Algebra with Base 10 Manipulatives

This little girl is doing some pretty big math.  Algebra doesn't have to be hard or scary. It' can be exciting easy and fun. I admonish all parents and teachers using this method to introduce algebra early. Four and five is not too young, Little kids enjoy algebra, especially when they don't know it's supposed to be hard.

In kid culture, they do know algebra is supposed to be hard. So when they see themselves doing algebra and it's easy and fun they think that they're smart. Their self talk is superior to those failing algebra, I assure you. 

The idea here is to introduce concepts gradually, but you'll find that with this method we cover a lot more ground a lot faster than the traditional symbol-based approach. Using base 10 blocks makes algebra visually obvious and so easy even very little children can do it and have fun at the same time.

Compare and contrast this to symbol based approach which often results in teenage tears. The problem I see in many mah textbooks is that they introduce too many concepts at once. This makes the "cognitive load" too high and algebra becomes frustrating. Instead, using base 10 blocks they can get their hands on it and we introduce one concept at a time. The algebra is actually used to teach addends and multiplication facts.  So a concept is introduced, we play with it, another concept is introduced and then we play with that.  While we are learning math concepts we are counting. But again don't be confused, computation is not all there is to mathematics. Mathematics is the development of logic and reasoning.

While we are learning basic math concepts, 45 addends and 400 multiplication facts can be internalized for instant recall not just memorized and forgotten again.

The fact that she still on her fingers doesn't matter either. Neither does the fact that she couldn't write all of these problems down quickly.  In fact if we took the time for her to write them down it would slow the lesson down to the point where he wouldn't get anything done. Learning math concepts can be done whether or not the child can write, in fact her ability to write is not reflective of her ability to learn math at all. Public schools seem to have this confused. Mathematics is intrinsic to the human mind. Concept based teaching of mathematics with base 10 blocks not only speed the process up but removes a lot of the pain.

In the short eight minutes we introduced some very powerful and important math concepts. The concept of the exponent, distribution; we reinforced counting by fours and nines did addends for 11 and 12 and 13. We didn't do stale worksheets. It wasn't boring, it was fun: child's play.

The deck is definitely stacked against little girls. In 2017, we still put little girls at a disadvantage. There still told math is a "guy thing." Girls are often discouraged from participating in math and science even if it's unconsciously. And mathematics is still taught to the male visual learner. Kinesthetic female learners usually have a difficult time with mathematics. But this method levels the playing field.

I charge $50 an hour or for $200.00 you get five classes. All you need is gmail vid chat and A set of blocks. This little girl could use a playmate and I have one other little girl would also like of playmate too.  If $200.00 is out of your price range, for $36 a month you can get passwords that allow you access to a plethora videos and webpages that show you how to do it yourself.  For example Raymond's page, shows you how to start off very young children. But there are many more password protected pages than that with PDFS and more.

Getting Started AMA1

Here is an email exchange that is all too typical. Before we begin let me say none of the little girls pictured are his little girl and this is exactly the time to start teaching math concepts right along with language and motor skills development. But her ability to push a crayon around is not indicative of her ability to understand basic math concepts which, when you think about it are just vocabulary.

How many is three?

What is three anyway?


Well, one and another one and one more. Or two plus one...half of six, the square root of nine...there's a lot to know about three. And at that age it's fun to learn it with blocks with your mom and dad or one or the other. And this is the right attitude. Explore and discover together and you shall see in short order, a little child shall lead them. 

I will say again consciousness rising: there was a time that they had you believing you might have bad math genes.  This dad understands that he has an opportunity to break a cycle forever. Once you learn how to do this they can teach others...like their own children. Kinda like riding a bicycle. This is the difference between rudimentary understanding via memorization, and knowing. Anyway I share this with you because it typifies a lot of mail I get but this one is exactly the right age...I hate it when I get mail like this but instead of three and a half it's 16...



Hi Crewton,

I have a 3.5 year old daughter.

My love of math was squashed when I was in the 5th grade and they introduced long division. I hated math in high school barely squeaked by Algebra and Geometry. I never took Calc or Trig but satisfied my last math requirements by taking "computer programming" classes.

So... here I am. Wanting to give a strong foundation for my daughter to LOVE math and have FUN with math and be GREAT at math.

And I think that learning how to teach Mortensens Math to my 3-year old would actually teach ME how to LOVE and have fund and be great at math as well!

I've looked around enough to believe that Mortensen's Math is the way to go.

And I've read enough great feedback about you on a number of forums, that I feel confident you have the tools, training, resources, etc.

I see that you are extremely generous with information on your website. However, (probably due to my previous bad association with math) I feel completely overwhelmed with the amount of information and seriously have no idea where to start.

Do you have a simple 1, 2, 3, A, B, C (buy this, DO this) recommendation for a math-phobic parent with a 3.5 year old?

Thank you!

J.R.
Austin, TX


J.R. If it was Dallas it would have been too perfect. But anyway my heart particularly goes out to little girls because the deck is so stacked against them. And the concept of transference is very real your show math anxiety THEY show math anxiety except they don't know why. So play and have fun and learn together--with my help.  Hundreds have now come before you. Quite a few get tutoring and then very quickly see all they have to do is play blocks. The cool thing about this is it works for the gifted and talented kids because it's accelerated learning due to multi-sensory input. Visual, Auditory, Kinesthetic...base ten blocks cover all the bases.

Getting Started AMA1  + New Year's Stealth Sale.

Yes.

Unfortunately the warehouse is down for the holidays and you just missed our product sale.

Get a password. Start, ANYWHERE--you've got years. But the getting started page is a great place to begin then the EZ PZ Overview, once you get a password. From there Parent teacher training...

 45 addends, 400 multiplication facts.

There is a lot of free stuff currently...look through it. But just like learning a new language it will take years to get comfortable...right now play and have fun and put concepts and math facts in. For everything there is a season this is an important post to understand the opportunity you have to make a change.

Get my free subtraction book and there is a Holiday bonus gift attached (I sent him the curious counter compendium). You can get my password for $349.00 if you do it before New Years, NORMALLY I say take advantage of the free stuff but I'd say get a password now because a lot of pages are about to go behind paywalls, and a combo kit combo ($135.00) or a deluxe combo kit combo and you are in for under 500 bucks and it's an investment that will last a lifetime. I can't do anything about the product price or availability but I can offer you a deal on the passwords and training. (And quite a deal considering I charge $50.00 and hour and those trainings go 4 or 5 hours at a shot.) And you'll be able to get started as soon as your blocks come.

Deluxe CKC

And I can't give you the same deal I gave people for the Christmas sale, BUT get a password and I'll throw training 2x in for free...good till new years. That's a $100.00 in real savings.

Season's Greetings.

And if three or more sign up I'll send you all my division book FREE, even the life time members paid for that.  Also I should throw this in, it's like meeting the parents.

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.

Base Ten Block Sample Lesson.

Math is fun when you use base ten blocks. Here is a young girl who isn't so very keen on math, she'd rather be playing with her bows and across or her sword but playing with nines and building walls can be fun too.   Measuring out how many nines in 27 turn out to be pretty easy.

Building walls of 24 can also be fun...here she sees quite clearly four sixes and six fours are the same also three eights and eight threes....and of course we counted by 3's, 4's, 6's and 8's...and we see counting by eights is the fastest...no need for worksheets. No muss no fuss. We talk about it she hears it she sees it.

She gets a math experience using base ten blocks that evolves more than just paper and pencil and memorization. She can get her hands on it.  She is in a math rich environment.   Everything we do is math during this lesson and counting.  Here we are doing multiplication and division and skip counting. It's visually obvious that the bigger the number is the fewer we need to count to 24...we see a relationship between numbers. Six 4's is the same four 6's...which is pretty cool when you are six.  But lets not get stuck doing the same thing over and over again...let's do something else.

Remove the no from the lesson.

So lets make some puzzles.  Build me x² + 7x + 12...and then count the sides...basically here the algebra is just along for the ride mostly we are cementing in the addends and doing some multiplication facts. Then we also see x² + 8x + 16 is (x+4)² which is just a shorter way to write (x+4)(x+4)...this also gives us a better understanding of just plain ol' x²...

10 to 15 Minutes per Topic.

Factoring is fun and easy. And it builds confidence because every kids knows algebra is supposed to be hard. So if they can do it with ease they must be just as smart as grandma says they are.

That moment when you see the answer.

 Keeping it small and easy makes it fun but there is plenty of math going on here none the less. Dividing by two, squaring a number, addends, multiplication she gets exposed to all of it in one simple problem.  If you put the child in a situation where they can not fail and feel like they are making their own discoveries rather than you just telling them math facts and practicing with drills and memorization you will find lower stress and more fun which leads to more learning and happy memories and associations.   Or you can bust out your work sheets.., and see how much fun that isn't.

It is a very simple concept, the making of positive associations with the mathematics instead of negatives ones. It should be pretty clear from the pictures that she is having a good time.  If you have doubts listen to her excitement in the video.

Once you get the thing factored counting is the easy part. While she is building it fine motor skills are being developed. Also recognition of spatial relationships...

Algebra is fun and easy.

Factoring Polynomials is Child's play.

Here is a picture that's fun because we are seeing quite clearly that 3 sixes and six 3's is the same thing. We made a purple sponge cake with pink frosting and as we frosted the cake we counted by threes.  We put them on top of each other and counted the sides...

Multiplication doesn't have to be drudgery, if you do it right the child see's that actually it's a time saver and learning to multiply makes life easier not harder because it allows us to count quickly which allows us to do more math with less pain. Discovering constancy of numbers is fun when you are six.

It's these little repeated exposures using base ten blocks that over time add up to a deeper understanding of how math fits together.

So here is a sample for you, showing us "jumping around" from topic to topic. The topic is math. so we are just playing math...we start off counting 11's...and then fool around with multiplication concepts...then we solved for x playing what's under the cup, told some stories...did some thinking...then we factored some polynomials and we were done...moved along in lively fashion didn't get bored doing the same thing over and over again even though we were doing the same thing over and over again...which is math...

Not just Theory.  Theory in Practice.  
I have HUNDREDS of FREE videos that show you how.

I don't want to tutor your kids I want you to tutor your kids. Play math and have fun. Spend quality time with your kids and learn together. This method will transform your math time into something your kids look forward to instead of dread. But don't take my word for it, here are testimonials, you can see many others have found that this is a better way to go. All you have to do is dive in.  Christmas is coming and it will be a great time to get some blocks and GET STARTED.  Get a set of blocks and a password and you are good to go.

House For A Duck.

Playing math often means learning math without really knowing you are learning math....when you are four or five. In this case we learned a lot of math, addends specifically, without worksheets without pencil, pens or paper. We just built a house for a duck and as an added bonus got a few more repetitions for these addends added to the long term memory. It takes many repetitions starting at an early age to get math facts (or any facts) into "the long term memory" and available for instant recall, but as you will see it's easier when they are younger and here is WHY.

Where most of you err particularly with multiplication is you try to cram the number of repetitions into a short time frame usually well after the brain is out of the "download mode". This can be effective but it has been my experience that this can also cause a host of problems particularly when it comes to math anxiety and attitude toward math in general. Instead of a fun and exciting language that underlies ALL of science and explains the universe around them via the physics and chemistry and biology it becomes drudgery and something that requires a lot of mental effort to memorize a host of math facts that don't seem to go together.

Using base Ten Blocks to Make A House For A Duck, You can also see a math bag in the background because we played what's under the cup too. We had fun while learning basic addends less than 10.

What you want to do is make positive associations with mathematics and avoid having to pound math facts into your children. This is what happens when you wait until they are past the age of 7 or 8 to teach them math. The very basics, 45 addends and 400 multiplication facts are learned easily before the age of 7; it is much harder after this age because the brain state has changed.

If you want to be an effective teacher you need to understand a little about how the brain works and how to put information in it. I will have more on this later but the basic is this:

When the child is naturally in "theta", they are basically in download mode. Learning anything is easier for ANYone while in theta, there is an entire industry dedicated to selling audio technology that puts the brain into these states for "super learning"...being happy and unstressed adds to this ability to learn easily. I cover this in Parent/Teacher training.

Removing "the NO" from the lesson is important because "NO" is a charged word that has all manner of negative associations attached to it even by the age of 5. Just hearing "no" is enough to make some children mad or sad or angry which activates the reptilian brain (cerebellum) which shuts down the prefrontal cortex which activates the fight or flight response where blood is pushed into the limbs NOT into the part of the brain that facilitates learning or higher order thinking.

By age six or seven "downloading" is no longer the default setting as it were and they begin spending more time in alpha and then by age 12 beta (and with training Gamma, a state not shown here and a state associated with "miracles" and the "paranormal" and other psychic abilities not easily explainable by modern science but which can be achieved with "practice.").  Logically the best time to teach a large amount of factual information is in the early years when it is easy down loaded or assimilated. The names of states and their capitols, Presidents, the ABC's and of course math facts like 7x8 and 17 squared are easily learned and stored in the subconscious for easy recall at earlier ages.  And if you make a game of it and make it fun, the learning is easier still.  Play math. Not worksheets.

At Crewton Ramone's House of Math as with Mortensen and Montessori, we emphasize whole brain activities...using both hands for example is VERY important, but can you also see that involving the other sensory cortexes would make learning easier? This is because we use more of the brain. This has been borne out by research at major universities.

This seems obvious to those of us that use manipulatives to teach math but quite a few others are only just now discovering that the more senses you involve the easier learning is.

WHEN you teach is also an important factor...as the child gets older more repetition is required to put information into the sub-conscious mind to be made available for instant recall.   In other words the older the child is the harder it will be to memorize multiplication tables...learn a new language or most any subject.  This does not; however, mean it can't be done. Obviously, it just means it will be harder,  take longer, and often involves a lot of tears and frustration.

Any student properly motivated and who is relaxed and happy can learn math at any age. I have proven this repeatedly for over 25 years with students of all ages including adults. But it is FAR easier if you get them young because by the time they are teens many factors are working against you, brainstate being primary among them but as you know, attitude and motivation may be lacking by the time they reach their teen age years, plus there is the added conditioning of past failures and the thought that math is hard instead of something easy and fun.

Here is theory in action. He sees the math facts. He hears the math facts. He experiences the math facts. He has fun. I should have put the camera on him when he told his parents he was done because you could see the satisfaction and pride in the smile on his face. Such a simple thing building a house for a duck, but terribly important for you to understand that through play we learn math, sans tears or fears and without "robbing them of their childhood", but instead making life far easier for him and others like him down the road.




Once (while) addends are mastered, multiplication which is just repetitive addition also becomes easy and we lessen the chance of losing them to multiplication tables and the stupidity that is the way we currently try to force feed students math at a late age.

Come join me on facebook. Share and like this post.

Trig For Little Kids

There is a FREE lesson on this page too:

How to teach trig to 8 year olds

to get you started

It's pretty easy once you understand some basic concepts. This short 5 minute video details what you get for your money. If you have already gotten a lifetime password this page is Gratis. Otherwise it's just $39.95.


The page contains several hours of video that will make trig into child's play. It also has several bonuses that make the page (more than) worth the 40 bucks you are going to pay...

You can pay 40 bucks and it will be more than worth it. Or you can get a "lifetime pass" and get passwords that get you into ALL my password protected pages AND the Parent Teacher training page. Use the button below. If you can't afford $250.00 all at once use the ten pay feature, And remember this page is FREE to those that already have lifetime passwords, but not to those that just have the P/T Training or Sitewide, or who just have annual password status.

Update:  These prices have changed.

Here is the one pay (choose $250.00):

use side bar

Here is the 10 pay (choose $26.00):

use side bar

Obviously, the only one that will get you the password to this page is the $26.00 Lifetime password. So when I say lifetime password I really mean 3 passwords. One for PT Training. One for ALL the other pages (Sitewide) and now one for How to teach Trig to 8 Year Olds. There will be more Al La Cart pages in the future but if you have a lifetime pass these come free with it...and as you can see eventually the price of the Lifetime pass is going to go UP.

If just want the password to this page buy it on the Entry Page and you are quite literally set for life. That 39.95 gets you into that page forever not just a week or month or year.  When the password changes, and it will, just email me for the new one.

Once you have you the correct password go:

HERE

Or direct to the page requiring your password here.

You get quite a bit of stuff for free, for example go to this page and get a some FREE simple trig lessons. You might also do a search for Crewton Ramone Trigonometry and see what comes back. And of course, if you don't think it was worth the money for the password ask for your money back.

Here is a photo set from the training...basically shots of the white board before I erased it and moved on. For an explanation of what you see here go to the page and watch the 40 minute screen cast...

Use these simple tools to make trig child's play.

Don't forget to check out the FREE lesson on this page:

How to teach trig to 8 year olds.

***Also be looking forward to a sale of sorts where you get a combo kit, a pass for two trainings AND, plus a lifetime password all for just 345.00. And because I will have the combo kits in hand you will get same day or one day PRIORITY shipping, so you will have the kit IN HAND in a week not 6 to 8 weeks. Stay tuned for that.

Another FREE Mirco LESSON:


You will see the reason for some of the vids on the password protected page once you see these little kids learning Trig...make math easy and do short lessons. Even this 15 minute lesson could be broken up. But I'm making videos to show you guys...note how I ask questions I don't just tell them facts to memorize. All this and more is covered in "How to teach trig to eight year olds." Note how I EXPECT hem to know and use basic concepts like square toot, divide a number by itself to get one, opposite addends, same and more...put it altogether with my help. 

Trig too much for you? Start with a FREE book on subtraction. Get Supremely Simple Subtraction here. If they can't do subtraction easily math isn't going to be any fun. Check the comments out on that page...people really like my free stuff I think you will find you'll get more than your money's worth when I ask you to pay for something. Get your FREE copy today.  Also go back up and hit like if you got some value out of this page whether to get "How To Teach Trig To Eight Year Olds" or not.

Trig With Base Ten Blocks

Base ten blocks are well suited for teaching trig and trig concepts in a very concrete manner.  Starting off simply with Pythagorean Theorem it becomes quite clear that the blocks make things much more tangible than even the simple formula a² + b² = c².

Basically we take a rectangle and cut it diagonally into a triangle and then study that and those relationships.  We have names for those relationships. SOH CAH TOA will help you remember those names but it's important to understand what those relationships actually mean.  As I have said about 1,000 times probably more, if all you know is sin30° = .5 and cos60° = sin30° you are going to have a bad time.

Even the entry page to the Trig page has valuable lessons you can use with your young students on it.  And judging from the instant and huge response there is some demand for a method that makes trig simple and easy. One the trig page you get hours of video including lessons that actual students were given that allowed them to get 100% scores when they were formally getting less than 50% of tests right.

Base Ten Blocks make Trig assessable.

Once you understand the concepts all they can do is change the numbers. Click this link to go see what I'm talking about. Then get yourself a password. The Trig page is worth the price all by itself, but you get 14 other password protected pages all for just 6 bucks...plus for a two and a half bucks more you get parent teacher training and that is also getting good reviews and blowing people's mind's when it comes to how easy math can be. If you let it.

The lessons on building squares are going to make Pythagoras easy to understand, Pythagoras made Trigonometry easy to understand and you will see the base ten block method makes it all understandable. On the entry page there is now a lesson about the definitions and how to use them for parents and teachers but students could benefit from it too.  There is also some quick info on what to expact on the password protected page and another vid showing simple definitions. Like any language you have to know what the words mean before you can use them properly. When you teach math try to think about it the way you would teaching any other language, lighten up and play math.

Crewton Ramone Teaching Math To Little Girls.

Here is the long version:



Here is the shorter version:

Base 10 Blocks & Algebra Teach The Basics

The points of this post are manifold.

One, for those who are thinking they might want to start a tutoring business, DO IT. NO ONE is out there teaching kids math like this...well, I can't really say that anymore because actually quite a few people are now using these techniques to teach math...more than six years ago when I started this nonsense anyway, but you know what I mean.  The number of people doing it this way is very, very SMALL. You should have no trouble finding a few parents who understand that giving their child, particularly if the child happens to be female, a real head start and are willing to pay well you for it. Don't undercut yourself.

You can charge decent money because of this, especially if you have been to several Friday trainings and/or have gotten passwords and watched all the videos (and played along with your blocks) on the Parent Teacher Training Page (there are quite a few more Hours about to added there BTW). Ask yourself where else are they going to get this? From me? I can only do so many students at a time and my time for teaching students is just about come to an end...I am interested in training teachers and ultimately training trainers and master trainers to replace myself. 

Two, when teaching older students who have massive holes like this child in their math knowledge and basic math facts it is important to preserve the child's self esteem. With younger remedial students playing like this is cool because in kid culture "everybody knows algebra is HARD" so although we are factoring polynomials not so much to learn algebra and distributive theory but more to learn addends and multiplication, the older students don't feel "dumb" because after all we are still doing algebra, and the younger students feel smart because after all we are still doing algebra. Get it? I think you will find this is a recurring theme here on this blog. I use third and fourth power algebra to accomplish this too.

Three, it should become abundantly clear after watching this video that having a calculator in hand wouldn't help him factor an expression like x² + 9x + 18...you have to know your addends, which will make repetitive addition (which some call multiplication) easy and fast and will bring home the concept that numbers are made up of other numbers and that there are many ways to express any number...as the sum of two (or more) numbers as the difference of two numbers as the product of two (or more) numbers or as the quotient of two numbers...

I also have another video with a 7 year old where you can see having played with square numbers and being familiar with addends and ratios and fractions makes trig EASY. But if you can't even recognize a square number when you see one...well...an "F" is much more likely than an "A".



Get a password, get a couple of my books and get going. Trainings on Fridays has become "a thing", cost is 20 bucks for 1 to 4 hours, lately they have been going for 4...if you come for an hour it's $20 if you come for all for hours it's $20, starts at 8am HST...you need gmail vid chat and you need to have the video plug in ALREADY INSTALLED. Email me for more info. I know you think 4 hours is a long time but trust me: time flies when you are having math...ask anybody that has come it won't feel like four hours.

Fractions Teach Multiplication Using Base 10 Blocks

This video is pretty self explanatory, so I won't put too much here in the way of words. People don't read these posts much anyway just look at the pictures and watch the videos...so:


But for those interested in a little more in the way of training for parents or teaches, with little kids you don't need to write symbols to start.  (By little kids I mean 6 and under.) Just do what you see here and talk about it. Later the symbols will make sense when we write them. Don't forget to spend some time DRAWING them too.  (Look at the second excerpt for more on this on the training entry page.)  Lastly, do symbols...but this kid is 17 so we went directly from manipulatives to symbols...because he's paying by the hour and it takes too long to draw and label them although it is a very worthwhile step, I told him to do it at home. I had other things I wanted to do in the hour. The idea is to teach concepts but this child needs work on multiplication...multiplication will make all of his math easier to understand because there is no time lost on computation (if multiplication is easy and fast, if not the math problem is compounded because they have to think about multiplication AND whatever the problem is too...once they have the multiplication down as Forest would say, "that's one less thing."

Here again I want to drive home the point that all we are doing is counting and basically I am teaching him to count and count quickly using fractions manipulatives. Counting quickly like this is called multiplication. The fractions are also discovered...and equivalent fractions understood and reducing fractions will not be difficult when we introduce that concept later...only then we will be using division instead of multiplication. I hope you can see the rectangles...


Introduce skip counting early and sing songs and play and this whole problem can be avoided...too many teen-agers have this exact same problem, they are having trouble with math (particularly algebra) because they can't even multiply and having a calculator doesn't help. In order to see relationships, ratios and multiples it is imperative that they know their multiplication tables bare ass minimum out to 9x9, out to 12x12 better than that and out to 20x20 (yes, 400 facts) best of all. We went thru a little period there where well meaning but horribly misguided math teachers tried to say that with the advent of cheap calculators students didn't need to know multiplication by rote memory. OPPS.

They were trying to spare students the pain of memorization and drill. I agree about taking the pain out of mathematics but not with taking the learning of multiplication out of the mathematics, which is why we didn't spend the whole hour on this...I assure you drill, worksheets, and flash cards will turn the kids off faster than you can say "modern mathematics teaching in America is an utter failure." But if you play games, sing songs, skip count, and do fun math activities starting at an EARLY AGE, multiplication can be mastered without tears, muss or fuss.

I have a book (my Curious Counter's Compendium) you can get for practically NO MONEY that will help you start teaching math to your toddlers, and another one (my Subtraction Manual) you can get for NO MONEY at all.  More manuals are being worked on as we speak, there will one day be 11 in all.

Side note: We measured the distance he walks using the odometer on my car and it was just over two and a half miles, one way. Math is either important or it isn't.

More side note: AFTER you go thru a lot of posts on this blog, videos on youtube and of course my website you might want to get a password...

Homeschool Math: Base Ten Blocks for long division...again.

I've been perusing the internet looking at what other people are doing with base ten blocks.  Sorry guys. It's appalling. No wonder teachers don't use them much...many of the presentations are very...uh, poor.  If you are a teacher showing other teachers how to use base ten blocks you have a responsibility to make sure you are doing it right. Even then there's no telling what the people you instruct will do...like a game of telephone after a very few generations things can go very, very far awry.

I remember once, we had a center in Salt Lake City.  I trained several people there and then went off traveling doing seminars and opening up a couple of other centers in places like Colorado and Nebraska and South Carolina along with the training tour I was contracted to do which was usually 3 cities a week...anyhow, I came back after about 3 months and was watching  a teacher that one of the trainers I had trained, trained do a lesson for a group of people who had bought kits, she was nervous because I was there but she did okay right up until she started presenting division.  I won't go into details but lets just say "there's no split and shift" in division. If you want to model multiplication that way fine, it will mirror what they see in public school but it doesn't work for division...at all. And if you don't know what "split and shift" means don't worry about it.

Lost In Translation.

So I understand. It's like a game of telephone where one person whispers a sentence into the next persons ear...by the time it comes back to you it can be radically different. Or things can get lost in translation. Like this:


Dboyz are still chuckling as I type this. Anyhow, behold! If you type in long division with base ten blocks into mother google this is THE number one video out there:


4 is contained in 532 how many times? What are we counting? FOURS. Here it is done showing how rectangles facilitate counting. As I watch this I see several things I could have done better too. But I think you'll agree one makes things a little clearer than the other.  The idea is to reduce these problems to simple counting.  Take a look at this video, "complex numbers" for 3rd power algebra made into child's play. Division shouldn't be hard or scary or cause tears. And once again we see the way things should as opposed to the way things are because currently the way we teach it in public schools kids learn to HATE long division.


Rectangles Facilitate Counting.


Now in order to do division a lot of you think you need to be able to multiply and subtract, as you can see (and I should make a vid with some actual 5 year olds) any five year old can count down one red one three blue ones and three green ones. 133. Building the rectangle and getting out the pieces would be the challenging part. But if you explain that it can only be four across they won't even reach for 100 squares...and again this is a dynamic problem that should only be attempted once many simple static problems have been done and mastered...I show and talk about some simple ones in the video.

I have already made several posts and pages about division with base ten blocks and on the Parent/Teacher training page I talk about the importance of starting in the concrete and moving to symbols after drawing whenever possible. Go to those pages for more. Here is yet more on division.

Multiplication is of course important and so is subtraction but again you can use division to teach multiplication...and subtraction, but all you need to do is be able to count to get started doing problems like this and you can baby step your way here in short order. Speaking of subtraction I just got a book on it finished and back from my illustrators. Supremely Simple Subtraction. You can have it for free, just give me your email. If you buy a password, it is of course included on the Password Protected PDF's page along with a lot of other cool Pdf's. Some people are reluctant to give me so much as an email lol because they expect that then they'll get bombarded with email from me. Is to laugh. If you get 12 emails from me in the next YEAR that will be a lot of emails...lol...there are people who sign up for emails and did so 5 years ago and still haven't gotten one...lol...they WANT an email telling them when I put up new vids or pages or what the new password is and...


They are still waiting for an email.

Things are a little different at the house of math. Go take a look. See any advertising? Casinos and Online schools and colleges solicit me quite often asking me to put links on my pages or ad words or what have you, and now that my site is doing well some of them are willing to pay a few hundred bucks for the privilege. Free money. They always get a "NO" from me. So if you want the book email me. I will email you the book and not a whole hell of a lot else. Seriously.

Here is one last video with a guy showing subtraction with base ten blocks...you may not be able to get through it.  I was going to make this it's own post but I think I'll just combine these two.  People always ask me why don't more people use base ten blocks to teach math...mostly because they don't know how and they end up doing presentations like this and teachers (and parents and/or homeschoolers) get turned off because really it's not much better than symbol based instruction and it seems more cumbersome and time consuming. If you just have rods, bars and units this isn't too far from correct because it takes forever just to set up the problem.  Anyhow here is exactly how not to do it:



How may units can we have in the units place in base ten? NINE. How many tens? NINE. It never gets past nine. If you want to see a super simple way to do subtraction get my subtraction book...or go to my subtraction page. But the word is in. The book is cooler and full color and spiffy as all get out.

Password protected pages give you even more detailed info in the form of vids and pdfs. They used to be super cheap...and guess what? Nobody bought them because I guess people figured they couldn't be worth much for just 5 bucks or what have you. Now I sell subscriptions and annuals and lifetimes at the rate of several per week...one password for $50 is the same as making 10 sales at $5...and I never ever made 10 sales even in a month at $5. Now even if I only do one a week that's 30x better than my best month when they were $5. Bummer for you. Bully for me. I might have a weekend sale in March on passwords not product,  (product is out of my control that's Mortco not me)....maybe. Probably people who got my book for free with an email or who got a password a long time ago would like to be informed of the sale with an email reminder...lol...but I doubt I'll get around to it.

Of course I have a FaceBook page and I'm on Instagram now too.

Divinely Dandy Non Difficult Division

Get Divinely Dandy Non Difficult Division for just $19.99. This book will show you everything you learned here and MORE laid out step by step with links to videos and pages that give simple concise explanations for how to use the rectangle to organize thought, how to introduce division concepts at a very young age, and how to make fun while you are doing it. I guarantee that video alone will expand your thinking when it comes to division and math.

Watch the video on the Preview and Purchase page that gives you a page by page over view of the PDF so you can "try before you buy", see exactly what you are getting and be confident it will be money well spent.

As always before you buy stuff be sure to check out all the FREE stuff first.

Crewton's Math Manipulative Manifesto

Math Manipulatives

Here is an article I wrote about math manipulatives for my website directing people to this blog. Some of the points here will be covered in more detail in the next parent teacher training.


Math Manipulative Manifesto

"Learning is not the product of teaching. Learning is the product of the activity of learners." ~John Holt

This blog is dedicated almost exclusively to showing you how to use manipulativess with your children at your house whether you home-school or not, and also to get you to use them in your classroom if you are a teacher. Note the lack of advertising, adsense, annoying pop up vids etc. The only things I advertise here are blocks, books, and passwords to vids and info.

While meditating it hit me why there is such a disparity of viewpoint between me and most of my "fans" regarding curriculum and organization. Whereas I see it all as just counting, others think of it in subjects, grades or levels or what have you, because the way you were taught was very compartmentalized.

It's been ingrained in you that FIRST you have to learn how to count, next you add next you subtract then you multiply then you divide next you do fractions etc.

What I'm saying and what this method teaches using math manipulatives, is that ALL that is, is counting. All of it. You're just counting. Since we are just counting, we can use division to teach it or we can use fractions to teach counting like addition and multiplication or we can use algebra to teach counting...most people think that in order to do division the student has to have learned how to multiply and subtract...NO. (Look at me! Breaking the rules: you are supposed to remove the no from the lesson.)

Students don't need to have gone through basic operations (addition, subtraction, multiplication, division) before they can do algebra, in fact algebra will teach basic operations. Division is also just counting and we can use division to teach a lot of math concepts as well as how to add, subtract, and multiply and they learn to multiply and subtract while they are learning to count. It's the same with fractions...or algebra.

Ask what is it we are counting?
"Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting." ~Ernst Mach

All mathematical questions boil down to "what are we counting?" When teaching math you can use division to teach counting or addition to teach counting or algebra to teach counting...you can focus on whatever you like but it doesn't need to be structured such that addition comes first and then subtraction, in fact you will quickly see it's very hard to separate the two and trying to do so may actually be harmful to their understanding.

I have sat in awe in grade schools while lessons on multiplication were taught without any reference to area, or division, or in some cases any reference to repetitive addition...just learn 7 x 8 = 56...and to this day it is amusing that 99.99999999999% of people I meet are wholly unaware that that division "thing" we use is just shorthand for a rectangle. Or what the equals sign means. Or where that percent sign comes from. Or that square numbers are square...but I digress.

The Mathematics is a language and it all goes together and shouldn't be segmented or compartmentalized to the point that the student is unaware that multiplication and division are inverse functions, manipulatives make that visually obvious. They will be able to see and understand this naturally...and then it's easy to point out to them, this is part of "directed discovery" you know what you want them to learn but you let them discover it. You facilitate this by putting them in a math rich environment.

The point is that while we are teaching basic operations we are just counting but don't get confused: basic operations is computation and computation is how we do math but math is much more than just computation. (The fact that I have to write that statement is a clue to the complete failure that is the current state of math education.)

There isn't anything more fun than seeing your own students or children learn something and have fun at the same time, and in knowing you are the one responsible for it. This is why some teachers are addicted to teaching no matter how poor the pay is and no matter how lousy the conditions are.

Math is the language of logic and reasoning combined with critical thinking skills. I have met many students who are great at computation but very,very poor at math. (Some of them go on to get degrees and then, ironically, attempt to teach others the math they don't really understand.

If you put the child in a situation where they CAN NOT FAIL, expect and allow for error, allow for self correction with direction...direct their discovery in a math rich environment: they learn math. They can't help it. AS an added bonus they have fun learning with math manipulatives and/or base ten blocks.

Give the child an algorithm for addition (wanna be a ten) that can be applied to multiplication and suddenly almost effortlessly (much to the amazement of parents and even veteran teachers) the students are adding and multiplying...multiplication is the first milestone because it allows the child to count quickly, once computation is easy the math becomes easy too because computation is how we DO math but again, it's not the math itself.

With computation mastery, math concepts that are understood can be applied to problem solving and answers are fun and easy to see. The combination of computational mastery and conceptual mastery combined with visualization is very powerful. The playful, curious attitude that problems are just games or puzzles removes fear and tears, and learning is seemingly effortless because they are having fun doing it.


Avoid the problems in the first place.

"Intellectuals solve problems, geniuses prevent them." - Albert Einstein

 
There is no greater joy for a parent (or any teacher) than seeing the ah-ha moments and light bulbs go off...it is especially poignant if the child had formally been struggling with math, but I prefer to avoid the problems in the first place.

The question should be "what kind of counting do you want to do today?" Or what kind of counting do you want to teach today? If you are a teacher. 1st graders as an example can learn division and thereby learn a lot about counting, and multiplication and subtraction...as well as addition...they can learn about fractions and thereby learn about addition, multiplication and division as well as concepts like SAME...the way we currently teach it children somehow come to the conclusion that rules have changed when we add fractions. They haven't. We can teach them problem solving, which at first is just recognizing same and "hero zero" and then "no fun get back to one"...all of which is just simple COUNTING even if they are little.

Please click on this link for more on "hero zero" and "no fun get back to one" and removing no from the lesson the other teaching concepts referenced in this manifesto. (Rant. Diatribe).

I've done lessons for 2nd graders on square roots...in order to do square roots we had to count the squares and the sides...so we learned skip counting, used addition skills to count 7 sevens which was more work than counting 4 fours and figured out what the symbol means--just count one side. We also learned about economy of symbol instead of 4 + 4 + 4 + 4 = 16, or even 4 x 4 =16 we could just use 4² =16. I wasn't just teaching square numbers I was teaching lots of counting. NONE of it would be possible without the use of base ten blocks. People are amazed that I go on to do lessons on Pythagorean theorem but they don't understand the part about it's easy when they can see it. I wouldn't even attempt to teach them any of this without math manipulatives.

Further students often never understand the relationship between Pythagorean theorem, distance formula and the first basic trig identity sin² +cos² = 1, it's just a bunch of stuff they memorize long enough to be tested on and then forget--never having made any of the  leaps of understanding or connections. My students avoid this because they've been playing with these concepts for years and baby step their way there instead of it being all new and confusing in all at once in high school.

Shift your paradigm.

What I have to do is get YOU to change YOUR paradigm and understand the way you were taught via compartmentalized, separate subjects, grades and levels might (just maybe, quite possibly) NOT be the best way to teach math, and is part of the reason the teaching of mathematics in general in the USA is an utterly abysmal failure. Most of you recognize that it is an utterly abysmal failure which is why you are here in the first place then the first thing you ask me is, "couldn't you teach and organize your blog and website more like the way we know doesn't work and is an utterly abysmal failure?"