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...
Make learning multiplication fun and easy playing with base ten blocks.
How to get multiplication mastered. You will have practice. There is no way around it. But you can make this practice fun. And you can make it easier by using some basic memory tools. The concept of a peg. And working in a more natural progression that complements the knowledge as it is acquired instead of just a jumble of facts in ordinal order.
Screencast with boys
Starting with Square Numbers and Pairs a lot of the multiplication can be understood. Then it is easy to add another for three's and of course 10's and 5's are easy so then it's easy to add one more or one less. For example fours can be thought of as one less than what ever number you were counting by fives...is of course four so 5 x 6 is thirty and one less six is 30 - 6 = 4 x 6 which is 24. Etc. This needs to be re-cut because the fan messed with the microphone but I STILL haven't had time.
Multiplication
You can use this same thinking with 9's and you can go up AND down with the square numbers...6 x 6 is 36 6 x 5 is 30 one less six and 6 x 7 is 36 + 6 which is 42 and the way you get there easily is with wanna be a ten, six needs 4 to be ten so it takes the 4 out of the six and we get another ten with two left over for 42...4 tens and two. Here is a screencast where I use addends to make multiplication easy for an Autistic student. If it works for her it will probably work for you. Multiplication by nine is EASY btw. So easy FIRST graders can do it. Click that link and watch the second vid. More explanation:
Using squares as a peg
Multiplication is THE milestone in mathematics and should be taught early and mastered so that all the rest of the math becomes easy...
There are books and worksheets that can help but more than anything you want to PLAY and have fun not beat them to death with math facts that make them hate math and turn them off at an early age. Play with blocks, sing songs do a little each day starting when they are very young and by the time they are 6 or seven most of it will be out of the way. Waiting until 4th grade is INSANITY.
Here is a web page of the books Mortensen uses. The facts mastery books are simply more practice and to be used to reinforce the PLAY you do, which should amount to much more time spent than time you spend on the books.
Also do some web searches for "Crewton Ramone Multiplication"...there are tons of pages and videos on this extremely important concept. And of course here is the Multiplication page at the House Of Math.
I strongly recommend you follow a lot of the links on this page. I know it's a lot but I can't stress how important multiplication is for making "the rest" of math easy and understandable because it allows you to see patterns and count very quickly. Then search "Crewton Ramone Multiplication" and see the plethora of pages and vids I've made.
My mother was a public school teacher for 30 years. She was certified for K thru 12 but settled into teaching second grade. At the time one of the major hurdles she had was teaching them place value. The curriculum that they had took a few weeks to get the concept across.
I went in there and had in done in two days literally. 100% competency every kid in her class understood the numbers have two parts "the how many part" and "the what kind part" and the numbers tell you how many the places tell you what kind combined with base ten blocks even the SPED kids had NO PROBLEM.
I remember my mother asking wryly, "now what are we going to do for math for the next too weeks?"
So I taught them algebra.
The principal of the school who had a minor in mathematics came to the classroom for something and he stopped at the door as I was casually teaching a group of 2nd graders to factor polynomials...by then they were giving me the factors of problems like x² + 9x + 20...
Anyhow, here are some vids covering a simple and expanded lesson on place value and the names of numbers.
When you start out you can just do the numbers from one to 1 million, three at a time, and then the next day do the numbers smaller than 1. Use a three period lesson. Treat place value like vocabulary...you are just learning the names of numbers and the pattern is easy to discover.
I did it all at once for this student because this student was older. He had some questions about the decimal point and where the one-ths place went the way MOST kids do.
Now you can get this handled and understood in a few days...give them a little home work and I would bet on 2 days. [b]THEN YOU CAN DO SOMETHING ELSE.[/b]
I bet if you as an adult were forced to do the same thing over and over again and the subject matter was presented in a way you really didn't understand they be telling to you had ADHD or ADD and would try and pump you full of drugs too.
Place value should be easy. By the time you spend some time on this page you should be quite comfortable presenting these concepts to your students. Remember to break it up and add more meaning as you go. Very little kids only need to learn up to 1,000 to start. Then you can play games and ask questions: what does the 2 in 1,257 mean? Which is more in that number the 2 or the 5? Etc.
Manipulatives make division easy and even fun. Here is the page at the House of Math on Division. Here are a couple of videos covering division mostly for parents and teachers. The first is much longer and the second is much shorter.
You don't have to teach division last you can teach it first if you want AND you can use it to teach subtraction and multiplication. Conventional wisdom is you have to know how to multiply and subtract to learn the algorithm for division.
Face it. Kids hate long division. They hate it for a lot of reasons. They haven't mastered multiplication; they don't like subtraction because counting backwards can pose challenges they aren't sure where to start counting. Manipulatives and the concept based base ten block methodology erase all of that. Mortensen Math rocks.
As you can see this is edited a little, the whole thing is available HERE. Only about 5 or 6 minutes is missing, the part covering negative polynomial division.
Here is a follow up video:
Between these to videos, the division page at the hous of math and this blogpost
you should be very comfortable presenting division concepts to your young students.
Practice with easy problems that have no remainders FIRST. Get comfortable. SPEND THE TIME, and do a lot of problems. THEN start doing problems with remainders and bigger problems and problems that are hard to model with manipulatives. All the while DO NOT leave out the part where they draw pictures. When we get to the problems that are hard to use blocks to model we can draw pictures and finally we can move to the the symbols ONLY. And the student knows what they are doing and why and although division may never be their favorite thing, it won't be confusing or hard either.
Now we are serious when we say that you can start with smiley face division books if you like because the baby step approach allows you to teach counting as you go. Here a couple of shots from the beginning of the smiley face series.
Keep in mind these books are made for PRE-SCHOOLERS. It should be obvious that older students can benefit from these books too. I suggest that they start at the beginning and "breeze through" until it begin to hit their level rather than skip the first books altogether. Here is book one:
Here is the end of book one. When you are 4 this is a lot of counting! I have seen people fool around with little 2 and three year olds where the child sits in their lap and just points to the right answer. Also because the price has gone up so far using a sheet protector and wet erase marker to get more milage out them is advised. They are no longer priced as consumables although they were originally intended to be.
He is a scan showing book 5. Expanded notation helps with understanding and is used as an intermediate step. I have a personal problem with the placement of the quotients and this was supposed to get fixed but we never got around to it. When Crewton Ramone comes out with a similar series it will be available in pdf form and some of these oversights and compromises will be fixed. It also had to do with the tech of the day 20 years ago but this is no longer an issue.
Remember bigger is funner. Also remember to let them make up a bunch of their own problems that are NOT in the books. As the parent or teacher you should make up some problems too. Practice.
Each booklet is 20 pages long and designed to be non-threatening. So you can see I am showing you page one and then the end of the books. This is the end of book 10. I have seen 5 years olds complete these books. Kindergarten math at a public school is pretty much a snap after that. Tee hee. If you can not afford the books just do lots of problems using the blocks and have them keep track of the problems they did in a journal. YOU may have to do a lot of the drawing and symbols for them because the whole point of these books is that they can learn math without the fine motor skills required to work a pencil.
Hat tip to Elizabeth Stevens for doing all the scans.
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.
More on the MAKE IT FUN theme. Here are couple of vids where we play math and the math portion is done many times because it's fun to shoot the walls down. They will do it over and over again because knocking down the walls with a Nerf gun is FUN.
These kids are having fun and the little boy you see there is only 5...note that the NO is removed from the lesson and he is encouraged to try and see if the pieces fit to make ten...ask questions: Is that tall enough...is that too short etc...build tens and nines and eights.
Out of an hour this was only a small portion of the math we did...this boy Tamu has Autism and is a little shy, but as you can see he is quite able to join in the fun. The idea is to keep the games quick and not to spend too much time on drill. They will get math facts as a matter of course.
Here what you see is us building a house for a lego craft. I also couldn't bring out the camera much because as soon as I did the dynamic changed, and as I have said before the first obligation is to the parents who are paying me money to teach their child. We also had fun building walls and shooting them but I didn't get these guys on camera.
As it turned out this was just the beginning of a large house...which I also didn't get on camera. Tamu got a lot of math facts presented to him and had fun while it happened. Many more exposures will be required before he "knows them" but this is a good start and the repetition is fun not drudgery.
We also did multiplication as well as addends for other numbers but most importantly we kept it fun and engaging. People always ask me how do you make math fun? Just play math.
Seriously. Get out your blocks and fool around, especially when the children are young. You just play and point out math concepts to them as you go. Simple things like a three and a four is the same as a seven...three 3's is square and the square root is 3...that means count one side...etc. Later when they see symbols the explanations make sense...
For more fun and games check Crewton Ramone's House of Math. This page has become popular: Math with Playing Cards. I keep meaning to add more games because there are a lot more games you can play using playing card this pages only gives you a partial list. Use your imagination and MAKE UP some games of your own.
The blocks are only limited by your imagination. Get creative. Have fun. Play math.
For those of you that come to the blog and don't see anything new for awhile go to my facebook page http://www.facebook.com/Crewton.Ramone There's always a fun assortment of pics and posts that don't make here to this blog. I try to keep the blog mostly math instruction. Go back and look at the old posts here not just the new ones, use the search engine lately I've been getting email from people asking, "how do I..." Or "where is a post on division...?" or what have you. Search Crewton Ramone division or Crewton Ramone fractions or crewton ramone plus whatever it is. If you don't see what you want and can come up with some specifics I can make a vid for you...just contact me.
Also password is about to change again...if you have paid for a password and don't get an email with the new one let me know...
Them college loans getting to be problematic. Here are several from my main man One Stone:
Make math simple. Make it fun. Make it child's play.
These are just a very few of the things you'll see on the facebook page. Here is a fun vid using lego to make a model of The Antikythera Mechanism:
Do really think the Koch brothers and a guy who has lied before and been caught red handed lying are doing science or are they doing politics? Anyhow, there are 215 comments as I post this and mnay of them are interesting. My favorite part about those with the strongest "belief in" global warming is they can't do basic math and when I say basic math I mean algebra, calc and statistics and yet they are smug and make comments about deniers and flat earthers when I can assure you most physicists that I know won't even enter into the conversation because "it's like trying to talk about geology with Christians who think the earth was created 6000 years ago. Not worth your time."
What is the heat index of CO2? What Percent is CO2 in the atmosphere?
“It is the greatest scam in history. I am amazed and appalled and highly and offended by it. Global Warming; it is a scam.” -Founder of The Weather Channel John Coleman.
The whole consensus thing is kind of a joke. BTW I worked briefly as a resource tech for the Solar Observatory on Haleakala. There was a time when Al Gore had me fooled too but then some solar physicists sat me down and made me do the math...there are a couple of them who are at the other end of the spectrum and are predicting a Mini Ice Age...search: "solar physicist predicts mini ice age". I am not allowed to name names or cite them due to a little non disclosure agreement I signed.
The point of the endeavor called Crewton Ramone's House Of Math is that the mathematics opens up a whole new world of analysis and critical thinking not available to the innumerate. It makes it easier to spot the BS you get in the news. It allows you to see through some of the lies when you can look at their data and see the flaws. For example with the hockey stick people who can do math pointed out that no matter what data imputs you entered you ALWAYS got a hockey stick...anyway the facebook page get stuff everyday from me and others to. Come join in the fun.
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.)
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 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.
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
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 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.
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.
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...
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.
