Distributive with base ten blocks.

Distributive theory EASY. Especially if you've been doing it since you were four. But even if you haven't base ten blocks make it easy to understand. This is an explanation the THE explanation. Makes the idea easy to see, the symbols become visually obvious and we take the concept from the abstract to the concrete with base ten blocks.

When working with young children the algebra is just along for the ride, we are much more interested in addends and multiplication.


You could use the blocks to show 3(2 + 7), use three's and you'd have two rectangles one with 6 and the other with 21, one above the other...three across and then 2 up and then 7 more up...

The Algebra is just as easy to get. Using the blocks and building bigger, funner problems makes it simple child's play.

More explanation can be done by flipping the blocks over and showing (10 + 3)(10 + 2), now instead of x squared and x's and units we have a hundred tens and units.  Same blocks we could do percentages too. Imagination is powerful and these tools help unlock it and put it to use...also helps with visualization.

Just that little line drawing can make such a difference for understanding but they have to get their hands on the blocks first. Just watching this video isn't enough if they don't have blocks it can still be confusing for some.  SO make sure they get their hands on the blocks...and don't start here you start with x² + 3x + 2 and if they have never seen it before let them discover how to build it don't just show them. Then after building a few and explanation like this can be helpful. This is just one example do several more where the child has to build it draw it and make symbols while you talk about it and factoring and division will make a lot more sense.

The distributive property is easy with base ten blocks and so it the associative property. That page BTW is far and away the most popular webpage I've ever built getting thousands of hits per month, month after month year after year. Why? Because base ten blocks make math concepts easy to understand.

My Two Cents On Common Core.

A little more than two cents on  Common Core

By Crewton Ramone

Let's be clear. I am not a fan.

How I feel listening to mathematicians defending common core.



But let me also be clear the way they are trying to teach addition using addends is a very good way to teach math. It would be visually obvious if they used base ten blocks.

Pictures and articles like this and like this have been making the rounds.

Taken out of context.

My position, with regard to the math at leaste, might be a little more unique than some others because I use manipulatives, so if you are "pro common core" before you dismiss this without even reading it as many who see an opinion counter to theirs are wont to do, take a moment and understand my focus is understanding and learning math, and after 24 years, several hundred videos made, and "too many" web pages and blog posts that detail down to the "nitty-gritty" on HOW TO teach math to every kind of student from the Autistic to the Gifted, I have a pretty good idea of what it is I'm talking about. My results speak for themselves. My students get 100's and can jump through whatever ridiculous hoop the school system puts in front if them because they understand it, they don't just memorize to take a test just to forget it later,  although certainly some do if they never see it again for years and years, myself included. 

Base ten blocks make math easy, and once again if the students understand the concepts all they can do is change the numbers for the test.

Further I am often finding the teachers of mathematics themselves lack understanding because many of them fell into the trap of just memorizing rather than understanding, they don't know why you invert and multiply and confuse dividing by a half and dividing by two. (See the work of Liping Ma,
"Knowing and Teaching Elementary Mathematics" and others for more, go to Amazon, look inside and just read the first few paragraphs of the introduction.) 

Anyway here are a two more articles:

Teach Common Sense not Common Core, April 20, 2014,  By Dr. Ileana Johnson Paugh

“Common Core will be raising good little socialists, who are in tune with their feelings, not so much their critical thinking skills.” – Author unknown


***
Pro-Common Core Deception Falling Apart, April 18, 2014 by Alex Newman

"Facing a growing avalanche of grassroots opposition from teachers, parents, and voters across the political spectrum, pro-Common Core forces — Big Business, Big Media, the Obama administration, and more — are striking back at their critics, oftentimes with outright deception and utterly ridiculous claims."


***   "Let's start common core standardized testing earlier...like third grade."




  A Little More Than Two Cents On Common Core.
Common Core Will Be Poorly Implemented.


If they start early enough they will avoid many of the problems detailed in "Un-Common, Not Core" by Cynthia Walker. This article was going great until the part about "cognitive development" which almost made me stop reading, but I did read the whole thing. Basically this is another report from the trenches and the reports are not good. Eventually people in this country will figure out government solutions are NOT solutions. The common core is not by accident but by design, and this person touched on, but did not develop the thought that education is being used to keep the classes in their place in Europe, and that common core is going to be used similarly here in the USA. Those wealthy can afford tutors to get their kids through it, the rest of you are screwed. Ha ha. Sorry.

I know Americans love to pretend they are free and live in a classless land of liberty where there is justice for all, while presidents of both stripes renew the NDAA and dare you to say anything at airports, but you do indeed have rulers and they DO intend to rule. Another word for rulers can be masters, and Americans hate that term even more. But your masters understand how to rule and education is a hugely important part of the equation. Well-educated people who understand mathematics are hard to rule. Emphasis on mathematics. The oligarchs had fixed the problem of upward mobility by making sure the very teachers in primary schools in the USA don't understand math but still can get a teaching degree "without taking very much math." They are further fixing the problem with common core.

This not an accident, it is by design.

This is not a mistake, it is by design.



No, really.  I'm not being dramatic.

They know how to use compartmentalization so that even the most altruistic teacher or administrator that does in fact love children and have high ideals about their education can be used to implement a plan that is exactly opposite of the reason they got into education in the first place. Point this out to them and they have been trained to scoff and shout "conspiracy theory." The combination of bullshit and bureaucracy is an exceptionally effective tool for implementing a system that negates and mutes the abilities of good people to use their skills to effect change or do the basic job of educating. At every turn they are hampered because they are limited to "approved" curricula and even when the teachers see it doesn't work or might even be harmful they are stuck with few alternatives. "Rogue educators" are fired. Veterans who were formerly effective quit. Those that would have become rogue teachers or veterans choose not to become teachers in the public schools. Those who understand math rarely go into teaching because they can get paid so much more elsewhere and they don't need the headaches.

Further, say what you will, but TEACHING IS HARD, that doesn't mean it can't be FUN and enjoyable and immensely rewarding but it is HARD even under the most ideal conditions. It is a lot of ridiculously hard, thankless work and the reward for most of them isn't the money, which is why this situation is all the more heartbreaking. I have walked in on teachers who literally had their heads in their hands sobbing, for various reasons...not all of them bad. I won't digress, but the point is that they care. A lot. They tend to get passionate and emotional. This does not stop them from being used by the system, however. When they quit caring, they quit teaching because the money alone isn't worth it.

It angers me to see certain pundits rail against teachers, as if they have it easy with summers off and lots of breaks and they don't really do anything and by the way some of them who do, are well aware of the system for sorting they've put in place; well aware that mathematics is a barrier to entry, and they intend to keep it that way. Others are just clueless.

I assure you teachers are not the problem. But teachers are part of the problem. The same way the government used lawyers to sell their ills and the same way the government allowed big pharma to use doctors to cover for, and sell their ills, is the same way government will use teachers to help implement a social structure that keeps the wealthy wealthy, guts the middle class and keeps the poor in line. Again-- a huge and well educated middle class is NOT in their interest. As an aside what has happened to the professional respect for doctors and lawyers over the years? Has it increased or decreased? The oligarch's social engineers are doing the same to teachers and police. This is also by design not by accident.

The huge increase in secular homeschoolers is a reaction to and symptom of this. The huge amount of social media devoted to the police's abuse of power is also a symptom of this.

The amusing part for me is most people dismiss this idea even as it becomes more pronounced, and can't seem to understand why they would even want this. George Carlin explained it to you several times in no uncertain terms and you all laughed.

It also angers me that most teachers, especially of mathematics, don't seem to see the problem or won't admit it. The primary teachers who on balance can't do math, also seem to be unaware that they have unwittingly become part of the problem when they got involved to become part of the solution. Such is the ability of a good master to cleverly use all assets to their purpose.

In case you've lost track of what the problem is in all these words:
The problem is that our children ain't learnin' no math.

The whole reason I've built and am building the Crewton Ramone "brand" is so that parents can do it themselves without having to pay 50 bucks or more an hour to help their kids with math. If you want it all for free you are completely out of luck, but I try to keep it more than reasonable.  Parent/Teacher training for ridiculously cheap for example. People are telling me it's worth many times the price.

Here is another article I have a slight problem with because this (pushing social agendas) has ALWAYS been done in public "education,"  it is not unique to common core.

http://dailycaller.com/2014/08/08/new-york-common-core-test-quizzes-kids-on-global-warming/

More with my comments:

CR: Don't worry they will figure out how to rig the numbers so it looks like they got C's and D's.

Utah students took their state's new Common Core tests this spring, and they struggled so badly that a majority of the schools could end up graded D or F.
http://www.orlandosentinel.com/features/education/os-testing-florida-utah-worries-20141004-story.html

CR: This article is from USA Today so you need to suspend your disbelief in order to get thru it. Standardized testing is making kids HATE MATH you hear it over and over again but who cares?: it's going well, most likely they have never heard of Liping Ma.


Several states have balked at requiring them and even comedian Louis C.K. last May took to Twitter to complain, "My kids used to love math. Now it makes them cry. Thanks standardized testing and common core!"

But teachers in states where the math and reading standards have been in place longest say that, in spite of the criticisms, Common Core is going well — and that most teachers feel prepared to teach new kinds of lessons.
http://www.usatoday.com/story/news/nation/2014/10/02/teachers-survey-common-core/16601335/




CR: And don't be confused. Common core is not curriculum, they just write curriculum for common core and put it on the text books they sell so teachers will know it's a common core text book...so children can pass a common core standardized test. So why should it matter what method you use if you teach them math and they understand it? Because if they don't do it a certain way it will be marked wrong even if the answer is right.

Common Core standards are not curriculum. The Common Core standards detail what K-12 students should know and be able to do in English/language arts and mathematics at the end of each grade level. The standards are similar to those used by top-performing nations.
http://union-bulletin.com/news/2014/oct/05/column-common-core-ensures-grads-are-prepared-coll/

"The standards are similar to those used by top-performing nations."
CR: Are top performing nations testing their kids to death? Is there money for a certain few corporations in testing?

CR: The answer for the most part is "NO" or you could say as ready as they were to implement "The New Math." Anybody old enough to remember how well that went?

Are teachers really ready for the Common Core?
The controversial standards are about to be tested for the first time, yet questions remain if educators have been adequately trained.
http://www.bostonglobe.com/magazine/2014/10/01/are-teachers-really-ready-for-common-core/bAhagn3zzkQ0bM9w8GgYzN/story.html

If it was easy to train all the teachers we'd have no problem. I've trained trainers (to teach teachers and to train other trainers), and teachers, and students...training teachers requires MANY hours. Training trainers more than that. I know for a fact the teachers in public school didn't get 40 or 50 hours of training and attain mastery. This isn't over. We have a long way to go. Be one of the parents that takes matters into their own hands and gives their kids a solid foundation in math...I have the tools you need and can teach you how to use them if you so desire.

Crewton Ramone is a pissed off math tutor who has been slogging away at math education for more than 20 years now. In that 20 years he has watched the situation steadily deteriorate...