Moving on with Manipulative Multiplication

Two weeks later we revisit multiplication as we make are way through the 20x20 matrix. The idea is not just to be able to do multiplication with symbols or blocks but to be able to do the multiplication quickly and easily in your head. In order to do this we need to be able to organize our thought and count very rapidly.

Manipulatives expedite this. The mind wants to work rapidly.  The device it uses is the brain. Brain and mind are not same, just like computation and mathematics are not same. Computation is how we DO math. Mind uses brain, brain does not use mind. But I digress.

As I am doing this video I try to impart some concepts not just on the students but on the adult viewers who may be parents or teachers. Concepts like the stages to competence. Do you see the blend of drawing symbols and base ten blocks? Driving home the point that "no" needs to be removed from the lesson. I was going to make the point that they are building neuro-pathways and now that we know some neurophysiology, you understand it takes a little bit of time for the child to form the thoughts and then vocalize them.  When they learn new things this takes up a lot of the brain and it takes a few seconds for the brain to process and compute and then make the information available for the mind verbalize. We are faster because the pathways have already been built. We are also going to use repetition to make the information available for instant recall and store it in the long term memory, but we are going to have FUN doing it. No muss, no fuss, no tears, no need for endless worksheets and drill.

The idea that the partial products model was supposed to be a way to help you count and organize thought and that it was a stepping stone to understanding multiplication and doing it fast was interrupted. Mortensen math uses the term "split and shift" to show this. Manipulatives illustrate partial products superbly, BUT here is a faster easier way to go about multiplication counting the big ones FIRST.

Already getting very positive feedback for this vid. People are stunned and amazed because one of the students is "only" six.



 I make one error in this presentation I expect you will see it easily but it doesn't slow us down or make a difference to the lesson. The blocks show 18x13 when I am doing 18x12 with the symbols. There are a couple of other subtle errors I caught while I was watching this, perhaps if you find them you can put them in the comments below. Lets see if YOU are paying attention, LOL.

Problem is, things got a little muddled along the way and many students get bogged down in the algorithm and instead of it unleashing speed it actually hobbles them. As you can see I am training them to go left to right. Count the big stuff first, understand that we're counting hundreds then tens and then units...adding them up is SUPER EASY IF you understand your addends. The youngest boy needs some practice with addends. He is going to build pyramids NOT do worksheets.

Since this first post we have maybe practiced this for an hour over two weeks. Maybe. There has not been drilling or worksheets, there has been some play (playing algebra and building math towns and such) and some practice. Soon we will make a game of practicing all 400 facts.

Note the order...first we get single digits facts mastered. Then we do the single digit times two digit facts. WHILE we are doing this, we have been building squares all the way out to 20x20. This helps us practice addends, addition and single digit multiplication. We have played with 11's (and nines) so those are easy. Also played with 12's. As we do this we are now also doing two digit by two digit which of course includes square numbers, 11's, 12's and the "easy ones where the tens addends add up 100, which are 11x19, 12x18, 13x17, 14x16 and 15x15. We can play with the little one like 12x13 and all those where there are no tens "hiding" first. These are great for building confidence with the little kids because it makes them feel like they are doing big kid math.

Concurrent and compounding lessons make all the difference.
Note that concurrently with learning addends, addition, and multiplication they are learning algebra which reinforces this...and also fractions, percentages and problem solving. You will also see compound lessons on square root and and the concept of square numbers tossed in as a matter of course.

I think you will agree they are making fine progress. And this is the way it works first you crawl, then you walk then you can jog and pretty soon you can run where you used to stumble and fall.

I hope you can hear the excitement. So much energy that many times I don't get to complete my thoughts...math learning should be FUN not done in silence to the scratching of pencils.

Raymond has his own page where you can track his progress. But you need a password. Great page if you have a five six or seven year old. Sarah's is a good page to visit if you are dealing with Autism. There are also tons of sample lessons and videos (free and password protected) on my site, and please come join me on Face Book.

Base Ten Blocks Teach Addends And Multiplication Of Nines.

Here is a classic lesson using base ten blocks. You could easily do this for 1st graders on up through highschool. The older kids tend to go ohh and ahh more...this class was especially unimpressed because they'd seen it once before. These are first graders and this is the nines times table. Obviously something is different here because many older students struggle with nines.

This is a short compound lesson, they can see addends for nines and tens, they can see all the combinations and why it works out that way and they can make sense of it for themselves.

We then went on to build pyramids like you see in this post and we only did nines and tens, this reinforces the lessons on making change and the algorithms surrounding "numbers are made up of other numbers" and "want to be a ten" plus gives them the first 10 multiplication facts for nines all in one short lesson.

Any teach can add this to their "canned lessons" and get good results. Here is the video:



By the time they see it the third time this will be super easy...imagine what they could know by 2nd grade if they had math like this an hour a day instead of an hour a week.

Of course at the end I pointed out a bit about square numbers with 81 and 9 because this was a lesson on nines. We talked about what the symbol means, that squares have sides that are the same, and that you can shape numbers into squares and that it's easy to count one side.

Share this information with parents and teachers you know.   More at:



Crewton Ramone's House Of Math.

Addition & Multiplication With Base Ten Blocks (Using Algebra)

Here is another video showing how you use base ten blocks to bring home the basic concepts of addition and multiplication. A very simple concept for very young students to grasp is numbers are made out of other numbers. You need to talk about addends...they get it when you tell them you can make a 5 out of a 3 and a 2. There are 45 addends but rather than doing the same thing over and over again for a whole year, addition in first grade for example, using worksheets and flashcards and drills...why not play and have fun and do many different activities that teach the same thing. Building towers, pyramids, walls and math towns are all activities that teach addends. (Search crewton ramone pyramids or crewton ramone addition) Variety is the spice of life.

 You teach addends, multiplication and the algebra is just along for the ride.

Here is another slightly more advanced way to teach three things at once using base ten blocks. You teach addends, multiplication and "the algebra is just along for the ride." Before you do this you get very comfortable with ONE x² before you add two or three. And you might check out this page that shows you how to present the basic concepts of addition and subtraction using manipulatives too. While you are using two of them you can really bring home the addends if you have a set of multiple tens. If you only have single blue (or whatever color you have) bars, not so much; BUT you can still get addends done if all you have is single bars just name the groups of x and add those.

As an added bonus you are factoring polynomials. I have discovered that a lot of older students have trouble with algebra because they haven't ever mastered their addends and they don't have their multiplication tables mastered either...yet they passed math several years in a row and find themselves in high school.

I left a few things out of the graphic because it was getting too busy. You should also see 9 + 9 and of course 1 + 1 (the x-squareds)  But when counting it up they may do 9 + 1 and 8 + 5 to get 23...at any rate LOTS of math goes on with each problem and the subconscious doesn't miss any of it...

Older students can take the time to draw the problems and write down the symbols. Younger students need speed and repetition so they don't get bored...and taking the time to write it all down slows things down too much...so we just talk about it...this also will come in handy later when you find they can do a lot of math in their heads. No Blocks. No pencil and paper either.




Other comments about this are regarding "mindset". Using algebra to teach basic math works well on all manner of students from various age groups because it changes their minds about math being hard. It's easy and even fun. Once they think it's easy: IT IS. If they think it's hard, math is much more difficult.

The next idea is working with older students who need to master multiplication and all 45 addends using traditional methods can make them feel stupid or inferior because they know they are doing work that is "beneath their level" or that younger kids do...this can be damaging to their self esteem and further turn them off to math. Recently a parent asked me what I thought of the math tutoring a public school had after school..."more math the same way they didn't get the first time. SO lets do it over again and perhaps they will get it this time." Even if they do they will have less than positive associations with math.

If you use algebra and it's fun and easy to start and stays easy, they have fun feel smart because they are doing algebra which they know in kid culture is supposed to be hard AND they get the practice they need to enhance their skill sets in addition and multiplication. Plus playing with base ten blocks is fun--they look like toys. They are toys. Powerful toys that teach math. Toys that make math child's play. In your hands they are powerful tools when used correctly.

They MUST get their hands on the blocks. This way you reach all learning styles and oddly enough several universities have recently made the discovery that the more senses you use the better and easier learning is...and the more learning takes place.

Also note BOTH hands make for a whole brain activity. This is why I have success with so many different students.

 The only way to learn math is to do math, have fun while you're at it.


I found early on as a salesman for this method that sales sky rocketed when we had enough kits for everybody in the room and everybody got their hands on the blocks...they understood it, they saw it made it easy they got a kit. Otherwise it was just more math.

Also athletes and other learners that are more kinesthetic excel using this method, and this is also why we do so well with special need learners.

I have made many posts about using algebra to teach basic operations. See the links below. You can also use fractions to teach addends and multiplication but that's another post and another video.

The previous post Algebra With Base Ten Blocks For Addends And Multiplication this could be considered part 1 and the one you are reading now part 2.

More on using algebra to teach other operations:
Using Algebra To Teach Multiplication.

Algebra its many uses.

Here is an older post, contains no video just words and pictures:

Using Algebra To Teach Basic Operations.

And here is a pile of screencasts on various topics:

Crewton Ramone on Screencast-O-Matic.

Use base ten blocks to explain the distributive property.

Shortly there will be another post with Commander Colby showing how to use algebra for remedial math without damaging the child's self esteem or making them feel stupid or like they are behind.

Algebra With Base Ten Blocks For Addends And Multiplication

Trying to get people to understand that you can use algebra to teach addends and multiplication can be a little frustrating. People (including teachers) are so stuck with the rigid and foolish way we have structured mathematics instruction in the USA that using algebra to teach addition or subtraction or fractions to teach multiplication are practically inconceivable. Compound teaching is; however, a very effective method for teaching math and base ten blocks definitely help.



In the picture above she has to tell me the whole rectangle...x² + 16x + 63...she has to add the x and multiply the 9 and 7...and we do it fast. There are only 45 addends, they need to be mastered. There are only We go through lots of problems quickly as you can see here:



This is video from an actual tutoring session. The little girl has all manner of distractions and yet we cover more math in an hour than she'll get in several days at school. And it's fun. Rather than spending days and days doing the same multiplication problems amd filling out works sheets, why not use base ten blocks and do lots of problems quickly. Remember the brain likes to work quickly. And the more impression it get the more likely the information is to be transferred from short term to mid term memory and finally into long term memory and with more impressions the info is available for instant recall. It is more likely to get there if you are having fun than if you are drilling and it's drudgery. The child is engaged, the brain is engaged learning is taking place.

By the time this video started we'd been playing for a good 10 or 15 minutes. Also it was self directed: she could use any two multi ten blocks she wanted, (these are base ten blocks that make building super fast because we don't have fool with getting out tens or x one at a time).

Also note you still have to work with them to get them to add two numbers instead of counting each block, and the more they do it, the faster they get. Same with the multiplication. All it takes is pratice and it's kind of fun to have the control of making up your own problems. She showed her little brother how easy it was to do algebra..."all you do is count," she says triumphantly.



With drill work and work sheets the brain eventually shuts down and it's boring you may even see them begin to yawn. Be careful with worksheets. Using base ten blocks engages all the senses. It's fun an you get more work done in less time. They learn more, faster.

When you can do your math and you get it, it's fun and it makes you feel good because learning is fun and sets off all manner of endorphins in the brain. Declaring yourself queen of math never hurt anything anyway. I am especially aware of little girls having their self esteem damaged when they fail at math. The psychology of the female is to take it personally, more so than boys as it was explained to me by a person who had a degree in the psychology of mathematics, little girls tend to think something is wrong with them when they don't get it, little boys tend to think there is something wrong with you if they don't get it. This is an over simplification and generalization but it is backed up with direct observation and anecdotal evidence during my travels.

You can play want to be a ten with the multi ten blocks...only it's actually, "want to be a hundred." 3 tens wants 7 tens...etc...7 ten and 6 tens is 13 tens...same blocks we are playing in algebra so 7x plus 6x is 13x...simple.

You will need a password but you can see the same principles at work when we work with negative factors: and we end up practicing adding integers. They learn about hero zero too, and they will often freestyle their way into concepts like the difference of two squares compare them to square algebraic expressions like (x+1)² and SEE what to do. [Soon there will be a link to a page and vid where a ten year old boy does so called, "advanced algebra." Meantime use the links below for more on using algebra to teach basic math.]

Here is another blogpost Algebra For Addends and Multiplication. You can also use algebra to teach remedial math, I have a student who has a hard time with multiplication and subtractions and fractions and...so we do algebra and then evaluate the polynomials for various numbers. This "tricks" him into doing his remedial work while he learns algebra and he doesn't realize we are doing stuff he should have learned already because he likes algebra, it makes him feel smart. Thus preserving his self esteem AND getting the work and practice done that he needs.

And here is a Video just learning about addends and playing and we don't do any algebra. But we could be doing algebra if we wanted and this student liked playing in algebra but in this vid she opted for building a town instead. This vid is about 30 minutes long. We just play blocks. I have been told this is a great video, might be worth your time:



The point is you can use algebra for teaching right along side, concurrently with, so called simple, basic lessons on addition, addends and multiplication.

More on using algebra to teach other operations:
Using Algebra To Teach Multiplication.

Algebra its many uses.

Here is an older post, contains no video just words and pictures:

Using Algebra To Teach Basic Operations.

And here is a pile of screencasts on various topics:

Crewton Ramone on Screencast-O-Matic.

and if you liked this page which is basically Algebra for little kids you should also like Trig For Little Kids too.

Now you can comment here using the blog commenter or with facebook:

Sample Lesson Math Vocab

Here is a sample lesson where we learn a little math vocabulary. It's important to know what the words mean...in the mathematics the words sound funny to little kids because they come to us from the Greeks and from Latin...but the concepts are easily understood.

You should also be able to see how the concepts of area and perimeter NATURALLY lead to practice with addends and multiplication and division. This goes well with basic lessons about addition.



I employ the three period lesson and you will note the repetition and lack of the word "no". If they get point to radius when I ask for diameter I tell them that's the radius show me the diameter...no need for the word NO.

The vid is a little long but it's a useful as a sample lesson and will appear on the Sample Lessons page.

Here is a short vid from a little later in the lesson where we are just playing with blocks and learning and reinforcing addends:

Online Math Video Tutoring Is Fun Too

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

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

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

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

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

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

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

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

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



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



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

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Make Math FUN

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

Here are a few:

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

Here is another blog post about making math fun.

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

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

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

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

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

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

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

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

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

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




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

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Or Just visit The House of Math.

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

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

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

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

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

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

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

Crewton Ramone Strikes Again! Sarah.

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



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

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



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

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

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

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

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



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

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

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

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

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.

Colby Completing The Square

This is a two part screencast on completing the square. This is where we are headed:

This is how we get there:

More on completing the square and making it easy by using the simple concept of degree of difficulty. Next after this is mastered we can head on to the quadratic or take a side trip into graphing them and talking about vertex form...and h and k.
But this won't be hard. And neither is this:


As I have said these are uploaded to both screencastomatic and my YouTube channel so if you can't see the screencast here look for it on YouTube.

"Colby Completes The Square Part 1"

"Colby Completes The Square Part 2"

You will find that giving them this formula isn't entirely helpful:

(x + a)² = x² + 2ax + a² nor does it deepen understanding. Further when combined with this:

ax² + bx + c = 0

with the instruction that completing the square just means replacing c with

(bx/2)² resulting in

ax² + bx + (bx/2)² = -c

might actually cause some confusion as well as fear and trepidation because they don't know what the symbols mean.

Students using base ten blocks and manipulatives know what that means because they can SEE it and rather than giving them rules and process and formula to follow they get an experiential understanding of what the formula means BEFORE they ever see the formula. THEN when they do see the formula it makes sense.

“To state a theorem and then to show examples of it is literally to teach backwards.” ~E. Kim Nebeuts


When I say they don't need the symbols I mean they can hear the problems and do them in their heads...if they have paper and pencil it's even easier.

Go here to see completing the square at Crewton Ramone's House of Math. My students SEE these concepts and more right from the very start. It teaches them how to count, how to multiply and also as a by-product algebra and factoring. Math is a language teach it all at once...

The screencast mentioned in the second vid is not yet up on the password protected channel...it will cover the problems you see in green above in intricate detail...with blocks but mostly with drawing and lastly symbols. You need LOTS of practice before you move on to the quadratic formula.


“The point is to develop the childlike inclination for play and the childlike desire for recognition and to guide the child over to important fields for society. Such a school demands from the teacher that he be a kind of artist in his province.” ~Albert Einstein

“A teacher is one who makes himself progressively unnecessary.” ~Thomas Carruthers

Crewton Ramone Cross Teaching Concepts.

Here is a longer video showing multiplication, algebra and division. The lesson is simplified by keeping in mind the five basic concepts, and having blocks the child can get her hands on. In my travels I found that the saying math is not a spectator sport was QUITE TRUE. Just watching is not enough, you need to get your hands on the blocks. It was became apparent the difference between everybody in the room "getting it" and "only" getting 80 or 90% of the room was to make sure everybody had a set of blocks or were sharing a set of blocks, but everybody had to be able to have their hands on the blocks.

If you don't "get it" you may be one of those people that needs to get your hands on the blocks.

This child is supposed to be special ed or SPED, I doubt many of her SPED-mates are doing math like this. Children doing math like this at 6 or 7 years of age would be considered gifted...but actually when they can see what they are doing ANY little kid (or big kid as the case may be) can do math. I often say if you can speak English, count to 9, identify a rectangle and tell whether things are same or different, you can do math...




You may want to watch this one first. The video above is a continuation of this lesson:



Crewton Ramone's House of Math

You also might want to subscribe to my youtube channel.

Why just teach one thing at a time?

Upon seeing this picture the youngest boy said, "That's us doing our shapes and counting!!" For him that's exactly what it was. For the older boy we were building rectangles and counting the parts....one big red one, five blue ones, two pink ones which are threes so six units. We do addition multiplication and counting all at once. We also pattern for 13 x 12 = 156 and we learn a little place value (count the big ones first).

I was at a party recently, handed someone my card and he said, "Math?!! My kid's only 3 years old." To which I replied, "are you teaching him English?"
Those nearby laughed and nodded...
"Math the way I teach it is a language. Just check out my website. Take what you like leave the rest."

Before this we did more place value. Then we just named the blocks one through ten and of course the hundred even though they already know it...Then did multiplication.

Started with 12 x 13 = 156 and spent time counting all the parts and counting the sides. Look at all the math:



**added 2 tens and 3 tens to get 5 tens
**counted 3 two times to get six
**saw that six can be a rectangle made with 2 threes or 3 twos...
**counted the big one then the blue ones and the units and talked about what each number in 156 meant.

Counted the sides very carefully to get 12 and 13...from 1 to 12 and from 1 to 13. then we counted fast, one ten and three more or one ten and two more is so much faster than counting 1,2,3,4,5,6....

Again they have to be taught to start at 10 even though they supposedly "know" one side of the red square is ten or the blue bar is ten...

Then we flipped them over and did algebra..and we were done...might have spent 20 minutes tops...on the entire lesson.

This compound teaching where each students takes away something different but where more than one concept is introduced at a time. Again the sub-concious mind logs all this information. It can (and will) be drawn forth later.