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.

## Wednesday, December 28, 2011

## Tuesday, December 27, 2011

### More Fractions Fun.

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)

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.

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.

## Sunday, December 25, 2011

### Fractions Despite SPED

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. ⇒

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. ⇒

## Wednesday, December 21, 2011

### Fractions Are Easy Too

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

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.

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

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.

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.

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.

## Monday, December 19, 2011

### Crewton Ramone And Comander Colby Get Radical

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...

Find us on FaceBook.

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...

Find us on FaceBook.

Labels:
Radicals,
Square Numbers,
Square Roots

### Crewton Ramone Doing Distribution With A Nine Year Old.

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

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.

Find us on FaceBook.

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

**we are learning about the distributive theory of multiplication.***while*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.

Find us on FaceBook.

## Wednesday, December 14, 2011

### Get Them Started Early.

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.

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.

## Tuesday, December 13, 2011

### Crewton Ramone Advanced Pythagorean Application

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...

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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## Thursday, December 8, 2011

### Do Your Own Math.

**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:

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:

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:

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:

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:

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

## Tuesday, December 6, 2011

### Fun Kindergarten Math Activities: Dboyz Play With Bigger Polynomials

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.

[Update: prices have indeed gone up. Look at the side bar for details.]

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."

## Saturday, December 3, 2011

### Big Blocks Big Fun Big Concepts.

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

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

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

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

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

Bust mostly we had fun building a castle.

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

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

1/2bh = A

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

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

Learn to use your base ten blocks.

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

## Sunday, September 11, 2011

### "Perpendicular To"

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.

Labels:
Algebra,
Geometry,
math symbols,
Perpendicular To

## Saturday, August 13, 2011

### Crewton Ramone Two Shorts on Geometry

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.

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.

ax

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.

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 Ï€r^{2}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.

ax

^{2}+ 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.

## Saturday, August 6, 2011

### Just Playing Math With Base 10 Blocks

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 x

^{2}+ 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.

## Thursday, August 4, 2011

### More Everyday Math

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...

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