Homeschool Math, Dboyz Playing Pascal with Base Ten Blocks

Here are a few recent vids. The point of them and this post is to illustrate and bring home basic concept number three: we form rectangles to facilitate counting. Rectangles make it easy to count and we can reduce many seemingly complex math problems to basic counting with the help of our friend the rectangle. In the first vid they make percentages EASY by using a rectangle.


What basic concepts do you see in these three vids?



Rudimentary Editing Skills Level 101: ACHIEVED. Mastery w/ percentages is being attained. THEN we can move on to ones that end in 5. Baby steps. Note the block serves as a "post" or memory anchor on what to do. They understand the CONCEPT so now I'm just changing the numbers...and we also get practice with multiplication and division.

Here is their little sister playing and learning addends...she had asked very nicely if I would play what's under the cup with her since her brothers were playing outside with two neighbor boys...and she wasn't being included. So I brought DBoyz in and shot that short vid and then sent them back out and played with her...we played what's under the cup and built tens and then she made a house for little ponies to stay in and then we cleaned up and it was time to go. She made the comment, "Time always goes so fast when I come to your house." Because time flies when your having math.



This next video is also edited. The full version is on Dboyz page at the house of math.  All three of these videos can be used for educational and training purposes...lets use them to focus on basic concepts.



You can stop here. The rest of this post is long and aimed at those who are interested in learning more from the perspective of a trainer or an aspiring master trainer. A link to this post will appear on the teacher training page too. Here is the whole converstion on Crewton Ramone's FaceBook page.

I highly recommend you click that link and read the thread, what follows are some (slightly edited) excerpts lifted from that thread starting with this: First things first, I don't write or make videos for Unicorns. Celeste is a unicorn. Female engineer. Statistically speaking they don't even exist. There are few Unicorns who have become interested in the house of math...Staci was another one: black female electrical engineer...Irene is another one I'm confident she knows more math and certainly more chemistry than I do...these are the exception not the rule...and it must turn tables and become the rule not the exception. I have been paid large sums by men who fully understood the mathematics well enough to apply it to physics or engineering or economics but could not explain why you invert and multiply to a seven year old's satisfaction...much less why the x's don't change when you add them...what has to happen is people who actually understand math have to be given the tools to be able to explain it to others.

Most parents statistically speaking failed algebra. Many teachers got a teaching degree because it "didn't involve taking a lot of math..." Teachers currently still think there's a trick to it:

Question: if you understand math and math concepts will you still need special techniques?
Answer: once you understand the concepts all they can do is change the numbers.


I'm starting to break lessons into small pieces for a couple of reasons, First: because we know the attention span of the average viewer is extremely limited...two minutes is optimal video length...what a laff: people want to learn math in two minutes....if not screw it...girls can become strippers and guys can always cut grass--wealthy people rarely do their own yard work. Second: because too many parents and teachers can't wrap their head around switching from topic to topic because they can't see how the lessons relate...we are learning about Pascal and summation but all we are doing basically speaking is addends and multiplication....the percentages practice was practice on multiplication and division. Once we get the CONCEPT down all we can do is change the numbers and then it just becomes practice with doing whichever of the basic operations are required because AGAIN computation is how we DO math but it's not THE mathematics.

You can do all the math with just addition and subtraction but it takes longer...further if you cannot DO computations quickly and easily mathematics is HARD because you have to contend with two things layered on top of each other: trying to remember the rules and process for the problem at hand and trying to remember the rules and process for the computation required itself. This overloads the system and results in failure, anxiety and incorrect answers which leads to negative feed back, which leads to more fear and anxiety, which leads to an aversion for the mathematics which leads to more of the preceding and a feed back loop is created that includes actual pain, mental anguish and damaged self esteem which leads to hating math, which leads to the dark side.

The concepts are very basic here. We form rectangles to facilitate counting. There are more as an exercise for those who are thinking about tutoring or maybe one day training others...what other basic concepts are covered in these three short videos?...you might also go over them in your mind even if you are "just a mom" teaching your own kids. You can put comments below if you like...but there are several more at work here. I mention some of them in that FB thread.

Now, the reason that this method is so effective is because if all math is counting and we can reduce any problem to simple COUNTING, then anybody can do math that can count. The trick, if there is one, is knowing how to reduce a problem to simple counting, which as it turns out is the genius of it all and which is why we say if you can count to nine form a rectangle and tell if something is the same or different or not we can teach you math...I add that they must already be able to speak a language generally it's English and if you can speak that language math should be EASY. Anyhow what basic concepts do you see in these vids? 

Mathematics is the study of relationships and we describe these relationships with symbols. pie is not just 3.14....it is the relationship between the circumference and the diameter, it's not just sin30° = .5, sin is the relationship between the side opposite 30° and the hypotenuse...addition and subtraction are inverse functions but basically the same thing in order to do one you need to do the other basically you are combining, the same with multiplication and division, things look scattered and random (even though the tab bar on my website basically goes in the order you will see it presented in the public schools) because you don't get how the language goes together or the gestalt of it...you can't study one part without studying some other part...using this method. You can certainly compartmentalize the mathematics and they do for an example think back to or visit your nearest public education institution.

 "Just show me how to do the problems" is the problem. My son is currently suffering under this line of thinking where he gets to do timed worksheets for multiplication facts. He doesn't do as well as other kids on these because he doesn't write quickly, therefore he must not be very good at math. They are majoring in minors.

When asked to be able to use and apply this knowledge to something like 28 is what percent of 70 or how many 4's in 72 they either can't do it at all or take forever and certainly can't do it in their heads...but they can whip out a 50 problem worksheet of single digit multiplication facts in under 3 minutes...but then ask them to figure out how much change they get if they buy 7 pounds of rice at 2.78 per pound and pay with a $20...no pencil, no paper...and they can't do it, because they can't organize and keep track of their thoughts.

Concept #3: Rectangles facilitate counting.
A = LW This gets totally LOST if you just memorize (n² + n)/2 which is what most of my students have done if they even know about this at all....they use summations on SATs and other standardized test to "separate the men from the boys..."

In the example for 14 we see various addends. a couple for 14 and also for 4, we also see the number 105 is 70 + 35 again numbers are made up of other numbers and that part will come in handy when doing division but also trainers should see the distributive theory of multiplication as we distribute the 7 across the 10 + 5 so the 70 = (7)(10) and the 35 = (7)(5)...students some how are mystified by this when they get to algebra even though they have been doing it all along, where the most common grade is "F" and when asked to multiply 7(x + 5) often have a very hard time even though it's easier than doing it in base ten because all we get is 7x + 35...whereas in base ten we have to combine like terms (the tens) which is a basic Concept #2: we only count things that are the same. If you were going to be a trainer and were asked to delineate the concepts on these vids and you came back with counting, forming rectangles and "The blocks help you see the patterns." I would FAIL you...because you failed to see the the basic concepts...

If you were being tested under Jerry or another Master Trainer named Brian you would fail and more than likely receive a  serious dressing down to go along with it...I remember one woman in particular in tears after she got done being schooled...although Brian would try to be a little nicer about it. I'm going to (try and) develop some Master Trainers...if I get 7 in the next 9 years I will have done phenomenally. When you are done you should be able to take any textbook and then take just about any problem and either show how to do it with the blocks or step back and show the basic concepts needed to do the problem because by now it should be clear that you don't want to model every problem with the blocks nor should you need to...and you don't need to hit the student over the head with them or take away the aha moments by just telling them....let them explore and discover for themselves. You nudge them in the right direction or point them down the path that will lead to the discovery you want them to make....but they walk down there alone. You are not far off, just in case and to catch them if the fall---control of error is important but failing your way to success is also important...not wrong just getting more information...that attitude leads to discovery and opens up the wonder. Control of error does not mean don't let them make mistakes ever or avoid making mistakes: it means learn from the mistakes, take that information and then use it to get it right.

Fear of failure or frustration of getting it wrong or worse being put in a position where they can not succeed shuts down learning decreases wonder and joy to zero or less--usually less, and makes the math what it is today. I see math memes like this:

And like this:

If you understood what you were doing how could you NOT know?  Yet this is a completely common response from many of my students who are not used to getting A's.  Try it some time ask your child or students how they did on their math test...

I would encourage to click this link and read the thread. The point is not to "talk down" or to deride other people who don't quite get it...entire companies have been built that purport to use base ten blocks to help you see the math...but some methodologies with base ten blocks are better than others. I can swing a hammer and work a saw...and my trig is strong, but I know quite a few carpenters who using the exact same tools, would get whatever it was built faster, better and prettier than I would.  My aim is to make you, if you so choose into a person who can teach math using base ten blocks and other math manipulatives, faster better and prettier than the majority of your peers. Unfortunately, I can't do it in an hour or even in 50 five minute videos...but I do have some parent teacher training more than 7 hours worth at VERY reasonable rates which many have found to be very, very useful.

If you would like to enter into a dialogue regarding concept number three, or make a comment about the teacher training (many have taken it now) please do so in one or the other of the comment boxes or ask questions about concept number three not 4 not 5 but 3 that would be concept number three the one about rectangles and how they facilitate counting.

Give me your email address and I will give you a subtraction manual in pdf.

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Homeschool Math: Base Ten Blocks for long division...again.

I've been perusing the internet looking at what other people are doing with base ten blocks.  Sorry guys. It's appalling. No wonder teachers don't use them much...many of the presentations are very...uh, poor.  If you are a teacher showing other teachers how to use base ten blocks you have a responsibility to make sure you are doing it right. Even then there's no telling what the people you instruct will do...like a game of telephone after a very few generations things can go very, very far awry.

I remember once, we had a center in Salt Lake City.  I trained several people there and then went off traveling doing seminars and opening up a couple of other centers in places like Colorado and Nebraska and South Carolina along with the training tour I was contracted to do which was usually 3 cities a week...anyhow, I came back after about 3 months and was watching  a teacher that one of the trainers I had trained, trained do a lesson for a group of people who had bought kits, she was nervous because I was there but she did okay right up until she started presenting division.  I won't go into details but lets just say "there's no split and shift" in division. If you want to model multiplication that way fine, it will mirror what they see in public school but it doesn't work for division...at all. And if you don't know what "split and shift" means don't worry about it.

Lost In Translation.

So I understand. It's like a game of telephone where one person whispers a sentence into the next persons ear...by the time it comes back to you it can be radically different. Or things can get lost in translation. Like this:


Dboyz are still chuckling as I type this. Anyhow, behold! If you type in long division with base ten blocks into mother google this is THE number one video out there:


4 is contained in 532 how many times? What are we counting? FOURS. Here it is done showing how rectangles facilitate counting. As I watch this I see several things I could have done better too. But I think you'll agree one makes things a little clearer than the other.  The idea is to reduce these problems to simple counting.  Take a look at this video, "complex numbers" for 3rd power algebra made into child's play. Division shouldn't be hard or scary or cause tears. And once again we see the way things should as opposed to the way things are because currently the way we teach it in public schools kids learn to HATE long division.


Rectangles Facilitate Counting.


Now in order to do division a lot of you think you need to be able to multiply and subtract, as you can see (and I should make a vid with some actual 5 year olds) any five year old can count down one red one three blue ones and three green ones. 133. Building the rectangle and getting out the pieces would be the challenging part. But if you explain that it can only be four across they won't even reach for 100 squares...and again this is a dynamic problem that should only be attempted once many simple static problems have been done and mastered...I show and talk about some simple ones in the video.

I have already made several posts and pages about division with base ten blocks and on the Parent/Teacher training page I talk about the importance of starting in the concrete and moving to symbols after drawing whenever possible. Go to those pages for more. Here is yet more on division.

Multiplication is of course important and so is subtraction but again you can use division to teach multiplication...and subtraction, but all you need to do is be able to count to get started doing problems like this and you can baby step your way here in short order. Speaking of subtraction I just got a book on it finished and back from my illustrators. Supremely Simple Subtraction. You can have it for free, just give me your email. If you buy a password, it is of course included on the Password Protected PDF's page along with a lot of other cool Pdf's. Some people are reluctant to give me so much as an email lol because they expect that then they'll get bombarded with email from me. Is to laugh. If you get 12 emails from me in the next YEAR that will be a lot of emails...lol...there are people who sign up for emails and did so 5 years ago and still haven't gotten one...lol...they WANT an email telling them when I put up new vids or pages or what the new password is and...


They are still waiting for an email.

Things are a little different at the house of math. Go take a look. See any advertising? Casinos and Online schools and colleges solicit me quite often asking me to put links on my pages or ad words or what have you, and now that my site is doing well some of them are willing to pay a few hundred bucks for the privilege. Free money. They always get a "NO" from me. So if you want the book email me. I will email you the book and not a whole hell of a lot else. Seriously.

Here is one last video with a guy showing subtraction with base ten blocks...you may not be able to get through it.  I was going to make this it's own post but I think I'll just combine these two.  People always ask me why don't more people use base ten blocks to teach math...mostly because they don't know how and they end up doing presentations like this and teachers (and parents and/or homeschoolers) get turned off because really it's not much better than symbol based instruction and it seems more cumbersome and time consuming. If you just have rods, bars and units this isn't too far from correct because it takes forever just to set up the problem.  Anyhow here is exactly how not to do it:



How may units can we have in the units place in base ten? NINE. How many tens? NINE. It never gets past nine. If you want to see a super simple way to do subtraction get my subtraction book...or go to my subtraction page. But the word is in. The book is cooler and full color and spiffy as all get out.

Password protected pages give you even more detailed info in the form of vids and pdfs. They used to be super cheap...and guess what? Nobody bought them because I guess people figured they couldn't be worth much for just 5 bucks or what have you. Now I sell subscriptions and annuals and lifetimes at the rate of several per week...one password for $50 is the same as making 10 sales at $5...and I never ever made 10 sales even in a month at $5. Now even if I only do one a week that's 30x better than my best month when they were $5. Bummer for you. Bully for me. I might have a weekend sale in March on passwords not product,  (product is out of my control that's Mortco not me)....maybe. Probably people who got my book for free with an email or who got a password a long time ago would like to be informed of the sale with an email reminder...lol...but I doubt I'll get around to it.

Of course I have a FaceBook page and I'm on Instagram now too.

Divinely Dandy Non Difficult Division

Get Divinely Dandy Non Difficult Division for just $19.99. This book will show you everything you learned here and MORE laid out step by step with links to videos and pages that give simple concise explanations for how to use the rectangle to organize thought, how to introduce division concepts at a very young age, and how to make fun while you are doing it. I guarantee that video alone will expand your thinking when it comes to division and math.

Watch the video on the Preview and Purchase page that gives you a page by page over view of the PDF so you can "try before you buy", see exactly what you are getting and be confident it will be money well spent.

As always before you buy stuff be sure to check out all the FREE stuff first.

Base Ten Block Subscription.

 

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Again by popular demand, now you can "subscribe"...just use the button below and you can break the cost of a password up into TEN payments. Get a lifetime (BOTH) for 10 payments of 26 bucks or an annual (one or the other) for 10 payments of 6 bucks...or both passwords for 10 payments of 8.50 for an annual pass...the subscription is a little bit more because paypal's fees on 10 payments are more than on one payment.


I have broken it up into 10 payments. So if you don't want to pay all at once in a lump sum you can pay for ten months and get a year of access, or pay $26.00 for ten months and get a lifetime of access...I don't think it could be easier. I know 250 bucks or even 50 bucks can be hard to come up with in these trying times but I think pretty much anybody can afford 6 bucks a month... if you would like to see MORE payments for the annual like 20 payments of 13.50 or something let me know...as always the password is the same for everybody, although that's getting to be problematic, .and when it changes (about every 3 or 4 months) just email me for the new one.  Because of all the options I can't make pop up pages or I'd have to make separate buttons, so your password will come in the form of an email with a link to a webpage that has the password on it...you will have it within 24 hours of your order...usually much less. And YES if you buy buy both for $8.50 you get BOTH upfront...I don't "drip" pages out to you. And you are in for 2 more months after your last payment...don't get overwhelmed with all the stuff. Just get started.

Options 10 Payments...

Annual Sitewide : $6.00 USD - monthly Annual P/T Training : $6.00 USD - monthly BOTH (Annual) : $8.50 USD - monthly Lifetime Pass (BOTH) : $26.00 USD - monthly

Alt Email.

Use alt email if the email you use for paypal "doesn't get checked" or is forgotten and/or you have an email to which you'd rather I send the links to your pasword(s).

No such thing as taking your love of math too far.

A "sitewide" pass gets you in to every page EXCEPT the teacher training...the teacher training password ONLY gets you into the teacher training page.  The training page currently has about 7 hours or video on it plus links to some hard to find pages.  More than 8 hours of vid is currently being edited to be added to the training page as I type this. [March 2015]  The sitewide pass gets you into lots of pages and anywhere it asks for a password (other than the teacher training page), the sitewide pass is it.  You will find hours and hours and hours available to you with the sidewide pass, I doubt very seriously that you will have gotten through everything by the time your ten months of payments is up.

Further, I add to these pages as time goes by, so during the next ten months there will be more videos and pdfs and web pages added...I think you find it's a STEAL for six bucks a month...or even 26 bucks a month...if you get an annual and then decide to get a lifetime (which many people have done once they see how cool it is...lol...) you will NOT be credited for the money you spent. In other words if you made some payments at 6 bucks that won't be subtracted from the cost of an annual.

People have in the past asked if they can get the lifetime for the difference of whatever they paid before. The answer is no.

Again, take advantage of the all  FREE stuff first. There is a lot of it. There is also now a lot of password protected stuff waiting for you if you want to do/learn more. Here is a page I built hastily describing what you get for the passwords it needs updating badly, now.  I have added lots since then and prices have gone up too... some people put a toe in with 6 or 8.50 a month...and they forget it's not 6 or 8 bucks for life it's 10 months for an annual. Then when they want to upgrade they get confused and think it's going to be $150.00 (the sale price that's ending SOON. for EACH password...$150 for the training page and $150 for the sitewide, but you get BOTH for that sale price (for most people your last chance will be June 25th)...the regular price is $250.00 and ask anyone it's worth the $250.00.



NEW UPDATE: Trig page has been built. See? Life time members from several years ago are STILL getting benefits because the sitewide password works on this page too.  Entry page has been built yet...it shows you the plethora of videos you get on the other side that are unlisted so you won't find them with searches.The trig page is worth the price of a lifetime pass ALL BY ITSELF.