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.

Patterning With Base Ten Blocks And 11's.

Here is a lesson where we basically play spot the pattern. We start off with base ten blocks and very quickly move to symbols only; however, this lesson does answer a lot of questions with regard to WHY some of the "tricks" with 11's you may have learned work the way they do.

This why we like math, the patterns are easy to see, the rules are consistent, you can prove your answers...but don't get caught up in the rules and theorems. Play and put the children in a place where they can discover the rules for themselves. Once they see the patterns they can often make up their own rules and then test them to see if they always work...if you do it right they will tell you the Pythagorean theorem you don't have to tell them. This is just more of that.



This is a simple lesson just playing with 11's. You could play with 9's (← note those are 1st graders in a classroom) or other numbers just for the fun of it. If the child is curious and having fun the lesson is much easier. We went pretty long considering it was just on 11's but they were fairly well engaged for more than a half hour.

In this lesson they got to practice their addends again, and do some addition and use their counting skills creatively and learn a little about patterns. More fun to be had at Crewton Ramone's House Of Math.

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Crewton Ramone Using Base Ten Blocks In The Classroom.

Here is a second post about how easy it is to incorporate base ten blocks into your classroom situation. Here is the other post I did called Crewton Ramone In the Classroom.

This is also great for stoking their imaginations as they tell stories about the ruins of Egypt and Great MATH Pyramids.

I've gotten into contentious debates about whether little kids can do math like this. What is so hard about it? They use their ability to discover SAME on both sides to discover x and then they have to do some more thinking to discover what the number is that is disguised on either side. You start off easy and work your way up...in both of the cases I cover here some students got the answers instantly.



You can hear one little girl in the class throughout that vid. She has been given lots of labels, I wanted her to stay in the class even though she is disruptive because like all the other kids given the chance she proves to be pretty good at math and this is valuable at repairing her damaged self esteem. Anyhow, there is a myth that employing base ten blocks will cause mayhem in the classroom. This doesn't have to be the case as seen here:



I will be the first to admit that it CAN get loud and out of control if you let it. Here some of the class is gone because they have remedial reading, but groups of four per combo kit works well and there could easily have been all 24 of them. I never really got any of the lessons on Pythagorean theorem I did on vid but factoring, fractions and percents are all easy to do with manipulatives. Here is an additional page on how to teach addition. (Get it additional!! C'mon--that's funny right there.) You could spend quite a bit of time there if you follow all the links on that page.

At the same time you introduce those concepts you play and build addends learn about integers and subtraction and practice multiplication so they can see the whole picture not just tiny compartmentalized parts.



This one shows them being creative, developing their fine motor skills and more. They not only built addends they had to work at getting the sevens fence to work using the posts...which are addends for 5...younger students would have a hard time making that fence work...these activities are great for preschool thru 3rd grade although older kids like to play too and some who never mastered their addends could also benefit.

Building and playing gives them a positive math experience.



They are in second grade. It shouldn't be work. It should be fun. These kids looked forward to Mondays with Crewton Ramone. They go home and tell their parents about what they did and the parents are amazed at their little second graders explaining factoring or Pythagorean theorem to them, I was at a birthday party and basically got mobbed by the parents there who were amazed that I was the math guy. They thanked me for teaching their kids math beyond adding and subtracting which is about the extent of the accepted 2nd grade curriculum... Adding subtracting a little measurement money and time telling.



This one can get out of hand because if they aren't careful the towers crash and there is a lot of excitement. Note that the point is to build addends NOT to build towers. I have seen teachers have them build using all the same blocks instead of the combinations...which defeats the purpose. Also you can count each level by the 4 or five blocks they used to get some skip counting in...in other words count the all the 7's on the 7 level...7, 14, 21, 28, 35...all the nines on the nines level etc just to get the patterns for the first few in.



For older kids (third or fourth graders) I make them build it and then tell me how many units they used...they have to do a lot of counting. That means count every block...including the hundreds...so lessee that's 100 plus 5 tens, plus another 100 plus 6 nines plus another hundred etc...some kids count all the hundreds then the pillars...no matter how they do t it's a great exercise in addition and multiplication.

Here is another fun exercise making a cube (it takes two top trays however) and I didn't make this vid in the classroom but at home with three home schoolers but there's nothing stopping you from doing in the classroom if you have the blocks. I did this with the first graders but never got it on vid. I made them line up and each kid built a combination and they went around and around their tables as fast as they could trying to build theirs faster than the other teams. A teacher could help keep the blocks straight and from falling down as it gets ten high. When you are done you can talk about cubes and notation if you want.



All in all it's EASY to use blocks in the classroom. You will find that just by playing they learn their addends and a lot more all on their own. Some direction from you can help but it's more fun and effective than worksheets and book work, the students learn more faster and you will earn a reputation as a good teacher and a fun teacher that students look forward to coming to rather than not.

Here is a page at the house of math that has a little more about using base ten blocks in the classroom and an instructional video with a million dollar idea in it...it basically links back to this blog post and the other one but it also contains a little more info and a couple of other vids to help you.

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Crewton Ramone In The Classroom.

Here are a few vids I've made while playing around at Haiku School with 1st and 2nd graders using base ten blocks.

We do math that is supposedly advanced for their age. Most of the time the kids don't seem to notice. We fool around with problem solving and algebra, Pythagorean Theorem and addition, multiplication and division. All it is is counting. No concept is beyond the child if presented at the child's level.

Teachers and teachers aides are always amazed at what I take for granted. Several teachers aides commented that they were doing the same thing at the local community college while they attempted to get their teaching degrees. Many of them are being held up because of the math. "Why don't they teach it this way?" is a common question.

I'll get into that some other time. I am building a six hour Audio Course that will cover that (briefly) and a whole lot more. Should be done this summer. To start off here is a rant. Fed up with teachers who tell me kids can't do simple algebra. Teachers can't do simple algebra, not the kids.



Then here is a CLASSIC lesson with first graders. We learn addends for 10 and nine and the nines multiplication table to boot.



Here is another lesson with is a lesson with 1st graders factoring polynomials but what we are really doing is learning addends and multiplication:



As one teacher put it when they get back to the stuff they are doing for "grade level" they ace it. Also In the 1st grade class I go to for an hour a week they blew away their piers on the standardized tests. Especially in "algebraic thinking" but also in general computation. These scores are confidential or I'd share them. Here is more:



I've been fooling with this for 23 years now. I have heard every excuse in the book from teachers as to why they can't do this their classrooms. This post is about removing excuses. ANYBODY can do this. I can train you. You can train yourself. I am working on courses that you can buy for a few bucks to help you implement this in classrooms or in your home or homeschool.

Meantime get a password for 24 bucks and start watching some vids and reading pages that interest you in your spare time. (That's a bit of a joke, my mom was a classroom teacher I know you don't have a lot of spare time.) Once you figure out how AWESOME this is you'll find the time.

Here are second graders doing slightly more advanced play. They are making square polynomials and you can hear the excitement in the room. It's fun. They know they are doing stuff that's supposed to be "hard." In kid culture algebra is hard, but they often ask for it by name.



Here is a lesson on square numbers:



We are getting ready for Pythagoras. Before you dive into more complex concepts it's good to get them used to the elements they will be faced with before hand...like squares and square root. Very important to know what the symbols mean.

And just for fun I took a trip down the radical path. Why. Because you can.



The we played with Pythagoras. The thing to remember is all we are doing is using our counting skills.



The classes with the first graders are about an hour long and 90 minutes with the second graders. I don't expect you to watch all these vids in one sitting but here they all are in one place. You can share them with teachers you know and they can get to them as time permits. Any young ambitions teacher that would like to turn these into lesson plans are welcome to do it...

It is hard to film and teach all at the same time, plus I am hampered by rules about filming children and etc. So I don't make many vids. Hopefully there will e another post like this before summer with a bunch more fun vids for you to watch.

95% of the time we have a great time. Once in a great while things can get rough. I had a Monday morning class with a substitute teacher where the second graders were having a hard time due to lack of sleep

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