Advanced Number Identification

Playing with the boys. Filling in the holes as I go.

There they are suffering through another math lesson.

The older boy stumbled at 21 + 7 (we were counting by 7's) he wasn't sure what to do when he already had a one for the units but not enough to make a ten...adding seven more didn't automatically mean 28 for him. He is careful, thoughtful, literal and meticulous...

Once I was playing fractions and I said "this is one to two" and he heard one two two and asked where the other 2 was...

1/2

More than once over the years the young ones have taught me they take you at your word, literally.

Anyway, here is a quick 5 minute lesson showing place value is well understood and they are well on their way to mastery of number naming. Soon I will begin correcting to one hundred seventeen, no AND. Then adding thousands and ten thousands and hundred thousands...just saying 137,596 is fun for them. As we start naming numbers we also talk about what the words mean just like you would when introducing any new vocabulary. How many is 100,000? How many is a trillion? (We'll get there later, but we will get there.)

Turns out most Americans can't conceive of that number.



What I didn't catch in the video was showing having two tens and a one and a seven, or two tens and a five and a three etc...we talked about doing the addition without worrying about what the tens were doing...the sad thing is there are plenty of parents and educators that take these powerful blocks and teach addition and subtraction and place value and then stop there...look over this blog for algebra, fractions and more...

Again note that there are barely any symbols being used...but when we do use them they know what they mean. Later a fun math activity is to write the numbers and then get out the pieces...the fun part is writing with the markers. Other than that don't be slowed down with making symbols because the little kids don't have the fine motor skills to write quickly. Do that after they have played blocks and named lots of numbers.

I used manipulatives once they didn't really seem to work. I shot a gun once: missed the target, the gun didn't work. Same reasoning.


Here is a fun vid showing how scarily innumerate the average American is...only 21% get the answer right. We are now growing the deficit at 2 trillion a year. People say I need to keep the politics off the blog; however, those people miss the whole point of why it is I do mathematics.

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The Difference of Two Squares

They call it that because it is.

This is a good place to start with the toddlers because the blocks are bigger and easier to get a hold of...also conceptually students can see the problem with more clarity.


The sample lessons are here. Look for the one called "Difference of 2 Squares." The vid is 34 minutes long. Scroll to the bottom for this one. As you may or may not know your password opens up a bunch of pages not just that one. Several people have told me that one page is worth a lot more than 3 bucks but so far only my friends in Namibia have been kind enough to actually put it writing.

Here we get into some very simple analysis of the blocks:

These very same questions have gone on in teacher trainings and it has at times taken me a lot longer to get a room full of adults to have the same light bulb go on as it did with the 6 year old after just a minute...literally. Watch. Sadly the camera was not pointed at his face when he had his ah-ha moment. YOU have to explain and show them and ask questions that they answer themselves NOT just tell them.

"Here: memorize this. Here is the formula. Now go do it." DOES NOT WORK. 20 years later and not much has changed except things have gotten worse...

Here is an opportunity to change. Start by going to the house of math and watching the vids or if you are more advanced break out three bucks and get a password...

x² - 25 = (x + 5)(x - 5)

Is obvious to these kids: they can SEE it. No big deal. The concept of zero is being introduced and later when they see zero identities it won't be scary or confusing just really, really obvious.

x² - 1 = (x + 1)(x - 1) and x² - y² = (x + y)(x - y) are also easy once the concept is understood. Several more impressions and it will START to be internalized. One of the main problems with high school and college courses is the fact that they don't go over concepts enough times (if at all) so the formula is stuffed into the short term memory recalled for a test and then forgotten. You also get to pay thousands per credit for the privilege.

Also added to their quiver will be adding zero to help with problem solving. Math concepts are never beyond a child if presented at the child's level. The next thing is negative expression and very shortly I was able and will be able to let them build and count problems that high school teachers will consider advanced. And we got there in baby steps...by the ripe old age of 4 in one case and 6 in the other...I have done this with HUNDREDS of students over the years. I know it works...we are past the testing stage. Soon there will be some pdf's with more evidence if somehow you can't believe your eyes here. Newspaper articles from 20 years ago and such.

Factoring Polynomials For Fun At Four

Here is the last 90 seconds of an hour lesson...


To see the whole lesson click here.

We just keep getting bigger and learning more math facts...building the rectangles is easy by now counting them poses the challenge...

Other systems wait far to long to introduce algebra, here I use it to teach other math facts. People are starting to notice these boys can count...your kids can be math geniuses too, and YOU can be the one who makes them that way...just get started. Watch vids for free on Youtube, go to CRHOM there's lots of stuff there...when you've burned trough all the free stuff in a few months get a password and check out hours of lessons which are free but for three bucks they are practically free. One page alone has several hours of vid on it.

The idea is to quit procrastinating, months gone by are months lost that could have been used to make multiple impressions on your kids/students. They need LOTS of repetitions to internalize math concepts and math facts...then they have instant recall of simple things like 4x7 or 7+8 but more importantly understanding of math concepts and how to apply the computation to problem solving.

Here we are doing addends for nine AND 10, 7 and 2 is 9, 2x and 7x are 9x, and 1*9 is 9...and the x plus the 9x is 10x...you can find the video on the sample lessons page...the mind wants to work fast, and factoring x² + 10x + 9 can teach a bunch of stuff at once...not just algebra and not just addends. Lastly they can see that (x+1)(x+9) = x² + 10x + 9

Many parents and kindergarten teachers are afraid of math like this. So of course the kids never see it until it's way, WAY too late. Parents got an "F" in algebra, teachers memorized enough to pass the test but hated it and now the 5 year old is going to have a fair shot and learning to enjoy math or not...somewhere along the line we have to break the cycle. All I can do is fill the pond with water. Horsey thirsty: horsey come drink. Better yet dive in and go swimming, the water's fine...

I hear it from parents all the time: "...what if I do it wrong?" Just play...there is no wrong play unless you are actually hurting somebody with a stick or something...other than that: play math! You can't get it wrong...even if you get it wrong, that will be a stepping stone to getting it right. Watch the vids, the blocks make it visually obvious for the novice and professor alike. Many "math people" are amazed because they can finally see what it is they know how to do...others are like, "...doesn't everybody see it this way?" And are amazed the answer is "NO!" (Actually that should come with an expletive not just an exclamation.) You might want to share these posts with people you know who have kids or teachers...they'll thank you for it.

Math enrichment for the masses is what this is all about. Here is a guy having fun with his daughter: math fun.

Once they are comfortable factoring and playing with with these, it's time to move on to negative expressions. See next post.

Factoring Fun With The Wee Ones

Little boys doing math, you can see their progress, and how they enjoy being mischievous as they are doing their lessons. Several inside jokes regarding counting can be observed. I especially enjoy teaching the 4 year old because he tests MY abilities every time.

You don't help them by doing it for them. Let them do it for themselves. Remove the no from the lesson...let them discover for themselves, teach them that failing is part of learning, and they they aren't wrong just getting more information. Tell them what they have not what they don't have...the basic concepts, I constantly remind myself of these things as I go along.

As a parent or teacher of course you want to show them how or help them when they are struggling to get the answer, but if you love them, let them do it themselves. You couldn't possibly do their walking for them, you could catch them when they fall (or kiss and make it better afterwards) and show them how to walk but the child has to get up and walk. It's the same with the math or any learning you can't just give it to them and expect them to know it, they have to discover for themselves. And when the light bulb goes off the satisfaction brings a smile every single time. Learning is fun.

Balance this by putting them in a situation where they cannot fail. Nothing is more cruel than a trick question or a question where they don't have enough knowledge to answer...it is frustrating and exactly not fun. Some teachers confuse this with "a challenge." Keeping it challenging is important and those challenges should come AFTER the child/student has attained a level mastery, occasionally on the way to attaining mastery but remember this ladder and the concept of degree of difficulty.

Which ladder you you rather climb?

In the half hour video which is on the sample lesson page the 4 year old exhibits some of the exact same thinking that many adults across the country did during my travels. He counts more than just the sides, he counts by fours instead of ones he is unable to move the pieces easily to form rectangles at first...but all of these things will be easy for him within the year...he's only 4. What is obvious to adults is not always obvious to children, your job is to make it obvious and let them discover it. Unlike the adults he doesn't have any judgment of himself when he gets it wrong or when he isn't getting it right, and he learns quickly from his mistakes and uses the knowledge instantly to help him solve other problems.

On the other hand, his brother who has more experience can see the answers easily and watching his brother really cements the knowledge in for him as he is dying to tell him the answers when the 4 year old doesn't get them right away. It was also fun to see the younger brother insist on making his different from his brother, different but still correct.

There is a lot more going on with this factoring lesson for me than just teaching them addends and multiplication.

He is still having fun learning and playing. Imagine where he will be with his understanding by the time he is 7 THREE years from now, 158 weeks away...300 or 400 lessons away...of course multiplication will be mastered by then, and all 45 addends and fractions and algebra and more. And I will be an even better teacher then than I am now because he will have had a chance to teach me so much more too.




The half hour lesson is available now with a password at the House of math. Factoring polynomials really is child's play, it's a shame more children don't get to play math this way and are relegated to addition and counting at this age.

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Time To Get Negative.

2x² + 5x + 3, sure, but what about negative coefficients?

I am constantly asked how to show and factor or work with expressions like

x² - 25

or

x² - x - 6

and some people start with a presumption, "That's great but I bet you can't show negatives very well." Well enough to get this autistic kid to get it. Or "...that's great but what about trig?" What you have here is a uniform methodology for the visualization of mathematics...not just the positive part not just the rectangles. Eventually there will be the derivation of πr² up on the sample lessons page, that 1/2 hour alone will be worth the price of admission. There are quite a few vids that I am told are worth the three bcks all by themselves. I am also told by marketers that the "problem" is the price is so low that people think there's no values there. I mean really, what can you get for 3 bucks?

Hours and hours of instruction that's what. Plus PDFs. Did I mention the PDFs?

I raised it from $1, apparently $19.95 is the going rate. MONTHLY. When I start getting some editing and some other paint and polish I will be raising the rates, meantime take advantage of the ridiculously low prices, NOW. It won't be long, this blog is already 3 years old, if you look at the first posts there were barely even pictures...lol...seems like yesterday.

Anyhow, here is Philip getting ready to go negative. Note how he is less than enthusiastic, because he has had bad experiences with integers due to that thing called the number line. I have lots of great stories about children who were taught about integers with this methodology compared to the way they did in school. One where the younger brother started solving problems faster than his older sister who "had learned all about negative numbers in school" but the method she had been taught was confusing and laborious...after seeing what her brother had been taught by me she said what most people say upon learning math this way: "I wish I'd had the blocks when I was learning this..."

For example:

Seems it would make sense to use blocks to teach about squares and the difference of two squares, or square roots or factoring...but they also come in handy for trig, pre-calc, and some basic concepts in calculus which I may never get around to here because there's hardly demand for it...well not nearly as much as algebra. But once you SEE an example of a derivative many light bulbs will start going off. Anyhow, once we are comfortable with factoring positive expressions THEN it's time to get NEGATIVE:



I see so many people who want to do too much too fast. "Okay, since they got that lets do this..." Remember degree of difficulty. Also the other thing to remember is you don't want to use the blocks for every single problem. The point is exactly the opposite...where you don't need the blocks once you understand the symbols anymore than you need pictures in your novels...but they were REQUIRED when you were first learning to read.

When you get to the Sample Lessons Page just look for the tittle "Show me the negatives." There are plenty more example on the password protected screencasts page too...going all the way up to 3rd and 4th power algebra.

BTW: I'd appreciate if a couple of people who do have passwords would comment on their experience with the password protected pages. Is it worth the 3 bucks or 12 bucks or what? If not here than on the facebook page and I'll screenshot it an paste it here.



Via email:

Hi there

Just read your blog where you ask for feedback about the password protected pages.

I visited once or twice with the password below, and the pages are great! The videos/screencasts are especially helpful. My only problem is that here in Africa (Namibia), our bandwidth is not enough to watch the screencasts without constant buffering etc. Far better for me is to be able to download the videos to watch later (and I might add, watch again and again!)

I have downloaded all your You Tube videos which are so helpful. Is there not some way that you can make it possible for us to download those screencasts?

OR, if you had some kind of full blown E-book/video course with an entire curriculum (k-12) in it to download, I’d definitely buy it. (?)

Anyway, thanks again for all the stuff that you’ve posted in various places already. I really is great!

Regards
Carol

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Math Concepts, Conceptualization vrs Memorization

Here is a short vid showing the wee ones doing a little math where you don't have to be there you can set it up walk away and come back and check it...then do more, walk away and check it. Math enrichment for them also means understanding what the powerful machines we have built are doing not just pushing buttons...I would be willing to bet that this six year old understands square root and what it means better than a lot of high school kids and even some college kids...

At this age just using a marker is fun in and of itself...the whole thing was a fun activity...took up about an hour of their day, it could have been shorter or longer depending how much fun they were having and how long their interest was held.

What you see here is a short part of it, but enough to give you the idea. I set up trays of blocks for them to count three different times...some days just one set is enough others times more or less...depending on their mood. Make it fun, not work...stress the concepts not the facts, mathematics is NOT computation. Remove the no from the lesson. If they give an incorrect response make them count again; tell them what they DO have not what they don't have, change the thinking from "wrong" to "acquiring more information."

Remember, it takes 18 exposures to get information back out again. We know that with one exposure the information is indeed stored but retrieval is hard, but after 18 exposures we can get more information from short term to mid term memory, and with more exposures we can move it into the long term memory and with yet more exposures we can make that information available for instant recall. Begin exposing your students to mathematical concepts EARLY. You will need to keep exposing them year after year for them to attain mastery and instant recall of things like addition and subtraction facts, multiplication, division and so fourth, but again you haven't taught them mathematics per se, just facts and computation skills which are how we do mathematics.

"Mathematics is a language plus reasoning." ~Richard Feynman

"Reality is consciousness, consciousness is expressed with language. Mathematics expresses reality numerically." ~me, standing on the shoulders of Terrence McKenna and John Paulos. Nanos gigantium humeris insidentes.

They have played with squares and rectangles before counting and building, here we begin introducing some symbols, later we will introduce more concepts and symbols so that we can write simple sentences like (3)(6)=18, 18÷6=3, 3x=18 and the symbols will make sense.

Same with building addends: 6+4=10, 6+x=10 will be simple and obvious and when explanations involving math terms like "additive inverse" are encountered they will also be understood even though they are cumbersome and oblique to most math students under the age of 12. I remember having 4 boys in 6th grade all bewildered, upset and offended by a set of problems like this:

5 + x = 14........x - 7 = 4

3x=24.............6x=24

3x + 5 = 20.......2x - 8 = 12

3x + 3 = 2x + 7 etc

It took about two sessions to clear all that up and get into negative expressions and I earned a couple hundred bucks in the process. (4 x $25 x 2) and people cannot understand why I find it all so ridiculous now...yet the parents and teachers both failed to explain it in a way they could grasp easily...and in the case of the parents some didn't even try, as soon as they see algebra they throw up their hands and say things like "well, I was never good at math so..." or "I get it but I can't explain it..." or "I don't remember any of that stuff even though I passed calculus with a B"....and are shocked when I tell them I failed calculus. FAILED IT. Not even close. Good thing I did. I can feel their pain and understand why it is they don't get it because I have the benefit of having been taught both ways. One way works and the other...uh, not so much.



These same kids play with 3rd power algebra, fractions, percentages and more. The ability to do all of that consists of countng to 9, being able to tell if something is same or different or not and being able to identify a rectangle.

More sample math lessons, tools and information are available at the house of math.

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Addends, Pythagoras and Math Fun

THIS IS A GREAT LESSON

The 36 minute vid requires a password and for 3 bucks (or 12 bucks for a year pass) it's worth it, if I do say so myself just for this vid alone. I just watched it again. It should really bring home certain points in the method and HOW you use blocks to reinforce the concepts. And that same password gets you onto pages with lots of worksheet PDF's and HOURS AND HOURS more video so you basically have no excuse for NOT using your manipulatives to teach math. All kinds of topics are covered and more all the time...

Here is a short clip from a tutoring session where we took it easy on a Friday afternoon and played...but it was serious play where we learned addends fooled with a triangle, learned lots of math concepts and worked toward mastery...of multiplication and addends using addends to count count by 6's and 7's well past 6x12 and 7x12.. All 45 addends and multiplication tables need to be mastered for instant recall...this will make all the other mathematics easier...and fun. In order to do that you need to make many, many impressions on the mind to build the nuero-pathway to that information. You'll see we go over 7+4 many times in this video...next time he comes back 7+4 be easier to recall and with a few more impressions it will be instant...like 2+2...all 45 need to be mastered.

This is a short segment of a lesson that's 36 minutes long at the house of math! It is a GREAT lesson if I do say so myself...you will enjoy it. Teachers will learn more about the lessons, students will get practice with understanding square root and what it means, we build one triangle, use a protractor, but mostly addends and their many and varied uses for making math EASY.

Check out the sample lessons at the house of math!

OR

You can burn it in there the old fashioned way, the way they do it at some learning centers with math worksheets and timed drills where the facts are repeated over and over again. This is effective BUT you may lose conceptual understanding and it compartmentalizes the information to the point where some students may have a hard time understanding how it all fits together, further you risk burning students out and creating a negative association with math...and just surveying the state of mathematics in this country how's that working out so far?

As you will see at the end of the full length video it's simple to tie it all together...and it's well past time for a different and fun approach.



Here is a little more from the lesson which actually happened before we shot the promo above...



If you want to see the full lesson, (you need a password). One of the things we did was count by 7's, and 6's well past 12 times, and I showed him how we could use addends to do it, we also fooled with a Pythagorean Triple and busted out a protractor to measure some angles...

Here is a two page test he did earlier in the week. Go here for a screencast covering these two pages. The screencast is titled Algebra Test. In the screencast they aren't sideways...

It amuses me no end that teachers and parents cannot understand how playing with blocks can lead to understanding mathematical concepts on such a profound level that 3rd degree polynomials eventually present "no problem." I am doing my best to remove the mystery and lay it as bare as possible...mostly for free. This system works, it's not an experiment it WORKS. It will make crappy math teachers into good math teachers and good math teachers into GREAT math teachers...it allows you to let your students see what the symbols mean. Therefore you can manipulate them...


http://www.crewtonramoneshouseofmath.com/


http://www.facebook.com/Crewton.Ramone

There are now hours of lessons, sample lessons pdfs for down load available with that same password. If you get materials through me you get a year pass to my sites if you already have materials or if you just want to see more, a start is 3 bucks, this gets you 60 days worth of time, for 12 bucks you get a year pass. You may need that much time just to get through the host of information available...and there's more going up every week.



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4 Year Old Factors Polynomials No Problem

Here is part of a longer video that you can find on the Sample Lessons Page. In it we see two little boys on a hot Hawaiian day playing algebra. You can see all the learning that takes place in this clip...they learn counting, addition, multiplication, factoring and algebra...and you can see it's fun and satisfying when they get it right.

God made it that way. Learning is fun. You can see when the endorphins go off by the expressions on their faces...you can hear the light bulbs going off in other videos with older students...ohhh, and ahhh, and "I get it now" are your verbal clues big smiles and clasped hands are physical clues.



Some day I would like to have a directors cut type session where I can pause the vids and talk over what's happening. The Mortensen Math methodology makes it easy for little kids to play math, it really does make math child's play...it's simple, once you understand the basic concepts. It's so simple some think it's magic, it's not magic: it's mathematics...and all we are doing is counting.

Too cheap to spend 3 bucks on a password? Go here for a FREE one hour overview on how to teach math using manipulatives, specifically using Mortensen Math.

Crewton Ramone Overview of Mortensen Math

Here is one hour covering various topics in math using the Mortensen Method.


Mortensen Math Video: The Amazing World Of Mortensen Math. You Can Get Straight A's In Math.




Here is the text of the Youtube vid page:

Visualization through our manipulatives based curriculum, is the means of translating intimidating equations to simple communication. Your children can get straight A's in math. We have 30 years of experience. VISUALIZING MATH IS THE KEY.

THE MISSION OF MORTENSEN MATH is to CHANGE the way students are taught. To help any student become an ACHIEVER, a BELIEVER in herself and himself. THE DIFFERENCE MORTENSEN MATH CAN MAKE: Students leave the "system" WITH THEIR DIGNITY INTACT. Students receive the GIFT of CHOICE. No one need be held back by a lack of confidence in math skills, causing avoidance of careers based on FEAR of math. Students now have the FREEDOM OF CHOICE based on their STRENGTHS in math to become Economists, Engineers, Robotics Developers, Astronauts, Scientists, TEACHERS, or even President!

VIEW MANY MORE Mortensen Math, JazzMath, iLuvMath.com Videos/Tutorials: http://vidgrids.com/mortensen-math

Visit Ben Rogers, Master Trainer, Teacher, Tutor for over 20 years using Mortensen Math on Maui HI and around the world:
http://www.crewtonramoneshouseofmath.com

Contact Us:
Toll Free USA: 800+4plus4=8! [800-475-8748]
Email Customer Svc: iLuvMath.Q@gmx.com
Web: http://www.mortensenmathdirect.com
Under Construction: MathNetwork.com, JazzMathChannel.com

Copyright 1981-2012 VJMCO, Mortensen Math World Headquarters, now iLuvMath, in Association with ReaL Love Song Media, Hollywood Ca

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Sample Lessons For Manipulative Math

Lola, Ruby and Opra help teach ALGEBRA.

Here is a bright 9 yr old girl, doing what most wouldn't consider math for 9 year olds and yet it's easy and fun with a little help from Lola, Ruby and Opra. As you will see we did a whole lot more than "just" factor

x² + 9x + 18

we also did some reduction of algebraic fractions and simple evaluations for x. Sounds complicated but this 9 year old never had any idea that it was hard...



The whole video is 21 minutes long and can be found along with some other exciting and fun vids here.

You can view them for as little as 3 bucks, which is what a two month password costs...or a year pass for 12 bucks...right now there are lots of math VIDEOS on that page alone lasting several hours. Everything from building tens to complex algebra...the page also contains links to a secret screencast page that has several more hours of vids on everything from percentages to 3rd and 4th power algebra, all presented in a way that even little kids can understand. All with one password. That same password unlocks pdf downloads too, including First Grade Math Worksheets, Fractions Worksheets and more.

If it works for them it will work for you...if you are a teacher or homeschooler or struggling student. I'm getting very good feed back...

Or you could spend 20 bucks on a crappy DVD filled with mindless entertainment...or a really overpriced (but delicious) sugar filled coffee drink for 3 bucks...if you get the small size. Feed your mind instead. And then you can feed the minds of others...of course there is a ton of FREE STUFF, pages and pages worth here on this blog and at Crewton Ramone's House of Math.

People on FaceBook ought to like this FaceBook page, you often get sneak peaks at video before they go onto the password protected pages, contests for free passwords and more...

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Crewton Ramone Expounds on The Math Methodology

Short screencast on using the methodology to teach a student math. The method is basically the same, get the basics down so then you can focus on problems, which are often one in the same...they can't do the basics so fractions and algebra are "hard" because they don't understand that math is just counting and fractions and algebra are just counting...and if you can multiply you can count fast and suddenly the math is EASY.

Use algebra to teach the basics like addends and multiplication, use fractions to teach multiplication...compound teaching makes things go faster. The student gets practice of basics like addends and multiplication WHILE they learn other math concepts like fractions and algebra...this is a simple screencast stay tuned for video of some sessions with him where he gets busted texting in my class...the full vid is here.

Addends Past 10

Here is a simple part of a lesson where we worked on addends with a 11 year old...he does math that is much more "advanced" by some standards but we know all math is, is counting so addends and algebra aren't much different on the "hardness" scale. Same goes for multiplication...the idea is to attain mastery in basic counting...addition, subtraction, multiplication and division.

The concept is simple: numbers are made up of other numbers. Here we practice the single digit combinations past ten...what you will find with any student of the mathematics is their knowledge has some gaps or holes in it. So occasionally it's good to go through and fill in some of the holes and gaps with fun practice.

Note that this is quite different from just memorizing facts or formula...they learn to figure out the formulas themselves, and if they forget the facts they have algorithms or tools to figure out the answers quickly for themselves if it is not part of their instant recall memory...and the more you practice the better the chance of it getting into the instant recall memory.

Adding some symbols to go along with the blocks certainly doesn't hurt anything. Notice it's just for keeping track and that he doesn't write out all the combinations, the blocks give a quick visual for that, especially with the colors for added instant recognition...we also did subtraction which is basically going "backwards and forwards."

If I have 15 and take away 8 I am left with 7 which is just the addend. You can also each them to just add 2 which is the 10 compliment for 8 to the 5 for a total of 7, or you could take five out of the 8 which leaves 3 and know that the 10 compliment for 3 is 7 or (leaste preferred) you could count backwards from 15, 8 places...students HATE the number line for a reason. It is ineffectual and can be confusing even when presented well. Knowing all 45 addends with emphasis on 9's and 10's will solve many problems later, in fact you won't just solve them you will avoid them altogether. I have had countless students who were failing algebra come to me unable to do simple addition and subtraction in their heads without aid of fingers or toes, not to mention multiplication...these addends lead to multiplication which makes all the math easy because it allows you to count very, very quickly....

Parents always ask me why don't you just cover the blocks why does it have to be a math bag (and why go to all the trouble to decorate the bag)? BECAUSE IT'S FUN. WHAT'S MORE FUN? COVERING THE BLOCKS WITH A PIECE OF PAPER OR GETTING INSIDE YOUR VERY OWN MATH BAG? Seriously: some adults are a sad shadow of the bright, fun loving, energetic, curious, infinitely inquisitive children they used to be.

Here as you can see is a youtube vid, with apologies to all my public school teacher friends who have to go home to view it. It's just a short (less than 3 min) vid where the unknown mathematician shows he knows some of the combinations without looking, without blocks or symbols (or fingers) just his imagination.



Find me on Facebook or Youtube. I'm told there are benefits to subscribing to youtube because sometimes I put videos up and then go back and un-list them as I put them on password protected pages. BTW lots more video has been added to the password protected pages...

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Autistic Integers

Here is the result of several lessons with factoring and integers presented in various manners:

It looks easy, but it took a long way to get here. You can see part of the journey as well as lessons on factoring negative expressions which is part of what I used to teach her to master her integers here at the house of math.

Of course in order to see that page you'll need a password. Passwords are cheap.

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Meet The Parents.

Here is a collection of Vids from the 70's, 80's and 90's...I got "involved" in 1990...

It's always interesting to see the what happened before. We have been higher than we are now and we have been lower...I plan to take it at leaste as high and as far as it has been in the past.

For those with really short attention spans or who are pressed for time here's 90 seconds:



Here we are going back in time:



Look how far we have come. Back in the day these vids were hard to make and expensive. Cameras and editing cost thousands. Now you can get a computer camera and other equipment all for less than $1000.00



Here is Jerry going over some simple problems using basic operations pieces that are no longer manufactured by anybody...one day we will revive them...the idea is not to spend so much time building the problem you lose sight of the concepts, getting out even 16 unites to build a square takes too long. These problems are whipped together quickly because he has the pieces handy and they are "stuck together"...meantime you can also draw them but make no mistake starting out in the concrete makes all the difference.



Also take a look at this promo vid from the 90's.

Find us on Face Book and be sure to go to the house of math for more on math, how to present it with manipulatives and make it fun.

Multiplication Math Town

Playing and having fun does several things. One of them is giving the child a positive feeling around numbers and math. I have more than a few students who fear math, or hate it. They come to me and have fun and I do my best to break that pattern but then they go back to school and the old pattern runs them over.  Just had a student tell me that she panicked when she took a recent test even though she knew everything on it and had even done some of the problems before...more than once.


"I don't know it was weird, I knew it all and I still froze up and got scared again."  These patterns are powerful and hard to break. Now imagine how much worse it is to NOT know everything and have those feelings...the point is if they feel good about math the learning comes easier. Math should be fun. When it's fun taking a test is just showing off.

Feynman said, "Math is a language plus reasoning." That reasoning leads to critical thinking. 

 So for about half of the lesson we built tens. We did subtraction and then although she always asks for it, we did just about no algebra and she didn't write a single symbol. We worked on counting and then we worked on counting fast which we call multiplication.

 As she built each tower she had to count it. Sometimes she just followed my lead other times she counted on her own...

 The town starts shaping up and she tells stories about each building and what happens there as we go.

 As we play the town gets built and rebuilt and changes...every time we knocked something down on purpose or by accident we counted it all over again...with lots of laughter.

 Just keep playing and adding stuff and pretty soon it starts to look pretty cool.

 Fine motor skills are further refined, counting and playing go together. We are doing multiplication ON a table but we aren't doing multiplication tables.  I was asked about math flash cards or multiplication flash cards and I said, "yes, they are great but not yet!"  When they have their facts close to mastered, they are familiar with for example 2's and 3's, and when you ask them what's 3 x 5 and it's almost on the tip of their tongues THEN flash cards. Using them as a a tool to teach math especially with young ones can lead to some very big misconceptions like the symbols 3 x 3 turn into the symbol 9!! I saw this over and over again during my travels. The kids had no conception that it meant three 3s. Here it's visually obvious as Maria Montessori used to say.

EVERYTHING gets counted, the tens the hundreds, we add, we subtract but mostly we have fun. It's math enrichment, so it should be an enriching experience, not drudgery. Especially when they are little or pre-teen...

Here is a 10  min screencast covering the pics you see above and more:



Find us on Face Book and be sure to go to the house of math for more on other topics.

Special Triangles, SOH CAH TOA and laughs...

Here is a short vid covering special triangles, but it's a refresher not a lesson from scratch or an introductory lesson...so it kind of starts in the middle and assumes the student has some familiarity with the subject.

The camera work is, as usual not awesome, but you get the info. You can also start to see how it all goes together, with square numbers and expressing numbers using radicals. We also again have the five basic concepts clearly on display we are just counting we never count past nine only count stuff that is same, concept of same, using rectangles to make it easy to count in this case squares, and of course the concept of ONE: No Fun Get Back To One, in both making one side of the triagle one but also by dividing out the sin cos or tan of an angle to get one x or y which is the length of a side or hypotenuse. This is where we begin to develop critical thinking skills and reasoning the computation is relatively easy...as expressed in the teenager terms, "OMG that's all there is to it?"



You can build triangles using the blocks as sides and learn a lot about the relationships that way. Here is a screencast on Pythagoras' Theorem:



Note that one you understand this, the special triangles make all kinds of sense and you are just playing with making one of the sides ONE, then you can use algebra to make generalizations about them. This math stuff is easy...as long as you can see the pictures and the pictures make sense. The last building block is of course square numbers because the worksheet wanted the sides expressed as radicals:



Here is a little more on that:



Yet more on radicals:


And how to introduce these concepts to little kids:



Find us on Face Book and be sure to go to the house of math for more on other topics.  Hit the trig tab once you get there for more FREE lessons....but if you want to see all the videos and the lesson that got Garret an "A" and not just an "A" 100% you will need to buy a password. You can get a lifetime pass for just $250.00 or get a "subscription" for as little as six bucks a month.