Here you will see students as young as 4 and 5 years old doing algebra and "advanced" math, without ever knowing it's supposed to be hard.
You are invited to learn how to use this method...

Monday, June 25, 2012

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.

long division with base ten blocks, math manipulatives, division

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 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

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The Curious Counter's Compendium.

math manipulative book, Base Ten Block Book

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.

Wednesday, June 13, 2012

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 can see more with Sarah on Sarah's page.

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Tuesday, June 12, 2012

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.

Monday, June 11, 2012

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.

Sunday, June 3, 2012

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.

base 10 blocks, base ten blocks, base ten manipulatives

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 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.