Here you will see students as young as 4 and 5 years old doing algebra and "advanced" math, without ever knowing it's supposed to be hard. You are invited to learn how to use this method...
"The teacher must take her materials from the school, and her principles from what she has learnt; and then she must face practically, for herself, the question of this recall. Only her own intelligence can solve the problem, which will be different in every individual case." ~Maria Montessori
I remember Jerry being quite amused that I wanted to be a master trainer yet had no concept or knowledge of Maria's work. I went home to escape winter and I had been reading "The Men of Mathematics" to try and figure out what the hell these guys were thinking, Newton did not develop the calculus to torture high school seniors, and college students. I also read "Innumeracy" by Paulos. He was surprised by this, so he took me down into his basement where he had a library set up and directed me to READ...particularly works by Mario and Maria. It was a large collection of books; I have an affinity for them, so I was quite content to spend hours down there, I found a book on Vedic mathematics, quite a few classics (Socrates, Plato, Aristotle etc) and many more. Jerry was content to have me down there because while I was down there I wasn't bothering him, and occasionally I'd come up with a topic of conversation "worth talking about."
Try to remember my lineage is direct. Me, Jerry. Mario. Maria. I don't recall Jerry (or Maria or Mario) talking about a standard curriculum that was to be applied to every child. Quite the opposite. The teacher was to be trained in such manner that each child's individual interests could be tapped, nurtured and developed. Discovery was directed by the teacher with regard to the child's individual interests.
Therefore lessons were developed for each class and each child in the class on subject matter at hand, in this case math. There was no cookie cutter approach. Even the books he developed were made with the understanding that the student picked where to start and the order. All books were to be completed but how and in what order was up to the individual student. And yes it's a hell of a lot more work, AND the education is far more effective and superior to what currently passes for education in the public school system of the USA. This year's class is not the same as last years class. How is it possible that the lessons would be the same?
"A teacher, by his passive attitude, removes from the children the obstacle that is created by his own activity and authority.". ~Maria Montessori
For example, today we are going to learn trigonometry concepts. The teacher introduces the CONCEPTS then directs the student to discover more and thru socratic method the child discovers axiom and postulate...and the formulas, they aren't hit over the head with them. Once concepts are understood mastery can be attained. Mastery is demonstrated by being able to make up and solve one's own problems. Again: once they understand the concepts all we can do is change the numbers.
"Education is a natural process carried out by the human individual, and is acquired not by listening to words, but by experiences in the environment." ~Maria Montessori
Your job is to create a math rich environment. Place the child in a math rich environment and they will learn math, in their own way and in their own time. This is the education of individuals in groups...how can the lessons be the same, in the same order at the same time. If you were educated in a public school yea verily this is completely foreign to you as everybody pledges allegiance and then opens their text book to page 123, or does the same worksheet in preparation for the standardized test. BTW it has become clear that homeschooled and Montessori students do incredibly well on standardized tests, because again, once the concepts are mastered all the givers of the test can do is change the numbers trying to ascertain if the math is understood or not. This has been circumvented by students and teachers who memorize answers to the test questions, rather than understanding the subject matter well enough to answer any questions. Once they understand addition they can add any two numbers. The principle is the same with regard to "advanced mathematics". The practice is another thing entirely: memorize long enough to take the test.
"Our care of the children should be governed not by the desire to 'make them learn things', but by the endeavor always to keep burning within them the light which is called intelligence." ~Maria Montessori
"The essential thing is to arouse such an interest that it engages the child's whole personality." ~Maria Montessori
Once interest has been pricked discipline and concentration flow as naturally as water downhill, time stands still, and learning takes place.
"The first essential for the child's development is concentration. The child who concentrates is immensely happy." ~Maria Montessori
"Discipline must come through liberty. . . . We do not consider an individual disciplined only when he has been rendered as artificially silent as a mute and as immovable as a paralytic. He is an individual annihilated, not disciplined." ~Maria Montessori
The only sale will be on annual and lifetime only, one time payment, no terms. Coming up with 50 bucks or a hundred and fifty bucks might ding your budget so I have now got a handy dandy subscription option where you can pay in installments, but as I said you won't get terms on the sale prices.
I'm going to have a password flash sale in March in honor of my elder's 10th and also the beginning of my second half century counting down the last few trips around the sun in this body...I pretty sure I've already had more than I'm going to get and that in itself is reason to celebrate...
If lifetime passwords are on sale for $150 and are normally $250 what % off is that? Those that answer with parts per million will be hunted down and summarily shot.
150 is to 250 as 3 is to 5 as x is to 8...therefore using this same ratio what should the sale price of the annual plus teacher training password sale price be? X will be the answer but you will have to us a multiplier to get the right answer what is the value of the multiplier? (I'm using round numbers to keep it simple.)
If a broke homeschooler asks me if they can apply the money they already spent on passwords to the sale prices what will my answer be?
Extra credit: Should the flash sale be 5 days, beginning on March 1st, 7 days Beginning on March 2nd or 10 days beginning on March 5th?
I can not put blocks on sale. Passwords do not require a phone number for delivery. Blocks do.
Meantime you can get this homeschool math subtraction manual for FREE, all you have to do is send me your email address; if I was smart I would have said email address and a promise that you'd go back and leave a comment....
I will be having a video training session FRIDAY, 27th Feb, 8am HST. 2 1/2 hours on Fractions. I just did a 2 and a half hour session with some Montessori teachers from SC and like a silly pants I forgot to record it...it was a pretty good training too...I think: never got much feedback from them.
Any how we'll go for an hour or so take a 15 minute break and then finish up the hour...I will start with this fractions kit. Fraction tiles. And if we have time spend a few moments showing how to use the multi tens to teach fractions...but remember all you really need is a combo kit...
Another training using the multi-tens and combo kit exclusively to teach fractions will happen some other day**...so if you have a fractions kit and want some training on how to use it email me to reserve a spot and let me know you can make it, cost will be 20 bucks. You need gmail video chat installed and you need to add me to a circle and I'll add you back...this would be a good time for me to actually email people who bought fractions kits and let them know about this...it could happen but I think my Girl Tuesday is going to go to the doctors instead of working her one day a week with me so...
**If not enough people with fractions kits respond I'll do the fractions training using a combo kit and multi tens because I know quite a few people have those. Then, I'll put it on the training page and perhaps on a PP fractions page as well. Also if you can't come for 2 and a half hours just come for an hour...you won't get lost. Which reminds me in March I was considering having a Saturday 6 hour training...50 bucks and you can come for an hour or two or all six or what have you come and go as you please...do 3 and 3 with a half hour break but I will need a quorum of ten.
Apparently, I should do an hour long subtraction seminar but it seems a little redundant now that the SSS manual is done. The whole point of the website and vids is to make myself obsolete...eventually you just pick any topic and there will be vids and pages there waiting for you...
You can also comment/sign up below using blogger or FB...
Using base ten blocks to teach Homeschool Math is the topic of conversation for a lot of people who have chosen to homeschoool...asking namely, "how am I going to teach these kids math if I failed math...?" And of course your first instinct is to teach math the way you were taught, even though you know from personal experience that it might not be the most effective way to learn math...here is a method that works and has been PROVEN effective--and best of all it's fun...and as an added bonus no number line to start with, just a noisy game kids love.
Here is that simple game for teaching integers.
I was going to make this a much lengthier post, but let's just keep it short and simple. My subtraction manual, Supremely Simple Subtraction is doing quite well, although I have now had several conversations where the gist of it is there is no way to describe how cool that book is...lol...still getting people who already have it to leave a simple comment is very difficult for a lot of reasons, but as you can see quite a few have done so now. Click that link get a FREE book...well, not entirely free you have to give me your email, but you won't have to worry about getting inundated with emails from me...in fact quite the opposite. There are people who have signed up on various email lists who have to this day not gotten a single email from me since. Even when they WANT an email to inform them of the new password or for notification of one of Mortco's extremely rare sales.
I haven't gotten around to making a list and getting an email program but I have hired an assistant, a Girl Tuesday if you will, and I think she will work wonders in getting things done and freeing up my time...so you may in fact get an email from me in March informing you of a special sale. And if you miss it you miss it. People have I think at last given up waiting for another sale from Mortco at these prices. And I warned people that prices were going up, but people are used to gimmicks so they thought prices would go up so we could mark it down and call it a sale...lol...no: prices have actually gone up. Same with my passwords...there might be two sales this year on them and they are not going to happen again...a Birthday Sale for the elder boy when he turns TEN...he won't turn ten again so don't expect a sale like that again...although the younger says we will also have a sale when he turns ten but that years from now, so I wouldn't wait...
I like this video because you can watch them learn in real time. Play along don't just watch math is not a spectator sport. Also would it be as much fun if it was just me and one student? This is why I like groups. More is learned faster. I have used this game for years and I can tell lots of different stories about kids learning with the number line and getting confused and then this game clearing things up. Also the explanations in Supremely Simple Subtraction work wonders.
I have had cases where the older sibling was taught with a number line and the younger learned with blocks thru me and the younger sibling blew the older sibling out of the water when it came to test time on integers...eventually I will have ten Series C Manuals done, subtraction is book three in the series, book one will be "Groovy Games & Addicting Activities" of which what you see here is just one. Series A Games and Activities is completely free no email or other interaction required there, hard copy costs about $3.20 (plus shipping) from Mortco. Don't say I never gave you nothin'.
You can also use algebra and factoring polynomials to teach integers...but if you want to learn to do so, you'll need a password (then just go to advanced algebra on my website...or be good at digging around on this blog and the internet. Here is a page regarding the teaching of addition and subtraction and more that you might find useful and may have had a hard time finding on your own.
Note the girls are at no disadvantage whatsoever, and you may note I make an effort to call on the girls more than the boys. The myth that girls can't do math must be busted and laid to rest along side the myth that woman can't learn to read, permanently. That myth about women and reading was prevalent just a few hundred years ago in western culture.
You can also use cuisenaire rods to play this game, just mark one side with a pen and make that the negative side. No biggie.
A few testimonials:
"By the way, YOU ARE AWESOME! I actually clapped for you when you explained some concept soooo simply and clearly.It is fantastic!" ~K Ontario, Canada.We are excited for math today!!! ~amazed parents from all over the globe.First, I wanted to thank you for being out there and for introducing me to the Mortensen Method. I'm a new homeschooler who's been searching for Math under every nook and cranny of the globe. Worksheets I can make. Flashcards I can draw. Concepts and vision...now THAT'S something to pay for.
EDIT
Also, as a believer in the separation of church and state from an educational standpoint, I felt really at home at your House. Thank you for that, too.
EDITFinally, thank you, thank you, thank you for mentioning somewhere, somehow, in some side comment that I can no longer find in your fantastic maze of a world the work of Liping Ma. I immediately bought her Knowing & Teaching Elementary Mathematics and have been forever changed as a result. It made me rethink the way EVERY subject is taught, learned and subsequently taught again. I never would have even heard of her if it weren't for you. EDITI am extremely eager to start having my "oh, I'm just not good at math, never was" mind blown. ~PF USA
"I've paid a lot more for a lot less." ~amazed parents from all over the globe.
"Ps. Your parents teacher training is great!" ~EM, UK
"The training is crazy. No one is offering anything like it that I know of...and your price is crazy too." ~JC, CA.
"The amount of stuff you get for the money is crazy."~JJ, New Hampshire.
"Just got the Parent/ Teacher Password.CR wasn't lying when he said 1 page was worth the price. Get it for yourself to learn how to think math." ~KY, USA.
" I really like how you do math. My kids do too! We were having problems and you made math good and happier for us. I sincerely say Thank You from the bottom of my heart." ~CS, Ohio.
"So, I am absolutely flabbergasted by the stuff I am learning just hanging out in the House of Math like four to five hours (literally) per day! Before the little one gets up, I'm on. Nap time, I'm on. After bedtime, I'm on with toothpicks bracing my eyelids. Even before purchasing the passwords! It's like a crash course re-education, and I am infinitely grateful..."
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.
I do not recommend my Tumblr because there's sex, and "naughty" pics, and swearing and all manner of content for grown ups, along with controversial topics...but the other ones are fairly tame, although still not tame enough for the Christian Homeschool crowd.
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.
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.
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.
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.
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.
Here is a lesson that uses bases for practicing math.
This is again cross teaching or a compound lesson. I am not interested so much in the student memorizing what one number in base ten is in another base, I am interested in the student being able to grasp some basic concepts like numbers are made out of other numbers, a deeper understanding of place value, a deeper understanding of division concepts...how many times is a number contained in another number--that's basic division.
When we convert from base ten to another base like 2 or 3 IT'S FUN to do. Kids enjoy it if you present it correctly.
This blog post is just to give you some ideas. I'll add more video on this later...I made this video on a lark because a parent was having some trouble explaining division. Play with this a little bit and long division will be a snap. I have lots of other videos on long division and using algebra to teach not only division but the other basic operations as well. Algebra is just generic math.
This video stops before we get to the repeating decimal. As I was doing this I was thinking too many concepts at a time. Keep it simple...next time we come back to this we can take it a step further and see what happens when we divide by sevens or nines...for not finding out how many time one number is contained in a another number with division should become much easier after converting to bases where you have to think about multiplication and subtraction with different numbers. For example converting 100 into base two...we don't need a 128, but we do 1-64, 1-32, no 16's, no 8's one 4 and no 2's or 1's...so 1100100. When you are a little kid that's a lot of thinking. But it makes sense and they can see that what they are basically doing is adding 64 to 32 to 4 to get 100...and keeping track with symbols in certain places...that one in the middle of the zeros means one four. Converting it into base three or 4 is also FUN.
I didn't get hung up in the details of notation, but instead focused on focused on the basic concepts. I assure you when they go do base ten or base x division it will be easier...and again doing division in base x makes "regular" long division easier too. Repetition is the mother of skill and memory but that doesn't mean you repeat the same thing over and over again. We want them to learn the 45 addends and their multiplication tables....this exercise practices all of that. For the little kids stat out with base two and maybe later do some base three. Do a few easy ones and work your way up.
I often start with base two and then make a table...from x⁰ to x10 across the top (largest on the left to smallest on the right) and then going down the right hand side binary, 3 to 10, 12 and then 16. Just making the table is a great exercise...do as much as you can without a calculator. Then it's fun to punch a calculator and get the answers, unless you are interested in the students practicing the computation. You might want to do it in stages over several lessons so it doesn't get tedious.
Here are the answers...
This gave me an idea for a password protected page called "solutions."
This post is mostly done, check back there may be more...Winter break is proving very challenging for getting things done....lol...
Prices for passwords are about to go up. Have gone up.
The sun is setting on the old prices.
These will be the new prices soon. As you can see prices are going UP. Use the buttons below to lock in your discount.
New Prices:
$20 A sitewide trail will last about 30 to 90 days and gives you access to everything but the training page. Anywhere it asks for a password other than the training page this password is it.
$27 or $49 A Sitewide password can be bought for 6 months or a year, it expires after one year unless you get a lifetime password which gives unlimited lifetime access to everything via two passwords. Up from $24.
$49 A Training password is only good on the training page, but that one page has hours of training on it...and more will be added. It is good for one year. Up from $15.
$79 You get both passwords if you buy them together for one low price...sitewide and training...will also offer an installment plan for this so you can make payments. Up from $39
There will be a few more password pages added soon too, geometry and some calc. Plus there are additional vids and pages added to the ones already there.
$249 is the new price for a lifetime password...you get both passwords and they never expire...will also offer an installment plan for this so you can make payments. Up from $100.
Those prices are a still a GREAT DEAL. People are constantly blown away by how much they get for so little money when they are used to paying a lot more for a lot less when it comes to math curriculum for homeschooling. I've been told the training page ALONE is worth the price of a lifetime password all by itself. I've been told the same about the value of just a few pages like percentages and sample lessons combined with Raymond's page, Dboyz' page and Sarah's page. There are a whole lot more passwords pages than that, some with books/pdfs too. I've also been told mine is about the best FREE site out there when it comes to explaining math and explaining how to teach math...don't forget you get tons of FREE stuff.
Take advantage of these prices for a few more days.
Not to mention there are several manuals and books there also--all for ridiculously low prices (and some are FREE like this.)
These LOW PRICES will end SOON
so take advantage of them NOW:
SALE PRICES
Too funny. I am getting emails asking if the Lifetime Pass really gives a lifetime of Access to
BOTH
Passwords.
LOL! The answer is YES. And yes, it is quite an outrageous deal.
People are thinking it's 100 bucks for a lifetime pass to either the Sitewide Password Pages OR 100 bucks for life time access to the teacher training. For 100 bucks you get BOTH, as in two passwords.
Prices even when I have sales will never be this low again. Even when I have a 50% OFF sale, half off will still be more than these "stealth sale prices" which are the current prices you have been enjoying. I'm not kidding: these prices end SOON. You will start seeing the buttons on my site and blog change...and shortly this page will be the only place to get the low prices.
*I can't put the plastic on sale because I don't own the plastic. I expect prices will go up again eventually on books and blocks especially as shipping prices continue to increase. A lot of you are waiting for a sale on those...lol...I will let you know if they have a sale and when i tell you it's a real sale for a limited time perhaps this time you will believe me.
**Have a few password protected pages to build vid is already shot and edited and mostly uploaded just have to build the pages one for subtraction to go with the new manual, one on geometry and another on pre calc, and also one on derivatives. Also Series C, Supremely Simple Subtractionwill beIS out SOON, it is almost done, just have a few simple edits to do...a full color, easy to understand subtraction manual.
"By the way, YOU ARE AWESOME! I actually clapped for you when you explained some concept soooo simply and clearly.It is fantastic!" ~K Ontario, Canada.We are excited for math today!!! ~amazed parents from all over the globe.First, I wanted to thank you for being out there and for introducing me to the Mortensen Method. I'm a new homeschooler who's been searching for Math under every nook and cranny of the globe. Worksheets I can make. Flashcards I can draw. Concepts and vision...now THAT'S something to pay for.
EDIT Also, as a believer in the separation of church and state from an educational standpoint, I felt really at home at your House. Thank you for that, too. EDITFinally, thank you, thank you, thank you for mentioning somewhere, somehow, in some side comment that I can no longer find in your fantastic maze of a world the work of Liping Ma. I immediately bought her Knowing & Teaching Elementary Mathematics and have been forever changed as a result. It made me rethink the way EVERY subject is taught, learned and subsequently taught again. I never would have even heard of her if it weren't for you. EDITI am extremely eager to start having my "oh, I'm just not good at math, never was" mind blown. ~PF USA
"I've paid a lot more for a lot less." ~amazed parents from all over the globe. "Ps. Your parents teacher training is great!" ~EM, UK
"The training is crazy. No one is offering anything like it that I know of...and your price is crazy too." ~JC, CA.
"The amount of stuff you get for the money is crazy."~JJ, New Hampshire.
"Just got the Parent/ Teacher Password.CR wasn't lying when he said 1 page was worth the price. Get it for yourself to learn how to think math." ~KY, USA.
" I really like how you do math. My kids do too! We were having problems and you made math good and happier for us. I sincerely say Thank You from the bottom of my heart." ~CS, Ohio. "So, I am absolutely flabbergasted by the stuff I am learning just hanging out in the House of Math like four to five hours (literally) per day! Before the little one gets up, I'm on. Nap time, I'm on. After bedtime, I'm on with toothpicks bracing my eyelids. Even before purchasing the passwords! It's like a crash course re-education, and I am infinitely grateful..."
Part of what makes this method so effective is the idea of compound lessons. Why learn "one thing at a time"? One thing at a time is great when introducing concepts...but once concepts are understood it's more fun to practice more than one thing at a time, which is why I emphasize compound lessons. And as you can see using base ten blocks to do it makes math fun.
A six year old factors x² + 11x + 30 all by himself and celebrates with his magical math microphone.
People ask me what they should get. Get a combo kit. A set of Multi-Tens and a password or both passwords...and you are good to go. Seriously. That's it.
In this hour we practiced mostly addition and multiplication but we did activities that were fun to practice them rather than doing worksheets over and over again. Using worksheets to memorize multiplication facts becomes counter productive at some point.
Just building addends over and over again would make math anything but fun. So even with this activity which by itself many kids find fun, we spice it up by racing your brother or mom or who ever happens to be around. Then we build some pyramids. All kids can benefit from building pyramids, the benefits are manifold. You get fine motor skills, addends which naturally include addition and subtraction skills, and the all important repetition which puts the facts in the memory for instant recall later...
Here the older boy is feeding his mother and brother combinations for their pyramids. and supervises the construction. They are building 11's, later we could build and find patterns with 11's.
Pretty soon he gets in on the base ten block building action. And his little brother hands over some combinations...sometimes we build all 45 addends at one sitting but today we just did all the ones from 8 to 10 and then 11's and 12's. How many math facts is that?
Children are always quite pleased when they complete one of these...or several of these. Sometimes we build towns or cities or temple complexes or moon bases (or whatever is in their imagination), made entirely out of pyramids built using base ten blocks, but today we played algebra which will give us addends and multiplication too. Started out with problems like x² + 7x +12 and worked our way up. We started there because he already has some experience factoring polynomials and I wanted to start easy...then we went on to x² + 8x + 12, and x² + 8x + 15, x² + 8x +16...Went thru several with 9x then on to 10x, those polynomials have lots of combinations.
x² + 9x + 8 you get addends for 9, 1 and 8, and 1 x 8 = 8.
x² + 9x + 14 you get addends for 9, 2 and 7, and 2 x 7 = 14.
x² + 9x + 18 you get addends for 9, 3 and 6, and 3 x 6 = 18.
x² + 9x + 20 you get addends for 9, 4 and 5, and 4 x 5 = 20.
You don't have to do every single one in order...mix it up and have fun. I did a couple with 10x like x² + 10x + 16 and then x² + 10x + 24...didn't do x² + 10x + 25...which is a good place to start if you want to go down the square numbers and square roots path which are made plain and EASY with base ten blocks. I had a mom tell me they completed the square with 24 once. I said go back and take a look at that...24 will complete a rectangle but certainly doesn't complete a square. 25 would complete a square...and completing the square is quite a useful skill to have later on when you are graphing polynomials and want to easily convert to vertex form.
Playing with squares and radicals are also fun math activities where you can compound the lessons and learn algebra, addends, multiplication, square roots and more. You decide the emphasis depending on the student. For some older students who are supposedly past addition and multiplication because of their age you can use these techniques for remedial math without them even knowing it.
Instead I gave him x² + 10x + 24 which he got pretty easily but then I gave him x² + 11x + 24, which is a challenge at this age when they are still learning their times tables. You can see he figured out he needed 8 and 3 to make it work.
Then I gave him a challenge. x² + 11x + 30...the dilemma after he figured out it was going to be (x+5)(x+6) was finding enough fives or sixes....they were being used in the pyramid...and he found that he could count by 5's but not by sixes as easily...remember this boy is 6 years old, he hasn't mastered his 6 times tables yet but he will....and there won't be tears or frustration. It will be part of fun memories spent playing with his mom instead of being angry at his teacher because of yet another worksheet.
After a little fooling around he decided to make 30 with 6's...which meant he was going to have to bust up his pyramid.
Completing the corner was important to him, later you will find students especially older students who know their times tables skip putting the units in because they already know 5x6...and that 5x6 is the same as 6x5...when they are younger this is still a fun discovery.
Challenge completed! It's time for some celebration which is where we came in. Also some high fives with mom never hurt nothin'.
This lesson took place way back in the beginning of October. Just got around to finishing it here. In this hour we basically practiced math facts in a very disorderly fashion...we didn't just do a bunch of addition or subtraction for an hour. We did both AND we did multiplication and some division AND we factored polynomials but the algebra was just along for the ride...as you can see it wasn't scary or hard and I used it to teach concepts and facts...most teen-agers I know FAIL algebra right at this point because they don't understand the distributive theory and never saw a polynomial until they were 12 or 13 years old...
Positive memories and positive associations with math are so important i don't have words. Wouldn't you rather have your child's or student's early childhood math experience be like this instead of rife with tears and frustration? They won't all be diamonds but more often than not you will find YOU the parent or teacher can make math fun and teach a whole lot of math all at once in compound lessons like this.
Want to get the materials you see in this blog post? GO HERE.
Therefore lessons were developed for each class and each child in the class on subject matter at hand, in this case math. There was no cookie cutter approach. Even the books he developed were made with the understanding that the student picked where to start and the order. All books were to be completed but how and in what order was up to the individual student. And yes it's a hell of a lot more work, AND the education is far more effective and superior to what currently passes for education in the public school system of the USA. This year's class is not the same as last years class. How is it possible that the lessons would be the same?
"The essential thing is to arouse such an interest that it engages the child's whole personality." ~Maria Montessori
