Homeschool Math, Dboyz Playing Pascal with Base Ten Blocks

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


What basic concepts do you see in these three vids?



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

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



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



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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

And like this:

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

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

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

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

Instagram.

FaceBook.

Twitter.

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.

More Compund Lessons With Base Ten Blocks

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.

Want a FREE PDF of the polynomials that cover the 45 addends and the multiplication facts that go with them?  Click here: POLYNOMIAL PDF

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.

Shift your paradigm.

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?"

A Glimpse Into Video Tutoring

People always ask, "how do you do it?" or "what goes on in a video lesson?"

See for yourself:



For teachers and parents the other thing I was looking for in the video was the addend you get when you figure out the problem... x + 9 = 15 is the same as 15 - 9 = x AND the same as 1 + 5 = 6...one being the addend for the nine.

And here is some Algebra where we learn a lot more than factoring...she gets addends and multiplication and more:



Pretty easy, and fun. The magic (if there is any) is in the blocks and the way they speak to the subconscious mind...also we know there is power in including more senses in the learning process. Getting her hands on the blocks makes a difference...more sensory input = more learning, easier and faster.

If you are interested in video tutoring there's more information here but basically I charge the ridiculously low rate of $40.00...you need a set of blocks on your end and google vid chat or skype and off we go.

Yet More Manipulative Multiplication.

Make learning multiplication fun and easy playing with base ten blocks.

How to get multiplication mastered. You will have practice. There is no way around it. But you can make this practice fun. And you can make it easier by using some basic memory tools. The concept of a peg. And working in a more natural progression that complements the knowledge as it is acquired instead of just a jumble of facts in ordinal order.

Screencast with boys


Starting with Square Numbers and Pairs a lot of the multiplication can be understood. Then it is easy to add another for three's and of course 10's and 5's are easy so then it's easy to add one more or one less. For example fours can be thought of as one less than what ever number you were counting by fives...is of course four so 5 x 6 is thirty and one less six is 30 - 6 = 4 x 6 which is 24. Etc. This needs to be re-cut because the fan messed with the microphone but I STILL haven't had time.

Multiplication


You can use this same thinking with 9's and you can go up AND down with the square numbers...6 x 6 is 36 6 x 5 is 30 one less six and 6 x 7 is 36 + 6 which is 42 and the way you get there easily is with wanna be a ten, six needs 4 to be ten so it takes the 4 out of the six and we get another ten with two left over for 42...4 tens and two. Here is a screencast where I use addends to make multiplication easy for an Autistic student. If it works for her it will probably work for you.  Multiplication by nine is EASY btw. So easy FIRST graders can do it. Click that link and watch the second vid. More explanation:

Using squares as a peg


Multiplication is THE milestone in mathematics and should be taught early and mastered so that all the rest of the math becomes easy...

There are books and worksheets that can help but more than anything you want to PLAY and have fun not beat them to death with math facts that make them hate math and turn them off at an early age. Play with blocks, sing songs do a little each day starting when they are very young and by the time they are 6 or seven most of it will be out of the way. Waiting until 4th grade is INSANITY.

Here is a web page of the books Mortensen uses. The facts mastery books are simply more practice and to be used to reinforce the PLAY you do, which should amount to much more time spent than time you spend on the books.

Also do some web searches for "Crewton Ramone Multiplication"...there are tons of pages and videos on this extremely important concept.  And of course here is the Multiplication page at the House Of Math.

I strongly recommend you follow a lot of the links on this page. I know it's a lot but I can't stress how important multiplication is for making "the rest" of math easy and understandable because it allows you to see patterns and count very quickly. Then search "Crewton Ramone Multiplication" and see the plethora of pages and vids I've made.

Monomials: Play Find The Ones.

 Monomials can look scary and be confusing for some, but if you make it a fun game they are actually easy and fun. Once the concepts are understood rules can be discovered by the student, not given by you as things to memorize.

Here is a poor screenshot showing a breakdown of the monomial with pictures and symbols so that finding the one is easy.  Little kids enjoy this game and students with various disabilities can really understand what they are doing and more importantly WHY.


Here is a very short vid covering one problem:



Algebra doesn't need to scary or hard. It can be fun. Endeavor to make a game of it whenever possible...make it child's play.

At Crewton Ramone's House Of Math there are tons of games and activities to make math fun.

"You make math fun and easy. I am so glad to have found you! Thank you so much." ~ALH

Find us on FaceBook.

Fractions And Autism Do In Fact Mix.

Here is Sarah really getting the hang of adding fractions...now that we have the idea of it, understand the concepts now it's time to move on to something completely different and wholly unrelated, right?

Only if we were in publik skool. NOW it's time to reinforce the concepts and increase the depth of understanding by doing more of the same, only different.

Here we are spending a little time on improper fractions so we know what to do when she "fills up the one." We make a game of it. They are not problems, the attitude is not a chore or drills but see if she can figure it out and how fast. So we do one refresher addition "problem" and then play this game where we rename the pieces and figure how many ones are hiding in there.

This is the beginning of the longer video below so skip this and just watch that one if you aren't pressed for time, or if you just want the idea of it watch this:



In the longer vid we add AND subtract fractions and do some work with improper fractions...she is about a third of the way through fractions...next we multiply which is easy, and then divide...and ten go back and work on more addition and subtraction with bigger number where we need to borrow. For example 3 1/5 - 3/4...

People are now having the opposite problem used to be there isn't anything about Mortensen Math. Now it's there's so much I don't know where to begin or it's overwhelming. GOOD. Now your excuses have to change. Where to start? Where ever you like but get started. Watch a few vids a week, play, practice, repeat.

At that rate it will take you about half a year just to cover the vids that aren't password protected. Go faster if you like slower if you have little kids or SPED kids. Math is a limitless topic. My focus is K thru 12, primary and secondary mathematics depending on where you are from. If you work with Autistic kids or have one, Sarah's page is a good resource although there are huge gaps because we went through a period where I didn't film anything. The longer video here is also there. Soon I will have to break Sarah page up into various topics...

Here she is doing the whole hour lesson condensed into 17 minutes or so. In the beginning you will note that many symbols are missing when we multiply by one but she understands what they mean. The first review of this series Fractions Despite SPED is here.



You can find us on FACEBOOK.

Want a fractions kit? Get one here.

Or just go to the house of math....

Big Blocks Big Fun Big Concepts.

Lately there seems to be a bit of a resurgence in understanding that those big wooden blocks had more purpose than meets the eye.



There are also articles appearing on blogs like this one and others. People seem to be rediscovering a very simple idea. Early is better when it comes to language, and math is a language. Further, the more senses you use the more learning takes place and the easier it is to understand. The brain likes multiple inputs.

Here is a simple wall made with the big blocks, also a lesson on proportion,  wholes, halves and quarters as well as addition and multiplication...just by asking simple questions. What if all the blocks were little ones...well them the bottom blocks would take four...in fact each row would be four...and we can sing a little song about fours as we figure out how many fours it would take if the wall was made of the small blocks, what if we used the halves? Then we'd be counting by twos...  For more advanced students (and teachers) we could do a quick lesson on bases...the most important part is to PLAY.  These kinds of lessons have to be quick and easy and as natural as possible so the kids learn without knowing they are learning...we're just playing using our imagination and asking silly questions as we build stuff.  It's not a formal lesson per se.

Here for sure we are playing. It's a fun preschool math activity AND they learn things that are not so obvious to the casual observer...as Doug Clements explains above.

We talked about the words symmetry, symmetric, symmetrical...

Bust mostly we had fun building a castle.

Then of course there was a little formal math where we practiced all 45 addends...this is a math activity that will be repeated MANY times before the recall is instant and mastery is achieved. Some of the slower teachers will drill these addends over and over again on a daily basis until the students have them down and have acquired a distaste for math in the process. The more enlightened teachers will make this one of a myriad of math activities that keep preschoolers, kindergartners, and first graders engaged for hours over many days and weeks.  Kids never get tired of playing.



Here is another fast easy lesson on finding the area of a rectangle where the students tell you the formula not the other way around. They will forget this in a few weeks, and you can teach it again as a fresh lesson. Seriously. After a a few times they will remember it...internalize it, understand it and not because they looked at these symbols and memorized a formula:

1/2bh = A

The lesson with the blocks above is SO much more powerful than even this lesson:



However, I posted that video several places and the comments about it were how powerful and easy a drawing can be to illustrate the simple concept. I find that presentation creates HUGE "AH-HA" moments in students and teachers alike. Picture worth a thousand words as they say. Kinesthetic experience with blocks worth exponentially more than that...

Learn to use your base ten blocks.

Find us on FaceBook or just go to Crewton Ramone's House Of Math.

Algebra Is Child's Play

Here we see a six year old knocking out factoring problems with ease. He doesn't know factoring polynomials is supposed to be hard and that I've had to work with kids 10 years his senior on these exact same problems...only they were frustrated and confused.

We just did a few problems for fun first thing in the morning. His brother chose not to play, opting for cars instead which I am told is equally fun not really MORE fun. Algebra doesn't have to be painful. The basic concepts can be mastered at an early age thus freeing up the teen age years for other things, more math if they want or whatever topic catches their interest. This child will have ALL the math currently taught in public schools through sophomore year MASTERED by the time his is about 9 or 10. Notice I use the word mastered. This is completely different from "memorized to be forgotten", which is what is currently the norm in classrooms through out the country, including our universities...

Here is a very short vid showing him developing his problem solving skills, along with a host of other math skills used for factoring polynomials.



Here you can see his progress. Algebra gets easier and easier as he gets better at counting and making symbols.


Learn more at The House Of Math.

Manipulatives For Conceptualization.

This is a good video illustrating the power of manipulatives to help conceptualize numbers and relative amounts. It uses pennies.



Base ten blocks and other math manipulates also help with this. Here you see base ten manipulatives called basic operations pieces, complete with a ten thousand square. You can change the scale several times and work your way up to trillions. They are very useful for teaching exponents getting a handle on 10², 10³, 10⁴, as well as higher power algebra.

In the picture you can see we have changed the scale and made what used to be a unit 100 and now the 10,000 square is a million!

But as you see at Crewton Ramone's House of Math, lots of things can be used for math manipulatives including macaroni, raisins, and oranges.

Algebra with toddlers using manipulatives.

These video shorts explain why it is I am underwhelmed with teachers who tell me they can't start algebra early on...less so with teaching methodologies that tell you NOT to teach math, (which is a language) early on because the students "aren't ready for it" thus reflecting the teacher's fear of math onto the students...in some cases these teachers have gone on to found methods that damage entire generations of children's mathematical abilities.

Learn how to use your base ten manipulaives.

UPDATE: there are now tons of full motion videos showing young students using base ten blocks to learn algebra and a whole lot more on youtube. Just search crewton ramone + whatever topic you want to see...

Then of course there are the text book writers who seem to start with the premise that math is hard and certainly not fun.

I've had parents (and Catholic Nuns) tell me that "math should be work"...it doesn't have to be.

Using manipulatives or base ten blocks makes math easy and fun. As you can see they learn math concepts quickly and easily.


Check out this post showing these same boys doing 3rd power math in their heads without any manipulatives. It should be clear that using base ten blocks avoids future problems it doesn't cause block dependence...they see the blocks in their heads.

It's child's play because they can see it. The manipulatives allow them not only to see the math but to get their hands on it. Couple this with the compound teaching algebra does for you and math concepts and facts are mastered in much less time with much less pain and difficulty.

YOU can learn how to teach your kids using this method. I don't care who you are or what your experience is with math. You can give your kids a head start and open the gateway to all manner of opportunities while at the same time preserving their self esteem. You can also give them a positive mindset toward math. If they think math is fun and easy it will be.

Crewton Ramone: Negative Three Distributes w/ a 4 & 5 yr old.



Crewton Ramone Intro To Negative Numbers.


Crewton Ramone Does Algebra With 4 and 5 Year Olds. (ScreenCast).



Crewton Ramone Distributes With 4 and 5 Year Olds.




Crewton Ramone Factoring With 4 and 5 Year Olds



Go to the ALGEBRA page at Crewton Ramone's House of Math where you can learn quite a bit of algebra for a few bucks (cost of a password)...most of it's FREE as you can see.

If I can explain algebra so that 5 year olds can do it, I bet I can explain it to you. Get set of blocks and get started. Previously you had to attend trainings or seminars to learn how to use these powerful tools but the internet has changed everything. You can now learn the basics for FREE and you can learn the more "advanced" concepts for just a few bucks. Get started NOW.

Here is the 4 year old working by himself...four year old math enrichment. ⇐ Click that and prepare to be amazed. Just because he can't write doesn't mean he can't learn math concepts. In the same way we don't wait for them to be able to write before teaching them their mother tongue in this case English.

This post is a couple of years old. You should see the math these boys are doing now, often without blocks and no paper or pencil either. Poke around on this blog and see for yourself.

http://www.crewtonramoneshouseofmath.com/

Updated Feb 2013.

Related:

Introducing a 4 year old to algebra.

http://crewtonramoneshouseofmath.blogspot.com/2014/03/manipulatives-introduce-4-year-old-to.html

Another 4 year get's some algebra.
http://crewtonramoneshouseofmath.blogspot.com/2010/12/4-year-old-math-enrichment.html

A classroom of 1st graders factoring polynomials.
https://www.youtube.com/watch?v=C3kGVv1IWHk

Get this book if you have children 7 and under...find out more about it, and a look inside here.  You can get it without a password for just $2.99. Give your kids a REAL head start with math and numbers with this book and my website.

"Great book for teaching how to use the blocks! Colorful, clear pictures and cute rhymes make the book fun to read and play around with. We printed the book out, and my 5yo loves how many of the block pictures are big enough to put his blocks directly on top of the pictures. The text plays fast and loose with niceties like punctuation, but is engaging when read aloud.

Most of the book focuses on playing with addition facts up to 10, which gives a solid foundation. But it also delves briefly into such topics as square roots, place value, addition of multi-digit numbers, and a glimpse at multiplication. And in true Crewton Ramone fashion, problem solving with 'x' (basic algebra) is sprinkled throughout. A great intro to playing with math." ~CS, GA.

"I have to tell you that when I first started to watch your videos I cried....after learning it myself in school (haha) then teaching my three daughters algebra using Saxon, Math U See and things from the Teaching Company, I never really had any idea of what I was doing. Watching the videos of you made everything make sense!!! I'm sure that this is a labor of love for you but I just wanted to say thank you! It is much appreciated." ~HS, Ohio, USA.



Tweet

10 Year Olds do the Math

These are a couple of exceptionally bright 10 year olds who came to a two hour session for enrichment not because they are having trouble.... If you would like more info about Math Tutoring on Maui go here.

They start the class with a simple whole brain warm up exercise where they have to build the addends for 7 thru 10. They have to use both hands simultaneously and they race me. I also have a tray. Right now they cannot beat me but soon the students will surpass the master...


Here is a shot of them using the blocks. They are racing to see who can get the problem st done first. We did the basic one step percentage problems, there are 3 kinds:
20% of 60 =?
24 is 60% of what number?
What % of 70 is 21?

We did a bunch of problems for each kind, then we did a mash up where all three kinds were in the problem set. It's always more fun with two or more students because we can race and get more problems done in less time.


Just for fun I taught them how to convert base ten to binary but forgot to snap a picture or two then we moved on to percentages. Here you see the problems and sketch of the solutions plus a matrix for the second problem so they can arrange their thoughts. They were using the blocks to figure these out at first then moved on to drawing them.


We spent a lot of time on binary conversion and percentages and they begged me to do algebra. That's not an exaggeration. So for the last 40 min or so we did some factoring. Started off easy and worked our way up. Here the student is doing a fast sketch and the writing the symbols...



What you don't see is the time we spent modeling these problems with the blocks. The base ten blocks are like training wheels, and these two wanted them to come off as soon as possible. Here we went directly to symbols no sketches no blocks...



You can tell how confident they are by asking "do you want an easy one or a hard one?" By the end of it they were saying, "give us some hard ones!!" Of course there are no hard ones when you understand what you are doing. (BTW x²-18x - 81 cannot be factored, but x² - 81 can. Look for a lesson on the difference of two squares soon.) They have fun and get a sense of satisfaction because they know much older kids who have a hard time with these...I will remind you that these are 10 year old boys.

This is a bad shot but shows economy of symbol. We don't need to write (x-9) twice. We talked about square numbers and what that meant. Soon they will be evaluating these for various values of x. Ie f(x)=5 or 10 or 2 etc...and they will see the result is always square. When it was over they thanked me profusely. One of them who was coming for the first time admitted that he thought it was going to suck but instead he had a good time and couldn't wait for the next session.

Neither can I.


Crewton Ramone Does Algebra With 4 and 5 Year Olds.


More at Crewton Ramone's House of Math.