Long Division With Base Ten Blocks

UPDATE: Here is yet another post on division due to the fact I see people showing how to use base ten blocks that are less effective than they could be. This one includes the #1 video hit for division with base ten blocks.

UPDATE: Divinely Dandy non Difficult Division is DONE! (See below.)

There is now an in-depth post at The House Of Math about Long Division With Base Ten Blocks.

Long Division. Not well loved among students. It's EASY if you understand the concepts. And here we will add a little about square roots too....just for fun. Just because we can. Just because you should cross teach whenever you get the chance so your students can see how it all fits together into one language.

Start simple and work your way up. Remember degree of difficulty...and the other 5 basic concepts. We are fooling around with rectangles and counting. Some call this multiplication and subtraction and others call it division. Bottom line: we are counting. And one more time computation is not mathematics. Computation is how we DO mathematics. Today I found myself with an older student and I told him I don't care about the computation at the moment...I want you to understand the concepts...we'll do the computation later...we trying to find the area of a shaded region with a square and a circle inscribed where the only information was the radius of the circle. But step one was knowing I had to do subtraction. But I digress.

Observe. Here is a very simple rectangle:

The question arises why don't you use this pattern (above) instead of this pattern:

Well, because we want to keep track of subtraction. Long Division With Base Ten Blocks allows us to see what we are doing.

We are counting a rectangle that is 4 across and contains 12.  4 is contained in 12, 3 times. The number inside the rectangle is the dividend the thing being divided, and the number outside (the 4) is the divisor and the 3 is the quotient.  We are humans we name everything. "I think I'll call this place Golgatha and move on."  Kids have a hard time reading division because of this. This is solved quite simply by saying 4 is contained in 12 how many times? We read left to right so saying 12 divided by 4 is confusing. Besides we denote that this way: 12 ÷ 4 = 3.

Dividend. Divisor. Quotient.  Simple no argument.  You be surprised at how many people can't figure out the syntax of Multiplier, Multiplicand, Product or think it doesn't matter. To little kids you are right it doesn't matter and you will note you do not hear these math terms in the video below because at the moment this is extraneous information. Later when they are comfortable with the concepts we can start naming names. Meantime we do Long Division With Base Ten Blocks so that it is readily understandable and visually obvious. Once we start getting it down they will be able to do long division in their heads with no blocks and no paper and pencil either. This is called mastery.

Note the lovely blend of symbol and manipulatives. It completely makes sense to he who is but 5.

Now because this is a demo video more or less and because my students are familiar with the blocks we jumped a bunch of steps to a much bigger problem. YOU would NOT do this with your students unless they were quite familiar with the blocks and even then. Do many smaller ones and have them count...you might also do a few where they have to give you parameter just for fun.  Many. More than three.

Here we are going to count how many times 12 is contained in 132. The obvious answer is 11. These are easy static problems. I used train teachers all the time and the first thing out of their mouths after their initial excitement subsided was how do do a problem like 7 is contained in 132. Pat answer: "you don't." You do lots of easy ones where it works out perfectly and then a few where we have remainders like 4 is contained in 13 how many times and 12 is contained in 133 how many times BEFORE you even think of moving to dynamic problems. By then they have the concept and they realize paper and pencil is MUCH FASTER than playing with blocks. Besides that's all the algorithms do is make counting fast. But long division is a bitch if you don't understand the basic concepts and you can't multiply.  Further let them figure out the algorythim for themselves as you direct their discovery in a math rich environment.

So now lets get even bigger and do one that just happens to be square. AGAIN, YOU would NOT do this until you had done many smaller ones and worked your way up here.

But I am going to illustrate and explain each step.  You could do this with 12 is contained in 132 or 13 is contained in 156 etc.

Because Mrs. Irma Hardbottom would accuse your little genius child of cheating if all he they did was write 19 and be done with it, we have to show our work which is again why we pattern with the blocks this way. Across and down.

And you can see other videos on Long Division With Base Ten Blocks where I talk about Hiram the Ant and use little men or animals or dinosaurs to walk along the edges and count. But you should point out that ten 19's are 190 and that one is one 10. Don't get confused with the edges, we are talking about the distance from one side to the other. 

Once we take 190 from 361 we had to do a little work to figure out what was left on this problem. After some figuring they counted 171 which with the blocks was 90 and 81 which was 19, 9 times. They were counting the blocks NOT doing subtraction, if they did subtraction it might have been even easier because all they would have to do is take 0 from 1 and get 0, add 1 ten to 6 tens to get 7 tens (see vids on subtraction)  leaving us with 2 hundreds because we had to take the 9 tens out of one of the hundreds which is how we end up adding 1 ten to the 6 tens and then taking 1 hundred from 2 hundred is EASY.

It's also easy to see that the square root of 361 is 19 and when it comes to notation this is much easier.

So we did 20 just for fun.

And then we were basically done. Here is all of the above in one fairly concise video:



Anyhow go check out the division page at the House of Math for a little more...long division shouldn't be hard. Look for another post about more advanced problems where the rectangles are more dynamic...these are best drawn or done with symbols AFTER the concepts are mastered.

Here is another GREAT post on long division that even has scans of pages from the smiley face books.

People get excited and ask me what they should get when it comes to blocks and stuff...go here for the simple answer.

Here are some more division worksheets (you need a password) and the video on that page teaches you how to use them. YOU could use that vid as a primer and instead of using pencil and paper use the BLOCKS.

Learn to use your base ten blocks.

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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. 



"Can you do Division? Divide a loaf by a knife - what's the answer to that?" ~Lewis Carroll, Through the Looking Glass 

 “We divided ourselves among caste, creed, culture and countries but what is undivided remains most valuable: a mere smile and the love.” ~Santosh Kalwar

PDF Prices

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

The Curious Counter's Compendium.

Get this book if you have children 7 and under...find out more about it, and a look inside here.  You can get it without a password for just $2.99

"Great book for teaching how to use the blocks! Colorful, clear pictures and cute rhymes make the book fun to read and play around with. We printed the book out, and my 5yo loves how many of the block pictures are big enough to put his blocks directly on top of the pictures. The text plays fast and loose with niceties like punctuation, but is engaging when read aloud.

Most of the book focuses on playing with addition facts up to 10, which gives a solid foundation. But it also delves briefly into such topics as square roots, place value, addition of multi-digit numbers, and a glimpse at multiplication. And in true Crewton Ramone fashion, problem solving with 'x' (basic algebra) is sprinkled throughout. A great intro to playing with math." ~CS, GA.

Ratios With Sarah

Ratios are easy. All you do is cross multiply. Why? And what if you for get the rules? Here is a series of videos staring Sarah who is studying for her GED. This series gets cut off before we finish but what is on vid is worth sharing. Remember this kid is autistic...but I don't treat her with kid gloves (anymore), and she is doing quite well with math. Look for other blog posts where she is featured and prepare to be amazed. Also look for a future post where the autistic savant rears it's head...she is beginning to recall math facts and remember seemingly random facts that she has seen before.

{I'll put a link in when I make the post. Note to self.}

In these vid we begin to see what do when presented with ratio problems and rather than give rules on when to multiply or divide we think about the relationships. Once we understand that then we can start making up rules to describe what's happening and what to do to get the answer. Note I give her no rules. Later she tells me the rules...unfortunately I did not get it on video. But by the last video you can see she understands it. Then and only then do we move on.



Note I put the P1 in front to make it easy to search and find the next vid...P1 Crewton Ramone and Sarah Playing Ratios and Relationships.



Note when I say tricky I am using her verbage because there's nothing tricky about these it's just math.



As they understand it they do it easier and faster.



And here is the final one where she shows she understands it.



After these we move on to problems where it's not just whole numbers but fractions but we didn't get any of it on vid...you can see more with Sarah on Sarah's page.

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Playing With Cubes

Getting to know a little about CUBES is important. Children need to have experience with numbers. Square numbers are good to be familiar with too and so are cubes. The problem with a lot of base 10 blocks is they represent cubes as...well, cubes. Which makes sense except that then the manipulatives are limited to the third power then. How do you show powers past 3? Simple you don't.


Here are the first 12 written out. But certainly DON'T just write them out as a drill until AFTER you have built them and talked about them and played with them a bit first. Here is a vid called Crewton Ramone Squares, Cubes and Division because it's about squares cubes and division. I'm creative like that.

Mortensen Math keeps it in two dimensions. Arithmatic not physics. (x)(x²) = x³ or (x²)(x) = x³ instead of (x)(x)(x) = x³ this is a subtle but important distinction which allows me to teach very young students higher powers and so called more advanced mathematics.

Before you get to cubes might be a good idea to play with squares and square numbers. My students will write them out several times during a course of lessons. So they see the numbers and have some experience with them. This will stand them in good stead when they take standardized tests. Many students get through high school without ever knowing their squares and cubes and at Crewton Ramone's house of math we go all the way to 25 with these. (And out to 20x20 on the multiplication tables.) Seriously, your kids know the names of the Pokemons but they don't know the name of 17² or 17³...or maybe it's all the characters in Harry Potter...or they can recite lines from Twilight, but you get the idea.

Squares and cubes should be familiar and easy and part of their instant recall just like 2x2 or 10x10x10...and make sure you eventually go out to 25. You have 12 years to get this accomplished. Here is a short video where Sarah and I are studying for her GED and cubes make their appearance...we only go to 12 here.

Crewton Ramone Takes Two

My favorite part about this vid is the comments: people just don't know what to make of me or it. This is a proof of concept vid...needs more work but I want to make math music vids that are current. Like Weird Al Yankovic except for math...change the lyrics of popular songs to explain math concepts...and then have puppets and good looking kids and base ten blocks dancing around to the beat.

This is just a proto-type if you will. I need a small crew to do camera, song covers and puppets and most of all editing.

Anyhow this one was designed for little kids...three to five. And it was designed to be watched more than once...the concept is multiplication by twos...and getting to know the names of the base 10 blocks.



Unconventional. Odd. Different. People not sure what to think. No pocket protector. No nerd glasses. Multiplication by two's for the little kids.

No. This ain't your grandma's mathematics. It's Crewton Ramone for the wee ones. Just a few math concepts at a time. Math needs to be cool again...currently it is the domain of nerds who do not reproduce...

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Go to Crewton Ramone's House Of Math for more.

Base Ten Blocks

Using base ten blocks to teach math is extremely effective.

As with any language: the younger the better. This child is 3.

It allows you to present concepts quickly and easily and because the students can literally grasp the concepts you are teaching because they have their hands on base 10 manipulatives you will find that they achieve greater understanding in less time. This is no longer theory. We've had proven and stunning results for decades now.



I have put up many pages and many videos of actual lessons using base ten blocks to teach algebra, using algebra with base 10 blocks to teach basic operations to even very young children or autistic students. The point is you can teach math this way no matter what you back ground or experience with math is. if you are already a math teacher base 10 blocks will make you a more effective math teacher. If you are just starting out you will find you get better results faster with base ten blocks if you are a seasoned teacher with lots of experience you will find you no longer need to fail half your algebra class because you can make math acseesible to ALL of you students using base ten blocks.

If you can get them to teach one another this is optimal.

If you are a homeschooler you can use base ten blocks and begin teaching math like a pro in no time. You will find that even if your math experience was poor you can teach a lot of things to your own kids and they will actually understand it. Factoring polynomials becomes child's play, solving for x, Pythagorean theorem, square roots and radicals percentages an more are EASY. All you need is a little initiative and and open mind. Take you time and you find lesson after lesson here and I often hear parents who are amazed that for the first time they understand distribution instead of just knowing a formula for what to do like FOIL.

One post couldn't possibly teach you how to best use your base ten blocks. But I can point you in the right direction. There has been some demand for a getting started page...so I will be working on that. Meantime, go to the home page at CRHOM and watch the short video with the little kid on the local news...this will give you an idea where you are going to eventually end up. Then watch the one hour overview. After that you can watch more vids or start reading about addition...which will lead you to multiplication and on the way you may do some subtraction and division.

Look where you can go with little kids. This seven year old is evaluating quadratics and it's child's play. Or you could just use these powerful tools for addition and maybe some place value.



Here we are playing with square numbers...again it shows you where we can go with ease. In between the vid above and the vid below check out this page on square numbers.



As long as you can count to nine and form a rectangle and tell if something is same or different we can pretty much go anywhere. Percentages for example or algebra are no problem. You don't need to know where the staircase leads just take the first step as my buddy Albert would say.

Using Math Materials To Best Effect

I would Like to introduce you to this woman who has started making vids on Vimeo.

Seriously. Could these kids be any cuter?
And it's even more important to teach girls early because they need every advantage. Our culture puts females at a disadvantage when it comes to math starting very early on.

Here is her channel, Education Unboxed. She has opted to use Cuisenaire Rods, I am hugely biased toward Mortensen Math base 10 Blocks/Manipulatives but she is correct that they are pricey and many parents already have Cuisenaire Rods because they are cheaper. (They are cheaper for a reason IMO.) With just a little work, a few "mods" as geeks and nerds like to say, they can be quite serviceable for teaching math beyond just addition and place value. Her point is to make vids that parents/teacers/homeschoolers can use to put the materials they may already have to better use. I highly recommend her channel and vids and hope she one day makes a blog and website too.

If you can't afford Mortensen math materials, perhaps you can afford a set of the Cuisenaire Rods...and you can get started teaching your kids math and learning math right along side them...with all the FREE suport you get from The House Of Math and this blog and now her vids too you can't afford not to get started and have very few excuses left.



She says she is "just a mom" who wants the best for her kids and wants to help others help their kids too. Even more I want to promote her because so many make excuses that they can't do it because they aren't good at math or don't have a degree or what have you...to which I reply: "just get started." You won't fail and you won't hurt or damage your kids. Errors can be corrected if you make them and can be turned into teachable moments.

My comments and critiques are for her improvement NOT to put her down or denigrate what she is doing. Her point and so is mine that if she (we) can do it SO CAN YOU.

CR:
Another great vid!

OMG: your kids are so cute it brings tears to my eyes.

Fine job removing no from the lesson and telling them what they have. Play a game with yourself how to I remove the negative completely. Instead of it's not 11, show me it's 11 or Hmmm, what's this side called again? (Answer is x, and then plus one.)

Improve your x² by putting a stip of paper over the sides because her observation that it is 10x is correct in this case you can clearly see it. I made a video about this...and it is a common question. Is 10x = x²? And the answer is a little complex involving 10, -10 and multiples of 10; they are after all base 10 blocks. That lesson would be best saved for another day...

Just telling them it's x when they can see it is 10 is usually not sufficient. Solve that problem with a strip of paper. I realize you are improvising with the tools you have and you are doing a FINE JOB.

This; however, is pretty important. Math concepts aren't because mom says so. lol

There is a Montessori concept called "visually obvious." It is visually obvious that that one side is ten...it must be visually obvious that that side and all sides is/are x.

A few side notes. At one point the younger child made and x to the second not an x square, which is good: it was one by nine...you could point that out in a later lesson. x² doesn't always have to be square! Especially if you are doing third power algebra...x³ dosen't have t be a cube either...in fact it will make higher power algebra impossible to present if you try and stay in three dimensions. You may casually mention this if she does it again...that way it's a natural discovery and not a "lesson".

Also they are never wrong. They are just getting more information. (You know this I am just reiterating for those reading.) You are a patent and gentle teacher. You may want to direct them a little more and let them figure out some of their mistakes on their own instead of just showing them so they can have their own ah-ha moment. You accomplish this by asking good questions using control of error and putting them in a situation where they can not fail...each one of those is a full dissertation and they are covered lightly on my concepts page.

Good questions:
Does yours look like mine? How could you make your square look like my square? Show me. How are they same, how are they different, what's the name of this. Etc.

You can also avoid and control error with use of the three period lesson.

Lastly you casually mention they are completing the square when they are in fact completing the square. That is great! You could take a second to ask how they do it...the answer you are looking for is by taking the x and splitting into two parts...this seems small but it's huge. Later when they do the quadratic the (b/2)² will make sense...

I would like your permission to your vids on my website or blog once in a while where they will get more exposure and hopefully encourage others to get started teaching their own kids math. I would also like your permission to put links in these comments because I have covered a lot of this in detail in other places.

Third please contact me via email...info is at my website. Just click the contact tab.
I am a master trainer. I was certified by Jerry to train trainers to train other trainers...not just train teachers to teach kids. The difference is understanding the why of things. You could be a mighty teacher if you wanted to be. You never know where teaching ends...somebody could see your vid and be inspired to do more...a kid could stumble across it and have an epiphany...you're making a positive difference.

One more time: FINE JOB.

Education Unboxed:

Yes, I absolutely do need to cover the sides with paper. I'll be doing that soon!

I THINK I understand what you are saying about "x squared" (not sure how to get the little 2 up there!) not having to be a square. Though I just learned last year that "squared" actually means a square! So, now you're saying that it doesn't HAVE TO BE in a square shape, right? Just that 9 is a square number because it COULD be made into a square? And when it's not in a square shape, then we call it "x to the second?"

Yes, please feel free to post my videos anywhere you'd like. The only reason I made them was to help other people (so they wouldn't have to do the hours and hours of research and reading I've done over the years). And, yes, links in the comments are fine.
I will contact you through your website. Thanks!!!

Then as you can see in this next vid she does...



A couple of notes for ALL teachers including myself: REMOVE THE NO FROM THE LESSON. Migrate to good habits early, but don't worry about doing it wrong if you are wrong just correct the mistake. Some students can be migrated to the correct way just by modeling, they see you doing it correctly so they change to make theirs the same as yours. Occasionally you get the child that wants to be different from you just to be different. These minds are to be encouraged but certain rules are not up for debate, we read left to right for example your blocks should mirror this...here are my comments so far:

Many comments to make. This is great.

Remove the no from the lesson.

Need an equals sign instead of a solidus...

We read left to right...the girls need to be (gently) corrected to put the units in the upper right. It doesn't really matter ( 3 + x )( 4 + x ) = ( x + 3 )( x + 4 ) however ( x + 3 )( x + 4 ) is more correct because we count in descending order. (Count the big ones first.) Also (minor details) move toward putting the parenthesis closer together. Again they aren't wrong they are acquiring more information...and you are simply moving them to more correct notation and mathematical syntax.

Also DRAW pictures. This is the bridge in the mind between the concrete and the abstract. A blend of symbol and blocks is great...
Will add more later.

Keep up the GREAT work.

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Online Math Video Tutoring Is Fun Too

Here are a few Screenshots and vids from some of the Online Math Tutoring I do.

I have found that online math tutoring is fun and the parents have found it is effective. All you need is a set of blocks.

Here is a 12 year old doing some high school math where we are exploring the concept of f(x) and what it means to evaluate algebraic expressions for various values of x. Sound complicated but his 8 year old brother gets it too. We do algebra because it teaches and reinforces basic operations, because of the algebra we have to do addition and subtraction multiplication and division. Their basic skills have improved since I've met them but we rarely drill multiplication facts...

This is one of my favorite students. She is a handful but she she is a free spirit, undisciplined and I dare say a bit naughty at times. But she has a creative mind that needs to be nurtured and rewarded, cultivated not punished for thinking differently and finding the structure of math a little boring. My job is to make computation easy and fun so that later she can "do math" which she will find is far more than computation. Computation is how we do math, but math involves problem solving logic and reasoning.

She is having fun learning addends...I had one parent ask me, "why not just cover the blocks why do you have to put a bag on their head?"
"Because it's more fun."

Building a tower is fun whether you are a boy or a girl. Here we are building the addends for 9 thru 6.  This child is eight. A pox on teachers who think math time can't be play time. She often goes through and tells me all the combinations she has made, although she doesn't have to. Her subconscious also develops a memory for the addends and this makes recall instantaneous.  She doen't have to think or compute...6+3 is the same as 9. We've built it many times. I should have taken pictures of the many times the tower fell over and needed rebuilding...which is also fun. Online Math Video Tutoring is pretty cool. We are as far apart as we can be almost...from Hawaii to the east coast. With the net distance doesn't matter.

After you get them built try playing Jenga with them...take out a block or two without knocking it down. Why? Because it's FUN.

I believe this photo captures a thing called pride. "I did this."  Good for self esteem.  Good for making math fun and giving a positive association with math instead of a negative one.

I find algebra much more useful for teaching math, building towers is fun but so is making these rectangles factoring quadratics not a problem...here she is completing the square and factoring x² + 10x + 25...she gets multiplication, addends, division and algebra all in one lesson. With the towers you get addition and subtraction of addends and fine motor skills but that's about it. Algebra is a much more powerful and effective way to teach more math all at once.



It still amazes me traditional teaching separates the inverse functions of addition and subtraction and multiplication and division. You can see the relationships when you play with the blocks. 6+3 = 3+6 and 9 is made up of a 6 and a 3 in this case so if you make a 9 with a 6 you need three and they see that 9 - 6 is 3 and 9 - 3 is 6...all in one shot where on paper it would take a but to list all those facts. Manipulatives make some operations MUCH faster and easier but eventually you will see paper and pencil really is the much faster way to do math. With Online Math Video Tutoring I can teach anywhere on earth, the concept should still boggle the mind. ANY subject can be taught this way including eye surgery as it turns out but, "dammit Jim I'm a mathematician not a doctor..."



Even when google's vid feed is messed up you can still do a lesson...and algebra is easy even being green. You may also note that I'm pretty generous with what constitutes "one hour" if we are having fun and they don't notice one hour can be 105 minutes...lol...sometimes it's a little less sometimes it more sometimes it really 60 minutes. I stress again with your kids math time shouldn't be rigid but more flexible and the lines between math time and play time should blur and merge.

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Make Math FUN

I think one of the most common questions I get is how do I make math fun? Well make math play and learning playFUL. Make a game of it. EVERYBODY like games. I have lots of posts about making math fun and interesting.

Here are a few:

Video tutoring making an addends house.
Note there a ton of screencasts for free and there is also a Password Protected Screencast page.

Here is another blog post about making math fun.

And another one where we play with monomials and play find the ones which makes it fun instead of scary. This child happens to be autistic but it doesn't matter and little kids like this game too.

Making a game of it is the beast way to make it fun...followed closely by incorporating it into everyday (math) activities. If you make it into a game all manner of things come into play, the students natural competitiveness will come out and everybody likes to get good at games so they can win at games. If you are smart you will make sure even the losers are winners...

You can teach some math with playing cards but you can also teach math by making up a game from whatever it is you just learned. Making it up together is the best way or having them come up with ideas like this video on polar coordinates where we brainstorm ideas for games (you have to skip to the end).

I once did a training in Utah where the homework over the week end was to come back with at leaste one math game...we had about 50 people in that training and we got well over 50 games and activities from Pre-school to "high school" algebra. If you are new here you might wonder why I have quotations around high school, the rest of you know it's because any little kid can do that algebra and they think it's FUN.

I have students on video begging me for algebra...because the way we do it IS FUN. It's like solving a puzzle. I guy who used to work for AMD figuring out why an AMD processor ran software differently than an Intel processor used those exact words...it's like solving a complex puzzle...and of course the way they solved it was with math. BTW he loved his job and was paid several hundred thousand dollars per year to do it. This is the attitude you have to instil in your students. That math is fun, and beautiful, and joyful...and when they think of math they are crying or conjuring up images of mental torture. I often make popcorn in my classes. The reason for this is manyfold.

First and foremost: I love popcorn. But so do most students and it gives them a positive association with math and me and my tutoring. Especially little kids. The smell of popcorn is associated with fun times...I am not above Pavlovian conditioning.

It doesn't have to be about smells and food although using M&M's or grapes or cookies or whatever snacks you like for addition and subtraction won't hurt anything. But making a game of the math itself is better yet...racing can also make a game of it when you separate kids into teams...I have even used this on video chat where one group is "live" with me and the other group is on the east coast...and they race to factor polynomials...we ended up going and extra half hour. Meantime the kids were literally squealing with excitement. You can create this same atmosphere in your classroom. You probably don't want to do it everyday but maybe once a week on Friday as a reward if they've been good.

Homeschoolers can get together once in a while and have family races where one group of kids gets together with one or more others. Use your imagination. Playing with the blocks makes math fun, but you can make math fun by making a game to ensure they attain mastery of whatever topic it is...often times the game they make will let you know how well they understand the related topic.

Here is a lesson you can use over and over again and make math fun while making the concepts understandable. Too many kids are confused by a whole year of multiplication and then a whole year of division and don't understand that they are indeed inverse functions. How you can separate the two is beyond me...

This is part of a long video (49 minutes it can be found here) and I edited down a little...the idea is you get a real time feel for what happens in a lesson. There's no magic to it you just play math and try and keep it fun. Part of having fun is removing the NO from the lesson. A lot of parents need to work on that...teachers too.




This is a compound lesson where we do multiplication, division, square roots, and word problems as well as area and addends, as well as integers watch as we move fluidly from one topic to the next...these boys are 5 and 7.

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Or Just visit The House of Math.

“The only way to learn mathematics is to do mathematics.” ~Paul Halmos

"Almost all creativity involves purposeful play." ~Abraham Maslow American psychologist 1908-1970

"Whoever wants to understand much must play much." ~Gottfried Benn German physician 1886-1956

"Play gives children a chance to practice what they are learning." ~Fred Rogers American television personality 1928-2003

"People tend to forget that play is serious." ~David Hockney Contemporary British painter

"Do not…keep children to their studies by compulsion but by play." ~Plato Greek philosopher 427-347 BCE

"Necessity may be the mother of invention, but play is certainly the father." ~Roger von Oech Contemporary American creativity guru

Crewton Ramone Strikes Again! Sarah.

Here is another testimonial. Sarah has hit a goal and removed a block to her progress. She passed her Compass Test.  This is kind of a big deal. Keep in mind when I met her she had no high school math credits.



Also keep in mind that her family swears up and down that this was a "normal" kid until she was three and she had a round of shots. When she was a baby/toddler she was happy and talkative and liked to draw and play with pencils.  Her mother says she was actually a little advanced because she was drawing not just scribbling and she started talking "early." (Sarah is quite an amazing artist.)  She got her shots and within days became quiet and withdrawn and for quite didn't play with pencils anymore and stopped talking altogether. The hubris filled medical profession coached by pharma has told her that her daughter had Autism all along she just didn't realize it. This is because her doctors know the child better than the parents.  In dealing with Autistic kids I have heard this story many more times than once...

I have also had to deal with schools and teachers that once they applied the Autism label limited what the students were allowed to do "for their own good"...in Sarah's case it was math. I will say her mother deserves quite a bit of credit for standing up for her daughter and getting her into some math classes.  She wants her daughter to be self sufficient. "I'm not always going to be around."



I can not take full credit for her progress because she has teachers and aides that now work with her too. I will say that when I first met her we started at square one...addends, adding numbers and multiplication.  There are still some holes I intend to go back and refill like fractions, ratios, money and problem solving.

I thought that once she passed this test which was the goal for which I was hired that we would be done but Sarah called me herself and asked me if I would do more tutoring with her even though she had passed the test. 

I have to admit that when her mom explained her goals I was among the ones with reservations, some of the school administrators flat out laughed at her,  I didn't go that far, I figured "we'll see." But I was not as optimistic as I should have been. I thought I was just being realistic. I have also been taught another valuable lesson.

Sarah has risen to the occasion. I like working with her because it increases my teaching skills as I figure out how to get her to discover some concepts on her own and how to get her to understand some of the things they teach her in school where she can mimic the algorithm but doesn't really understand what she is doing. She is beginning to understand and "know" the math not just memorize long enough to take the test which I see too many students who are not autistic doing.

I will take credit for this though because I know for a fact she would never have gotten it the traditional way...just like a lot of "normal" kids don't.



I prefer enrichment students and students who are already good at math and want to learn more. I also don't care to get put in a niche where I only work with autistic students; however, I am happy to do video tutoring with students who need help. Scheduling might prove interesting depending on your time zone but I think you find my rate of $40.00 per student quite reasonable. It's not about the money, it's about the math.

Sarah has her own page at the house of math. There are many vids there you can't find anywhere else. I put up quite a few lessons and will add more as well as a link to this post. I was wanting to to film more but sometimes this adds a dimension that is disturbing to the process. There is quite a bit there...it will take a few seconds for all the vids to load.

The idea is you learn how to help your own kids not pay me...you can get a password for 5 bucks.  I also have more video sitting on my hard drive that needs to get edited and added so check back and refresh the page there as I add more in the coming year.  I was working on a book, Crewton Ramone's Completely Cool Curious Counters' Kindergarten Compendium which took quite a bit of my time, but I was sill tutoring and making vids, they just didn't get loaded up to youtube and are sitting on my hard drive. Get the book and read it to your young child autistic or not, repeatedly.

New improved version I added an "r" to the title.

Quick Lesson Inverse Functions

You need more than one example but this is a quick 3 and a half minute lesson on how to find the inverse of a function.



In this case what is the inverse of

y = -4x² + 2 ?

Due to my math experience I looked at the multiple choice answers and knew which one it had to be...however due to my carelessness when I tried to show him why I got the wrong answer because I left off a negative when I copied down the problem. We did the problem more than once and this vid shows the last time we did it.

Two principals here:

One: NEVER TRUST THE TEACHER.

Two: You aren't wrong you are just getting more information.

Too many parents (and some teachers) are afraid to work with their kids because they might get it wrong and be embarrassed or what have you. Just get to work and see if you can get the answers...sometimes it's good to get the answer first and then look at the problem. I have had more than one student say it's easy when you know the answer. That's true and then with the thought this is easy you can see how to solve the problem and you know where you are going.

Another thing with some multiple choice tests: you can see answers that reflect common mistakes or misunderstandings of concepts that would lead you to pick the wrong answer. Talk about them. Talk about why they would put that answer as a choice on the test. This often helps deepen understanding.

Now in order to learn how to do these it requires more than on 3 and a half minute video. They can get the rule "just switch the variables and solve" but they will forget the rule in just a few weeks...

You need at leaste three examples of which this would be one of the last ones. They should have also spent some time understanding the basic concepts of Hero Zero and No Fun Get Back To One. (HZ & NFGBT1)

Here is the first example I showed this particular student:

y = x² therefore the inverse would be y = ± √x

First we "swap" the variables: x = y² which is the same as y² = x and solve (NFGBT1) by "square rooting" both sides: y = ± √x

Then you just make them slightly more complex: y = x² + 1 etc...

Then you get two thumbs up because they "get it."


"Example isn't another way to teach, it is the only way to teach." ~AE

More at the house of math.