see. The concepts are simple and any little kid will get it especially if you read 30 or 40 times (or more) over a couple of years...I know little kids who have "The King, The Mice, And The Cheese" memorized. Might as well memorize some math facts too...but up until now there hasn't been a book like this where they can SEE the numbers.

I will also make a screen cast where I point out what I had in mind when I made this book and how you might use it to best effect, and I will also point out a few things you might want to emphasize to your child. Also I would like to point out that older students will also enjoy this book because with our public school system the way it is the concepts in this book may be considered appropriate for students who are older. Perhaps much older.

I know I was supposed to work more on my website, especially the fractions page but this book kind of took on a life of it's own so I went with it. I am pleased with the result and think it will be worth the five or ten bucks it takes to get yourself a copy in whatever form you like best.

The Password Protected PDF's Page costs 5 bucks to get into. Once you have a Password you not only get this book for down load but a bunch of other PDF's and videos you won't find anywhere else. Hopefully this is just h beginning of the books. Supremely Simple Subtraction is partially finished and so is a coloring book and a few other things. Plus I have an endless amount of ideas for the many and varied topics that make up the mathematics, in such a fashion that they make sense and people can see how it all ties together to make up the beautiful language in which the universe is written.

http://www.facebook.com/Crewton.Ramone 

UPDATE: some of you just want the book, go HERE, scroll down and you can get the book all by itself, no password required:

PDF Prices

CCCCC $19.99 USD SSS Prinable $9.99 USD DDnDD $19.99 USD PDF Page Only $39.99 USD