Crewton Ramone's Blog of Math

Problem Solving Concepts Made Easy

2012-01-29T11:12:00.007-10:00

Note that depending on age the emphasis changes...for the older girls it's about the concepts and seeing the rules they have been taught, for the younger students it's about finding same and building addends.

The basic concepts are hero zero and no fun get back to one...but it's all about using those to find same and SEE what x is...the equals sign tells us what x is...and x can be anything depending on the problem.

For all of them it's about making it easy and fun. Let's start with older students:

Now as is typical of many high school math students, they have yet to master multiplication and resort to fingers when adding. I will get them off their fingers and they will have to master multiplication on their own...

Then Watch a six year old doing basically the same thing, CONCEPTS are the same. (BTW it's a piece of organic all natural endangered species chocolate which he picked out from the health food store.)

And the older kids (begin to) SEE the rules:

They are hampered by a mental paradigm that math is hard even when it's this easy...it takes a while for them to realize really math is easy; but when that shift happens the math becomes easy and with or without me A's can be achieved. In the vid we did not evaluate for x = 6 but I did so with them and with Dboyz who figured out that 30 plus 3 is the same as 18 plus 15...and they were quite proud of their skip counting skills...counting by 6's all the way to 30 with the younger boy in the lead. When doing 18 plus 15 they knew five wants to be ten so it takes a five from the 8 leaving 3 tens and three...they also did 8 takes the 2 from the five and again we get 3 tens and 3...lots of DO-able math for kids of all ages. 10 years from now this will be old hat for some students. More to come on the problem solving page at the house of math...the question will come up, how do you do a problem like this?

3x - 2 = 2x + 5...there's no -2 in five. True. You need hero zero again, none of this balancing stuff...you just see same on both sides.

Or

5x + 3 = 2x - 12 again many people can't see same on both sides...that's because of hero zero again. Want a detailed explanation? You need a password. PPPSP = The Password Protected Problem Solving Page.

There are tons of different problems on the PPPS and vid that make them ALL super easy. Remember those boat and current problems? Or how about constant rate problems? AND of course the ones you see here where you might think it's not same on both sides because things got negative...just a few minutes and you will see your way clear...

I have heard from a student that has since moved to the mainland that she is getting A's for the first time in math...all I did was adjust her thinking and hand her some concepts she can use no matter what the topic...beliefs are powerful things. She now believes math is easy...she knows it...so of course she's getting A's. I don't need to be there. And that's the point of all this.

Why Invert and Multiply.

2012-01-14T15:53:00.004-10:00

Used to be to get this info you had to come to a seminar or training, usually held in Idaho...now I think the next one will be in LA or maybe Las Vegas...if we ever do one again. It's on my list but it could be a while. Nothing like in person training but it's costly and you have to travel and all that goes with it and blah, blah, blah.

Now you have the house of math and this blog. First we see fraction multiplication and why nothing is getting smaller we are just counting parts of a part and if you insist yes a third of a half is smaller but we were counting not doing magic and with 1/2 ÷ 1/4 = 2 really nothing got bigger we were counting quarters. Two of them. Observe:

Here is a quick lesson with the symbols no blocks for why invert and multiply. Division of fractions. Also easy to understand. If you want to see the whole lesson go to Sarah's page. There you will see us use manipulatives to make fractions clear and easy. And you will get the joke about "clear"...

If you actually take some time to study the picture above you can see that the symbols are quite confusing to some students particularly to deaf students who couldn't for the life of them figure out the relationship between those numbers if they didn't understand division, or even if they did. How the heck does it turn into 2/9?!?

Well, it doesn't turn into anything: we are counting. The rectangle we see has the one sixth in lowest terms instead of 6/36 which is what you get if you multiply 3/4 x 2/9...which is equal to 1/6...but getting there with symbols only and no concepts is impossible and modern math teaching doesn't even attempt to clear this up they just give you the rule INVERT AND MULTIPLY.

WHY?

And it's right about here many students make the fatal decision that math doesn't make any sense...I mean the rules changed for addition and subtraction, you can just add 1/2 and one 1/3 and get 2/5, it works for multiplication though, and then it's some crazy rule for division and they get bigger when you divide: this math is arbitrary crazy stuff.

No. It's not. It is consistent and beautiful and simple. The five basic concepts are alive in well in our fractions games...knowing what one is, same, rectangles, the how many part the what kind part, and economy of symbol...but the problem with that last part is 95% to include the teachers don't understand what the short cut is doing. It's economy of symbol: fewest symbols possible, and it's a short cut and work saver. Now, if you want to see more with manipulatives to make it clear why we invert and multiply a 15 minute video on this (and a lot more vids) is on Sarah's page you need a password. Just get a month and I think you will see an annual pass is worth it because you won't get through everything I have up in a month and as the months go by I add more and more. I will be offering a special where you can apply your monthly to the annual if enough people get a monthly pass.

One example with symbols only may not have been enough, a couple more examples with manipulatives should clear the whole thing up. The idea being if an autistic student can glean the concepts SO CAN YOU. Same when you see me using 5 and 6 year olds as students for algebra...if they can "get it" so can teen-agers.

Passwords used to cost a buck. Now they cost 5 times as much...inflation and the fact that there's 10 times as much stuff on the password protected pages and then someone sending ma a $24.99 vid that had basically 30 minutes on it, and not even a good 30 minutes just 4 concepts poorly explained with lots of special effects and production. Here you get ZERO special effects and very, very low production value but very heavy on the information and concepts, well explained...or so I am told. AND HOURS AND HOURS ARE NOW UP. It's worth the 5 bucks.

What we are doing is finding how many times one number is contained in another number. In order to do this we have to make them same or we can avoid all that work with the rule...basically we are just skipping a lot of steps and in the process skipping a lot of students who throw in the towel and change their belief to math is hard and arbitrary. How do teachers teach students who already know they can't learn whatever math it is later on in high school? This will be discussed in depth with another little girl who got a convenient label put on her. She loves playing math but as soon as we bust out the school work, math is no longer fun and she knows it's hard even though we were just doing it with ease a minute before. That's how powerful beliefs and paradigms are. Her page is here. Both of these pages will grow over the coming months, and are especially good for home schoolers and teachers.

Also now lots of Mortensen Math Materials available on my site, if you buy something there, a password if free. The fractions Page was going to go up in it's new form Monday but it's MLK day so I will have Dboyz and I doubt it will get done...although it is on the agenda for Wednesday...fractions from beginning to end.

Find us on Face Book.

People on face book and twitter got the vid FREE for a day...it has since been taken down...joining us there has it's benefits.

Fraction Subtraction Simplistic Though Autistic

2012-01-12T12:52:00.001-10:00

Sarah is getting better at fractions. Her mom wants the focus on algebra because the test coming up will have a lot of algebra on it, but I see students all the time that have trouble with algebra because they don't understand fraction concepts. Rules and process are quickly forgotten. Concepts aren't.

So far we have covered addition and a little subtraction of fractions and she understands that "the name of the game is to make them same." Then we can add, subtract or divide...with multiplication we just multiply and I'm going to try and get her to discover WHY we can just multiply without making them same and why we invert and multiply when we divide. Hint for you it's a short cut to making them same.

For now we spent a little over an hour doing this and by the end of the hour she was getting pretty good.

Here is 15 minutes of that hour.

Note there are fewer pictures and symbols here but we started with the blocks and drew pictures and then I remembered to turn the camera on for a bit. You always start in the concrete then draw THEN go to symbols only, and here at the end I went back to tie it together. You can gauge your students understanding by their facial expressions. Here I could see she was "getting it" but more reinforcement is needed not just because she is autistic but because repetition is the mother of skill for ALL children. If you have young students, you can do these lessons and then months or years later do them again...after many impressions the knowledge is ready for instant recall.

Homeschoolers have the opportunity to cover the same ground like it's new if you start them very young. The idea that they cover it once in 5th or 6th grade and then they'll have it forever is ludicrous to my mind.

The idea that autistic kids can't do this is being disproved right before your very eyes. Due to the brain damage caused more than likely by mercury injections, she will need EXTRA repetitions but that's all. Once she understands it the nuero-pathways can be built and reinforced.

You can now get fractions materials at the house of math. That page has lots more info than just how to by a kit plus some free PDF's and a caution on using fraction worksheets too early in the game. Fractions FUN begins with manipulatives not worksheets.

Also Sarah's page is expanding. More vids are there, some of which you won't find here or anywhere else...but you need a password.

Find me on FACEBOOK or Twitter. Crewton Ramone, there is only one.

Moving Toward Mastery

2012-01-11T11:01:00.002-10:00

If this is you first exposure to Crewton Ramone's House Of Math, I highly recommend you go to the homepage and watch some introductory videos too, before you watch these because these are a little advanced. People think it's magic or the kids are geniuses (which they are going to be) and that they could never do this with their own kids or learn to teach math this way or whatever poppycock springs to mind when see 6 year olds doing algebra in their heads.

Note for some of the problems we only SPOKE the symbols we didn't even write them down and he still solved the problems! This should put to rest the silly objection that they will have to take the blocks with them to school in order to do math. My boys sit patiently through the simplistic kindergarten math lessons they get at school and then pretty much ace whatever they are given as work or home work...or tests. They have some basic concepts mastered...and are working on mastering more concepts each day, which makes their math at school SUPER EASY.

One of the concepts that was mastered early on is the concept of addends for ten. They both have instant recall for most of their addends but especially for 9 and 10. No pause, seven needs what to be ten? Three! INSTANTLY. This is extremely important and is a building block on the way to mastering addition, subtraction and multiplication and therefore division.

Here we see the older boy who has not yet mastered multiplication working out another set of factors for 24...he knew 6x4 but didn't immediately know 8x3...but he will and this helped him to add that fact to his storehouse of math facts.

They have yet to master their multiplication tables but we are getting there easily and gradually. They both see that knowing how to multiply makes math easy and when it's easy, it's fun. In the vids you see here we stay positive. If you want to see them start learning to do problems like this with their friend hero zero you need a password. I have also created a page just for certain lessons with Dboyz and other students (like Emma and Sarah) that will be instructional to all.

For those that have been following their progress this vid may be a little hard to follow due to the lack of symbols but you understand what's happening, for brand new people often times the take away is that's amazing but what are they doing? What they are doing is seeing pictures in their head.

Here is a short intro, (skip this one and watch the next one if you have a little time the next one IS this one plus six more minutes):

Here is the above vid plus a few more problems, listen to the 5 year old say, "we're so good at math it's easy!" Compare to some students I have that are sure math is HARD.

In which we answer the question do they have to carry their blocks with them to schoool.

Now don't get the idea that I'm some kind of Math Wizard. Naturally, I am better at it than a novice (most of the time) but I have trained teachers all over the country to use this method, and I have trained trainers and have trained trainers to train trainers to train teachers...all of whom are still amazed at the results they get sometimes even after years of doing this. I have had teachers call me excitedly saying "it works!" Or "it never ceases to amaze me." Me either.

Of course it works. You have the right tools for the right job.

Now if you want to see all 26 minutes which is the above plus about another short 15 minute lesson on negative expressions where we use lots of the symbols you are used to go to the Dboyz page or find it on the sample lessons page. Password is changing and prices are going up. Dboyz page has the NEW password...those who want to renew (can you believe it's been a year) at the annual rate will get the old rate if you already have a password. You use the old password to get to the page to renew. Clever, huh? New Password has gone out. Look for it. If you don't get it contact me at gmail.

Price is now $24.00. That's two bucks a month. One month which always works out to more than one month (ask anybody) is now $5.00...3 months for $10.00. Lifetime memberships are now available to those who already got a password.

It's hours and hours of vids and pages and pages of PDF's, and more are added monthly all for $24.00 It will take you months to get through it all or weeks if you are diligent and spend hours each day. But for those who spend a few minutes a day and maybe an hour or two on weekends there is more there than you can shake your finger at. Don't get overwhelmed, just get started...watch the intro and then go to whatever topic you like. You may never see it all because I am always adding and might stay ahead of you at this point. That's okay you are always learning. Even old pro's enjoy watching the vids because they get something out of it each time.

Crewton Ramone Playing Math With A 7 Year Old. Intro Lesson.

2012-01-10T19:20:00.001-10:00

Here is a good lesson for those with young children. This was a first time student who is being turned off to math at school. We had fun and she wants to come back for more.

What's Under The Cup Quickly Became Her favorite Game

Look for this lesson on the sample lessons page too. You need a password to see the other hours (and hours) of lessons there but here is this one for FREE. Soon Emma will have her own page because she is an excellent case study. She has been labeled ADHD or ADD and is on her way to SPED and I'm sure part of that is due to her not "getting" math and other subjects the way they are teaching it...thus she get bored or frustrated and acts out. This is a 7 year old child. I have seen no indication that she can not learn or stay engaged for 1 hour at a time. But what do I know...?

I am extremely biased against drugs for 7 year olds. I am also dubious when it comes to the ADD and ADHD diagnosis for bright little kids.

Mostly we played games like what's under the cup and making rectangles:

Building Rectangles and Playing Algebra? No problem.

She never figured out that most kids think algebra is harder than subtraction...which she informed me she doesn't like at all because "it's kinda hard and confusing." We will work on addends and clear all this up over the coming weeks. And you can watch the transformation at http://www.crewtonramoneshouseofmath.com/index.html. We didn't do any subtraction at all that she was aware of...but we will soon master that as well as quite a few other math concepts.

BTW password is going to change soon and prices for passwords are going UP this year.

Anyhow, here is a half hour of math...the hour went by in no time at all.

Find us on FB.

Now available all manner of Mortensen Math Materials.

Fractions And Autism Do In Fact Mix.

2012-01-03T19:27:00.002-10:00

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 public 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? Whereever 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 jusy go to the house of math....

Fractions and Addends

2011-12-28T13:54:00.002-10:00

It doesn't matter what the lesson is with the younger students, it can be aided by practicing addends. Playing with addends makes it all easier. Drilling with addends is not fun but building walls and filling trays and racing to fill trays with addends IS fun. Right now she is getting the hang of it but soon she will race me and may even beat me like Sarah does. Kids naturally like competition.

We did a lot of things in our hour one of them was finding out what pie means...

c/d = ∏ and yes ∏ = 3.14 but now we see what it means...

We played with fractions:

And at last we built some addends. No magic to it. Just solid conceptual understanding of the basics.

She is 10 so the emphasis will be using fractions to learn addition and multiplication...same with the algebra when we do algebra the emphasis is not so much on algebra as it is on multiplication, the algebra is just along for the ride as it were. If this sounds odd to you spend a little time digging around this blog and over at the house of math.

More Fractions Fun.

2011-12-27T21:44:00.005-10:00

You have to do a lot of preparation before you dive in and start adding problems like these.

You need to understand basic concepts like SAME and ONE. But basically all you have to be able to do is count. You don't have to be able to add and multiply although it helps.

Fractions concepts are easy. Any little kid can learn them and understand them, it's that much better if you let them fool around and DISCOVER concepts and how things work for themselves while you give copious amounts of encouragement and direction.

Working with very young students is similar to working with SPED and other "learning disabled" or "special needs" children because often what you have is "developmental retardation" or to be plain many Downs Syndrome and Autistic students who are in their teens are in about the same developmental stage as very young children. Very young children can learn math concepts as proved consistantly on this blog, ergo: SPED kids CAN learn math.

This isn't rocket science. Simple logic.

Here are a five and six year old playing math. Fractions. They have very limited experience with fractions and still can't multiply easily because the don't know their multiplication tables completely yet, but they can learn fractions and begin to understand the concepts. Now if SPED kids and little kids can learn fractions then certainly high school kids and adults can also learn it, even the "problem" children...who aren't particularly disabled or SPED but may be special needs because of circumstances at home, like poverty or parents who use drugs or alcohol etc. Sadly most of you know what I'm talking about because it's more and more common in public schools.

Here they are playing a game where they try to discover the fraction from the disguise it's wearing and they literally get to pull off the disguise once they figure it out.

They do not have enough experience to go about it methodically, but they do have natural thinking skills...and with me as a guide they can be directed to the answers by simple questions. Remember remove the "no" from the lesson. Allow them to explore and discover for themselves. Ask "what if" questions, count, see what they have.

Once we get through some of this we can do some simple addition and see how that works. Also we are headed for story problems and these activities get them ready for that too. There are also everyday math activities that help them make sense of the symbols and numbers when they see them. Also check out this post where they fool around with food and no symbols to help them understand what's going on with fractions.

Also note how the younger boy is very much a participant in this and often gets the answer before his older sibling.

Let them discover and have fun! You will even hear them say "Don't tell us!" The joy of discovery makes learning math (or anything else) FUN.

The whole video in one piece is available on youtube and on my website here. [Link not built yet.]

To get a fractions kit,

check my expanding product exchange:
http://www.crewtonramoneshouseofmath.com/product-exchange.html

Also don't forget these free fractions worksheets.

Fractions Despite SPED

2011-12-25T19:49:00.007-10:00

People often ask me if there is a special way to do it for SPED students, the answer is no.

I've had conversations with students that went along these lines. "I know everybody calls you special, but in my class your just like any other kid that's going to learn math. I know you can learn math because you understand English. So quit telling me how special you are and count this."

95% of the time they shock everyone except me...they even shock themselves sometimes. Bear in mind when I met Sarah they weren't even teaching her math because there was "no point to it." they knew she couldn't learn it, and as we say in Hawaii they were wrong but true. She would never have learned math with just paper and pencil and rules and process out of a traditional text book.

(There was a time in my life when I was shocked. After I got over it, I said to myself more people need to see this. And, since no one else has stepped up to the plate it seems to have fallen to me. Hence this blog and my website and the many things that will be made manifest in the next 7 years or so...word is getting out.)

If you try to teach SPED students (or even "regular" students) rules and process the results will be poor. There was a time when I used to have to argue the point but the dismal performance of American math students as reflected by ANY metric saves me the trouble; not to mention that in the 22 years I've been doing this the results have gotten WORSE not better....Fractions and long division still top the list of leaste favorite math subjects pre-algera.

But I digress.

This is an excerpt from an email exchange between myself and a parent of a child with Downs Syndrome.

First off:

Treat them like "normal" kids.

How is her speech, does she speak English well? If she speaks English she can learn math. Period. There are no special needs lessons plans. Do the same lessons you see on the blog and website. You may have to go slower and for shorter periods...but that's it. MAKE SURE SHE gets her hands on the blocks and isn't just watching you play with the blocks. I have had success with downs syndrome, deaf kids, blind kids, autistic kids, kids who climb on rocks...kids is kids no matter what "the experts" tell you. Use all the senses or as many as possible. Play, have fun, learn math. Don't approach it as math time so much as play time. Sing songs. Play games. Watch vids and then DO the stuff in my vids...don't worry about getting it wrong. You can't play wrong.

Sarah is Autistic use your password and check out her page: http://www.crewtonramoneshouseofmath.com/Sample-Lessons-Sarah.html

Here Sarah is doing fractions (again):

After about half an hour she starts "getting it." We have covered fractions before in different ways...we started from scratch, like she had never seen them before and went from there. And this is the result:

As you can see it's becoming easier and easier. You do the same thing with "normal" kids especially younger children. Teachers lament that they have forgotten everything they were taught over long summer breaks. This is normal and natural and often shows mastery has not been attained, although sometimes the are doing as fast as you can write a problem looking very much like mastery has been attained and then a week later they can't remember how to do it. This shows it takes many exposures to put information in long term memory and more than that to make knowledge available for instant recall. Expect this.

She did this one in her head as soon as I wrote it down...however mastery has not been attained, one small change in the process and she gets flustered. As the picture where the problem is scratched out above shows...watch the vid and you'll see what happens when a change is made to the process.

I do the same lessons several times separated by time, they seem new for some, but usually I say the first time it's new, and might seem strange and maybe even a little hard. The next it's I've seen this before, the third time it's I got it already lets do something else. With SPED students it may take an extra time or two beyond that.

If you want to see the whole lesson (you need a password)...just go to Sarah's page. The vid is 24 minutes long. You will see the ups and downs. Here you just see the success. There you will see how we got there...and future vids will make even more sense.

I recommend this for people who don't have SPED students too. The lessons are basically the same...now that she has this lesson mostly mastered and I have watched the lessons, I will emphasize different things, next time we will focus on "filling up the one" and work on improper fractions and then we will be able to do more fractions where we add and then subtract and eventually have to borrow out of that one...we can also go back and forth with reducing fractions and equivalent fractions....then multiplying fractions will be easy and at last division will be covered and you can be assured she will discover WHY we invert and multiply. Again.

If you have teen age students that are doing algebra you might go over fractions again with them because consistantly I see kids in algebra that can't do fractions...or forget how or can sort of do fractions but hate them which is silly when they're so easy.

One last note. Several parents have told me they get lost watching the vids and sometimes don't understand what they are seeing...although it looks fun and easy they don't get it. "Do you have a set of blocks?"

"No."

Therein lies the problem. I can't stress enough that in all the time I've been doing this the ONLY time we lost people is when they didn't have a set of blocks to play with in front of them or wouldn't put their hands on the blocks...the blocks get you through your mental blocks. That's why Jerry used to say "Math is NOT a spectator sport." You have to participate.

If your are an extremely visual learner just watching vids may be enough, but if your are kinesthetic or auditory or a mix where visual is not the primary learning style then hands on is a must. Not saying this to sell you blocks. I'm telling you this because my experience has proven beyond any shadow of a doubt that this is TRUE.

Crewton Ramone's House Of Math

Search this blog for "fractions." (There's like 8 pages of results worth.)

BTW if you want a set of fractions tiles like the ones you see here it's $105.00 shipped to your door and is available on my site at Products and Passwords now. Or order at right. ⇒

Fractions Are Easy Too

2011-12-21T22:17:00.003-10:00

This is a simple introduction to fractions tiles. Fractions concepts are great for teaching counting and multiplication to young students.

Most students hate fractions because after four years of learning math one way suddenly the rules change. You can't add

1/2 + 1/3 and get 2/5...some kids will put 1/5

showing an utter lack of understanding and confusion about the rules. But the rules haven't changed. They just didn't understand them in the first place or more likely were never even taught the rules properly to begin with.

If you go back to the 5 basic concepts, you will find under concept 2, we only count things that are the SAME. Also it's key to understand that numbers have two parts the what kind part and the how many part. Fractions are cool because they tell you the how many and what kind all in one place, whereas with whole numbers you need to understand place value.

Note how in this introduction we don't cram in adding fractions in the first lessons all we do is play with simple concepts. We see how many make up a one, and we count and we learn their names. Later we will learn about numerator and denominator and build on the concepts of "same" or equivalent fractions. Also we will use other base ten blocks to represent fractions and fractions concepts. One crucial concept is the idea that x/x = 1. Right now they are seeing 2/2 = 1 and 3/3 = 1 and so fourth on up to 9/9...let them discover that anything over itself is 1...except for our hero. Plus they will discover this concept from multiple angles. Right now it's counting (three of three is one), but later it will also be division, (three is contained in three one time).

But for now we just play a little and tell stories about fractions wearing disguises.

In this fractions intro I cover the same info but without video. Be sure to get the free fractions worksheet. It's free. Note with me "free" doesn't mean "give me your email address." It means free. If you want more, get a password if not I don't want to waste time with you and an email list.

It should be quite obvious you can use fractions to teach counting and addition and multiplication. These students are advanced so the lessons are easy and fast but if you had a student that hadn't even mastered counting to nine these same fractions tiles would help them learn that. Compare and contrast with the thinking that says they have to have mastered multiplication before they learn fractions which is still ridiculously prevalent in math instruction in the USA and elsewhere.

The fractions page at the house of math has been in disrepair for about a year now...but that is getting fixed. It is very near the top of the to do list now. Look for more updates and improvements to that page over the next 30 days as I cut videos and add lessons and hopefully some more pdf's. Right now there are some videos there and a list of terms but it will become much more cohesive shortly.

Next there will be a video where we add simple fractions and find out what 1/2 plus 1/3 is and more importantly WHY, and we won't just learn some silly rule about multiply this, this and this...and then add this and this...but keep this the same...stay tuned.

BTW if you want a set of fractions tiles like the ones you see here it's $105.00 shipped to your door and will be available on my site at Products and Passwords shortly.

Another Fun First Grade Math Activity

2011-12-21T20:37:00.001-10:00

There are plenty of games you can play that teach math. At Crewton Ramone's House of Math there are pages of them. The page called "how to teach addition" has a bunch of games for addition but there are games for multiplication and algebra and more on my site and here on this blog. I put fun first grade math activity in the title but it could just as easily be a fun preschool math activity or a fun kindergarten math activity.

This is a story Jerry Mortensen came up with for teaching addends below ten...the numbers are having a party. Addends* are quite important and help students with many other aspects of mathematics (like subtraction). They are a basic building block that so many systems skip completely.

With little kids you want to play math...not drill math, and you need to play it enough so that they attain mastery and have instant recall. 2 + 2 = 4 is instant for most kids but 4 + 3 can take a a little longer and then 7 + 5 takes longer than that and they may resort to fingers. Get them off their fingers...but you start on their fingers.

There are only 45 addends in all. They should be mastered but don't spend all your time just doing addends, play other math games, do multiplication, sing songs, do algebra, fractions, problem solving etc. WHILE you are mastering addends...and all of these topics can be used TO master addends...and multiplication. Math is a language: it all goes together.

This idea of segmenting it down into individual parts that never become a cohesive whole ISN'T working.

*Addends: two numbers added together that make up another number. 7 + 3 are addends of 10 for example.

Crewton Ramone And Comander Colby Get Radical

2011-12-19T19:52:00.002-10:00

Playing with square numbers can lead a lot of places.

You can end up doing square roots, or distance formula or Pythagorean Theorem...or in this case we ended playing with radicals. You could also start playing with completing the square or finding the difference of two squares...all of these concepts are centered around squares, although some math text books and therefore some math teachers seem to have forgotten this. Really it's about squares.

We have built square numbers before, but this time we ended up expressing numbers in terms of radicals.

We talked a little about why we call them radicals, used our imaginations to make a two into a square and played around with the ideas. I was under the mistaken impression that we had done this before but actually this was his first introduction to them, had I know that we might have used some clay to really conceptualize the fact that we were turning these numbers into squares. I have quite a bit of video and pages and posts devoted to this topic. This should be a clue as to its import.

The sad thing is that it is SO EASY and yet so many kids come to me frustrated and unable to do what their classes require...because they are confused with rules and process. Like factoring polynomials once they see how easy expressing numbers as a radical is they actually get mad. All we are doing is playing around with squares. After a few lessons like this when they see the way it is presented in school and it makes sense...the symbols and lessons are just short hand as it were, for making squares and applying them to mathematics.

The nice thing with this student is he will never know it's supposed to be hard...in fact a lot of times he makes it harder than it is because ever since he got bumped up to Honors Math he tends to over think things...and do whatever it is the hardest way possible.

The second part of this video takes it up a notch replete with some Jazz and blender sounds in the back ground. Eventually this will be on a password protected page...and I really should make a PDF or two...

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Crewton Ramone Doing Distribution With A Nine Year Old.

2011-12-19T17:13:00.001-10:00

This positive factoring of polynomials is easy and fun for all ages. At the house of math we also do negatives, higher powers and more. If you would like to see problems like this factored then you need a password and there is an abundance of material on the advanced algebra page.

We did problems like to to help work on integers, this nine year ld has little problem with basic operations, and is having fun with fractions already, we will be covering more on this because right now he understands fractions from the point of view of the rules instead of the concepts. In other words he knows how to invert and multiply but he doesn't know why, he knows how to add fractions but he doesn't understand that he is making them "same" so he can add them...and the concept of multiplying by one is lost. But that's another post, this one is about factoring polynomials and it's many and varied uses for teaching math concepts beyond "just" distributive theory.

With young students you use if for cross teaching addends, addition, and multiplication as well as or in addition to factoring and how the distributive theory works. Once we get into negative factors we can use it to teach integers while we are learning about the distributive theory of multiplication.

This was just the warm up, we got into factoring the problems above and more. You can find them on the advanced algebra page, scroll down near the bottom. You will also find hours of other fun algebra there...but as you will see you need a password.

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Get Them Started Early.

2011-12-14T13:23:00.001-10:00

Here is a little article I'm hoping to get published in a local circular called Mauimama aimed at parents with very young children.

There was a time in the not to distant past when educators and parents thought it better not to confuse young children by teaching them too many languages at once. This was the common wisdom. As it turns out this was completely false. The younger they are, the easier it is for them to learn a new language, pronounce the words correctly and even hear the subtle differences in intonation. In fact, there is a window of opportunity that can be missed if the language is introduced too late.

Math is a language. The longer you wait to introduce math concepts the greater the chances of the child having difficulty with math are. Conversely the earlier you introduce math concepts, the easier math will be as they get older. This may seem obvious to some but the great problem lies in the fact that for the bulk of Americans (including teachers) math was not a positive experience. The thought of inflicting math pain and suffering on their toddler is unbearable. They imagine the poor child suffering through lessons and being exposed to formulas they have to memorize. They want to stave that off as long as possible so that their child can enjoy their early childhood unspoiled by math. Or as with some systems (particularly Asians), the child is taught to write early and then they do endless drills that literally burn mathematical nuero-pathways into their brain that will never be forgotten.

There is a better way. What do children like to do most? PLAY. How about you play math? "Preposterous!" you say. Math is anything but fun. The way you were taught math was probably anything but fun. This is true. There are ways that are quite powerful using manipulatives and blocks that with just a little direction from the parents can instill math concepts in tots without them even knowing they are learning math. They are ways to teach math through play that although the child may know they are doing math it's still fun. Imagine having your kids ask if they can play math. It happens. Try searching Crewton Ramome Math Enrichment.

With little kids up to about seven or eight you can just use your hands and show all the addends for numbers up to 10. Start with one hand, hold up 5 fingers and then grab two. 3 plus what makes 5? 3 + x = 5, 5 + x = 10 etc. How many is in my hand? Same principal but have raisins or something put 4 in one hand 3 in the other close the hand with three and say I have seven how many in this hand?...if they get it right they get to eat the three raisins, and you can say 7 minus 3 is 4. If you have big wooden blocks there should be a block that is equal to two smaller blocks and maybe even 4 smaller blocks, Have them show you "half." Then "a quarter" or one fourth show them two fourths is the same as a half. Keep it simple and fun. Don't make it a lesson, make it a game, or just point things out while playing with blocks.

There are now many pages and hours of FREE videos that show direct proof that math can be fun. Little kids actually like algebra, it's fun! They don't need to write symbols to learn math concepts. For little girls an early positive math experience is especially crucial. What does it do for a child's self esteem to be considered smart at math? Have fun. Play math. Learn how.

Crewton Ramone Advanced Pythagorean Application

2011-12-13T15:48:00.005-10:00

a² + b² = c² Is easy to understand when you can see it. I need a new white board this one has gotten quite a bit of use...anyhow the vid at the bottom of the page shows how to find the height of a triangle when you only know the sides.

Here is a young bright Honor student who has all "A's" in everything but math. All students (and a lot parents) blame the teacher first when they fail or don't understand. Sometimes this is true and sometimes the teacher is doing the best they can with the tools they have. Other times the student is a little brat and it wouldn't matter who the teacher was the kid would be failing or getting "C's" or what have you on their own account, not because of the teacher. There is also the personality factor, I don't get along with everybody, I don't know about you but I figured out a long time ago you can't please everybody and you will be unhappy if you try.

I always spend a little time getting to know the student first before I take them on, sometimes it's better to refer them elsewhere or say no than yes. It's pretty rare, but it happens. But I digress.

This student is smart, quick minded and when whatever it is, is explained she usually gets it right away or takes meticulous notes so she can study it later if it's iffy. This way we cover the most ground possible. This student does; however, have huge gaps in her math skill sets that need to be addressed but we usually spend all our time studying for the tests instead of increasing her conceptual knowledge base and brushing up on her computation. As with most students I meet, multiplication tables are not mastered, nor are fractions or the basics of algebra specifically hero zero and no fun get back to one.

Happily Pythagorean Theorem (⇐ click that to go to go to CRHOM's page on it) made sense to her because it is pretty straight forward and my explanation using blocks is visually obvious as the Montessori folk like to say.

Here she is being introduced to Pythagorean Theorem the Crewton Ramone House Of Math way. Note this student is advanced and we are pressed for time so this isn't the best presentation for little kids, go to the house of math for that.

I want to stress this is a sharp high school student. (A little freaked out by math but still very quick minded.) This is NOT how you would present it to a young student or a 6th grader or even a not so sharp junior. More examples and don't jump to subtraction after just one problem. You cab see the confusion this causes, happily I am there to clear things up, but I am not always there. And most often things don't get cleared up. Note how I use easy problems that have answers that are whole numbers that don't require a calculator. She can easily see 10 as an answer as compared to a problem with a long decimal for the answer. This also adds to the confusion. Once you understand the concepts all they can do is change the numbers...

After a very short time she is getting it. But three passes do not a quarterback make. PRACTICE is required. Also note how for the most part she told me the formulas, when I told her the formulas she had already got them she just had a little trouble verbalizing them. Contrast this with just telling them to memorize the formula.

Not the best lesson but a good lesson overall. In my defense we were rushing because we had a lot of ground to cover, she had an upcoming test, and she was flustered. Now, this would normally only be on a password protected page, but in the spirit of Christmas, the Flying Spaghetti Monster appeared to me in a dream while driving a fast car, and told me specifically to make this video available to anyone who could find it. In a few weeks this post will be buried on this blog like many other great posts I've made over the years and you will have to search to find it. I have 100's of videos on youtube now. Finding the one you want is made easier with a password because on my website they are grouped by subject. Also many of the vids are unlisted so like the one below you have to know where it is to find it, it won't show up on a search.

It is also on a couple of the password protected pages like advanced algebra, because the problems shown are classic algebra problems that appear in every textbook ever written about algebra...or just about. Now you might have to be in Algebra II but it's basic algebra application as far as I'm concerned. Very few kids figure out how to do this on their own and over the years many kids have come to me failing to understand how to do these kinds of problems...

Find h.

Students and teachers who have spent time at the house of math have very little trouble understanding this problem because they understand the basic concepts behind each step and the computation doesn't pose a problem. (Get it? I crack myself up.)

You can also see for sure that the drawing on her paper is "not to scale."

I have been told by more than one person the vid above is actually fun to watch because they "get it." A lot of that goes on at the house of math.

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Do Your Own Math.

2011-12-08T09:26:00.006-10:00

Research Citations Linking Vaccines To Disease

I did not write this or gather this information, I just found theis PDF and put on the web. Please feel free to cut and paste this elsewhere. Soon I will have post about a certain Danish study analyzing their graphical data from a purely mathematical point of view. ~Crewton Ramone

http://preventdisease.com/news/pdf/Research_Citations_Linking_Vaccines_To_Disease.pdf

Bichel, "Post-vaccinial Lymphadenitis Developing into Hodgkin’s Disease", Acta Med Scand, 1976, Vol 199, p523-525.

Stewart, AM, et al, "Aetiology of Childhood Leukaemia", Lancet, 16 Oct, 1965, 2:789-790. [Listed under Vaccine Adverse Reactions.]

Glathe, H et al, "Evidence of Tumorigenic Activity of Candidate Cell Substrate in Vaccine Production by the Use of Anti-Lymphocyte Serum", Development Biol Std, 1977, 34:145-148.

Bolognesi, DP, "Potential Leukemia Virus Subunit Vaccines: Discussion", Can Research, Feb 1976, 36(2 pt 2):655-656.

Colon, VF, et al, "Vaccinia Necrosum as a Clue to Lymphatic Lymphoma", Geriatrics, Dec 1968, 23:81- 82.

Park-Dincsoy, H et al, "Lymphoid Depletion in a case of Vaccinia Gangrenosa", Laval Med, Jan 1968, 39:24-26.

Hugoson, G et al, "The Occurrence of Bovine Leukosis Following the Introduction of Babesiosis Vaccination", Bibl Haemat, 1968, 30:157-161.

Hartstock, , ""Post-vaccinial Lymphadenitis: Hyperplasia of Lymphoid Tissue That Simulates Malignant Lymphomas", Apr 1968, Cancer, 21(4):632-649.

Allerberger, F, "An Outbreak of Suppurative Lymphadenitis Connected with BCG Vaccination in Austria- 1990/1991," Am Rev Respir Disorder, Aug 1991, 144(2) 469.

Omokoku B, Castells S, "Post-DPT inoculation cervical lymphadenitis in children." N Y State J Med 1981 Oct;81(11):1667-1668.

Vaccines and Chromosome Changes Leading to Mutations:

Knuutila, S et al, "An Increased Frequency of Chromosomal Changes and SCE’s in Cultured Lymphocytes of 12 Subjects Vaccinated Against Smallpox," Hum Genet, 1978 Feb 23; 41(1):89-96.

Cherkeziia, SE, et al, "Disorders in the Murine Chromosome Apparatus Induced By Immunization with a Complex of Anti-viral Vaccines," Vopr Virusol, 1979 Sept Oct, (5):547-550.

[Note: SCE means sister chromatid exchange and is an indication that genetic mutations are occurring, which could possibly lead to cancer-causing mutations.]

Vaccines and Auto-immunity Citations:

Romanov, V A, et al, "Role of Auto-immune Processes in the Pathogenesis of Post-Vaccinal Lesions of the Nervous System", Oct 1977, Zh Mikrobiol Epidemiol Immunobiol, 10:80-83.

Grachev, V P, et al, "Formation of Auto-antibodies in Laboratory Animals After Inoculation of Viruses With Different Virulence. I. Results of Studies ..., July 1973, Acta Virol (Praha), 17:319-326.

Movsesiants, AA, et al, "Experimental Study of the Ability of Different Strains of Vaccinia Virus to Induce Auto-Antibody Formation", Vopr Virusol, May-Jun 1975; (3):297-302.

Negina, IuP, "Comparative Study of Auto-antibody Formation Following Immunization With Different Types of Typhoid Vaccines", Zh Mikrobiol Epidemiol Immunobiol, May 1980; (5):69-72.

Vaccinations and Diabetes Citations:

Sinaniotis, et al, "Diabetes Mellitus after Mumps Vaccination", Arc Dis Child, 1975, 50:749.66

Polster, H, "Diabetes insipidus after Smallpox vaccination", Z Aerztl Fortbild (Jena), 1 Apr 1966, 60:429-432.

Patan, "Postvaccinal Severe Diabetes Mellitus", Ter Arkh, Jul 1968, 40:117-118.

Classen, JB, MD, "The Timing of Immunization Affects The Development of Diabetes in Rodents", Autoimmunity, 1996, 24:137-145.

Classen JB, "The diabetes epidemic and the hepatitis B vaccines," N Z Med J, 109(1030):366 1996 Sep 27. [letter]

Classen JB, "Childhood immunisation and diabetes mellitus," N Z Med J, 109(1022):195 1996 May 24 [letter]

Poutasi K, " Immunisation and diabetes," N Z Med J 1996 Jul 26;109(1026):283. [letter; comment]

Other Articles Linking Diabetes to Vaccines:

Dokheel, T M, "An Epidemic of Childhood Diabetes in the United States? Evidence from ....", Diabetes Care, 1993, 16:1606-1611.

Parent ME, et al, "Bacille Calmette-Guerin vaccination and incidence of IDDM in Montreal, Canada," Diabetes Care 1997 May; 20(5):767-772.

House DV, Winter WE, "Autoimmune diabetes. The role of auto-antibody markers in the prediction and prevention of insulin-dependent diabetes mellitus," Clin Lab Med 1997 Sep; 17(3):499-545.

Zeigler, M et al , "[Autoantibodies in type 1 diabetes mellitus]" Z Arztl Fortbild (Jena). 1994 Aug; 88(7- 8):561-5

Vaccines and Nervous System Changes:

Bondarev, VN et al, "The Changes of the Nervous System in Children After Vaccination", Pediatria, Jun 1969; 48:20-24.

Ehrengut W, "Central nervous sequelae of vaccinations," Lancet 1986 May 31;1(8492):1275-1276.

Provvidenza, G et al, [On a Case of Benign Acute Cerebellar Ataxia in Childhood], Arch Ital Sci Med Trop, 43:189-194, Apr 1962.

Katsilambros, L, "[The Phenomenom of Apathy in Man and Animals After the Injection of Viruses in Very High Doses. Clinical Data]", Rev Med Moyen Orient, 20:539-546, Nov – Dec 1963.

Vaccinations and Autism Citations:

Eggers, C, "Autistic Syndrome (Kanner) And Vaccinations against Smallpox", Klin Paediatr, Mar 1976, 188(2):172-180.

Kiln MR, "Autism, inflammatory bowel disease, and MMR vaccine." Lancet 1998 May 2;351(9112):1358.

Selway, "MMR vaccination and autism 1998. Medical practitioners need to give more than reassurance." BMJ 1998 Jun 13;316(7147):1824.

Nicoll A, Elliman D, Ross E, "MMR vaccination and autism 1998," MJ 1998 Mar 7;316(7133):715-716.

Lindley K J, Milla PJ, "Autism, inflammatory bowel disease, and MMR vaccine."Lancet 1998 Mar 21;351(9106):907-908.

Bedford H, et al, "Autism, inflammatory bowel disease, and MMR vaccine." Lancet 1998 Mar 21;351(9106):907.

Vijendra K. Singh, Sheren X. Lin, and Victor C. Yang, "Serological Association of Measles Virus and Human Herpesvirus-6 with Brain Autoantibodies in Autism," Clinical Immunology and Immunopathology, Oct 1998, Vol. 89, No. 1, p 105-108. ["None of the autistic children in the study had measles in the past, but all had the MMR" stated David Whalgren.

Vaccines and Demyelination Citations:

Herroelen, L et al, "Central-Nervous-System Demyelination After Immunization with Recombinant Hepatitis B Vaccine", Lancet, Nov 9, 1991, 338(8776):1174-1175.

Kaplanski G, Retornaz F, Durand J, Soubeyrand J, "Central nervous system demyelination after vaccination against hepatitis B and HLA haplotype." J Neurol Neurosurg Psychiatry 1995 Jun; 58(6):758-759.

Matyszak MK, Perry VH, "Demyelination in the central nervous system following a delayed-type hypersensitivity response to bacillus Calmette-Guerin." Neuroscience 1995 Feb;64(4):967-977.

Tornatore CS, Richert JR, "CNS demyelination associated with diploid cell rabies vaccine." Lancet 1990 Jun 2;335(8701):1346-1347.

Adams, JM et al, "Neuromyelitis Optica: Severe Demyelination Occurring Years After Primary Smallpox Vaccinations", Rev Roum Neurol, 1973, 10:227-231.

In 1988, Dietrich used MRI to show that developmentally delayed children had alterations in their myelin. Coulter described that central nervous system damage can be exhibited as abnormal behavior of the child. In 1935, Thomas Rivers, experimental allergic encephalitis (EAE) can be the result of a viral or bacterial infection of the nervous system. "The fact of the matter is that it is a matter of record that it was known that vaccination produced encephalitis since 1926." The authors stated, "In regions in which there is no organized vaccination of the population, general paralysis is rare. ... It is impossible to deny a connection between vaccinations and the encephalitis (brain damage) which follows it."

Vaccines have been linked to seizures, convulsions and epilepsy.

Vaccinations and Seizures:

Hirtz DG, Nelson KB, Ellenberg J H, "Seizures following childhood immunizations", Pediatr 1983 Jan; 102(1):14-18.

Cherry JD, Holtzman AE, Shields WD, Buch D, Nielsen, "Pertussis immunization and characteristics related to first seizures in infants and children,"J Pediatr 1993 Jun;122(6):900-903.

Coplan J, "Seizures following immunizations," J Pediatr 1983 Sep;103(3):496.

Barkin RM, Jabhour JT, Samuelson J S, "Immunizations, seizures, and subsequent evaluation," JAMA 1987 Jul 10;258(2):201.

Griffin MR, et al, "Risk of seizures after measles-mumps-rubella immunization," Pediatrics 1991 Nov;88(5):881-885.

Griffin MR, et al, "Risk of seizures and encephalopathy after immunization with the diphtheria- tetanus-pertussis vaccine," JAMA 1990 Mar 23-30;263(12):1641-1645.

Cizewska S, Huber Z, Sluzewski W, "[Prophylactic inoculations and seizure activity in the EEG]," Neurol Neurochir Pol 1981 Sep-Dec;15(5-6):553-557. [Article in Polish]

Huttenlocher PR, Hapke RJ, "A follow-up study of intractable seizures in childhood." Ann Neurol 1990 Nov; 28(5):699-705.

Blumberg DA, "Severe reactions associated with diphtheria-tetanus-pertussis vaccine: detailed study of children with seizures, hypotonic-hypo-responsive episodes, high fevers, and persistent crying."Pediatrics 1993 Jun; 91(6):1158-1165.

Vaccinations and Convulsions Citations:

Prensky AL, et al, "History of convulsions and use of pertussis vaccine," J Pediatr 1985 Aug; 107(2):244-255.

Baraff LJ, "Infants and children with convulsions and hypotonic-hypo-responsive episodes following diphtheria-tetanus-pertussis immunization: follow-up evaluation," Pediatrics 1988 Jun; 81(6):789-794.

Jacobson V, "Relationship of pertussis immunization to the onset of epilepsy, febrile convulsions and central nervous system infections: a retrospective epidemiologic study," Tokai J Exp Clin Med 1988;13 Suppl: 137-142.

Cupic V,et al, "[Role of DTP vaccine in the convulsive syndromes in children]," Lijec Vjesn 1978 Jun; 100(6):345-348. [Article in Serbo-Croatian (Roman)]

Pokrovskaia NIa, "[Convulsive syndrome in DPT vaccination (a clinico-experimental study)]," Pediatriia 1983 May;(5):37-39. [Article in Russian]

Vaccinations and Epilepsy Citations:

Ballerini, Ricci, B, et al, "On Neurological Complications of Vaccination, With Special Reference to Epileptic Syndromes," Riv Neurol, Jul-Aug 1973, 43:254-258.

Wolf SM, Forsythe A, "Epilepsy and mental retardation following febrile seizures in childhood," Acta Paediatr Scand 1989 Mar;78(2):291-295.

Vaccines and Brain Swelling:

Iwasa, S et al, "Swelling of the Brain in Mice Caused by Pertussis ... Quantitative Determination and the Responsibility of the Vaccine", Jpn J Med Sci Biol, 1985 , 38(2):53-65.

Mathur R, Kumari S, "Bulging fontanel following triple vaccine." Indian Pediatr 1981 Jun;18(6):417- 418.

Barry W, Lenney W, Hatcher G, "Bulging fontanelles in infants without meningitis." Arch Dis Child 1989 Apr;64(4):635-636.

Shendurnikar N, "Bulging fontanel following DPT" Indian Pediatr 1986 Nov;23(11):960.

Gross TP, Milstien JB, Kuritsky JN, "Bulging fontanelle after immunization with diphtheria-tetanus- pertussis vaccine and diphtheria-tetanus vaccine." J Pediatr 1989 Mar;114(3):423-425.

Jacob J, Mannino F, "Increased intracranial pressure after diphtheria, tetanus, and pertussis immunization." Am J Dis Child 1979 Feb;133(2):217-218.

Dugmore, WN, "Bilateral Oedema at the Posterior Pole. Hypersensitivity Reaction to Alavac P injection." Br J Ophthalmol, Dec 1972, 55:848-849.

Vaccines and Neurological Damage:

Nedar P R, and Warren, R J, "Reported Neurological Disorders Following Live Measles Vaccine", 1968, Ped, 41:997-1001.

Paradiso, G et al, "Multifocal Demyelinating Neuropathy after Tetanus Vaccine", Medicina (B Aires), 1990, 50(1):52-54.

Landrigan, PJ, Whitte, J, "Neurologic Disorders Following Live Measles-virus Vaccination", JAMA, Mar 26, 1973, v223(13):1459-1462.

Turnbull, H M, "Encephalomyelitis Following Vaccination", Brit Jour Exper Path, 7:181, 1926.

Kulenkampff, M et al, "Neurological Complications of Pertussis Inoculation", Arch Dis Child, 1974, 49:46.

Strom, J, "Further Experience of Reactions, Especially of a Cerebral Nature in Conjunction with Triple Vaccination", Brit Med Jour, 1967, 4:320-323.

Berg, J M, "Neurological Complications of Pertussis Immunization," Brit Med Jour, July 5,1958; p 24.

Bondarev, VN et al, "The Changes of the Nervous System in Children After Vaccination", Pediatria, Jun 1969; 48:20-24.

Badalian, LO, "Vaccinal Lesions of the Nervous System in Children," Vop Okhr Materin Dets, Dec 1959, 13:54-59

Lorentz, IT, et al, "Post-Vaccinal Sensory Polyneuropathy with Myoclonus", Proc Aust Ass Neurol, 1969, 6:81-86.

Trump, R C, White, T R, "Cerebellar Ataxia Presumed Due To Live Attenuated Measles Virus Vaccine," JAMA, 1967, 199:165-166.

Allerdist, H, "Neurological Complications Following Measles Vaccination", Inter Symp, Brussels, 1978, Development Biol Std, Vol 43, 259-264.

Finley, K H, "Pathogenesis of Encephalitis Occurring With Vaccination, Variola and Measles, Arch Neur and Psychologist, 1938; 39:1047-1054.

Froissart, M et al, "Acute Meningoencephalitis Immediately after an Influenza Vaccination", Lille Med, Oct 1978, 23(8):548-551.

Pokrovskaia, Nia, et al, "Neurological Complications in Children From Smallpox Vaccination", Pediatriia, Dec 1978, (12):45-49.

Allerdist, H, "Neurological Complications Following Measles Virus Vaccination. Evaluation of the Cases seen Between 1971-1977'', Monatsschr Kinderheilkd, Jan 1979, 127(1): 23-28.

Ehrengut, W et al, "On Convulsive Reactions Following Oral vaccination Against Polio", Klin Paediatr, May 1979, 191(3):261-270.

Naumova, R P, et al, "Encephalitis Developing After Vaccination without a Local Skin Reaction", Vrach Delo, Jul 1979, (7):114-115.

Goswamy, BM, "Neurological Complications After Smallpox Vaccination", J Ass Phys India, Jan 1969, 17:41-43.

Schchelkunov, SN et al, "The Role of Viruses in the Induction of Allergic Encephalomyelitis," Dokl Akad Nauk SSSR, 1990,315(1):252-255. [Vaccines contain viruses, too]

Walker AM, "Neurologic events following diphtheria-tetanus-pertussis immunization," Pediatrics 1988 Mar;81(3):345-349.

Shields WD, et al, "Relationship of pertussis immunization to the onset of neurologic disorders: a retrospective epidemiologic study," J Pediatr 1988 Nov; 113(5):801-805.

Wilson J, "Proceedings: Neurological complications of DPT inoculation in infancy," Arch Dis Child 1973 Oct; 48(10):829-830.

Iakunin IuA, "[Nervous system complications in children after preventive vaccinations]," Pediatriia 1968 Nov; 47(11):19-26. [Article in Russian]

Greco D, et al, "Case-control study on encephalopathy associated with diphtheria-tetanus immunization in Campania, Italy," Bull World Health Organ 1985;63(5):919-925.

Ehrengut W at Institute of Vaccinology and Virology, Hamburg, Germany states, "Bias in the evaluation of CNS complications following pertussis immunization are the following: 1) Notifications of post-immunization adverse events, 2) Publications by vaccine producers on the frequency of adverse reactions, 3) Comparison of permanent brain damage after DPT and DT immunization, 4) Pro- immunization, 5) Immunization associated viral encephalitis, 6) Accuracy of statistics, 7) Personal. A review of these points indicates an underestimation of CNS complications after pertussis immunization."
Reference: Ehrengut W, "Bias in evaluating CNS complications following pertussis immunization." Acta Paediatr Jpn, 1991 Aug; 33(4):421-427.

Vaccinations and Unexplained Diseases:

Hiner, E E, Frasch, C E, "Spectrum of Disease Due to Haemophilus Influenza Type B Occurring in Vaccinated Children", J Infect Disorder, 1988 Aug; 158(2): 343-348.

Olin P, Romanus, V, Storsaeter, J, "Invasive Bacterial Infections During an Efficiacy Trial of Acellular Pertussis Vaccines — Implications For Future Surveilance In Pertussis Vaccine Programmes", Tokai J Exp Clin Med, 1988; 13 Suppl: 143-144.

Storsaeter, J, et al, "Mortality and Morbidity From Invasive Bacterial Infections During a Clinical Trial of Acellular Pertussis Vaccines in Sweden", Pediatr Infect Disorder J, 1988 Sept; 7(9):637-645.

Vadheim, CM, et al, "Effectiveness and Safety of an Haemophilus Influenzae type b Conjugate Vaccine (PRP-T) in Young Infants. Kaiser-UCLA Vaccine Study Group," Pediartics, 1993 Aug; 92(2):272-279. [The vaccines caused fevers, irritability, crying, and seizures, but were declared to be "safe and ... effective ... ".]

Stickl, H, "Estimation of Vaccination Damage", Med Welt, Oct 14, 1972, 23:1495-1497.

Waters, VV, et al, "Risk Factors for Measles in a Vaccinated Population", JAMA, Mar 27, 1991, 265(12): 1527.

Stickl, H, "Iatrogenic Immuno-suppression as a Result of Vaccination", Fortschr Med, Mar 5, 1981, 99(9);289-292.

Vaccine Citations Linking the Vaccine to the "prevented" Disease:

Nkowane, et al, "Vaccine-Associated Paralytic Poliomyelitis, US 1973 through 1984, JAMA, 1987, Vol 257:1335-1340.

Quast, et al, "Vaccine Induced Mumps-like Diseases", nd, Int Symp on Immun, Development Bio Stand, Vol 43, p269-272.

Green, C et al, "A Case of Hepatitis Related to Etretinate Therapy and Hepatitis B Vaccine", Dermatologica, 1991, 182(2):119-120.

Shasby, DM, et al, "Epidemic Measles in Highly Vaccinated Population", NEJM, Mar 1977, 296(11): 585-589.

Tesovic, G et al, "Aseptic Meningitis after Measles, Mumps and Rubella Vaccine", Lancet, Jun 12, 1993, 341(8859):1541.

Johnson, RH, et al, "Nosocomial Vaccinia Infection", West J Med, Oct 1976, 125(4):266-270.

Malengreau, M, "Reappearance of Post-Vaccination Infection of Measles, Rubella, and Mumps. Should Adolescents be re-vaccinated?" Pedaitric, 1992;47(9):597-601 (25 ref)

Basa, SN, "Paralytic Poliomyelitis Following Inoculation With Combined DTP Prophylactic. A review of Sixteen cases with Special Reference to Immunization Schedules in Infancy", J Indian Med Assoc, Feb 1, 1973, 60:97-99.

Landrigan, PJ et al, "Measles in Previously Vaccinated Children in Illinois", Ill Med J, Arp 1974, 141:367-372.

NA, "Vaccine-Associated Poliomyelitis", Med J Aust, Oct 1973, 2:795-796.

Vaccine Failures Citations:

Hardy, GE, Jr, et al, "The Failure of a School Immunization Campaign to Terminate an Urban Epidemic of Measles," Amer J Epidem, Mar 1970; 91:286-293.

Cherry, JD, et al, "A Clinical and Serologic Study of 103 Children With Measles Vaccine Failure", J Pediatr, May 1973; 82:801-808.

Jilg, W, et al, "Inoculation Failure Following Hepatitis B Vaccination", Dtsch Med wochenschr, 1990 Oct 12; 115(41):1514-1548.

Plotkin, SA, "Failures of Protection by Measles Vaccine," J Pediatr, May 1973; 82:798-801.

Bolotovskii, V, et al, "Measles Incidence Among Children Properly Vaccinated Against This Infection", ZH Mikrobiol Epidemiol Immunobiol, 1974; 00(5):32-35.

Landrigan, PJ, et al, "Measles in Previously Vaccinated Children in Illinois", Ill Med J, Apr 1974; 141:367-372.

Strebel, P et al, "An Outbreak of Whooping Cough in a Highly Vaccinated Urban Community", J Trop Pediatr, Mar 1991, 37(2): 71-76.

Forrest, JM, et al, "Failure of Rubella Vaccination to Prevent Congenital Rubella,"Med J Aust, 1977 Jan 15; 1(3): 77.

Jilg, W, "Unsuccessful Vaccination against Hepatitis B", Dtsch Med Wochenschr, Nov 16, 1990, 115(46):1773.

Coles, FB, et al, "An Outbreak of Influenza A (H3N2) in a Well-Immunized Nursing home Population," J Am ger Sociologist, Jun 1992, 40(6):589-592.

Jilg, W, et al, "Inoculation Failure following Hepatitis B Vaccination," Dtsch Med Wochenschr, Oct 12, 1990, 115(41):1545-1548.

Hartmann, G et al, "Unsuccessful Inoculation against Hepatitis B," Dtsch Med Wochenschr, May 17, 1991, 116(20): 797.

Buddle, BM et al, "Contagious Ecthyma Virus-Vaccination Failures", Am J Vet Research, Feb 1984, 45(2):263-266.

Mathias, R G, "Whooping Cough In Spite of Immunization", Can J Pub Health, 1978 Mar/Apr; 69(2):130-132.

Osterholm, MT, et al, "Lack of Efficacy of Haemophilus b Polysacharide Vaccine in Minnesota", JAMA, 1988 Sept 9; 260(10:1423-1428.

Johnson, RH, et al, "Nosocomial Vaccinia Infection", West J Med, Oct 1976, 125(4):266-270.

Vaccines Causing Another Vaccinal Disease:

Basa, SN, "Paralytic Poliomyelitis Following Inoculation With Combined DTP Prophylactic. A review of Sixteen cases with Special Reference to Immunization Schedules in Infancy", J Indian Med Assoc, Feb 1, 1973, 60:97-99.

Pathel, JC, et al, "Tetanus Following Vaccination Against Small-pox", J Pediatr, Jul 1960; 27:251-263.

Favez, G, "Tuberculous Superinfection Following a Smallpox Re-Vaccination", Praxis, July 21, 1960; 49:698-699.

Quast, Ute, and Hennessen, "Vaccine-Induced Mumps-like Diseases", Intern Symp on Immunizations , Development Bio Stand, Vol 43, p 269-272.

Forrest, J M, et al, "Clinical Rubella Eleven months after Vaccination," Lancet, Aug 26, 1972, 2:399-400.

Dittman, S, "Atypical Measles after Vaccination", Beitr Hyg Epidemiol, 19891, 25:1-274 (939 ref) Sen S, et al, "Poliomyelitis in Vaccinated Children", Indian Pediatr, May 1989, 26(5): 423-429.

Arya, SC, "Putative Failure of Recombinant DNA Hepatitis B Vaccines", Vaccine, Apr 1989, 7(2): 164- 165.

Lawrence, R et al, "The Risk of Zoster after Varicella Vaccination in Children with Leukemia", NEJM, Mar 3, 1988, 318(9): 543-548.

Vaccination Citations and Death:

Na, "DPT Vaccination and Sudden Infant Death – Tennessee, US Dept HEW, MMWR Report, Mar 23, 1979, vol 28(11): 132.

Arevalo, "Vaccinia Necrosum. Report on a Fatal Case", Bol Ofoc Sanit Panamer, Aug 1967, 63:106-110.

Connolly, J H, Dick, G W, Field, CM, "A Case of Fatal Progressive Vaccinia", Brit Med Jour, 12 May 1962; 5288:1315-1317.

Aragona, F, "Fatal Acute Adrenal Insufficiency Caused by Bilateral Apoplexy of the Adrenal Glands (WFS) following Anti-poliomyelitis Vaccination", Minerva Medicolegale, Aug 1960; 80:167-173.

Moblus, G et al, "Pathological-Anatomical Findings in Cases of Death Following Poliomyelitis and DPT Vaccination", Dtsch Gesundheitsw, Jul 20, 1972, 27:1382-1386.

NA, "Immunizations and Cot Deaths", Lancet, Sept 25, 1982, np.
Goetzeler, A, "Fatal Encephalitis after Poliomyelitis Vaccination", 22 Jun 1961, Muenchen Med Wschr, 102:1419-1422.

Fulginiti, V, "Sudden Infant Death Syndrome, Diphtheria-Tetanus Toxoid-Pertussis Vaccination and Visits to the Doctor: Chance Association or Cause and Effect?", Pediatr Infect Disorder, Jan-Feb 1983, 2(1): 7-11.

Baraff, LJ, et al, "Possible Temporal Association Between Diphtheria-tetanus toxoid-Pertussis Vaccination and Sudden Infant Death Syndrome", Pediatr Infect Disorder, Jan-Feb 1983, 2(1): 5-6.

Reynolds, E, "Fatal Outcome of a Case of Eczema Vaccinatum", Lancet, 24 Sept 1960, 2:684-686.

Apostolov. et al, "Death of an Infant in Hyperthermia After Vaccination", J Clin Path, Mar 1961, 14:196-197.

Bouvier-Colle, MH, "Sex-Specific Differences in Mortality After High-Titre Measles Vaccination", Rev Epidemiol Sante Publique, 1995; 43(1): 97.

Stewart GT, "Deaths of infants after triple vaccine.", Lancet 1979 Aug 18;2(8138):354-355.

Flahault A, "Sudden infant death syndrome and diphtheria/tetanus toxoid/pertussis/poliomyelitis immunisation.", Lancet 1988 Mar 12;1(8585):582-583.

Larbre, F et al, "Fatal Acute Myocarditis After Smallpox Vaccination", Pediatrie, Apr-May 1966, 21:345- 350.

Mortimer EA Jr, "DTP and SIDS: when data differ", Am J Public Health 1987 Aug; 77(8):925-926.

Vaccines and Metabolism Citations:

Deutsch J, " [Temperature changes after triple-immunization in infant age]," Padiatr Grenzgeb 1976;15(1):3-6.[Article in German]

NA, "[Temperature changes after triple immunization in childhood]," Padiatr Grenzgeb 1976;15(1):7- 10. [Article in German]

[Considering that the thyroid controls our Basal Metabolism, it would appear that vaccines altered (depressed) thyroid activity.]

Vaccines Altering Resistance to Disease:

Burmistrova AL, "[Change in the non-specific resistance of the body to influenza and acute respiratory diseases following immunization diphtheria-tetanus vaccine]," Zh Mikrobiol Epidemiol Immunobiol 1976; (3):89-91. [Article in Russian]

Vaccinations and Deafness Citations:

So I did a background check to see if there was any scientific evidence linking vaccines to deafness and hearing loss. Here are some of the articles I found:

Kaga, "Unilateral Total Loss of Auditory and Vestibular Function as a Complication of Mumps Vaccination", Int J Ped Oto, Feb 1998, 43(1):73-73

Nabe-Nielsen, Walter, "Unilateral Total Deafness as a Complication of the Measles- Mumps- Rubella Vaccination", Scan Audio Suppl, 1988, 30:69-70

Hulbert, et al, "Bilateral Hearing Loss after Measles and Rubella Vaccination in an Adult", NEJM, 1991 July, 11;325(2):134
Healy, "Mumps Vaccine and Nerve Deafness", Am J Disorder Child, 1972 Jun; 123(6):612

Jayarajan, Sedler, "Hearing Loss Following Measles Vaccination", J Infect, 1995 Mar; 30(2):184-185

Pialoux, P et al, "Vaccinations and Deafness", Ann Otolaryng (Paris), Dec 1963, 80:1012-1013.

Angerstein, W, et al, "Solitary Hearing and Equilibrium Damage After Vaccinations", Gesundheitswesen, May 1995, 57(5): 264-268.

Brodsky, Stanievich, "Sensorineural Hearing Loss Following Live Measles Virus Vaccination", Int J Ped Oto, 1985 Nov; 10(2):159-163

Koga, et al, "Bilateral Acute Profound Deafness After MMR Vaccination- Report of a Case", Nippon Jibiin Gakkai Kai, 1991 Aug;94(8):1142-5

Seiferth, LB, "Deafness after Oral Poliomyelitis Vaccination – a Case Report and Review", HNO, 1977 Aug; 25(8): 297-300

Pantazopoulos, PE, "Perceptive Deafness Following Prophylactic use of Tetanus anittoxin", Laryngoscope, Dec 1965, 75:1832-1836.

Zimmerman, W, "Observation of a case of Acute Bilateral Hearing Impairment Following Preventive Poliomyelitis Vaccination (type 3)", Arch Ohr Nas Kehlkopfheilk, 1965, 185:723-725.

Vaccinations and Kidney Disorders Citations:

Jacquot, C et al, "Renal Risk in Vaccination", Nouv Presse Med, Nov 6, 1982, 11(44):3237-3238.

Giudicelli, et al, "Renal Risk in Vaccination", Presse Med, Jun 11, 1982, 12(25):1587-1590.

Tan, SY, et al, "Vaccine Related Glomerulonephritis", BMJ, Jan 23, 1993, 306(6872):248.

Pillai, JJ, et al, "Renal Involvement in Association with Post-vaccination Varicella", Clin Infect Disorder, Dec 1993, 17(6): 1079-1080.

Eisinger, AJ et al, "Acute Renal Failure after TAB and Cholera Vaccination", B Med J, Feb 10, 1979, 1(6160):381-382.

Silina, ZM, et al, "Causes of Postvaccinal Complications in the Kidneys in Young Infants", Pediatria, Dec 1978, (12):59-61.

Na, "Albuminurias", Concours Med, Mar 1964, 85:5095-5098.[vaccination adverse reactions]

Oyrl, A, et al, "Can Vaccinations Harm the Kidney?", Clin Nephrol, 1975, 3(5):204-205.

Mel’man Nia, "[Renal lesions after use of vaccines and sera]." Vrach Delo 1978 Oct;(10):67-9, [Article in Russian]

Silina ZM, Galaktionova TIa, Shabunina NR, "[Causes of postvaccinal complications in the kidneys in young infants]." Pediatriia 1978 Dec;(12):59-61, [Article in Russian]

Silina EM, et al, "[Some diseases of the kidneys in children during the 1st year of life, following primary smallpox vaccination and administration of pertusis-diphtheria-tetanus vaccine]." Vopr Okhr Materin Det 1968 Mar; 13(3):79-80, [Article in Russian]

Vaccines and Skin Disorders Citations:

Illingsworth R, Skin rashes after triple vaccine," Arch Dis Child 1987 Sep; 62(9):979.

Lupton GP, "Discoid lupus erythematosus occurring in a smallpox vaccination scar," J Am Acad Dermatol, 1987 Oct; 17(4):688-690.

Kompier, A J, "Some Skin Diseases caused by Vaccinia Virus [Smallpox]," Ned Milt Geneesk T, 15:149- 157, May 1962.

Weber, G et al, "Skin Lesions Following Vaccinations," Deutsch Med Wschr, 88:1878-1886, S7 Sept 1963.

Copeman, P W, "Skin Complications of Smallpox Vaccination," Practitioner, 197:793-800, Dec 1966.

Denning, DW, et al, "Skin Rashes After Triple Vaccine," Arch Disorder Child, May 1987, 62(5): 510-511.

Vaccinations and Abcesses:

Sterler, HC, et al, "Outbreaks of Group A Steptococcal Abcesses Following DTP Vaccination", Pediatrics, Feb 1985, 75(2):299-303.

DiPiramo, D, et al, "Abcess Formation at the Site of Inoculation of Calmette-Guerin Bacillus (BCG)," Riv Med Aeronaut Spaz, Jul-Dec 1981, 46(3-4):190-199.

Vaccinations and Shock:

Caileba, A et al, "Shock associated with Disseminated Intravascular Coagulation Syndrome following Injection of DT.TAB Vaccine, Prese Med, Sept 15, 1984, 13(3):1900.

Vaccines: The Weird, The Wild and The Hilarious Citations:

Sometimes there are articles published about the strangest facts related to vaccines that defies our imagination and ability to understand them. They were written seriously by well-meaning scientific persons, but their titles can be seen differently. Some are funny, some are sad and some are purely scientific folly. See if you can figure these out:

Pathel, JC, et al, "Tetanus Following Vaccination Against Small-pox", J Pediatr, Jul 1960; 27:251-263. [Now you need a tetanus vaccination!]

Favez, G, "Tuberculous Superinfection Following a Smallpox Re-Vaccination", Praxis, July 21, 1960; 49:698-699. [Super means large/big/great!]

Bonifacio, A et al, "Traffic Accidents as an expression of "Iatrogenic damage", Minerva Med, Feb 24, 1971, 62:735-740. [But officer I was just vaccinated!]

Baker, J et al, "Accidental Vaccinia: Primary Inoculation of a Scrotum", Clin Pediatr (Phila), Apr 1972, 11:244-245. [Ooops, the needle slipped.]

Edwards, K, "Danger of Sunburn Following Vaccination", Papua New Guinea Med J, Dec 1977, 20(4):203. [Are vaccines phototoxic?]

Stroder, J, "Incorrect Therapy in Children", Folia Clin Int (Barc), Feb 1966, 16:82-90. [Agreed.]

Wehrle PF, "Injury associated with the use of vaccines," Clin Ther 1985;7(3):282-284. [Dah!]

Alberts ME, "When and where will it stop", Iowa Med 1986 Sep; 76(9):424. [When!]

Breiman RF, Zanca JA, "Of floors and ceilings — defining, assuring, and communicating vaccine safety", Am J Public Health 1997 Dec;87(12):1919-1920. [What is in between floors and ceilings?]

Stewart, AM, et al, "Aetiology of Childhood Leukaemia", Lancet, 16 Oct, 1965, 2:789-790.

Nelson, ST, "John Hutchinson On Vaccination Syphilis (Hutchinson, J)", Arch Derm, (Chic), May 1969, 99:529-535. [Vaccinations and STDs!]

Mather, C, "Cotton Mather Anguishes Over the Consequences of His Son’s Inoculation Against Smallpox", Pediatrics, May 1974; 53:756. [Is it for or against?]

Thoman M, "The Toxic Shot Syndrome", Vet Hum Toxicol, Apr 1986, 28(2):163-166. [Animals are not exempt from vaccination damage either!]

Johnson, RH, et al, "Nosocomial Vaccinia Infection", West J Med, Oct 1976, 125(4):266-270. [Nosocomial means a disease acquired in a doctor's office or hospital.]

Heed, JR, "Human Immunization With Rabies Vaccine in Suckling Mice Brain," Salud Publica, May-Jun 1974, 16(3): 469-480. [Have you had your suckling mice brains today?]

Tesovic, G et al, "Aseptic Meningitis after Measles, Mumps and Rubella Vaccine", Lancet, Jun 12, 1993, 341(8859):1541. [AM has same symptoms as poliomyelitis!]

Buddle, BM et al, "Contagious Ecthyma Virus-Vaccination Failures", Am J Vet Research, Feb 1984, 45(2):263-266.

Freter, R et al, "Oral Immunization And Production of Coproantibody in Human Volunteers", J Immunol, Dec 1963, 91:724-729. [Guess what copro- means .... Feces.]

NA, "Vaccination, For and Against", 1964, Belg T Geneesk, 20:125-130. [Is it for or against?]

Sahadevan, MG et al, "Post-vaccinal Myelitis", J Indian Med Ass, Feb 16, 1966, 46:205-206. [Did I mention myelitis?]

Castan, P et al, "Coma Revealing an acute Leukosis in a child, 15 days after an Oral Anti-poliomyelitis Vaccination," Acta Neurol Bekg, May 1965, 65:349-367. [Coma from vaccines!]

Stickl, H, et al, "Purulent [pus] meningitides Following Smallpox Vaccination. On the Problem of Post- Vaccinal Decrease of Resistance", Deutsch Med Wschr, Jul 22, 1966, 91:1307-1310.

[Vaccines are the injection of viruses cultured from pus ... ]

Mercury:

You will want to watch these several times they are PACKED with info:

Packed with info but he never does tell you how to detox mercury...

Here is this:

10 biggest vaccine news stories of 2011

(NaturalNews) A lot happened in the vaccine industry in 2011 -- a year of accelerating change and increased awareness among the people. One of the big realizations that hit home in 2011 is that vaccines are far more dangerous than most people previously thought, and even conventional scientists are starting to question the over-vaccination of infants and children.

Here are the 10 biggest vaccine news stories of 2011, reported on NaturalNews.com:

http://www.naturalnews.com/034525_vaccines_news_stories.html http://www.naturalnews.com/034525_vaccines_news_stories.html

Fun Kindergarten Math Activities: Dboyz Play With Bigger Polynomials

2011-12-06T20:57:00.004-10:00

Here are some fun problems:

We cover all of these in the longer 20 minute video. Here is the short version, but you can get to the longer vid from here if you like:

In order to get here we played with basic concepts for months. With a password you can have access to hours and hours of video, sample lessons, PDF's and more and you can see step by step how a 6 year old got here. People are quite amazed at just how much you can get for 3 bucks or 12 bucks for an annual pass. Those who buy annual passes before the end of the year are in for some pleasant surprises next year, along with those of you who have already bought a annual pass to show your support...prices will be going up and there are more products being worked on as we speak that will be available at good discounts for those who have already gotten an annual pass. Also there are going to be separate passwords for various topics but right now one password does it all. For those who just want to take a peak 3 bucks gets you a good 60 days worth...but don't expect any special treatment.

For a more complete blog post on with these very same videos go to Math Genius Making.

Of course be sure to find us on FaceBook, and go to the House Of Math for much more on the best use of base ten blocks and manipulatives for math enrichment so your child or students can be doing math like this with no problem.

Stay tuned like I say on my website, "I'm just getting started."

Big Blocks Big Fun Big Concepts.

2011-12-03T12:04:00.008-10:00

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....

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

"Perpendicular To"

2011-09-11T10:42:00.001-10:00

Short explanation of a symbol in geometry, with a very lame explanation of how to use a negative inverse to make a perpendicular line.... After further review we did a much more thorough lesson on how to make perpendicular lines with slope intercept form. Anyhow math really is no fun if you don't know what the symbols mean.

Crewton Ramone Two Shorts on Geometry

2011-08-13T14:43:00.001-10:00

Remembering complimentary angles and supplementary angles can be tricky. It also causes some people to think all math is, is memorization.

I always hear questions like, "can this do algebra, can this do geometry, can this do calculus?"...with "this" meaning Mortensen Math and the blocks. How do you apply manipulatives to Geometry or Trig? The basic concepts remain the same throughout the mathematics.

In cases like this all we are doing is learning vocabulary:

So there is a fast way to remember vocabulary. The problem is when you confuse vocabulary with understanding concepts or where you confuse memorization with conceptualization and problem solving. Some seem to think there is no difference between memorizing vocabulary words and memorizing formulae or addends or multiplication tables. Nothing could be further from the truth. We can "figure out" or use an algorithm that requires some thinking and doing to derive the quadratic, or even πr² or something simple like how to remember 9's times tables rather than just commit a bunch of facts to memory but with definitions there is no "figuring out" per se you either know it or you don't.

Although with reasoning and logic you may use induction or deduction to figure out a word's meaning it's not quite the same as knowing enough algebra to solve for x when given a second degree polynomial in standard form set equal to zero.

ax² + bx + c = 0 and coming up with the quadratic formula...and just memorizing the quadratic formula. With complimentary angles and supplementary angles it is very difficult to deduce which one means two angles which when added add up to 90 degrees and which one means two angles which when added add up to 180 degrees, unless you know quite a bit more English than the average highschooler has at their command...you either know what "table" means or you don't. Same with complimentary angles and supplementary angles. Don't confuse memorizing definitions of words or terms with wrote memorization of formula.

Now once we have the definitions down we can start to do some simple problem solving.

Turns out this stuff was super easy after all. We also covered distance formula which as just slightly advanced Pythagorean Theorem and a few or math terms and definitions that come with geometry like parallel and perpendicular, and then the names of angles, and poof, a few problems and the hour was over.

Just Playing Math With Base 10 Blocks

2011-08-06T21:09:00.004-10:00

At my house this doesn't even qualify as "math time" anymore. It's just playing blocks. The fact that they are learning their addends and other math facts as well as refining their motor skills is an added bonus.

When we did do math we basically fooled around with factoring quadratics and distributive theory.

They multiplied problems like 5(3x + 2) = 15x + 10.

And factored problems like x² + 12x + 27...

They learned LOTS of math doing these and more problems like them. We laffed, we cried, we spent some time learning addends and multiplication and factoring via the algebra. Most places you are supposed to know your math facts BEFORE you get to algebra. If you want to watch the lesson you will need a password so you can go to the sample lessons page. If you click that link you will go directly to it or click the picture below...it will ask you for your password and should redirect you to the vid, or just click on the URL in the address window of your browser and hit enter, if not just scroll down until you see the video titled More Algebra for Basic Ops. Also check out the vids right ABOVE it.

Here is a super short sample of the 36 minute video.

Passwords are cheap and easy to get and don't change near as often as they should. # bucks will get you in for at leaste 60 days, and it will take you about that long to watch all the stuff I have up.

Find us on FaceBook and Twitter.

More Everyday Math

2011-08-04T15:18:00.003-10:00

Basically all we did was play with our food. By the time I thought about getting the camera out we were down to about 20 grapes...we had already eaten more than half. We practiced the all important concept "numbers are made of other numbers".

I was mostly focusing on addition and subtraction and multiplication he threw in division on his own at the end...so we covered all the basic operations. We could have easily gone down the fractions road...but we didn't. Main thing is to keep it simple and fun. Talking about math concepts as you manipulate real world objects helps them understand and add meaning to the abstract symbols they see.

Also the theme of late is math rich environment. That doesn't mean you have to be rich and spend a lot of money on manipulatives you can create a math rich environment pretty easily...just takes a little imagination and an idea of what you want to impart that day. Everyday math activities should be relatively short simple and fun.

You can't go wrong just play math. This is a great preschool math activity...or depending on where your child is and how late you started it could be a first grade math activity, or even second grade. I teach math concepts early using this method compared to public schools. By the end of second grade this boy will know his 45 addends and multiplication tables thru 12. Very little of it will come from drills with pencil and paper or math worksheets. Most of it will come from play. The worksheets and paper and pencil will reinforce what he already knows it won't be the primary tool for learning these math facts and concepts. He will also have tools and algorithms for figuring out problems he hasn't been exposed to and will quickly find there are quite a few patterns and rules that are immutable. A basic concept for teachers to understand is all math is IS COUNTING. So you can do adding or algebra, counting or calculus from day one. It's all just counting.

Seriously. Which way would YOU have rather learned?

FACEBOOK.

For new comers this may be a little hard to digest. Search this blog and my website you will see how we actually use algebra to teach counting and other basic concepts instead of the mindset where these concepts have to be mastered BEFORE we introduce algebra...

Addends Towers In Full Motion.

2011-07-30T20:37:00.001-10:00

You have seen pictures and descriptions of addends towers and other games at Crewton Ramone's House of Math since pretty much day one, but here it is on video for the first time. This is a staple of Mortensen Math. You HAVE to set the rules for the lesson: they have to build the levels with addends not just four 7's or whatever.

These two little girls are a ton of fun and a bit of a challenge when it comes to behavior management. This was part of a lesson that engaged them the whole hour. At the end of it we did algebra but we barely got started and it was time to go...it felt like they were there for 5 or 10 minutes. Thus proving my own axiom to myself: "make it fun."

With these two I just have to get a little more creative and keep things moving so te have little or no time to quarrel with each other...and certainly no time to get bored. I fully understand in a classroom situation you can't make it exciting every single minute, that would be exhausting for everybody; however, on the other hand some classrooms are so boring the kids get diagnosed with ADD or ADHD, they're not attention deficient, they bored to tears. Solution: drugs.

I have a different solution. Engage the student with MRE's. Math Rich Environments. Make sure those MRE's are activity rich too. Book work is boring. Necessary, but boring for little kids. As they get older you will be moving to symbols anyway but at the younger ages they need hands on activities. Think of it the same way you think of teaching reading. In the beginning the books have a lot more pictures than words and gradually move to words, but by 7 there is still lots more page devoted to pictures than to words.

Same for math...remember start in the concrete, then move to pictures and lastly to symbols. If you do it right the symbols might even be a reward and something they look forward to...drawing with pens on the board is fun, and along with the pictures move them to making symbols...

And as always don't just use these powerful tools to teach addition and place value. You can use them to teach counting through calculus...and one day you will see that as I use algebra to teach counting you can use calculus to teach counting and multiplication too...so literally teach counting through calculus.

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Simple Symbols Lesson

2011-07-30T10:58:00.003-10:00

The best way to start any lesson on Math Symbols is with a three period lesson. You may need to repeat it once or twice...it's important that they hear you read the symbols and that you add meaning as you go.

Here is a synopsis of about 30 minutes of a lesson on some math symbols. We had also done this several times before. This student is Autistic which doesn't mean can't learn, it means takes more time and impressions to get info into the part of the brain where it can be recalled. This one is often missed by students who have made the rule hard and fast in their heads two negatives equal a positive: -|-3| because they don't understand the concept of absolute value and fail to read the math symbols correctly.

When doing absolute value I often just talk about the block itself doesn't matter what side it's on a four block is "four" long. In her case though this explanation didn't sit as well because she wanted to be sure the block was on the positive side since all absolute values are positive. Other students seem to get the idea of "it's four from here to here" no matter which way you go. This also explains why the difference of two negative numbers is still positive.

Bright young students might inquire why it is that -22 - ^-28 = 6 where all the numbers are negative and we're even subtracting! The answer somehow ends up positive.

The difference can be explained in terms of direction on a number line, but as far as I have seen number lines and direction help confuse things, not clarify them. It's not about direction, it's about distance. The amount of "space" between the numbers, delineated by numbers themselves. Most kids don't ask. Might be wise not to bring it up especially with students who have poor self confidence in math. For the inquisitive ones and older students it can quickly devolve into a discussion on philosophy. How do you know the distance from here to here is four...? Keep it simple instead.

Explain what the math symbols mean and use blocks to bring the points home. Integers are no problem if presented properly. Look for more lessons on integers here on this blog and at the house of math where Sarah has her own page. The way I see it if you can explain it to Autistic students or little kids in a way they can understand then adults and older students as well as "gifted" students should be duck soup. Most of the time this is true. Often you have to get through math anxiety and other problems first with the older students.

Bottom line keep it simple.

“If you can't explain it simply, you don't understand it well enough”. ~Albert Einstein

I have made 100's of dollars re-explaining integers and reading symbols to all manner of students and have almost universally heard that using blocks makes it easier. Of late I have run into a lot of students who just want something to memorize rather than wanting to understand...understanding concepts is better.

Problem Solving Is The Whole Point

2011-07-15T14:30:00.002-10:00

I used to keep a overhead slide of a Far Side Cartoon By Gary Larsen with me as I introduced my two hour lecture on Problem Solving. It showed a picture of the devil and a bunch of books; on closer inspection all the books were story problems and the caption read "Libraries in Hell".

It was worth a chuckle. The point of learning the language of mathematics is for problem solving. Counting and computation as I have said many times are for doing math but the point of being able to count quickly (using basic operations) is to solve problems. Story problems show some of the uses for algebra and computation, build up problem solving skills. Problem solving skills include logic and reasoning, which together help form critical thinking skills. Some of the skills learned along the way include using mathematics to express reality, that is, translating real world situations into mathematical symbols and then knowing what those symbols mean. Turns out the same symbols can be used to express lots of different things...

Of course the vid gets cut off at the very end. If you watch it we will see that Spaceman Spiff catches him after 3 minutes. How far away from the moon base are they when he does? An astounding 90+% of students can NOT do two stage problems, that is solve a problem to get the answer to another problem. Once I find X, I can evaluate the equations and see if they are same. In mathematics once we find one variable we can usually find other variables easily. If we understand the concepts.

In calculus we study one and several variables. I used to start my pre-calc lecture where we just did linear algebra by asking the people in the room especially college graduates and teachers to give me a short definition of calculus anybody could understand. 99.99999% of the time none of them could. They might come up with some convoluted definition that even they were somewhat unsure of or come up with a very complex definition that they understood but when asked the rest of the room was not able to make sense of it...and I we would all laugh. This happened in cities from Maine to Maui and everywhere in between. The stress test was always could a little kid "get it." I have a simple definition. Look for it in an upcoming blog post meantime think of one for yourself if you've studied calculus.

In linear algebra we just begin to delve into calculus concepts and the most basic concept of all: the idea of a variable and how two variables interact. For now we are just fooling around with X. Later, as we see at the bottom of the page we can get into Y. (Make up your own joke.)

"The most powerful single idea in mathematics is the notion of a variable." ~K. Dewdney

So we start off with X.

Lets take this problem for example. 3x + 4 = 2x + 9 we can tell a story about Spaceman Spiff, or snowball fights, or we can just play with the blocks and add more meaning later. The idea is not to just give them a set of rules. Give them concepts and algorithms that make sense and that they can see in action.

The basic concepts in use here are Hero Zero, No Fun Get Back To One and of course the rectangle.

They can then use those concepts and algorithms to DO math, rather than just memorizing rules and process...which we have seen DOES NOT WORK. But who is in charge of math education? The 5% who easily memorized rules and process...see the problem? Good, because they don't.

The problem solving page is starting to grow. There is also a Password Protected Problem Solving Page now with more stuff on it. There are tons of common, perennial classic, story problems that students get exposed to during their journey through mathematics. Rate and Distance, Boat and Stream, Percents, Mixture and Solution, (I have some 5% solution and some 12% solution, how much 12% solution do I have to mix with 5% solution to get 8% solution)...there also some like in the case of ordered pairs that they don't get exposed to and never get to understand. I know a ton of students that could not tell you that an ordered pair could be a story about a water tank or a doughnut factory and the resulting equation could be a graph of the production or amount of water as it fills the tank. All they "know" is slope intercept form, y = mx + b, and points on a graph. Half the time they can't remember which is the x and y axis. How this relates to a story about a tank of water or factory or anything else.

In that short 60 second clip I don't tell the story that went with the symbols but in the longer video OF COURSE I do. Here is a story:

I have a doughnut factory. After 3 hours, there were 16 cases of doughnuts, and after 8 hours, there were 31 cases of doughnuts how many cases where there to begin with and how many cases do they make per hour? That's the most basic story. You can do the same with a tank of water, after 3 hours 16 feet of water after 8 hours, 31 feet of water in the tank. How fast is the tank filling up and and how much water must have been in there to start?

Then you can throw extra bells and whistles like the tank holds 40 feet of water how long does it take to fill? Go negative and drain the tank...use 39 and make them do fractions...but make sure the concepts are understood before you do any of that.

You can find many amazing and easy ways to explain these in the Series A Manuals from Mortensen Math. Eventually, I will make videos of all of these kinds of problems but it takes time because I take the many steps in the degrees of difficulty...and don't just dive in and do the problems. Parents and Home schoolers seem to appreciate this, but it's driving some of the math teachers crazy.

This method is slower at first but pretty soon it goes faster and faster until it surpasses traditional methods by far and you see little ten year old kids that seem like geniuses...it all starts with a game for 4 year olds called "what's under the cup?"

There is also some problem solving going up on Sarah's Page.

Playing With Nines Again

2011-07-15T12:24:00.001-10:00

Nines seem to pose a bit of a problem for a lot of students but actually it's one of the easiest times tables because there are so many "tricks" you can use to count and multiply by nines.

Here is another video showing yet another way to do it...there are more ways. Here is counting by nines with younger students.

There is a way to use your fingers too. I have to make a short vid on that one too...meantime here is a short post on a simple way to count rapidly by nines.

Advanced What's Under The Cup

2011-07-10T18:57:00.003-10:00

Math is more fun if you make a game of it. But eventually games are no fun if they are too easy and present no challenge. They are also no fun if they are too hard. There is a game called "what's under the cup?" that many think is just for little kids.

The idea is to start easy then advance by degrees. You will find that pretty soon your students are doing some pretty "serious" algebra. The idea is to understand the concepts and the way you do that is obviously not to memorize a lot of rules and formula. In fact, you will see students begin to make up their own rules as they get better at playing "what's under the cup?"

At first problems like these pose a challenge as the students are learning to count, and can pose a problem for some students when these are first introduced in 5th or 6th grade. They get confused with "inverse addends" and "inverse functions", as well as rules about walking across the equals sign...just tell me what has to be under the cup.

Once this game becomes easy, you can move on to more advanced what's under the cup. Problem Solving is easy and you will see their thinking skills improve as they use their computation skills to start doing math via algebra. I thought this lesson was about 10 minutes long, turns out it's 25 minutes long. Times flies when your having math.

This was their first time playing advanced what's under the cup like this. The next time will be easier and the time after that easier still. Each time we play another concept can be introduced and other concepts reinforced. Look for more vids with other kids in the coming weeks where we start adding negative numbers...they will be on the advanced algebra page...

The video above will be added to the Problem Solving page. Which is about to undergo a revamp...or I may have to add a another page or two. Meantime you can search "Crewton Ramone Problem Solving" in your favorite search engine or on Youtube.

Here is a video that gives an overview for older students who don't have the luxury of taking one concept at a time. This is really advanced what's under the cup:

And the little boys can do this also...the game is called find stuff that's same on both sides...

So nice to have the luxury of time! When I made that video I had 10 minutes to get the point across and Youtube gave you one minute grace and I used every second of it. Now I can pause and blab about food and whatever bounces into their heads...and eventually you will see the boys doing some of the exact same problems you see in the second video. If you keep it simple and make it so the answer ends up being x equals a number they are actually easier than some of the problems in the first video...

Look us up on Facebook and Twitter...you might consider a password as a donation. This project is pretty much 100% powered by passwords and some larger donations I have received. People are quick to send me emails asking questions, advice, and for videos on specific topics but pretty slow to send even three bucks. Those who buy combo kits or take lessons get free passwords and those who donate 25 bucks or more have found they get vids made for them pretty quickly and everybody gets a response to email eventually...some quicker than others, but I generally answer them all. If you already have base ten blocks or know somebody who does, make sure you let them know about this site and encourage them to get a password.

I always enjoy the emails that basically say, "what can I do to help?" Some people have some great and creative ideas. The best thing you can do is spread the word. That doesn't mean sell passwords for me. That means just post on your Facebook page, share posts or vids with friends, hit the "like" button, or "tweet" button, make comments, that's the best help. Eventually I will take some of you up on some of the offers...but for now just spread the word...oh, and get a password. Even three bucks helps...

Algebra Is Counting and Not Really That Complex

2011-07-10T10:59:00.003-10:00

Algebra is just generic math. We count stuff. That stuff has names. We can use it for lots of things. Problem solving. Honing our critical thinking skills. Learning to count. Simple stuff like that.

This nine year old can already count, so all I'm doing is giving him new stuff to count. That stuff has names, like "x to the third" and "x squared" and "x", you can also teach kids who are just learning the names of numbers these too: it's just more vocabulary. Mostly I find that the teachers themselves are the ones who have a bias against counting "x to the thirds" due to their own ill experiences with math, but really, to little kids it's just counting.

Little kids actually enjoy algebra because it's like learning with puzzles...the teacher can add more or less meaning as needed, depending on age and skill level.

This little snippet may look impressive but if you watch the whole thing which is on the "advanced" algebra page you can see it was easy and fun and it was a natural progression. The child even made up the problem himself.

I watched the long version of the video with a certain pair of students who were four and six and they made me stop the video so they could answer before the child in the video did. You can also do this with your students. I know three bucks is a lot to pay for a home made 22 minute video but you also get pdf's and access to literally 50+ more videos. Go crazy and spend 12 bucks and you get that access for a year and you'll see how much stuff I add weekly is worth a buck a month.

It will be a while before we move into negative expressions and we still have to play around quite a bit before we start setting these equal to zero and solving them and then move on to graphing them. One step at a time.

Also for homework you could take that last problem we did and draw it so that one side is x² + 2x + 1 and the other is 3x + 2. You'll get the same thing just in a different shaped rectangle. There's often more than one way to factor third and fourth degree problems.

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Addition, Multiplication, Fractions and Algebra, Oh My!

2011-07-09T13:10:00.004-10:00

This is a short snippet from a video that's 26 minutes long which you can find on the sample lessons page.

This is short and simple, all the lessons in this class were too. Math is always easy when you can see it and the concepts are "visually obvious".

We started reducing fractions and SEEING the common factor, he was getting them all correct but then got snagged on this one. He only saw the symbols not the blocks as soon as they can see the blocks it's easy, and only requires the most basic counting skills. 14/35 without the blocks requires some multiplication and/or division skills in order to discover the common factor.

Then we moved on to other basic operations like addition and subtraction, and of course we played around a little in algebra, factoring polynomials. The whole video requires a password...although some people got a link to it free on Facebook.

As you watch the longer video you should be able to see the five concepts in action and why I stress multiplication facts mastery. You need to be able to count quickly, and being able to do so will allow you to see patterns and relationships easily. For example 14/35 is the same as 2/5. Further, it's easy to see (2/5)(7/7) = 14/35 and of course (14/35)/(7/7) = 2/5. Later when the numbers are more complex, the basic concepts will remain the same. Also 2/5 = x/35 will also be easy.

Anyhow, the 26 minute video is full of math; short lessons that should be easy for you to duplicate. They all blend together into what we call basic operations. For more go to the House Of Math. If you are new to all of this you can watch a short vid that shows what happens to little kids when they are taught this way, watch an overview of the Mortensen Math method and peruse a ton of videos on various topics.

Crewton Ramone Math is Counting With Savmack.

2011-07-05T14:01:00.001-10:00

The twins who have both now figured out first had that having fun with math and fooling around are not exactly the same thing, and they both have the time outs to prove it had a great fast fun lesson with math. We learned a few concepts and mostly practiced what we already knew. We practiced addends, algebra and factoring also spent time seeing that multiplication and division "go together".

When 60 minutes seems like 5 minutes I know I'm on the right track. This video basically covers everything we did...it's about half an hour:

The idea is to introduce simple concepts one or two at a time. that way it's never scary or overwhelming. Traditional approaches seem to confuse introducing concepts into bite size pieces with segmentation to the point where the whole is lost. You want to trickle feed the information but the feed has to be continuous and cohesive. What often ends up happening is reduction to the ridiculous where students get lost in computation without seeing the whole picture. They get confused and think computation IS math, instead of understanding that computation is part of doing math.

You can rarely separate the two, just like it is difficult to separate water from milk...although it can be done it's usually better to just drink the milk. I could continue on with this metaphor but I think you get the point. I can't figure out if they end up with water or powdered milk in public schools although if you are thirsty powdered milk isn't going to quench your thirst...

Anyhow, the idea is to keep it simple and keep it at or below the child's level and add "challenges" as they are ready. The worst thing you can do is put a child in a position where they can't succeed. Note who they tell me how easy it is and this is the cue to make it a little harder using two red squares...they get it after a little work, and it's self correcting. Keep the basic concepts in mind as you introduce more math concepts.

See what happens when this approach is used early on...here.

Reducing Fractions

2011-07-01T12:51:00.003-10:00

This shot is from the end of the lesson where we squeeze in a couple of problems in Algebra, he factors a couple of polynomials. It's fun and easy and a nice break from "all the fractions stuff."

This lesson brought home the point that multiplication makes ALL the other math easier because it allows you to count very quickly. You can do these problems without having multiplication facts down but it sure takes longer. Little kids who only have the ability to count should still be exposed to these concepts but the problems should be smaller and easier to count.

The concept of one, common factors, and equivalent fractions and multiplication and division are all bundled up into one here and should be deconstructed for the student so they can see each part and how it goes together.

This video covers the hour lesson from start to finish. We start with all 45 addends, move to multiplication mostly just to see his progress, and we do a little subtraction, he asks for help with fractions and so we do some and then end with algebra again the hour flies by. This vid is packed with concept rich content.

You may notice that we discuss the basic concepts in passing as we go along. This is a longer video and I've found many people won't watch it as soon as they see the time. If you have children who are learning fractions concepts you may want to take the time at some point to show them this video as they will SEE the common factor and why it is that "as we do above so we do below." Rather than just giving the rule of dividing both the numerator and denominator by the same number. We we move on to more complex algebraic fractions the concept remains the same.

My fractions page is still in disarray but you can find links and more vids there too, plus some PDF's, people seem to want fractions worksheets and I need to get more made, but there are a few there right now.

Find me on Facebook, and Twitter and you might want to subscribe to my Youtube channel as many videos go there that don't make it here. You can find sessions that I document for parents and such. On the entire internet there is only one Crewton Ramone. Also now you can usually easily find follow up vids if you notice the P1 in front of the tittle...just go to the password pages and look for P2 and P3 with identical titles.

3rd Power Algebra? It's Just Complex Counting.

2011-06-29T14:29:00.001-10:00

Here is an excerpt from a lesson where we played around with some third degree algebra made rectangles and counted the sides.

You can see from the vid we are in the drawing stage, but we still get out manipulatives so we can get a solid handle on what we are doing which is counting. We start off with all positive expressions and basically factor them. Then we move on to expressions with negative coefficients and do division too. When you are first starting out just doing one problem can take up 15 minutes or more...but then as the understanding increases it will go faster and faster.

The way to increase understanding is not to do the same thing over and over again just using symbols and changing the problems, the way to get them to "get it" is to start in the concrete move to drawings and increase the degree of difficulty gradually as concepts are understood and mastered. This also shows how important neat writing is...lol...sloppy symbols can make the difference between an A and a B, or worse a C and an F. Also, for those with a password you will see on the follow up vids on the Advanced Algebra Page. Password costs all of 3 bucks or $12 for a year pass. Buck a month is hard to beat.

You will note sometimes I say one thing and mean another in these vids when I read the problems and say "x-squared" instead of "x to the third" and so on. I watched one vid where I did it over and over again...but eventually I say it right. Painful for me to watch.

Problems like x³-4x²+x+6/x-2 take a long time just to say but they are quite instructive. They are also intimidating to some students who find them confusing and scary just because of all the symbols, but once we get into it and it becomes familiar, they see that actually it's pretty easy...just have to count and keep track. Here we are going over the positive ones:

As usual I forget to turn the camera on until we've done a lot of them. Remember always start in the concrete, use three period lessons and make sure drawing is part of the lesson too, don't just use symbols.

Here we see that base x also has place value and answer the question "why do they go where they go?"...you'll see this on the next video look for "P2 Crewton Ramone and Syd Play with the 3rd Powers" on the Advanced Algebra page. Scroll down to the part that covers 3rd and 4th power.

My friends in Africa have shown that the passwords are valuable enough to steal, and enjoy putting jibberish in the email list box to let me know they have gotten into the password pages without paying. So far the ISP's trace back to Ghana and Nigeria. It's good to know they have enough value to some that they are worth stealing. Passwords will change soon so put your name in when you get in, that way you can be kept up to date on the new password and the new stuff that's being added so you can get the most out of your password while it works. Also Next year prices will go up a little again as more and more people find out about how cool this is. Those who have passwords or have bought passwords will get special discounts on renewals. If you buy kits or products from me or take tutoring you automatically get a password gratis.

Be sure to find me on Facebook or follow along on Twitter. There's only one Crewton Ramone so searching out vids and pages should be pretty easy.

Happy Tau Day

2011-06-28T14:34:00.002-10:00

This is fun especially since it's the 28th. Of course it's even more fun when you look at the symbols, π and τ, Tau looks like half a Pie to me and Pie looks like 2τ, stuck together but that besides the point.

When we talk about radians tau really does simplify things. And math is about simplicity and beauty although you would be hard pressed to get the average high school algebra student to agree.

The boys have π memorized out to 3.14 lol, but they beginning to understand what it means...c/d. I will slowly increase this week by week...until they get out well past 20...JFSAG. 3.14159625...1971.

And while I posting other people's Youtube vids might as well put this one up. Note how he tries to make it clear that mathematics is just the language we use to describe the philosophy, math in and of itself cannot BE the philosophy of economics. And way back when, when I used to study economic theory as an aside when I was teaching people to pass the standardized tests to get securities licenses I too though these freaking formulas don't mean anything!! Turns out I wasn't the only one.

More Autistic Intergers Plus Algebra Too

2011-06-28T14:15:00.001-10:00

This is a pretty good lesson for beginners on integers. I believe in introducing integers EARLY. The one thing missing in this lesson is the time consuming task of drawing the problems. This step should not be left out especially for the younger students.

Again you don't want to draw every single problem (or build every single problem with the blocks) but you don't want to skip drawing them either. This vid is a lesson AFTER lessons where we drew quite a few of them. I did not get vid of the preivious sessions where she drew them. On the internet that means it didn't happen...lol..but I assure you it did. DRAWING IS A MUST. It's not optional. Why? Because it works. It bridges the gap between the symbols and the blocks. For some students this gap is wider than others, so more drawing may need to be done.

The drawing and symbols can go together and they can be very simple. In fact the better understood the concepts are, the less complex the drawings need to be, so some kids may start off with complex drawing of whatever it is, in this case integers and you will encourage them to move to simpler drawing and finally symbols only.

Drawings of integers usually involve holes in the ground, not a number line. Or up in Washinton and Idaho and a few other places a log standing on end can be put in holes and then figure out how much is sticking out...make up stories that the kids can relate to in their own situations. In the city that might be telephone poles or whatever. You can also combine drawings and blocks on a white board quite easily...draw a hole 3 deep, and then put a nine block in it. Show the various ways we can write this. -3+9, 9-3, 9+(-3), -3-(-9), etc...

Got to The House Of Math and find Sarah's page, the tab says Sarah SL for the complete vid P1 and P2 and also P3 which is another 6 minutes on algebra with negative factors. These vids might create greater understanding for students and teachers who are NOT autistic or working with SPED students too.

11 Year Old Math Enrichment

2011-06-23T14:31:00.002-10:00

Here is an 11 year old who is just getting started at the house of math. His primary assignment is to work on multiplication.

While he is doing that, I expose him to various basic math concepts. He has played in algebra and fractions, and he is seeing that multiplication helps because it allows you count quickly. This gives some motivation to work on his multiplication. I specifically tell him (and his parents) not to just drill on multiplication tables but to play games, listen to music, and generally mix it up so it doesn't become tedious and boring.

We also work on addends...addition and multiplication are just ways of counting quickly. We need to be able to count quickly in order to math but math IS NOT computation in and of itself.

In just three lessons he has already come a long way.

The third lesson is a lesson on fractions if you'd like to see it you need a password and you can find it here (currently at the bottom of the page) called Fractions with Koa. My fractions page needs work, but there is a lot of stuff there and I have a few fractions worksheets for beginners up too. You can download the pdfs and see more vids with a password.

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Algebra Is Child's Play

2011-06-18T12:55:00.003-10:00

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.

Math Erichment For Two (Twin) Girls

2011-06-18T11:23:00.001-10:00

These two are bright and energetic...their math experience is limited so it's more fun and exciting for them than a lot of kids their age...each lesson is full of discoveries. Makes it fun for me two. Now the trick will be trying to capture some of the ah-ha moments on video.

Here is a snippet of my first meeting with them. They informed me that they don't do multiplication.

We played and had fun and the hour went quickly. Their mother and little sister stayed for the first one. A good time was had by all.

The next lesson was just the two of them and we covered a lot of ground...their homework was and will be "do multiplication."

Normally you need a password to see vids like this but just for fun and because it's basically a compilation of a bunch of other stuff with other students you can already get for free on Youtube or my Screencast channel, I put it here for you for FREE. Lets other parents see how to run a lesson for beginners too.

As you can see we cover lots of ground and lots of concepts just to expose them to the mathematics, not expecting them to retain it all for a test later. They are being exposed to math. We will focus on the basics of counting and then get to more complex counting as we move along but they are seeing first hand is that all math is, is counting. Multiplication allows you to count very quickly and therefore MUST be mastered.

There are many half hour and longer sample lessons on the password protected pages at Crewton Ramones's House of Math along with pdf's and detailed explanations of how to teach various topics of math using manipulatives...there are also tutorials for parents and teachers as well as links to an hour over-view of Mortensen Math.

Math Erichment For Any Age

2011-06-04T11:52:00.003-10:00

Look at these problems. They would pose a challenge for most high school kids and even college students...but actually they are child's play:

Here you can see both the symbols and the drawings if you know what you are looking for...the skill required to solve these is quite simply the ability to count.

Here is a simple video:

Find out more:

http://www.crewtonramoneshouseofmath.com

Advanced Number Identification

2011-05-31T19:49:00.004-10:00

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

There they are suffering through another math lesson.

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

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

1/2

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

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

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

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

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

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

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

The Difference of Two Squares

2011-05-31T17:41:00.003-10:00

They call it that because it is.

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

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

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

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

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

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

x² - 25 = (x + 5)(x - 5)

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

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

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

Factoring Polynomials For Fun At Four

2011-05-31T16:07:00.002-10:00

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

To see the whole lesson click here.

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

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

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

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

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

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

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

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

Factoring Fun With The Wee Ones

2011-05-24T12:01:00.001-10:00

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

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

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

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

Which ladder you you rather climb?

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

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

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

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

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

Come play with us on Facebook.

Time To Get Negative.

2011-05-22T15:38:00.005-10:00

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

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

x² - 25

or

x² - x - 6

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

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

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

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

For example:

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

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

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

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

Via email:

Hi there

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

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

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

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

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

Regards
Carol

Math Concepts, Conceptualization vrs Memorization

2011-05-21T14:06:00.004-10:00

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

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

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

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

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

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

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

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

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

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

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

3x + 3 = 2x + 7 etc

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

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

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

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Addends, Pythagoras and Math Fun

2011-05-20T18:25:00.011-10:00

THIS IS A GREAT LESSON

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

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

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

Check out the sample lessons at the house of math!

OR

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

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

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

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

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

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

http://www.crewtonramoneshouseofmath.com/

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

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

4 Year Old Factors Polynomials No Problem

2011-05-19T23:47:00.002-10:00

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

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

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

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

Crewton Ramone Overview of Mortensen Math

2011-05-19T12:20:00.004-10:00

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

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

Here is the text of the Youtube vid page:

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

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

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

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

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

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

Sample Lessons For Manipulative Math

2011-05-18T12:05:00.006-10:00

Lola, Ruby and Opra help teach ALGEBRA.

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

x² + 9x + 18

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

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

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

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

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

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

Crewton Ramone Expounds on The Math Methodology

2011-05-17T14:06:00.002-10:00

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

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

Addends Past 10

2011-05-16T16:32:00.005-10:00

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

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

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

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

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

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

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

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

Autistic Integers

2011-05-15T19:41:00.003-10:00

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

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

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

Meet The Parents.

2011-05-04T16:10:00.002-10:00

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

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

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

Here we are going back in time:

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

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

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

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

Multiplication Math Town

2011-05-04T15:41:00.001-10:00

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

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

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

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

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

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

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

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

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

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

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

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

Special Triangles, SOH CAH TOA and laughs...

2011-05-04T11:07:00.004-10:00

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

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

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

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

Here is a little more on that:

Yet more on radicals:

And how to introduce these concepts to little kids:

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

Patient Problem Solving.

2011-04-28T22:42:00.005-10:00

Yeah, what he said:

I don't have patients I have students..but still really captures a few issues in a short period of time. I watch this every couple of months...

I need to put more math problem solving videos up.

Here are a few:

Problem Solving with Crewton Ramone.

Crewton Ramone Problem Solving w/ Fractions.

Crewton Ramone Problem Solving With Sarah

Crewton Ramone Simple Systems of Equations

Find us on Face Book...I'm the only Crewton Ramone.

Mortensen Math Squeeks Back To Life...

2011-04-25T23:12:00.002-10:00

Here is a video from the early 90's...

People always wonder about the nature of the relationship between Matt Dillon and Miss Kitty, likewise the relationship between Crewton Ramone and Mortensen Math. Let's just say we go way, way back...

Due to a shall we say, a slight altercation between myself and the Marketing Company that produced the promotional video I was edited out of the vid with the little boy who does the Algebra, even though it was my idea to use him and I'm the one that taught his parents, (particularly his mother) how to use the kit they just bought.

I'm bringing up another generation of testimonials on Maui as we speak. For example:

Multiplication and algebra are the two things we focused on, when I met her she was still adding on her fingers...now: 100's. Before she got a 28 on one test...we haven't even done 10 lessons yet. It's not that Crewton Ramone is so awesome, it's that the methodology IS.

Here is a FAQ at the house of math.

Crewton Ramone I just wanna Play Math all day.

2011-04-20T18:18:00.000-10:00

Play. Play Math.

I've said it over and over again. Play is important. It's crucial. Note how he talks about problem solvers having to use their hands. Mechanics. Engineers. Kids with blocks. Something happens when you get the tactile sense involved. Kinesthetic learner or not, adding the sense of touch and being able to get your hands on it makes such a big difference mere English words do not adequately convey the importance of it.

2011 and the world of mathematics has still not caught on to how important manipulatives are for increasing comprehension and learning of math concepts. It's still something for special education or minorities. "Real" math teachers don't use manipulatives and certainly not on adults. I note the "real" math teachers are failing miserably as a whole, with a very few bright spots here and there.

Here is yet another TED talk on the subject of play:

"Almost all creativity involves purposeful play." ~Abraham Maslow American psychologist 1908-1970

"Whoever wants to understand much must play much." ~Gottfried Benn German physician 1886-1956

"Play gives children a chance to practice what they are learning." ~Fred Rogers American television personality 1928-2003

"People tend to forget that play is serious." ~David Hockney Contemporary British painter

"Do not…keep children to their studies by compulsion but by play." ~Plato Greek philosopher 427-347 BCE

"Necessity may be the mother of invention, but play is certainly the father." ~Roger von Oech Contemporary American creativity guru

Not to hit you over the head with it, with these math quotes but perhaps maybe, you just might want this to become part of your teaching philosophy. I try to keep these quotes in mind when I play math with my students. Grander men than me have left behind these words so that I might also understand the crucial role of play.

"We didn't do anything dad, we just played with blocks." ~My favorite quote from a little girl who went from "F" to "A".

Here are a few blog posts as a reminder:

http://crewtonramoneshouseofmath.blogspot.com/2010/12/4-year-old-math-enrichment.html

http://crewtonramoneshouseofmath.blogspot.com/2010/09/make-it-fun.html

http://crewtonramoneshouseofmath.blogspot.com/2011/02/math-rich-environment-ii.html

Crewton Ramone Quikie on Ordered Pairs.

2011-04-20T13:02:00.002-10:00

Pre-calc concepts are not hard either if you can SEE the relationships.

Here is a short video that shows how an 11 year old can begin to MASTER the concepts related to constant rate problems and make ordered pairs into simple linear equations without being given formulas to memorize...in fact given time they will be able to come up with the formulas themselves.

We never once talked about dy/dx. He quickly began to see that the fastest way to do it was to take the largest number that would divide equally into each of them and is just beginning to find out that the result is dy/dx but he is doing it by multiplying and subtracting...which by the way is division. Do you see how math really is a language? If you are a layman that paragraph might be jibberish, but if you are a teacher I encourage you to pause and reflect. If you are a homeschooler with math issues of your own take a while and play with the concepts and you will see that it becomes easier the more you play with it.

This student did 15 or 20 minutes for a few sessions over a few days, later one 30 minute session of which this video is part and we haven't been back since but we will and each time we do more understanding is created.

More at my house of math.

Crewton Ramone Playing with Radicals.

2011-04-20T12:00:00.000-10:00

First off apologies to public school teachers who can't watch YouTube a school the screencasting software is buggin' out and won't let me copy it to a screencast without it being herky jerky video or bad audio...so for now all I have is this youtube video.

It shows me doing a few problems with radicals. Adding and subtracting (combining) them and doing other operations is actually pretty easy when you keep the 5 basic concepts in mind and can see what you are doing.

You might want to look at the square numbers page at the house of math, too.

You might also note there is a new tab on the navigation bar there for percentages. It's password protected though. Progress is being made. Albeit slowly. All it has is two Youtube vids showing how to do percentages with base ten blocks on it at the moment but there's more to come.

Meantime the completing the square page which certainly is related is growing too.

Square numbers are fun and easy.

Find us on FaceBook.

Response to Radiation in Hawaii Milk.

2011-04-13T00:07:00.001-10:00

Look, first things first. Drinking water limits and limits for milk are two very different things.

The limits for drinking water are 3 pCi/L that is 3 picocuries per liter, and assumes long term exposure. The average person doesn't drink as much milk as water, nor do you bathe in it, brush your teeth with it, cook (as much) with it etc. The amount is minute because it assumes constant exposure to potable, drinkable water.

The milk they sampled contains 18 pCi/L which would be 6 times the limit for drinking water but not 6 times for milk for I-131. (The limit for milk is 4,700 pCi/L or 261 times higher.) For Cesium-134 they found 24 pCi/L, and for Cesium-137 19 pCi/L, which would be 8 times and 6 1/3 times over the limit for WATER respectively.

This translates into 600%, 800% and 633% for each of the three isotopes respectively; however you CANNOT then ADD the percentages and come up with 2033% over the limit. What kind of math is that? It's not a cumulative total for radiation in general, and besides it's milk, NOT drinking water. No one isotope was 2033% over the limit for water or milk.

That said, how did the radioactive isotopes get into the cow to get into the milk? I would assume from drinking water and eating grass contaminated with those isotopes. We have no measurements for rainwater in Hawaii available to the public.

What is the ratio of isotopes in pCi/L that a cow has to consume to produce milk that has a pCi/L of the isotopes. I doubt it's one to one, because the "experts" have constantly repeated how poorly the uptake for those isotopes is in humans and animals. Now, I don't know what the ratio is and though I bet there is a study or two on the subject I have yet to find it.

If for example, if the ratio is 2 to 1 then the cow would have had to consume 36 pCi/L of water/grass I-131. For Cesium-134 48 pCi/L, and for Cesium-137 38 pCi/L...if it's 3 to 1 or 4 to 1 you can hopefully do the math yourself. Maybe it's 10 to 1: I don't know. Were the cows drinking straight undiluted rainwater? Doubtful. Was the grass soaked in rainwater that just contained 48 pCi/L of Cesium-134...again doubtful. I would think that the rainwater that fell on the cows had many multiples of 3 pCi/L of I-131 because it would be diluted in water troughs and on the grass and feed that they consumed. This is all conjecture on my part. I have no numbers with which to work, only a little logic, reasoning and critical thinking skills of which certain bureaucrats seem to be blissfully bereft.

I look at rainwater readings elsewhere and find them to be in the from 79 pCi/L in MA to 543 pCi/L in CA (San Fransisco) for I-131 but in all cases they also found Cesium and Te-132. On the day they measured 543 pCi/L of I-131 they found 13 pCi/L of Te-132 and Ce-137 in San Fransisco along with a few other isotopes. The point is, for it to show up in the milk it has to be in the rainwater in many multiples of what it is in the milk, but we have no measurements for rainwater in Hawaii that I have seen. NONE. ZIP. NADA. ZILTCH. ZED. ZERO. Not any. Squat.

All I can gather from the exceedingly limited data I can find is that it has been more than 18 pCi/L of I-131 in the rainwater. I doubt it was 500 pCi/L of I-131, on the other hand I doubt it was only 36 pCi/L of I-131. I am thinking the range is some where between 100 and 400 pCi/L of I-131 in our rainwater but that's a guess. Problem is rainwater IS drinking water for some of the state where catchment and surface water make up a good deal of the water supply.

Again the amounts are minuscule in the main water supply because even so the contaminated water mixes with the drinking water in ratios that would knock down the pCi/L count by factors: Waikamoi Reservoir is a 30 million gallon (MG) reservoir and Kahakapao Reservoir is 100 MG. One gallon is 3.7854 liters. So doing a little math even if 100,000 liters of contaminated rainwater got directly into the reservoir when it was only about half full it would be diluted far below the 3 pCi/L for the isotopes. It makes for some nice math problems: 100,000 liters of 200 pCi/L I-131 water mixes with 200,000,000 liters of uncontaminated water...assuming a somewhat even distribution what is the new contamination level?

I just made these numbers up to make the math easy. We have had a wet winter and the reservoirs are better than half full and 100,000 liters would be an extremely heavy rainfall so that would be a conservative (read unlikely) guesstimate using made up numbers erring on the side of contamination. Possible but not plausible and you'd still be 30 times under the limit for drinking water. A thought exercise for the sake of example.

After all that, people on catchment do not have the luxury of large numbers, and rainfall directly on you is not diluted...100 to 400 pCi/L of I-131 and even the smaller amounts of the other isotopes that are basically here permanently due to their much longer half lives are not amounts to be flippantly ignored. Cesium accumulates. It also bio-accumulates. Stay out of the rain for a while and don't drink rainwater. Especially if you are pregnant or a small child.

This is FRANCE where the numbers are smaller and they are much farther away:
http://www.euractiv.com/en/health/radiation-risks-fukushima-longer-negligible-news-503947

The people who have catchment tanks should have been warned, one good rainfall can take a tank from 3/4 full to full and then the dilution is only 1:4. I know quite a few people who use catchment

Up until March I collected rainwater on Maui for watering plants and occasionally for drinking...fresh vog free rainwater is delicious. This is no longer the case. Over time the longer lived isotopes could be cause for concern in our drinking water but right now this is not the case. It is indeed cause for caution when it comes to direct exposure to rainwater. The "nothing to worry about" mantra becomes annoying.

It would be nice if our government would do it's (expletive removed) job and inform the people of the measurements in the rainwater instead of just the lack thereof. Still, it's better than Canada were they aren't even testing the milk because they are so certain there is no cause for concern. The point is it's not the milk itself but the amount of radiation it took to get the cows to produce contaminated milk in the first place. Also to be noted is not all the rain has radiation in it all the time, but obviously it has had some in it recently or they wouldn't be detecting it in the milk and that's the problem: we don't know how much or when.

Math Might Be fun

2011-04-09T00:06:00.001-10:00

Here is a short vid with a student who is figuring out that math might be fun after all. At Crewton Ramones House Of Math it's hard not to have fun with it...

This has been a great week with two of my former "F" students (both of whom who happen to be teenage girls) getting perfect scores on homework and tests and quizzes. One parent quipped "I guess your worth the money..."

Yeah.

This little girl is well spoken, therefore I know I can teach her math because English is a messed up language and math is a beautiful one.

Here you can see they have a set of base ten blocks but they are not suitable for teaching all the math concepts the combo kit can. Also note 1000 as a cube which makes third power mathematics difficult at best and fourth power mathematics impossible...

Here you see the algebra again being used to teach addends and multiplication. By know the method should be familiar to some. Each lesson is tailored to the individual student but the method is the same. The problems are presented the same way in the same order...

She has some friends to help her count the rectangles. x² + 10x + 24 is "no problem..."

Here is the screencast covering the lesson:

The password protected pages keep growing with contect. The price is still a buck a month but now you have to buy 12 months worth to get it for a buck a month or you can buy one month (which ends up being 60 days or so...) for 3 bucks...just added a cute vid of an 11 year old and 6 year old playing algebra together. The footage is raw but it is charming...or so I have been told.

There is about 4 hours of password protected screencasts and many pages of pdf's for that price and like I said more being added all the time...if you buy a combo kit or tutoring the passwords are free.

Find us on FACEBOOK.

And yes, I'm on Twitter.

Yet More Factoring With Positive 3rd Power Polynomials

2011-04-04T21:45:00.001-10:00

Here is a session with an 11 year old, I tacked a short segment on the end of if with a 15 ear old high school student so there can be no question it's basically the same stuff...the textbook problem at the end uses M's instead of X as if that makes it more interesting...

Again if you want to see negatives you need a password...

More advanced algebra at Crewton Ramone's House Of Math...

Find us on FACEBOOK.

And yes, I'm on Twitter.

Even More Factoring with 3rd and 4th Power Polynomials

2011-04-04T19:52:00.003-10:00

Factoring is fun and easy or hard and incomprehensible depending on how you learn it. I once had a high school student tell his mother he was math learning disabled due to his inability to "get" problems like these. He quit tutoring one lesson before we got to these...

This student on the other hand is 11 and he'll never know this stuff is supposed to be hard. Note how we stay positive until we really have a handle on how to make these go together. Textbooks always jumble the degree of difficulty and start of with negatives and positives. Then wonder why students don't "get" it...that and they haven't figured out how to show third and fourth power algebra in two dimensions...

There are a lot of posts on factoring polynomials on this blog and also on my website. If you want to see how to do ones that contain negative coefficients as well as how to do division and more you need a password and you will find it on the password protected pages (advanced algebra tab) at Crewton Ramone's House Of Math...

Find us on FACEBOOK.

And yes, I'm on Twitter.

Crewton Ramone Start In The Concrete!

2011-04-04T19:04:00.000-10:00

Start in the concrete, there's no better way to cement the facts into their heads than to start with hands on experience of the math...

Some people find it amusing that kids who have trouble with addends and multiplication can factor third power polynomials...that's because they fail to understand proper application of the 5 basic concepts. Math is just counting. Multiplication and addition as well as 3rd power algebra are just counting.

The main idea here though is start in the concrete and watch your success rate go up...

Here is a short screencast covering this lesson.

Find us on FACEBOOK.

And yes, I'm on Twitter.

Flying Blind: Factoring by Grouping Without The Pictures

2011-03-28T17:49:00.001-10:00

Here is a fast lesson where I show a 15 year old what her text book is trying to teach her when they talk about factoring by grouping. You can see the distributive theory if you have mastered the concept, but if you haven't trying to take these third power polynomials apart and factor them can be intimidating. But once yo know how, it's easy and once you can actually SEE what you are doing it's easier still.

Here you see no pictures, which can make it very difficult to do the math, most students (and by most I mean 99%) like it when they can actually see what they are doing rather than just using rules and process to factor these problems. Most teachers and professors I show this to are absolutely STUNNED.

For problems like these you need a password. They are covered on password protected pages at CRHOM click on Advanced Algebra. (You need a password). There's plenty of 3rd power algebra on this blog and on my website for free though. The term advanced algebra is amusing when you see how easy it is.

Once you understand the concepts, bigger is just funner.

Here is a quick video I made covering basic factoring by grouping...staying positive, I put three short videos together and the last one shows what the picture looks like. We spent lots of time going over the pictures and suddenly the rules made sense. This is the second example and by the time we got here it wasn't very hard. If you look around on this blog you'll see an 11 year old doing this and more.
And of course little kids can get in on the act too, since all math is is counting once you know what to count and how to count it...here are 4 and 5 year olds playing with "advanced" algebra. For them they are basically learning how to build rectangles and add and do some simple multiplication. 3rd power algebra is a "by-product" of the lesson not the focus of the lesson.

More algebra at CRHOM.

Find us on FACEBOOK.

And yes, I'm on Twitter.

Algebra For Addends and Multiplication.

2011-03-28T16:34:00.004-10:00

By now you have seen me use algebra for teaching more than just factoring to little kids. Here we see the boys playing with one problem, using their critical thinking skills to make rectangles. They learn many math concepts in addition to addition and multiplication, they also get to practice writing their symbols which is a source of a great sense of accomplishment for youngsters. The 6 year old again much more impressed with his 5 and 2 than his ability to factor x² + 7x + 10. People don't think of algebra as one of the fun preschool activities but it is...if presented correctly.

I cannot stress enough that you must be patient and let them do it. Don't do it for them and don't give hints...just let them fool around with it. AFTER they have done the work talk about their discoveries and emphasize the fact that they weren't/aren't wrong just getting more information. Also when the older boy starts building his with the blocks on the wrong side he was building for you the viewer, being a silly adult I thought he was building it the "wrong" way. He wanted to make so "the people could understand it"...so he was going to try to build it up side down and backwards for your benefit. Next time I'll let him....

Here are the problems we did in order. At about 5 minutes a problem this is an hours worth of work. They had to get out the blocks, and form them into rectangles and count the sides. I talked about the partial products and made them point to them but that is ancillary to learning the addends and the multiplication of the factors. I also talked about the distributive theory and what that meant but again the main lesson was about counting out x and figuring out how to make the numbers fit in the corner.

x² + 2x + 1.
x² + 3x + 2.
x² + 4x + 3.
x² + 4x + 4.
x² + 5x + 4.
x² + 5x + 6.
x² + 6x + 5.
x² + 6x + 8.
x² + 6x + 9.
x² + 7x + 6.
x² + 7x + 10.
x² + 7x + 12.

The discoveries made here are too numerous to mention but a few I noted were, you can't build a 10 with 3's. 3 times x and x times 3 are the same thing, 5 twos and 2 fives are the same thing but it's easier to get out 2 fives than fooling around with all those twos...adding x's is easy...x² + 2x + 1, x² + 4x + 4 and x² + 6x + 9 are square numbers. Again these are their discoveries I didn't tell them these things...

You may note that there are 45 addends and thus 45 problems you can build and master. Ending with
x² + 18x + 81. Soon there will be worksheets on the Password Protected Pdfs Page with all of these problems on them. You should get comfortable with these and positive problems with two or more x² BEFORE you move on to negative expressions.

Here is the Password Protected PDF's Page. You need a password. Buy one, they are cheap.

Find us on FACEBOOK.

And yes, I'm on Twitter.

Cabbage For Your Brain

2011-03-28T15:52:00.000-10:00

The lowly cabbage is a super food. Excellent for the beneficial flora in your stomach and also good for your brain. Find out more about cabbage with the help of your search engine.

Gas however can be a problem, so if you let it ferment for a few days you get salted cabbage and many of the benefits of cabbage without the gas...there is nothing like raw cabbage though, packed with enzymes and phyto-nutrients...but really this couldn't be easier. Sun, Salt, Cabbage a Sterilized Jar. Put the lid on loosely after you pack it with cabbage, so the gas can escape and unwanted stuff doesn't get in while you are waiting...not pictured a wooden spoon to pack it with and the sun that makes it all happen.

Factoring Positive 3rd Degree Polynomials

2011-03-03T19:16:00.002-10:00

Factoring 3rd degree polynomials can be intimidating not to mention frustrating if all you have to go by is some rules in a textbook, but when you can see it it's EASY. This student is autistic and we just made a game of it once we had done a few examples and were familiar with the names of the pieces. Refer to the concepts page and use the 3 period lesson to make sure we know the names of the symbols and and what the symbols represent. The use of color markers helps but isn't necessary.

"Whoa! That's big," she exclaimed upon seeing the symbols.

Just count the sides and you're done.
"Well, that's EASY!" She laughs and writes it down. We do a few not pictured here and then she has a chance to make one up of her own. Of course she makes a big one:

The picture and the symbols are fast and easy to write. Much faster than drawing it, which is the point.

Now we make a trickier one with some square x²'s...

But of course that easy too because she can SEE it. Factoring polynomials is a snap, and kind of fun and builds the child's math confidence and self esteem.

Then we start making a game of it. I draw a picture give her the symbols and she has to make a drawing that matches mine. We have fun and a few laffs as she tries to figure it out...in no time she gets the hang of it. "My mind is warmed up now." I made some for her so it's only fair that she gets to make some for me. This helps her with mastery and makes the game more fun.

So she reads me her drawing next:

I start out like this because of all the clues in the terms.

Factoring polynomials: pretty easy once you are used to it and have had some practice. One hour does not a pro make. Also it gets more complicated when the terms get negative, so lets get comfortable with the basic concepts and stay positive. Children under 5 can also do this! All we do is count.

Then the rest just falls together. A better explanation is given in the screencast below, because for some of you it can't be this easy so you need more than just pictures.

Then we move on to a little problem solving with hero zero and no fun get back to one...

Then a few problems with fractions which she says are harder and not as much fun as the algebra!!!

After a few problems she remembers what to do and why we have to make them SAME kind before we can add them. Again it's just rectangles and counting.

And there it is done.

Here is the screencast:

Here is a much better explanation of factoring by grouping on YouTube. The one on the sccreencast is verbal only and lame...the YouTube vid is an actual lesson with a 15 year old cheerleader who is freaking out because of all the symbols...

Find me on Facebook and be sure to dig around at the house of math and on this blog for more. There is and will be a lot more on this on the Advanced Algebra Page which is password protected; how to do negative expressions for example is well covered as are many other topics.. Passwords now cost 3 bucks for a month, and 12 for a year pass. And soon they will cost more than that.

Slightly More Advanced Problem Solving, 3 Variables.

2011-03-02T11:51:00.000-10:00

We see Slightly More Advanced Systems Of Equations in this video...three variable problem solving is easy. The math concepts are simple. Use the information you have to find the information you don't have. Isolate a variable and the whole thing comes into focus. Hero zero and no fun get back to one...done.

Soon he will be doing systems of equations where all three equations have all three variables and he has to eliminate to solve them but we aren't there yet; however, this is where we are going:

3x + 2y + 4z = 9
-x + 3y + 2z = 1
4x - 5y - z = 3

For now he is doing problems like this:

L + T +3D = 8
T + 3D = 14
L + 2D = 0

There are a lot of intermediary steps between those two sets of problems. Steps that are ENTIRELY ABSENT in modern day text books. Now they give you three or four examples a few rules and some process and "off you go...and hey graph it while you're at it even though this is your first exposure to a "Z" axis."

Here are several vids strung together with my poor (but improving) editing skills:

For those pressed for time here is a short video covering just the one problem shown above:

To see how we started off and why I'm using L, T and D check out this post Simple Systems Of Equations.

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Playing With Nines

2011-03-02T10:12:00.002-10:00

Here is a simple vid where two little boys learn about nines and multiplication using stuff they already know: addends and counting...

The older boy who BTW turns six today said upon review of the video..."I thought they were supposed to be hard."
"Really?"
"Yeah, but that was almost TOO easy."
"Yeah, too easy," chimes in the four year old...

Now it's just practice and more games and more play until the nines are part of their instant recall memory.

I was working with a 14 year old and discovered her multiplication was severely lacking and nines in particular were not there. This same lesson was used to similar effect: she found nines to be easy. I also showed her "one less make a ten."

In other words 3 x 9 is one less than three which is 2 and 3 needs seven to be ten so 27. 6 x 9 is one less than 6 which is 5 and six needs four to be ten so 54. OR you can just take 30 minus 3 or 60 minus 6...unless of course you suck at subtraction because they taught you to count backwards and you're 14 and still 100% dependent on fingers.

That day we also watched Multiplication Rock vids, which upon reflection is where he might have gotten the idea that nines were supposed to be hard...lol...and counted by threes and sixes which they are getting very good at, and talked a little about what numbers they heard that were the same on three (read 3, 6 and 9) multiplication tables.

Those two boys are never going to have the problems with math that I commonly make 40.00 an hour to "fix" with children who are 13 thru 18. Further by the time they are 7 or 8 there will be very little math that high school kids can do that they can't do.

Passwords Change End of Month.

2011-02-27T13:51:00.000-10:00

Passwords are changing and going up in price on (or about) March 1st.

If you already have a password and want a free update email me...if you have ordered a kit through me you get free passwords all year long...if you made a donation of a buck or more get a free update by just emailing me...

If you have been putting off the major decision on whether or not to sped a buck you have a few days left to get one for $1.

A password gets you into the screencast page the pdfs page and the advanced algebra page as well as the password test page which just has links to the pages where the password works.

More stuff is being added, and more blog posts will be up this week...thanks for all your support.

Division Worksheets

2011-02-23T11:55:00.006-10:00

Here is a short screencast on how to use the division...

This is just one activity among many. No need to spend day after day on division. That link takes you to the division page at Crewton Ramone's House Of Math.

This is just more fooling with rectangles and counting the sides, in this case we know the whole rectangle and one side and just have to count the other side. We also have to remember to stop and record when we get to TEN.

Here is the Password Protected PDF's Page. You need a password. They cost a buck till the end of the month.

Very quickly THEY will see (and if you are a clever teacher THEY will discover) the algorithm "multiply and subtract."

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Simple Systems Of Equations

2011-02-19T13:51:00.001-10:00

Start off easy and it will stay easy. What are we doing? Understanding basic concepts and ten seeing how we come up with te rules and process they teach for solving equations. This student is 11. This is his second exposure.

l + d + t = 12
l + t = 8
l + d = 7
Solve for l, d, t...

Now make up some of your own...

Then lets go back to some "regular" problem solving, which seems extra easy now that we only have one variable to figure out...later once the concepts are fully understood we can go back and have multiple lions and tigers and dogs, oh my. (I couldn't resist.) Later we can introduce two lions, then maybe two lions and three tigers...etc...

Right now what to do when a negative number shows up?...understand same, hero zero and no fun get back to one.

Here is a quick screencast on it...for more go to the problem solving page at Crewton Ramone's House of Math.

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Look they practically give the thing away...get one if you haven't already got one tucked away somewhere. Great for making highskool kids see how easy it can be...