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...

## Wednesday, August 27, 2014

### Want Fries With That?

Once I was doing some demo teaching for an eighth grade class of whiners. They would often interrupt lessons on algebra and factoring with questions like, "when are we ever going to use this?" or "why do we have to learn this?"...etc. Even though they were easily getting it with their base ten blocks.

My answer is the same everytime, "if you are working in fast food, you are right you will never use it but if you are working in engineering or architecture or the sciences you will use algebra just about every day. So I tell you what. Let's practice something else. Repeat after me, 'Would you like fries with that?'"

Stunned silence. From the back of the class, "This guy's harsh."

Later that same year in that same class they gave me a standing ovation...

Learn to use your base ten blocks.

anonymous said:

I make \$15 an hour doing work that actually requires my brain, if they raise the minimum wage and I'm quitting and finding a career flipping burgers lol

Take my job for example. You may call what I do “unskilled” or what a line cook does “just flipping burgers”, but that is because of a classist bias against blue collar work. I am a prep cook. Every day I utilize my knowledge of physics to successfully balance and carry multiple dishes and ingredients in my hands, as well as to lift objects that someone of my size should not be able to lift. I use my logical analysis skills to figure out which recipes need to be made first, and even then to further prioritize on a number of criteria, because it is paramount that certain items are ready before open and that all items are made as soon as possible. I use basic division and multiplication to determine ingredient amounts for recipes depending on how many times we need them made, which has been projected given the day and other criteria like weather that affect our guest volume. I will do this math across multiple measuring systems, converting up and down on two different scales depending on how a recipe is written. I use a knowledge cache of cooking techniques, which require studying and practice, to execute dishes to perfection and I must do it perfectly every time, or else it’s waste.

And the line? Try making 30 burgers at the same time. All of these have side dishes that guests pick from a list of five sides. All 30 entrees came to you at the same time. You’re on grill and hot sides, and you have a coworker on pantry and a coworker on hot box that fulfill other sides and entrees that don’t require the flat top, convection stove, or fryer. All of these have to go out around the same time, but you can only make two or three plates at a time tops. This is pretty complex time management man, especially when you factor in the fact that beef is ordered to different taste and you have to keep track of that too.

Judging by this question, you aren’t qualified to “flip burgers”.

## Tuesday, August 26, 2014

### Base Ten Blocks Make Algebra Child's Play

Base Ten Blocks Make Advanced Algebra Child's Play. For those of you wondering if the work I do with younger kids makes a difference when they are older...that picture was taken with some very young students (8 and 9 years) who at the time were learning much more about 8 + 8 and 8 x 8, and that 64 is square, than they were about algebra.

This post will eventually be on one of the password protected pages (Advanced Algebra) but you are getting these videos here for FREE. Eventually, this post will get buried on this blog and people will have a hard time finding it. As I have often said these posts get old but they don't get out dated...use the methods you find here on your students. They work.

And again if they work on little kids they will work on high school kids and college students too. The idea is to introduce CONCEPTS in stages and get comfortable with them THEN add more and a little more. It is good to start with something easy and familiar so they get the grasp of it..."it" being the concept or idea rather than deluge them with a huge amount of unfamiliar math all at once. This is what textbooks do. They put too much together at once and it becomes overwhelming and confusing.

Start with completing the square. I have lots of vids and pages devoted to that, making it easy and using it to teach children more than just algebra but also counting and dividing by two and addends and multiplication. But when the time comes they are quite familiar with completing the square and factoring. Being thus grounded, it's easy to add new concepts and more understanding. So lets begin with this:

This video is not listed so please don't share it unless you are sharing this whole post.

Being able to count by square numbers all the way to 25 is also a good skill to have...

Note that I start off with lessons on making squares and square numbers. Imagine that.
Being able to square numbers quickly and easily makes this vastly simpler for understanding because that part is out of the way as it were. So when we want to take half of the x and square it it's no problem (get it?) even if the amount of x is odd...as Forrest would say: "That's good, that's one less thing." [To worry about.]

Being able to square numbers that end in 5 is a good skill to have but rather than memorize some rule I show them where the rule comes from and math is less mysterious.

You may also note that using base ten blocks to make algebra easy has benefits where kids can see the relationship between squaring 35 and getting 1225, and taking half of 7 and squaring that and getting 12.25...a lot of older students just go, "OH! Well then that's easy..." Usually they hate any of the ones that have fractions in them...but that's easy too. I find fractions are almost universally a stumbling block.

After you've watched the first one up there lets go back and really get the concepts down.

So lets back up, keep it easy and start with something REALLY familiar and focus:

And then a little practice.

And a little more:

And now they look like the little geniuses they are and are ready to play with the quadratic:

This video is not listed so please don't share it unless you are sharing this whole post.

I spent another class where instead of dividing by "a" we multiply by "4a" to make it easier but that video is lost. You can see a stale presentation of it here though:

With the DBoyz I some questions and really got into why we complete the square with b²...

And now we are ready to start playing with ones that have more negatives...and instead of real roots imaginary ones and so on...what do you think? By the time they are in high school will this stuff be easy or hard for them?

And it all started with taking x² + 2x + 1, taking the x and putting them on the sides and putting the one in the corner...then moving on to 4x and 6x and 10x...with base 10 blocks they can see what they are doing get their hands on it and then when we move to mostly symbols it makes sense.

This is one of they key differences we find with kids who learn math using base ten blocks they can see the relations ships and math isn't a confused segmented set of mysterious rules. And then completing the square and vertex form are much more easily understood and relate-able, the students see how it all goes together. I have found that using base ten blocks makes things like distance formula, Pythagorean theorem, and the first trig identity go together in the students heads too...instead of being completely separate things.

Using base ten blocks in a step by step approach can make math child's play for your students too. Manipulatives make math easy and fun, it's just counting. I've tried to give a detailed explanation via the videos here but if I left something out or you have further questions please comment below...

## Tuesday, August 19, 2014

### Crewton's Math Manipulative Manifesto

 Math Manipulatives

Here is an article I wrote about math manipulatives for my website directing people to this blog. Some of the points here will be covered in more detail in the next parent teacher training.

Math Manipulative Manifesto
"Learning is not the product of teaching. Learning is the product of the activity of learners." ~John Holt

This blog is dedicated almost exclusively to showing you how to use manipulativess with your children at your house whether you home-school or not, and also to get you to use them in your classroom if you are a teacher. Note the lack of advertising, adsense, annoying pop up vids etc. The only things I advertise here are blocks, books, and passwords to vids and info.

While meditating it hit me why there is such a disparity of viewpoint between me and most of my "fans" regarding curriculum and organization. Whereas I see it all as just counting, others think of it in subjects, grades or levels or what have you, because the way you were taught was very compartmentalized.

It's been ingrained in you that FIRST you have to learn how to count, next you add next you subtract then you multiply then you divide next you do fractions etc.

What I'm saying and what this method teaches using math manipulatives, is that ALL that is, is counting. All of it. You're just counting. Since we are just counting, we can use division to teach it or we can use fractions to teach counting like addition and multiplication or we can use algebra to teach counting...most people think that in order to do division the student has to have learned how to multiply and subtract...NO. (Look at me! Breaking the rules: you are supposed to remove the no from the lesson.)

Students don't need to have gone through basic operations (addition, subtraction, multiplication, division) before they can do algebra, in fact algebra will teach basic operations. Division is also just counting and we can use division to teach a lot of math concepts as well as how to add, subtract, and multiply and they learn to multiply and subtract while they are learning to count. It's the same with fractions...or algebra.

Ask what is it we are counting?
"Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting." ~Ernst Mach

All mathematical questions boil down to "what are we counting?" When teaching math you can use division to teach counting or addition to teach counting or algebra to teach counting...you can focus on whatever you like but it doesn't need to be structured such that addition comes first and then subtraction, in fact you will quickly see it's very hard to separate the two and trying to do so may actually be harmful to their understanding.

I have sat in awe in grade schools while lessons on multiplication were taught without any reference to area, or division, or in some cases any reference to repetitive addition...just learn 7 x 8 = 56...and to this day it is amusing that 99.99999999999% of people I meet are wholly unaware that that division "thing" we use is just shorthand for a rectangle. Or what the equals sign means. Or where that percent sign comes from. Or that square numbers are square...but I digress.

The Mathematics is a language and it all goes together and shouldn't be segmented or compartmentalized to the point that the student is unaware that multiplication and division are inverse functions, manipulatives make that visually obvious. They will be able to see and understand this naturally...and then it's easy to point out to them, this is part of "directed discovery" you know what you want them to learn but you let them discover it. You facilitate this by putting them in a math rich environment.

The point is that while we are teaching basic operations we are just counting but don't get confused: basic operations is computation and computation is how we do math but math is much more than just computation. (The fact that I have to write that statement is a clue to the complete failure that is the current state of math education.)

There isn't anything more fun than seeing your own students or children learn something and have fun at the same time, and in knowing you are the one responsible for it. This is why some teachers are addicted to teaching no matter how poor the pay is and no matter how lousy the conditions are.

Math is the language of logic and reasoning combined with critical thinking skills. I have met many students who are great at computation but very,very poor at math. (Some of them go on to get degrees and then, ironically, attempt to teach others the math they don't really understand.

If you put the child in a situation where they CAN NOT FAIL, expect and allow for error, allow for self correction with direction...direct their discovery in a math rich environment: they learn math. They can't help it. AS an added bonus they have fun learning with math manipulatives and/or base ten blocks.

Give the child an algorithm for addition (wanna be a ten) that can be applied to multiplication and suddenly almost effortlessly (much to the amazement of parents and even veteran teachers) the students are adding and multiplying...multiplication is the first milestone because it allows the child to count quickly, once computation is easy the math becomes easy too because computation is how we DO math but again, it's not the math itself.

With computation mastery, math concepts that are understood can be applied to problem solving and answers are fun and easy to see. The combination of computational mastery and conceptual mastery combined with visualization is very powerful. The playful, curious attitude that problems are just games or puzzles removes fear and tears, and learning is seemingly effortless because they are having fun doing it.

Avoid the problems in the first place.
"Intellectuals solve problems, geniuses prevent them." - Albert Einstein

There is no greater joy for a parent (or any teacher) than seeing the ah-ha moments and light bulbs go off...it is especially poignant if the child had formally been struggling with math, but I prefer to avoid the problems in the first place.

The question should be "what kind of counting do you want to do today?" Or what kind of counting do you want to teach today? If you are a teacher. 1st graders as an example can learn division and thereby learn a lot about counting, and multiplication and subtraction...as well as addition...they can learn about fractions and thereby learn about addition, multiplication and division as well as concepts like SAME...the way we currently teach it children somehow come to the conclusion that rules have changed when we add fractions. They haven't. We can teach them problem solving, which at first is just recognizing same and "hero zero" and then "no fun get back to one"...all of which is just simple COUNTING even if they are little.

Please click on this link for more on "hero zero" and "no fun get back to one" and removing no from the lesson the other teaching concepts referenced in this manifesto. (Rant. Diatribe).

I've done lessons for 2nd graders on square roots...in order to do square roots we had to count the squares and the sides...so we learned skip counting, used addition skills to count 7 sevens which was more work than counting 4 fours and figured out what the symbol means--just count one side. We also learned about economy of symbol instead of 4 + 4 + 4 + 4 = 16, or even 4 x 4 =16 we could just use 4² =16. I wasn't just teaching square numbers I was teaching lots of counting. NONE of it would be possible without the use of base ten blocks. People are amazed that I go on to do lessons on Pythagorean theorem but they don't understand the part about it's easy when they can see it. I wouldn't even attempt to teach them any of this without math manipulatives.

Further students often never understand the relationship between Pythagorean theorem, distance formula and the first basic trig identity sin² +cos² = 1, it's just a bunch of stuff they memorize long enough to be tested on and then forget--never having made any of the  leaps of understanding or connections. My students avoid this because they've been playing with these concepts for years and baby step their way there instead of it being all new and confusing in all at once in high school.

What I have to do is get YOU to change YOUR paradigm and understand the way you were taught via compartmentalized, separate subjects, grades and levels might (just maybe, quite possibly) NOT be the best way to teach math, and is part of the reason the teaching of mathematics in general in the USA is an utterly abysmal failure. Most of you recognize that it is an utterly abysmal failure which is why you are here in the first place then the first thing you ask me is, "couldn't you teach and organize your blog and website more like the way we know doesn't work and is an utterly abysmal failure?"

### Base Ten Block Battle

Playing with base ten blocks. You can't help but make learning fun. Again building stuff over and over again because they want to shoot it down is more fun than worksheets. It is important to use two hands for optimum whole brain sensory input. When the student uses both hands more learning takes place easier, it's that simple.
Using base ten blocks to get addends mastered make learning math almost effortless. First they learn their addends which helps them add two numbers which is basic addition; which helps them add series of numbers which helps them learn to multiply which makes math easy because it allows the student to count quickly.  Math is a whole lot easier when you can multiply because it allows you to divide and discover patterns and a whole lot more. Problem solving and fractions are much more difficult  when the student can't do simple computation. Addends are the basic building block. Gets the kids off their fingers, makes addition a snap...also builds confidence. He built walls of 10 on down to 5 and made a little fort.
I think you can guess what comes next. Knocking them down is the most fun...why not use a nerf gun? We're just playing and having fun while we learn math. Kids will often build walls or set up addends over and over again so they can shoot them down...I wish I had video. That gun couldn't hit the broad side of a barn. LOL!
Okay, fort destroyed, clean up and on to some algebra where we played what completes the square...
Here he is putting 25 in the corner, to complete x² + 10x + ___, he had started from x² + 2x + __, then x² + 4x + __, x² + 6x + __, x² + 8x + __. Again the algebra is along for the ride, he is getting lessons in addends, square numbers and dividing by two...not memorizing formulas involving b/2a...when the time comes though those formulas will make sense...

***

Now onto his brother. Again we start with addends he got a lot more done faster using the tray.  The other way is "cooler" but usually takes longer. If you are playing at home time is not an issue but when you are paying 50 bucks an hour it can be. The one thing I will say about building the tower is that he gets more practice because the walls fall down and have to be rebuilt as you go...it took him a while to build the second story without knocking down the first story...each of those wall was built and repaired more than once. In the tray he does it once and moves on...
Except when he takes the tens out fo no apparent reason and had to put them back in again. AGAIN note the use of both hands because I made him do it...and reminded him verbally more than once...

He was quite proud of the finished product because it looks cool. Kids also find out that building walls out of addends are cooler to shoot at than walls all built out of the same block over and over again...
Then we factored some quadratics started small and worked our way up. First one we did was x² + 5x + 6. Here he is doing x² + 8x + 15. But what he is really doing is learning an addend for 8 and figuring out that 3 x 5 = 15. Also that 15 can be 5 threes or 3 fives...also some division concepts and as an added bonus factoring a quadratic. He is learning counting skills...just happen to be using algebra to teach them, could just as easily be using fractions. I use algebra because it is known to be HARD in kid culture so it builds confidence and self esteem in students like these who are having problems learning math at school
Now I made him get out two tens and a four and measure it with various blocks...he already tried nines...didn't come out evenly...24 is two nines and some more, three nines is too much...eights fit perfectly and he can see 3 eights is the same as 24...but with sevens 3 isn't enough and 4 is too many...and he counted out 7 x 3 = 21 and 7 x 4 =28...he wasn't wrong to get out sevens he was just getting more information and learning as he went. Soon he had eights, and sixes and fours and threes...and calculated that it would take 12 twos...quite a bit of math from just building a wall of 24...
And now he gets some base ten block battle action too. Here he is setting up 12's. Gets the addends for twelve and counts by twelves...note the use of two hands.
And then shoots the twelves.  But never did hit one with that gun. Got a nerf pistol out and made quite a few hits. Kids will usually make more targets and shoot them down over and over again which requires building them over and over again. Tom Sawyer taught me well. SO much more fun than doing a work sheet adding little numbers together. Plus you get fine motor skills AND a whole brain activity instead of just using the dominant writing hand. Here is an article that provides a clue.

"Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting." ~Ernst Mach

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## Tuesday, August 5, 2014

### Base 10 Block Book for Preschoolers & Kindergarteners.

There aren't a whole lot of base ten block books like this out there. This one is designed for young kids. The idea is you read it to them at bedtime just like any other story book. If you have children that are a little older, 2nd or 3rd grade they could read it to themselves. If you have children older than that check out this blog and website for lots of instruction using base ten blocks to make math EZ! If little kids can do it your highschool kids can too.

Now you can get this content packed base ten block e-book: Crewton Ramones Completely Cool Curious Counters' Kindergarten Compendium for just \$19.99. No need to buy a password (if you already have a password this book comes with, just go HERE and click on the picture or the big red "here.") If you don't, get this book and start learning math NOW.

No need to buy a password,  now you can get the book all by itself, I'll send you the file direct to your inbox. Until now this base ten book was only available if you bought a password. now you can get this book by itself.  Put it on your laptop, tablet, or reader or print it out.
As you can see it shows your younger children some crucial math concepts using base 10 blocks to make it easy. It helps you help them master their addition facts, introduces square roots, place value, multiplication and more. Give your child a head start in mathematics. This book makes understanding math concepts fast and easy. Mathematics is the gateway to scholarships, the sciences, and higher paying jobs. Get them started off right.
Read your children this book the way you would any other children's book except with this book they will learn math because base ten blocks make it visually obvious. For ages 9 and under but especially aimed at children ages 3 to 5. That's right PRESCHOOL, (even though it says kindergarten). They can see the math...take a look for yourself...and at this age you can read it to them over and over again.
Just like any language they aren't going to learn it all the first time you read it to them. They aren't going understand it all the first time but after a very few short weeks the concepts in this book will be understood because it's simply written, it almost rhymes, and it's full of pictures of base ten blocks, the same way any picture book for toddlers is.
Plenty of brightly colored fun pictures explain basic math concepts, that will put your kid well ahead of their peers when they get to kindergarten or preschool. Kids that can do even just a little math at an early age are considered SMART or advanced or even geniuses whether they are or not...but one thing people have noticed over the years is that if you treat kids like they are smart they will act like they are smart. If you put kids in a class known to be advanced they will usually live up to the expectations...the opposite is also true. Put then a class in SPED or the "F Troop" they will often live up (or down) to the lowered expectations.

I have been in plenty of second grade classrooms where many of the students don't know their addends for ten without thinking about it or using their fingers. Some of these kids have to think about it when asked what does five need to be ten?! Base ten blocks help get them off their fingers and into math.

Or how many left if you take three out of nine...? This book will ensure your kid isn't one of them. Basics like this can handicap your children for life. That's no exaggeration. At the other end of the spectrum getting them off on the right foot can give them advantages for the rest of their lives...
So yeah, it's kind of important. And it has been my experience that even if they hit third grade and they don't know their addends teachers don't usually take these kids aside and give them the extra help and time they need to master them. A downward spiral often ensues as these children never learn to add single digit numbers easily, then adding them over and over again (multiplication) becomes difficult and then they try to circumvent this with memorization of multiplication tables via worksheet and flash cards. Then long division is HARD and hated, fractions are poorly understood and mathematics in general becomes PAIN. Sound familiar? Statistically more of you had a poor experience with math than a good one which is usually part of the reason you found your way here.
The homeschool market is growing by leaps and bounds and many of those parents HATE MATH, but are smart enough to understand they need break the cycle...but don't really know how. Plenty of homeschool moms know they suck at math and are concerned they won't be able to teach their children math because they can't do math...well I'm here to show how you can both learn math together. This book is a good start. Lots of teachers are also using this book to help them introduce math to their young students.

This book

Makes math fast, fun and EZ.
Concept based.
Builds a firm foundation in addition facts.
Shows them how to add numbers with ease.
Introduces Square Roots
Problem Solving
Place Value
Multiplication

“My kids love this book.”
“I like it because it makes math easy for them to understand because they can see it.”
“We started out counting and before you know it he was doing some pretty impressive math for a 5 year old.”

More pics and stuff:

Crewton Ramone's Completely Cool Curious Counters' Kindergarten Compendium at the house of math. If you click this link you'll need a password to get it...remember the book is included with a password this page was built for those who just want the book.

here on blogger. Again this page will direct you to a password protected page. If you just want the book order below. Please allow up to 12 hours for delivery...I will email you the actual pdf.  The email you use for paypal is the email I will use unless otherwise specified. No messing with pop ups or download buttons unless you want to. [Haven't built the pop up page yet so...] But you will have to check your email...if you want to me to send it to an email other than the one you used for paypal put in the box.

 PDF Prices CCCCC \$19.99 USD SSS Prinable \$9.99 USD DDnDD \$19.99 USD PDF Page Only \$39.99 USD

Here is a short explanation of the options. Remember if you have a Life Time Pass, the book is INCLUDED, this page was built by request for those that just want the book and only the book...but of course I added extra options to the button just in case you decided to do a little math and figure out getting the book by itself might not be the best option.  Also by now there are people who have gotten an annual password two or more times...and every time they get a new one there's even more stuff than the last time...and their kids are still little. Probably should have gotten a lifetime pass. This button will change soon because the \$15.00 price for the PT training is limited to the first 50 paid.