Base Ten Blocks for 2017

SO much to do.

Got fractions videos to put up on the fractions page...it's been a couple YEARS that that page has needed work...passwords really are going to change shortly and many pages are going behind paywalls when in doubt use the sitewide password....and there's a slight chance that I have a live seminar/playshop here in Southern California...somewhere in "the valley"...in January meantime sometimes people figure rapidly that what's at the house of math currently is worth a whole lot more than $349.99. And I am quite serious when I say if you can find lessons that make math easy using base ten blocks post them here. 

This is what gets me out of bed in the morning.

Got in another conversation about Khan Academy. Which is great, free lessons BUT they are "traditional" symbol based lessons with no pictures. No compound lessons and lots of memorization...and I have heard more times than I can count that watching the videos over and over again does not lead to understanding although you can remember the steps long enough to take the test--sometimes. I have had high school students tell me over and over again teachers basically let Khan Academy teach their classes for them and homework can consist of watching vids there.

"if I didn't get it the firs time watching again and again isn' going to help although once in a great while watching it over and over again makes something click. I still have an "F" though." ~16 year old girl, with regard to Kahn. Same girl: "Holy crap! I watched your video one time and totally got it why didn't anybody tell me this before?"

I find the explanations clear and usually concise, but again the algorithms are symbol based and I have an ace up my sleeve because I know what the symbols mean and the pictures they represent due to my familiarity with base ten blocks. Again it's not me it's the tools and understanding of their best use.   Also you get compound lessons that teach more than one thing at a time.

High school kids who tell me they hate the site because they hate math have no pictures or blocks. You'd hate English too if all you learned was letters like c o w but never saw a cow; chair could be confusing because they both have four legs and start with "c" but you've never seen a chair either...and nobody ever explained to you that those letters mean the thing you sit in as opposed to an animal from which milk can be had assuming you get a female. I have talked to more than one teen that was confused by Khan Academy not because Sal is a bad teacher but because he lacks tools other than symbols. Many have benefited from the vids there and he has many, many more than I do.

Despite appearances I did not pay for this testimonial.

The idea is that free or not, a huge amount of videos that explain math or not--it's not fun, kids often don't "get it" and it helps but still falls short for too many students, particularly female kenesthetic learners but also males. If you go through my blog and website, Crewton Ramone's House of Math you will see why this is a problem. It's just more of the same. It will work for a certain percentage of students...but my method works for a much greater percentage. "Gifted and talented" as well as challenged or remedial. I guarantee you most autistic kids do not prosper there at Khan Academy although there are a few for whom the method is perfect.

The point is the base ten block method works for more students more often.

Healthy Sibling Rivalry is a good thing.

Problem: most people don't know how to use base ten blocks effectively and completely. They fall off right after basic operations and usually explain division incorrectly...and no one shows you how to subtract with addends. Nobody. Most base ten block use is limited to addition & subtraction (regrouping) and that's it.

Nobody is showing you how to teach trig to 8 year olds or calc and 3rd & 4th power algebra to ten year olds...

My website needs a lot of work and I basically lost a year trying to build the Kajabi site out...so many lessons never saw the light of day because the threads weren't finished...so the pages never got published...all you got was the teacher training but I had several other stands like trig and algebra partially built. Oh well. Pretty much all of it is at the house of math NOW, just not in such a snazzy format and some of the vids are low quality because they were uploaded when I was having net problems...well I wasn't: the cable company was, but now it's all high speed. have to replace the low quality ones but first I have to replace or re-cut the screencasts that don't work at all anymore.

CKC

Anyhow, I will work on the house of math this year and I think CrewtonRamone.com will come back online this year...also there are going to be some more Crewton Ramone in the kitchen vids...lots of stuff to do in the new year. Also many have asked for more "getting started guidance." More what to do first type stuff and then what to do after that...which is more concrete than "anything you want."

Also need to revamp and add to the parent/teacher training and add more elsewhere too. Even where it's at now, if you go through all the training I have up currently you will be head and shoulders above most elementary math teachers. That's not hyperbole. Experienced teachers have been amazed. I show you how to use the tools to get more done faster without pain and tears but with joy and laughter. As I have heard more than once, it's life changing.

DO not discount this blog and old blog posts, once you get some instruction or training you can see the method/theory in action here. There is information you won't/can't get anywhere else, like this.  Here is a collection of vids showing a little history.

Here is a new MATH PDFs page for people who don't want to buy a password but still want PDFs

Also working on my book,  "How to teach Math o Young Children" (trying to bang out chapter 4)...and tutoring an interesting set of students this year. Nice to get these from password purchasing people:

"Thanks so much! I love your videos and materials and look forward to using them with my kids!

Best regards,

Anne-Marie
...
Anne-Marie Tan, Ph.D.
Certified Reading Specialist, K-12"

Base Ten Block Battle

Playing with base ten blocks. You can't help but make learning fun. Again building stuff over and over again because they want to shoot it down is more fun than worksheets. It is important to use two hands for optimum whole brain sensory input. When the student uses both hands more learning takes place easier, it's that simple.

Using base ten blocks to get addends mastered make learning math almost effortless. First they learn their addends which helps them add two numbers which is basic addition; which helps them add series of numbers which helps them learn to multiply which makes math easy because it allows the student to count quickly.  Math is a whole lot easier when you can multiply because it allows you to divide and discover patterns and a whole lot more. Problem solving and fractions are much more difficult  when the student can't do simple computation. Addends are the basic building block. Gets the kids off their fingers, makes addition a snap...also builds confidence. He built walls of 10 on down to 5 and made a little fort.

I think you can guess what comes next. Knocking them down is the most fun...why not use a nerf gun? We're just playing and having fun while we learn math. Kids will often build walls or set up addends over and over again so they can shoot them down...I wish I had video. That gun couldn't hit the broad side of a barn. LOL!

Okay, fort destroyed, clean up and on to some algebra where we played what completes the square...

Here he is putting 25 in the corner, to complete x² + 10x + ___, he had started from x² + 2x + __, then x² + 4x + __, x² + 6x + __, x² + 8x + __. Again the algebra is along for the ride, he is getting lessons in addends, square numbers and dividing by two...not memorizing formulas involving b/2a...when the time comes though those formulas will make sense...

***
Now onto his brother. Again we start with addends he got a lot more done faster using the tray.  The other way is "cooler" but usually takes longer. If you are playing at home time is not an issue but when you are paying 50 bucks an hour it can be. The one thing I will say about building the tower is that he gets more practice because the walls fall down and have to be rebuilt as you go...it took him a while to build the second story without knocking down the first story...each of those wall was built and repaired more than once. In the tray he does it once and moves on...

Except when he takes the tens out fo no apparent reason and had to put them back in again. AGAIN note the use of both hands because I made him do it...and reminded him verbally more than once...

He was quite proud of the finished product because it looks cool. Kids also find out that building walls out of addends are cooler to shoot at than walls all built out of the same block over and over again...

Then we factored some quadratics started small and worked our way up. First one we did was x² + 5x + 6. Here he is doing x² + 8x + 15. But what he is really doing is learning an addend for 8 and figuring out that 3 x 5 = 15. Also that 15 can be 5 threes or 3 fives...also some division concepts and as an added bonus factoring a quadratic. He is learning counting skills...just happen to be using algebra to teach them, could just as easily be using fractions. I use algebra because it is known to be HARD in kid culture so it builds confidence and self esteem in students like these who are having problems learning math at school

Now I made him get out two tens and a four and measure it with various blocks...he already tried nines...didn't come out evenly...24 is two nines and some more, three nines is too much...eights fit perfectly and he can see 3 eights is the same as 24...but with sevens 3 isn't enough and 4 is too many...and he counted out 7 x 3 = 21 and 7 x 4 =28...he wasn't wrong to get out sevens he was just getting more information and learning as he went. Soon he had eights, and sixes and fours and threes...and calculated that it would take 12 twos...quite a bit of math from just building a wall of 24...

And now he gets some base ten block battle action too. Here he is setting up 12's. Gets the addends for twelve and counts by twelves...note the use of two hands.

And then shoots the twelves.  But never did hit one with that gun. Got a nerf pistol out and made quite a few hits. Kids will usually make more targets and shoot them down over and over again which requires building them over and over again. Tom Sawyer taught me well. SO much more fun than doing a work sheet adding little numbers together. Plus you get fine motor skills AND a whole brain activity instead of just using the dominant writing hand. Here is an article that provides a clue.

"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

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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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Playing With Squares Would Have Made Quite A Difference.

Here is a quick set of vids on completing the square. You can find all 5 parts here on the Advanced Algebra page. Basically we take playing with squares to the next level and out of necessity we have to cram a lot of info into a short period of time because he has grades to make and tests to take.

If he had been playing with squares and building square numbers for a while previous to this, everything would come a lot easier and with less stress. Get your students started early...and by "early" I mean as early as possible, five or six year olds can do a lot of this math as seen on my website and other posts on this blog. For them, you go slow and make a game of it...but they learn and discover all kinds of things that will come in handy here.

Take a look at this picture:

In a moment it will make more sense. You can see that instead of a red square and blue bars which are the x we have orange twos...the red square is now a two square and the 9 has twos around it because each x = 2 (and of course x² = 4), and 25 = 25...when x = 2. What would get for x² + 6x + 9 if x = 3?

Watch this vid:


All we are doing is some simple problem solving, trying to figure out what x is. Then we immediately begin adding more meaning and information with graphing...but first we practice without the blocks:



And as you can see he has a bit of difficulty so we go back to the blocks and practice some more. Check out this page on completing the square [link not built yet] for the full story, the page contains a link to both the entire 23:30 minute video and the 5 separate videos on a page very similar to this but with a little more explanation and pictures and video and links...that vid cuts off abruptly and you will need a password to get into the pages that contain the rest of it.

Here is Part 5 where we do one more problem that looked a little daunting but many of my young students have built that very square just playing on their own. Self directed students often get out four or even nine red squares and put x's and units around them...building bigger squares is fun. They can also see the similarities between x² + 6x + 9 and 169 and see the square root is 13 in the case of 169 and (x + 3) in the case of x² + 6x + 9 and certainly if each x is two then x² + 6x + 9 = 25. In fact substituting for 1, 2, 3 and 4 is no big deal and not scary at all for a 6 year old. But the teen-agers who are being exposed to this for the first time do not agree. Too bad they didn't get to play with these blocks when they were kids.



Little kids would just build it draw a picture of it and that would be it. Later we could set it equal to zero or another square number and solve for x. As I mention in the vid, first you introduce the positive root then as they become more familiar with square numbers and integers you can introduce the negative root. 5² = 25 and so does -5².

±5 = 25 is just economy of symbol.

Here is the 5th part, in part 3 and 4 we cover graphing and more completing the square with a negative middle term...which is also ridiculously easy and visually obvious. If you have a set of blocks see if you can figure it out for yourself without using your password to look at the video...

Being familiar with the concepts ahead of time solves a lot of problems. For students who are struggling to pass algebra the blocks make the concepts assessable and easy to SEE and therefore understand and remember.

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Problem Solving Concepts Made Easy

Note that depending on age the emphasis changes...for the older girls it's about the concepts and seeing the rules they have been taught, for the younger students it's about finding same and building addends.

The basic concepts are hero zero and no fun get back to one...but it's all about using those to find same and SEE what x is...the equals sign tells us what x is...and x can be anything depending on the problem.

For all of them it's about making it easy and fun. Let's start with older students:



Now as is typical of many high school math students, they have yet to master multiplication and resort to fingers when adding. I will get them off their fingers and they will have to master multiplication on their own...

Then Watch a six year old doing basically the same thing, CONCEPTS are the same. (BTW it's a piece of organic all natural endangered species chocolate which he picked out from the health food store.)



And the older kids (begin to) SEE the rules:



They are hampered by a mental paradigm that math is hard even when it's this easy...it takes a while for them to realize really math is easy; but when that shift happens the math becomes easy and with or without me A's can be achieved. In the vid we did not evaluate for x = 6 but I did so with them and with Dboyz who figured out that 30 plus 3 is the same as 18 plus 15...and they were quite proud of their skip counting skills...counting by 6's all the way to 30 with the younger boy in the lead. When doing 18 plus 15 they knew five wants to be ten so it takes a five from the 8 leaving 3 tens and three...they also did 8 takes the 2 from the five and again we get 3 tens and 3...lots of DO-able math for kids of all ages. 10 years from now this will be old hat for some students. More to come on the problem solving page at the house of math...the question will come up, how do you do a problem like this?

3x - 2 = 2x + 5...there's no -2 in five. True. You need hero zero again, none of this balancing stuff...you just see same on both sides.

Or

5x + 3 = 2x - 12 again many people can't see same on both sides...that's because of hero zero again. Want a detailed explanation? You need a password. PPPSP = The Password Protected Problem Solving Page.



There are tons of different problems on the PPPS and vid that make them ALL super easy. Remember those boat and current problems? Or how about constant rate problems? AND of course the ones you see here where you might think it's not same on both sides because things got negative...just a few minutes and you will see your way clear...

I have heard from a student that has since moved to the mainland that she is getting A's for the first time in math...all I did was adjust her thinking and hand her some concepts she can use no matter what the topic...beliefs are powerful things. She now believes math is easy...she knows it...so of course she's getting A's. I don't need to be there. And that's the point of all this.

Fraction Subtraction Simplistic Though Autistic

Sarah is getting better at fractions. Her mom wants the focus on algebra because the test coming up will have a lot of algebra on it, but I see students all the time that have trouble with algebra because they don't understand fraction concepts. Rules and process are quickly forgotten. Concepts aren't.

So far we have covered addition and a little subtraction of fractions and she understands that "the name of the game is to make them same." Then we can add, subtract or divide...with multiplication we just multiply and I'm going to try and get her to discover WHY we can just multiply without making them same and why we invert and multiply when we divide. Hint for you it's a short cut to making them same.

For now we spent a little over an hour doing this and by the end of the hour she was getting pretty good.

Here is 15 minutes of that hour.



Note there are fewer pictures and symbols here but we started with the blocks and drew pictures and then I remembered to turn the camera on for a bit. You always start in the concrete then draw THEN go to symbols only, and here at the end I went back to tie it together. You can gauge your students understanding by their facial expressions. Here I could see she was "getting it" but more reinforcement is needed not just because she is autistic but because repetition is the mother of skill for ALL children. If you have young students, you can do these lessons and then months or years later do them again...after many impressions the knowledge is ready for instant recall.

Homeschoolers have the opportunity to cover the same ground like it's new if you start them very young. The idea that they cover it once in 5th or 6th grade and then they'll have it forever is ludicrous to my mind.

The idea that autistic kids can't do this is being disproved right before your very eyes. Due to the brain damage caused more than likely by mercury injections, she will need EXTRA repetitions but that's all. Once she understands it the nuero-pathways can be built and reinforced.

You can now get fractions materials at the house of math. That page has lots more info than just how to by a kit plus some free PDF's and a caution on using fraction worksheets too early in the game. Fractions FUN begins with manipulatives not worksheets.

Also Sarah's page is expanding. More vids are there, some of which you won't find here or anywhere else...but you need a password.

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Crewton Ramone Playing Math With A 7 Year Old. Intro Lesson.

Here is a good lesson for those with young children. This was a first time student who is being turned off to math at school. We had fun and she wants to come back for more.

What's Under The Cup Quickly Became Her favorite Game

Look for this lesson on the sample lessons page too. You need a password to see the other hours (and hours) of lessons there but here is this one for FREE. Soon Emma will have her own page because she is an excellent case study. She has been labeled ADHD or ADD and is on her way to SPED and I'm sure part of that is due to her not "getting" math and other subjects the way they are teaching it...thus she get bored or frustrated and acts out. This is a 7 year old child. I have seen no indication that she can not learn or stay engaged for 1 hour at a time. But what do I know...?

I am extremely biased against drugs for 7 year olds. I am also dubious when it comes to the ADD and ADHD diagnosis for bright little kids.

Mostly we played games like what's under the cup and making rectangles:

Building Rectangles and Playing Algebra? No problem.

She never figured out that most kids think algebra is harder than subtraction...which she informed me she doesn't like at all because "it's kinda hard and confusing." We will work on addends and clear all this up over the coming weeks. And you can watch the transformation at http://www.crewtonramoneshouseofmath.com/index.html. We didn't do any subtraction at all that she was aware of...but we will soon master that as well as quite a few other math concepts.

BTW password is going to change soon and prices for passwords are going UP this year.

Anyhow, here is a half hour of math...the hour went by in no time at all.



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Now available all manner of Mortensen Math Materials.

More Fractions Fun.

You have to do a lot of preparation before you dive in and start adding problems like these.

You need to understand basic concepts like SAME and ONE. But basically all you have to be able to do is count. You don't have to be able to add and multiply although it helps.

Fractions concepts are easy. Any little kid can learn them and understand them, it's that much better if you let them fool around and DISCOVER concepts and how things work for themselves while you give copious amounts of encouragement and direction.

Working with very young students is similar to working with SPED and other "learning disabled" or "special needs" children because often what you have is "developmental retardation" or to be plain many Downs Syndrome and Autistic students who are in their teens are in about the same developmental stage as very young children. Very young children can learn math concepts as proved consistantly on this blog, ergo: SPED kids CAN learn math.

This isn't rocket science. Simple logic.

Here are a five and six year old playing math. Fractions. They have very limited experience with fractions and still can't multiply easily because the don't know their multiplication tables completely yet, but they can learn fractions and begin to understand the concepts. Now if SPED kids and little kids can learn fractions then certainly high school kids and adults can also learn it, even the "problem" children...who aren't particularly disabled or SPED but may be special needs because of circumstances at home, like poverty or parents who use drugs or alcohol etc. Sadly most of you know what I'm talking about because it's more and more common in public schools.

Here they are playing a game where they try to discover the fraction from the disguise it's wearing and they literally get to pull off the disguise once they figure it out.



They do not have enough experience to go about it methodically, but they do have natural thinking skills...and with me as a guide they can be directed to the answers by simple questions. Remember remove the "no" from the lesson. Allow them to explore and discover for themselves. Ask "what if" questions, count, see what they have.

Once we get through some of this we can do some simple addition and see how that works. Also we are headed for story problems and these activities get them ready for that too. There are also everyday math activities that help them make sense of the symbols and numbers when they see them. Also check out this post where they fool around with food and no symbols to help them understand what's going on with fractions.

Also note how the younger boy is very much a participant in this and often gets the answer before his older sibling.



Let them discover and have fun! You will even hear them say "Don't tell us!" The joy of discovery makes learning math (or anything else) FUN.

The whole video in one piece is available on youtube and on my website here. [Link not built yet.]

To get a fractions kit,

check my expanding product exchange:
http://www.crewtonramoneshouseofmath.com/product-exchange.html

Also don't forget these free fractions worksheets.

Fractions Despite SPED

People often ask me if there is a special way to do it for SPED students, the answer is no.

I've had conversations with students that went along these lines. "I know everybody calls you special, but in my class your just like any other kid that's going to learn math. I know you can learn math because you understand English. So quit telling me how special you are and count this."

95% of the time they shock everyone except me...they even shock themselves sometimes. Bear in mind when I met Sarah they weren't even teaching her math because there was "no point to it." they knew she couldn't learn it, and as we say in Hawaii they were wrong but true. She would never have learned math with just paper and pencil and rules and process out of a traditional text book.

(There was a time in my life when I was shocked. After I got over it, I said to myself more people need to see this. And, since no one else has stepped up to the plate it seems to have fallen to me. Hence this blog and my website and the many things that will be made manifest in the next 7 years or so...word is getting out.)

If you try to teach SPED students (or even "regular" students) rules and process the results will be poor. There was a time when I used to have to argue the point but the dismal performance of American math students as reflected by ANY metric saves me the trouble; not to mention that in the 22 years I've been doing this the results have gotten WORSE not better....Fractions and long division still top the list of leaste favorite math subjects pre-algera.

But I digress.

This is an excerpt from an email exchange between myself and a parent of a child with Downs Syndrome.

First off:

Treat them like "normal" kids.

How is her speech, does she speak English well? If she speaks English she can learn math. Period. There are no special needs lessons plans. Do the same lessons you see on the blog and website. You may have to go slower and for shorter periods...but that's it. MAKE SURE SHE gets her hands on the blocks and isn't just watching you play with the blocks. I have had success with downs syndrome, deaf kids, blind kids, autistic kids, kids who climb on rocks...kids is kids no matter what "the experts" tell you. Use all the senses or as many as possible. Play, have fun, learn math. Don't approach it as math time so much as play time. Sing songs. Play games. Watch vids and then DO the stuff in my vids...don't worry about getting it wrong. You can't play wrong.

Sarah is Autistic use your password and check out her page: http://www.crewtonramoneshouseofmath.com/Sample-Lessons-Sarah.html

Here Sarah is doing fractions (again):



After about half an hour she starts "getting it." We have covered fractions before in different ways...we started from scratch, like she had never seen them before and went from there. And this is the result:



As you can see it's becoming easier and easier. You do the same thing with "normal" kids especially younger children. Teachers lament that they have forgotten everything they were taught over long summer breaks. This is normal and natural and often shows mastery has not been attained, although sometimes the are doing as fast as you can write a problem looking very much like mastery has been attained and then a week later they can't remember how to do it. This shows it takes many exposures to put information in long term memory and more than that to make knowledge available for instant recall. Expect this.

She did this one in her head as soon as I wrote it down...however mastery has not been attained, one small change in the process and she gets flustered. As the picture where the problem is scratched out above shows...watch the vid and you'll see what happens when a change is made to the process.

I do the same lessons several times separated by time, they seem new for some, but usually I say the first time it's new, and might seem strange and maybe even a little hard. The next it's I've seen this before, the third time it's I got it already lets do something else. With SPED students it may take an extra time or two beyond that.

If you want to see the whole lesson (you need a password)...just go to Sarah's page. The vid is 24 minutes long. You will see the ups and downs. Here you just see the success. There you will see how we got there...and future vids will make even more sense.

I recommend this for people who don't have SPED students too. The lessons are basically the same...now that she has this lesson mostly mastered and I have watched the lessons, I will emphasize different things, next time we will focus on "filling up the one" and work on improper fractions and then we will be able to do more fractions where we add and then subtract and eventually have to borrow out of that one...we can also go back and forth with reducing fractions and equivalent fractions....then multiplying fractions will be easy and at last division will be covered and you can be assured she will discover WHY we invert and multiply. Again.

If you have teen age students that are doing algebra you might go over fractions again with them because consistantly I see kids in algebra that can't do fractions...or forget how or can sort of do fractions but hate them which is silly when they're so easy.

One last note. Several parents have told me they get lost watching the vids and sometimes don't understand what they are seeing...although it looks fun and easy they don't get it. "Do you have a set of blocks?"

"No."

Therein lies the problem. I can't stress enough that in all the time I've been doing this the ONLY time we lost people is when they didn't have a set of blocks to play with in front of them or wouldn't put their hands on the blocks...the blocks get you through your mental blocks. That's why Jerry used to say "Math is NOT a spectator sport." You have to participate.

If your are an extremely visual learner just watching vids may be enough, but if your are kinesthetic or auditory or a mix where visual is not the primary learning style then hands on is a must. Not saying this to sell you blocks. I'm telling you this because my experience has proven beyond any shadow of a doubt that this is TRUE.

Crewton Ramone's House Of Math

Search this blog for "fractions." (There's like 8 pages of results worth.)

BTW if you want a set of fractions tiles like the ones you see here it's $105.00 shipped to your door and is available on my site at Products and Passwords now. Or order at right. ⇒

Fractions Are Easy Too

This is a simple introduction to fractions tiles. Fractions concepts are great for teaching counting and multiplication to young students.

Most students hate fractions because after four years of learning math one way suddenly the rules change. You can't add

1/2 + 1/3 and get 2/5...some kids will put 1/5

showing an utter lack of understanding and confusion about the rules. But the rules haven't changed. They just didn't understand them in the first place or more likely were never even taught the rules properly to begin with.

If you go back to the 5 basic concepts, you will find under concept 2, we only count things that are the SAME. Also it's key to understand that numbers have two parts the what kind part and the how many part. Fractions are cool because they tell you the how many and what kind all in one place, whereas with whole numbers you need to understand place value.

Note how in this introduction we don't cram in adding fractions in the first lessons all we do is play with simple concepts. We see how many make up a one, and we count and we learn their names. Later we will learn about numerator and denominator and build on the concepts of "same" or equivalent fractions. Also we will use other base ten blocks to represent fractions and fractions concepts. One crucial concept is the idea that x/x = 1. Right now they are seeing 2/2 = 1 and 3/3 = 1 and so fourth on up to 9/9...let them discover that anything over itself is 1...except for our hero. Plus they will discover this concept from multiple angles. Right now it's counting (three of three is one), but later it will also be division, (three is contained in three one time).

But for now we just play a little and tell stories about fractions wearing disguises.



In this fractions intro I cover the same info but without video. Be sure to get the free fractions worksheet. It's free. Note with me "free" doesn't mean "give me your email address." It means free. If you want more, get a password if not I don't want to waste time with you and an email list.

It should be quite obvious you can use fractions to teach counting and addition and multiplication. These students are advanced so the lessons are easy and fast but if you had a student that hadn't even mastered counting to nine these same fractions tiles would help them learn that. Compare and contrast with the thinking that says they have to have mastered multiplication before they learn fractions which is still ridiculously prevalent in math instruction in the USA and elsewhere.

The fractions page at the house of math has been in disrepair for about a year now...but that is getting fixed. It is very near the top of the to do list now. Look for more updates and improvements to that page over the next 30 days as I cut videos and add lessons and hopefully some more pdf's. Right now there are some videos there and a list of terms but it will become much more cohesive shortly.

Next there will be a video where we add simple fractions and find out what 1/2 plus 1/3 is and more importantly WHY, and we won't just learn some silly rule about multiply this, this and this...and then add this and this...but keep this the same...stay tuned.

BTW if you want a set of fractions tiles like the ones you see here it's $105.00 shipped to your door and will be available on my site at Products and Passwords shortly.

Equivalent Fractions With The Wee Ones

Equivalent Fractions teaches multiplication. It all goes together so while they learn fractions concepts they learn multiplication or in this case they get to practice it...but when we get to the higher numbers they'll be learning the higher multiplication tables.

It's easy to see that 1/3rd and 6/18ths are the same. They can see it.

People often ask the ridiculous question: "Do they need to have the blocks with them to do math?"

The other night without blocks or even symbols just verbally I asked him what the factors of x² + 3x + 2 where and he looked up for a moment and said X plus one and X plus 2...then before naps today I asked him, "if the sides are x plus 2 and x plus 3 what's the whole thing?"

He thought out loud and said, "one x square, three and two...five x's and four...no I mean six...six would fit in there cuz it's three and two."

No blocks or symbols. It's the same when you teach any language to babies: they hear it FIRST before they ever see an ABC...just because they can't write symbols doesn't mean they can't learn math.

Further the average student can't multiply 15 x 17 in their heads...because they need to have the symbols and a pencil and something to write on. My students can see the answer is 255 or at worst can add 100, 120 and 35...

Here in this video they have seen this a couple of times before without symbols and for the first time they see the symbols for fractions today, and the symbols make sense and are easy to comprehend because they have heard them before.





You can see their progress with multiplication if you have been following this blog...they still can't tell you 4 x 5 off the top of their heads but give them a little time and they can figure it out...and the more we learn fractions the better they'll get.

Find us on FaceBook

Go to the House of Math. (Home Page.)

“Men must be taught as if you taught them not, And things unknown proposed as things forgot.” ~Alexander Pope

Algebra with toddlers using manipulatives.

These video shorts explain why it is I am underwhelmed with teachers who tell me they can't start algebra early on...less so with teaching methodologies that tell you NOT to teach math, (which is a language) early on because the students "aren't ready for it" thus reflecting the teacher's fear of math onto the students...in some cases these teachers have gone on to found methods that damage entire generations of children's mathematical abilities.

Learn how to use your base ten manipulaives.

UPDATE: there are now tons of full motion videos showing young students using base ten blocks to learn algebra and a whole lot more on youtube. Just search crewton ramone + whatever topic you want to see...

Then of course there are the text book writers who seem to start with the premise that math is hard and certainly not fun.

I've had parents (and Catholic Nuns) tell me that "math should be work"...it doesn't have to be.

Using manipulatives or base ten blocks makes math easy and fun. As you can see they learn math concepts quickly and easily.


Check out this post showing these same boys doing 3rd power math in their heads without any manipulatives. It should be clear that using base ten blocks avoids future problems it doesn't cause block dependence...they see the blocks in their heads.

It's child's play because they can see it. The manipulatives allow them not only to see the math but to get their hands on it. Couple this with the compound teaching algebra does for you and math concepts and facts are mastered in much less time with much less pain and difficulty.

YOU can learn how to teach your kids using this method. I don't care who you are or what your experience is with math. You can give your kids a head start and open the gateway to all manner of opportunities while at the same time preserving their self esteem. You can also give them a positive mindset toward math. If they think math is fun and easy it will be.

Crewton Ramone: Negative Three Distributes w/ a 4 & 5 yr old.



Crewton Ramone Intro To Negative Numbers.


Crewton Ramone Does Algebra With 4 and 5 Year Olds. (ScreenCast).



Crewton Ramone Distributes With 4 and 5 Year Olds.




Crewton Ramone Factoring With 4 and 5 Year Olds



Go to the ALGEBRA page at Crewton Ramone's House of Math where you can learn quite a bit of algebra for a few bucks (cost of a password)...most of it's FREE as you can see.

If I can explain algebra so that 5 year olds can do it, I bet I can explain it to you. Get set of blocks and get started. Previously you had to attend trainings or seminars to learn how to use these powerful tools but the internet has changed everything. You can now learn the basics for FREE and you can learn the more "advanced" concepts for just a few bucks. Get started NOW.

Here is the 4 year old working by himself...four year old math enrichment. ⇐ Click that and prepare to be amazed. Just because he can't write doesn't mean he can't learn math concepts. In the same way we don't wait for them to be able to write before teaching them their mother tongue in this case English.

This post is a couple of years old. You should see the math these boys are doing now, often without blocks and no paper or pencil either. Poke around on this blog and see for yourself.

http://www.crewtonramoneshouseofmath.com/

Updated Feb 2013.

Related:

Introducing a 4 year old to algebra.

http://crewtonramoneshouseofmath.blogspot.com/2014/03/manipulatives-introduce-4-year-old-to.html

Another 4 year get's some algebra.
http://crewtonramoneshouseofmath.blogspot.com/2010/12/4-year-old-math-enrichment.html

A classroom of 1st graders factoring polynomials.
https://www.youtube.com/watch?v=C3kGVv1IWHk

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. Give your kids a REAL head start with math and numbers with this book and my website.

"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.

"I have to tell you that when I first started to watch your videos I cried....after learning it myself in school (haha) then teaching my three daughters algebra using Saxon, Math U See and things from the Teaching Company, I never really had any idea of what I was doing. Watching the videos of you made everything make sense!!! I'm sure that this is a labor of love for you but I just wanted to say thank you! It is much appreciated." ~HS, Ohio, USA.



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