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page1&2 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

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  page1&2 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-24 09:48 -0700
    Re: page1&2 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium  - Yet another repeat of crap. alouatta.coibensis@gmail.com - 2018-05-24 10:01 -0700
      2Alouatta talks Berkeley-- Denis Auroux, Richard Bamler, Robert Bryant, never a Picture of Fundamental Theorem of Calculus//are you as dumb as Alouatta //your students deserve better Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-25 11:16 -0700
        Re: Archimedes Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-25 18:48 +0000
          Moroney calls MIT Harvard coneheads// Bernard Burke, George Clark , Jeffrey Goldstone//never  realizing the Real Electron = muon, proton=840MeV, .5MeV = Dirac's monopole Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-25 12:14 -0700
    page3&4 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-25 11:18 -0700
      page5&6 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-25 20:17 -0700
        page7&8 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-27 07:36 -0700
          page9&10 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-27 13:07 -0700
            page11&12 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-27 13:28 -0700
              Re: Archimedes Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-27 20:55 +0000
          Re: _Burse calls 25 years crazy-- Manfred Einsiedler, Paul Embrechts, Giovanni Felder of ETH, no picture diagram of Calculus proof// still believing proton is 938MeV electron .5MeV when they are 840MeV, 105MeV moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-27 20:24 +0000
    Re: page1&2 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium bursejan@gmail.com - 2018-05-27 12:58 -0700

#413764 — page1&2 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

Newsgroups: sci.math
Date: Sat, 24 Mar 2018 11:16:31 -0700 (PDT)

Subject: *TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Sat, 24 Mar 2018 18:16:31 +0000

TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

Chapter 1 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium 

Preface: 

Alright I devote the entire years 2018-19 to doing this textbook on math. A textbook like none other for it takes the student from age 8 through to age 26 for all their math studies, throughout the subject of mathematics. The one book for all of mathematics. Of course we supplement with some outside sources like the common core curriculum, although I have found most math books are full of error. 

This book is historic in the sense that it cleans out all the errors of Old Math, and believe you me, the errors in Old Math were vast. So vast, that the best thing is to rewrite all the math textbooks, throw out the old-- so to speak. 

And historic in the sense the book is used from ages 8 to 26 as a single math text, where teachers supplement blank pages to tailor fit their class. I write this textbook with the Common Core Curriculum in the USA, in mind. So I know what Grade level students are taught specific topics. But here the teachers have to help this book along as to what is most appropriate for their classrooms, and have to tailor-make many lessons. 

I write this textbook in a style never seen before in science textbooks, for I am talking most often to the student, but also, talking very much to the teacher. So both the student and teacher are addressed in this textbook. 

This book is unique, in that you need only this text of math for all school needs. None of this buying a new book for each course. And it requires work by the teacher to fill in blanks. I cover only the very basic. But the beauty of that, is many students bored with the lessons under study at the moment, will keep on looking further ahead in the pages, at more advanced math-- for it is available and open to their eyes to wander on into what their future math lessons are going to be-- what we now call surfing the book in our age of computers. 

I am a pragmatist teacher myself, and know that if math is available, only more advanced, that the students will often exceed expectations and learn what was meant for them years into the future. I see it the case that some very bright High School students will have mastered the College level math from this textbook before they even get to college, just because it is in plain sight starting at age 8. 

Now in writing this text I need commentary along with lessons. So the structure of the book is lessons and then commentary. Arranged in chapters, and arranged for age level of students. The 8 year old starts at the beginning. Then 9 through 13 year olds has a chapter. Then 14 year olds have their own chapter. Then the High School students starts have their chapters on geometry, algebra, trigonometry and precalculus. The college student starts near the middle and takes up over half the book. The need of the College student is all the math that can take them through physics. Any other math a college student can read on their own time. But all ages can wander through this textbook learning more and more about math. And I myself remember that the worst nightmare for me, often in College, was that I could not remember a past year's teaching to understand what was before me at present. So in this textbook, if a student has trouble in later pages, well, just flip backwards to a earlier section and pick up what is needed. 

And this textbook is unique in another way, it is written Logically, a logical minded author, am I. Logic means clarity and order. So few, so very very few books of science and math are written by authors who possess a logical mind. 

But, I was a teacher myself, and know the key number one element of being a teacher, a good teacher, is that a good teacher teaches students at a level of age, that the student can readily comprehend and understand the material. If a student cannot understand what is being taught, cannot understand the teacher, cannot understand the book, gets frustrated and is turned off by math. It is not the student's fault, but the teachers and book fault. The teacher or book is not at the level where the student can learn. The teacher and book is "over the heads of the students". And that is the worse kind of education situation. Over the heads of the student and makes the student fear math, and forever turned off by math. Math, never needs to be feared. 

But another sign of a excellent teacher, is he/she comes to class every day, prepared, not ad-lib an hour, but prepared the night before. 

So, teacher, to young students, tell them this book is used by them throughout their life, but for the classroom at a certain age, only this part of the book are they going to learn. Tell them the rest of the book they will learn in later classes in later years, not your class. Your class only is responsible for this part of the textbook. And of course, well, the brightest students will be bored with what they are responsible for, and will peek ahead into future lessons. And, let them do that. 

But, in all my lessons of this textbook, I strive for CLARITY, strive for Understanding, and strive for Logic and Order. A text on math written by a logical author. 

Bon voyage 


#1-1 Decimals  Counting, and "What are Numbers" TEACHING TRUE MATHEMATICS, 2018 

Now we start mathematics with the students memorizing multiplication tables. Sad to say, that is how math should start for 8 year olds. Memorization. They learned some math in prior years, but now starts their formal education of math. And it starts with memorizing a table: 

2x2 =4 
2x3 =6 
2x4 =8 
2x5 =10 
2x6 =12 
2x7 =14 
2x8 = 16 
2x9 =18 

3x3 = 9 
3x4 = 12 
3x5 = 15 
3x6 = 18 
3x7 = 21 
3x8 = 24 
3x9 = 27 

4x4 = 16 
4x5 = 20 
4x6 = 24 
4x7 =28 
4x8 = 32 
4x9 = 36 

5x5 = 25 
5x6 = 30 
5x7 = 35 
5x8 = 40 
5x9 = 45 

6x6 = 36 
6x7 = 42 
6x8 = 48 
6x9 = 54 

7x7 = 49 
7x8 = 56 
7x9 = 63 

8x8 = 64 
8x9 = 72 

9x9 = 81 

Now, some students would benefit by seeing rectangles on graph paper such as 7x8, of 7 rows of 8, or 8 rows of 7 and count the smaller blocks as 56. Show pictures as often as you can.

Teach them the word "commutative" in this Multiplication Table, by saying commutative is switching around is the same as not switching around and do the table all over again. Switching around does not change the answer for 2x3 is the same as 3x2. That 9x6 is the same as 6x9.

3x2 =6 
4x2 =8 
5x2 =10 
6x2 =12 
7x2 =14 
8x2 = 16 
9x2 =18 

4x3 = 12 
5x3 = 15 
6x3 = 18 
7x3 = 21 
8x3 = 24 
9x3 = 27 
  
5x4 = 20 
6x4 = 24 
7x4 =28 
8x4 = 32 
9x4 = 36 

6x5 = 30 
7x5 = 35 
8x5 = 40 
9x5 = 45 

7x6 = 42 
8x6 = 48 
9x6 = 54 
  
8x7 = 56 
9x7 = 63 

9x8 = 72 

Now, teacher, make sure all the 8 year olds have that table memorized, to where they say the answer from rote memory. A few of the above are tricky for youngsters-- such as the 54, 56. And teach the students that you have the same answer (commutative) going in either direction. I mean that 5x7 = 35 is the same as 7x5 = 35. 

Now I do not recall how I learned this table, and teachers probably know better than I on how to teach this table rote memory. Whether daily out loud questions where all the students answer, so the teacher says 7x3 is what? Then 8x6 is what? so on and so forth. 

Students have to memorize the multiplication table because when you do division, you have to have memorized multiplication to do division.

Now, teacher, stay with that table of memorizing multiplication, until you feel that the students have it rote memorized. It is important to have it memorized because division depends on the students memorizing multiplication. If they do not memorize it, and go to division, they are frustrated. 

Sad to say, the most important use of mathematics by every person alive is to be able to know how much money, count money and know numbers to count money correctly. But, then again, that is why everyone needs to learn math-- to be able to handle money. Very difficult to live in modern society and not be able to handle money because you have no math. 

We start this book for 8 year old students and to Count and then from Counting learn "What is a number". 

Have the students write out all the numbers from 0 to 100. They are Counting 

Something like this:: 

90, 91, 92, 93, 94, 95 96, 97, 98, 99, 100 
80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 
70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 
60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 
50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 
40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 
20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 
00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 

Now, teacher, warn the students that writing 1 as 01 or 2 as 02, etc, does not affect the number. Teach them a 0 in front of a number does not affect the value, but a 0 after does affect the value. Such as 1 is 01 but 10 is ten, and 02 is 2 but 20 is twenty. So, teacher, spend a good deal of time teaching when 0 affects the value of a number. Tell the students that the reason they are writing a 0 in front of 1 or in front of 0 itself is so there are two digits, yes two digits for all these numbers, except for 100. 

Now, ask the students to Count those numbers as if they were whole dollars (in other countries, they may not or may have a currency- a money in decimal, if they do not, well, just use USA dollar with cents). 

So, zero dollars, 1 dollar is 01, 2 dollars is 02, etc, etc. Have the entire class count up to 100 dollars. 

90, 91, 92, 93, 94, 95 96, 97, 98, 99, 100 
80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 
70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 
60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 
50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 
40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 
20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 
00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 


Now I am a firm believer in repetition by students, for they memorize and it boosts their confidence-- that they can do this, do math. They understand it and do it easily. 

Now, we take our chart and place a decimal point "." between digits. We just took our above table of numbers 00 to 100 and added a decimal point. Teacher, it is not far away where we teach Decimals, but let the students do mostly counting for now, and the decimal explanation will come soon enough. 

9.0, 9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0 
8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 
7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 
6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 
5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 
4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 
3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 
2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 
1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 
0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 

Now, have the students count these numbers. 
Zero point zero, zero point 1, zero point 2, zero point 3, zero point 4, etc etc. Count all the way to nine point nine, ten point zero. 

Now, teacher, have them count that same table as if they were dollars and cents. Zero cents, ten cents is .1, twenty cents is .2, thirty cents is point .3, forty cents is .4, on up to 9 dollars and ninety cents is 9.9, ten dollars is 10.0. 

  

Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 



On Saturday, March 24, 2018 at 9:35:18 PM UTC-5, Archimedes Plutonium wrote:
#1-2 Decimals TEACHING TRUE MATHEMATICS, 2018 

Picking up where we left off the last time. Only this time we move the decimal point over one more time. 

.90, .91, .92, .93, .94, .95, .96, .97, .98, .99, 1.0 
.80, .81, .82, .83, .84, .85, .86, .87, .88, .89, 
.70, .71, .72, .73, .74, .75, .76, .77, .78, .79, 
.60, .61, .62, .63, .64, .65, .66, .67, .68, .69, 
.50, .51, .52, .53, .54, .55, .56, .57, .58, .59, 
.40, .41, .42, .43, .44, .45, .46, .47, .48, .49, 
.30, .31, .32, .33, .34, .35, .36, .37, .38, .39, 
.20, .21, .22, .23, .24, .25, .26, .27, .28, .29, 
.10, .11, .12, .13, .14, .15, .16, .17, .18, .19, 
.00, .01, .02, .03, .04, .05, .06, .07, .08, .09, 
  

Now teacher, prepare for class the night before, for students deserve to have a teacher that prepares, and does not walk into the class just ad-libing, just winging it. Come prepared for each lesson. The difference between a excellent teacher and those beneath, is preparedness. Although Grade schoolers may not recognize a prepared teacher from not prepared, by High School, the students do recognize. 

That is why I like to blend in one lesson with the next, so that the blend shows the preparedness. 

Now, have the students make the above table where we moved that decimal point over once more. Now count these numbers. 

Point zero zero is 0 cents. Point zero 1 is 1 cent, point zero 2 is 2 cents, point zero 3 is 3 cents. Count all the way to point nine nine is 99 cents, one point zero is 1 dollar. 

Bring some coins to class, for students always deserve visuals to go along with learning. Bring a penny, nickel, dime quarter, half dollar, even a dollar (Susan B coins).

Now, teacher, if the class is not fluent in these tables, repeat them until they are fluent and do other exercises, until they are very good at this. In fact do exercises focused on decimals. 

Now the next exercise once the students are fluent in the above tables-- homework, quizzes, tests, and make them easy quiz and test, build confidence. Is the teaching of Decimal Numbers themselves. From a look at the Common Core Curriculum, either the students of 8 years age has seen the decimals before, or they have not. So the teacher here has to determine if the students have been already taught the decimal numbers or not, and with that determination the teacher must supplement my teaching with a  good chapter of common core on decimals. I do not know how the Common Core teaches decimals. And my own personal memory can no longer pull that experience up and what age I was. I vaguely recall doing fractions, multiply, add, subtract even divide fractions. And here is where I argue with Common Core. That more time needs be spent on Decimals for decimals are the True Numbers in mathematics, whereas Fractions are a bit of exotica, for fractions are just Long Division without actually doing the division. So, what I propose is that Fractions be cut deeply from the curriculum and with that extra time, devote it to Decimals. Do not eliminate fractions altogether, just pare away about 1/2 the time spent on fractions and give it to decimals.

One memory does stick out in my youth, of around the age of 8 or 9. I would go across the street to the neighbors and play with their kids of my age. And one day, the father was home and wanted to see me especially. He wanted to see if I could Long Divide a number he wrote down on a pad of paper. Sorry to say, I could not do it, and being a kind father, he went ahead and showed me how to Long Divide. So, that scene stuck in my mind through my life. What the father was testing, was not whether I was smart enough, but seeing whether his own sons of my age should be able to do it. For if I could do it, he would be angry that his own sons could not. And, well, that scene perhaps in some manner, made me think, math was special, and I had to be better in math than I was.

Now this is just my gut instinct, but I think, Decimals as a concept are far more difficult to learn than is fractions, because of the definition of Decimals, with its place values. Place values for 8 year olds seems too difficult. So, what I propose is teaching Decimals every year, just gradually a bit more and more, so that by High School, they surely will have comprehended the Decimals, and its tough definition. For me, I vaguely just vaguely remember that the definition I would gloss over, sort of like surf the definition-- only the word "surf" was never around when I was in Grade School in 1958 an 8 year old. And the first time I used the word surf was from some songs out of California in the 1960s. But now we have surfing the web and internet. So, why not surf the definition of Decimal. By surfing Decimal definition at age 8 and for the next 6 years reinforce that understanding of the Decimal number. 

I must emphasize that Decimals are a key crucial part of mathematics, a essential part. So the teacher must have Decimals taught long and hard. 

So here is a juncture point for the teacher and me as author. I am not going to write long lessons on teaching decimals or long division. But at this moment of this textbook, what the teacher has to evaluate and accomplish, and the student has to learn well and hard. First Decimals and then Long Division. 

Google Internet search: 
        1.        Number & Operations in Base Ten - Common Core State Standards ...www.corestandards.org/Math/Content/5/NBT/‎
Read, write, and compare decimals to thousandths. CCSS.Math.Content.5.NBT.A .3.a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 ...‎CCSS.Math.Content.5.NBT.B.7 - ‎CCSS.Math.Content.5.NBT.B.5 


Now the above Google Search hit of common core on decimals is fine except it is written in fractions. Here we want to eliminate fractions as much as possible, because they are not numbers but division of numbers.

And I would be content if they, the 8,9,10 year olds, only learned to the thousandths place value in decimals. The above number 347.392 is good for 8,9,10 year olds. 

Now, here Teacher, you decide which is appropriate for your classroom. Whether they can learn this, shown below or if that is too hard for 8 year olds: 

Definition of Decimal:: a number such as 347.392 = (3 × 100) + (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) + (2 x (.001)) 

Obviously the students are going to need to know what .1 is, and remember our number graph that .1 was a dime or ten cents out of 1 dollar, as fraction .1 is 10/100 = 1/10, and then 1/100 is 1 cent out of a dollar as .01,  and .001 is 1/1000 as a fraction, but this is all probably too hard for 8 year olds. You, the teacher find out where you can teach to 8 year olds, whether they can understand 7.3, one decimal place. If 8 year olds can understand one decimal place to left and right of decimal point, then teach that and no more on place value. Save the harder for another year. Never frustrate students. 

I do not know if that is too much for 8 year olds? If they have seen this before, and if not, well, we never want to frustrate, so start the 8 year old on this. 

Definition of Decimal:: a number such as 7.3 =  (7 × 1) . + (3 × (.1)) 

With exercises like this -- write out what 2.4 = 

what 1.7 = 

what 9.8 = 

what 5.3 = 

etc, a lot of practice exercises 

Then at 9 years of age we come back and do a little more this time 

47.39 = (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) 

write out what 21.48 = 

what 33.25 = 

what 19.17 = 

etc 

Finally by age 9, 10 we come back for more on the definition of decimal 

Definition of Decimal:: a number such as 347.392 = (3 × 100) + (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) + (2 x (.001)) 

Make sure you point out the parenthesis marks as that you want to operate inside those parenthesis-- take some time to teach parenthesis and order of doing math operations. 

So, teacher, give the students many numbers and let them write that number according to the definition. 

By the time they are 12, 13 year olds they should easily do these two and much more. 

135.687 written out is (1x(100)) + (3x(10)) + (5x(1)) . + (6x(.1)) + (8x(.01)) + (7x(.001)) 

980.002 written out is (9x(100)) + (8x(10)) + (0x(1)) . + (0x(.1)) + (0x(.01)) + (2x(.001)) 

So, do many exercises of writing out decimals, and point out the Place Values. The "ones" place value, the tens place value, the hundreds place value. Point out the decimal point then the .1 place value, etc etc. Review fractions so that they know 1/10, 1/100, 1/1000 are division problems. 

And use the Common Core, a proven teaching guidelines. Find out what old books used as teaching the Decimals.

Now out of curiosity I had to see what age is Long Division taught, and apparently in 5th grade, ages 10-11. So here the teacher has to decide whether 8 year olds can handle Long Division. If not, well, wait for 10 years of age. So here I need guidance by teachers who teach 8, 9, 10, 11, 12, 13 year olds. When does Long division start and how is it best taught? So let the teacher decide on this. 

But in the meantime. I wonder if we can add, subtract, multiply decimals, keeping it very simple for 8 year olds. 

So here I ask the teacher to determine how much the students know of decimals and know how to add, subtract, multiply. If weak, then months go by with the teacher using Common Core materials to ground the students well in Decimals. Use other books for the teacher to do the lessons. That means the teacher has to well prepare these month long lessons. 

DECIMALS: 

So here, let us focus on Decimals. And according to Core Curriculum, the 8 to 14 year old students learned what Decimals are, and how to add, subtract, multiply and divide with them. 

It would be nice, very nice to repeat lessons on Decimals in all the age groups from 8 to 14, giving them refreshment exercises each year. Unless they learn decimals well, they cannot go into science or engineering or medicine. 

So, first, let me repeat the meaning of a decimal with an example using the number 321.987. 

Decimals are place values and that number represents (3x100) + (2x10) + (1 x 1) . + (9x .1) + (8 x .01) + (7x .001) 

Teacher, show the students the progression leftward of the decimal point starting with 1 then 10 then 100 according to the place value. Then show them the progression of place value going rightward. 

I think the Common Core even shows diagrams and pictures of place value. 

So let me get a list of practice exercises, and the teacher preparing each day for months on end with practice on decimals, and add, subtract, multiply with decimals. 

With add and subtract, it is pretty much the same as if we dealt with numbers without a decimal point, just make sure you ___line up the decimal point___ before adding or subtracting. 

1.6 
4.5 
7.8 
----- 

 7.9 
-6.7 
---- 

5.3 x 4 

1.2 x 2.8 

87 x .1 

Here the idea is to introduce Decimals by age 8, make it extremely simple, and then build on that introduction in ages 9 to 14. Never do we want to frustrate students. 


Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 

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#413767 — Re: page1&2 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium - Yet another repeat of crap.

On Thursday, May 24, 2018 at 9:48:38 AM UTC-7, Archimedes Plutonium wrote:

> I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      
> 
> Read my recent posts in peace and quiet.
> 
> https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
> Archimedes Plutonium

So post your shit there.  That way nobody will smell it.

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#413827 — 2Alouatta talks Berkeley-- Denis Auroux, Richard Bamler, Robert Bryant, never a Picture of Fundamental Theorem of Calculus//are you as dumb as Alouatta //your students deserve better

On Thursday, May 24, 2018 at 12:01:31 PM UTC-5, alouatta....@gmail.com wrote:
> 
> So post your shit there.  That way nobody will smell it.

2Alouatta talks Berkeley-- Denis Auroux, Richard Bamler, Robert Bryant, never a Picture of Fundamental Theorem of Calculus//are you as dumb as Alouatta //your students deserve better
1 post by 1 author  

Alouatta is not only a failure of math, must have have been burnt out at school-- but also an insane stalker on sci.math. I have often asked Google to please engineer a delete key so original authors of a thread can develop their thread without these insane poopers pooping up (Jan is a 20 year stalker). Let original authors delete any post in their thread which is unfit. 

MAKE sci.math a Level Playing field, and stop tilting sci.math in favor of moron stalkers. 
--------------------------------- 

Univ California Berkeley math department 

Carolyn Abbot-- geometry group theory 
Ian Agol -- low dimensional topology (what a relief that is for me and him, for dimensions beyond 3rd are all fakery) 
Alexander Alldridge * -- Supergeometry (never heard of such a thing, let's hope he can super solve Jan's error of never understanding that a entry cut near the cone apex has a asymmetrical arclength compared to exit cut) 
Denis Auroux-- symplectic topology and mirror symmetry (this expertise in symmetry is called for-- so many think a cut of a cone is a ellipse when anyone with a halfbrain can see it is a oval) 
Richard Bamler-- geometric analysis, differential geometry (sounds like a heavy weight in geometry and this cone problem should be easy for Richard) 
Robert Bryant *-- many geometry expertises 
Zhiqi Chen -- differential geometry and although a visiting scholar, we should never play bias to whomever can answer the question of no ellipse is a conic but only a cylinder section 
James Conway-- contact and symplectic geometry (what in the world is symplectic-- better not ask) 
Heinz Cordes-- classical analysis (hope that does not mean classical Old Math) 
Ved Datar-- differential geometry (now, how fast can these guys compute the arclength along sections of the cone-- fast as in 5 minutes or fast as in 2 days) 
David Eisenbud-- algebraic geometry 
Mark Haiman-- algebraic geometry 
Jenny Harrison-- geometric measure (perhaps measuring the arclength of cone sections is what is needed) 
Robin Hartshorne-- history of geometry (well, well, why does it take till 2016, for any mathematician to realize the ellipse was never a conic section, rather, it was the oval) 
Wu-Yi Hsiang-- differential geometry (and a long long time ago Dr. Hsiang sent me his manuscript of a alleged proof of Kepler Packing, thanks) 
Michael Hutchings-- geometry 
Marina Iliopoulou-- incidence geometry 
Brian Krummel -- geometric analysis 
Tim Laux -- geometric analysis 
David Li-Bland-- differential geometry 
John Lott-- differential geometry 
Kathryn Mann-- geometry 
David Nadler-- geometric representation 
Martin Olsson-- arithmetic geometry 
Kenneth Ribet-- algebraic geometry 
Alan Schoenfeld-- math education 
Vivek Shende-- geometry 
Isadore Singer-- geometry 
Zvezdelina Stankova-- algebraic geometry 
Bernd Sturmfels-- algebraic geometry 
Hongbin Sun-- hyperbolic geometry (the hyperbolic geometry may come in handy in showing that the cone section cannot be an ellipse) 
Peter Teichner-- geometric topology 
Dmitry Tonkonog-- geometry 
Michael Viscardi-- geometric representation 
Alan Weinstein-- geometry 
Lauren Williams-- geometry 
Mariusz Wodzicki-- geometry 
Joseph Wolf-- geometry 
Hung-Hsi Wu-- geometry 


   /\-------/\ 
   \::O:::O::/ 
  (::_  ^  _::) 
   \_`-----'_/ 
You mean the classroom is the world, not just my cubbyhole in Berkeley? 

And, even though you-- professors of math, want to remain silent and stupid in Calculus, your students deserve better. 

SEE PICTURE DIAGRAM of FUNDAMENTAL THEOREM OF CALCULUS below, professors hate teaching this for it shows their "limit calculus to be a joke" 

PICTURE DIAGRAM OF FUNDAMENTAL THEOREM OF CALCULUS 

By April 2015, was there for the first time a picture diagram proof of the Fundamental Theorem of Calculus, FTC, not just an analysis argument, but a geometry proof (see below). Old Math could never assemble a picture diagram of the FTC. All they could do is argue with limit concept an analysis argument, never a geometry proof of FTC. 

A picture diagram proof of FTC changes all of calculus and thus, changes all of mathematics for it requires a infinity borderline to produce an actual number for the  infinitesimal, and that number is the inverse of the infinity borderline. Requiring a infinity borderline to produce the infinitesimal changes all of mathematics, and throwing out the limit concept. By changing all of Calculus and thus correcting mathematics, all of math before 2015 was just trash math. 

Picture Diagram needed for Fundamental Theorem of Calculus 

Why no continuum and no curves exist in Math, so that the Calculus 
can exist, and does exist 

by Archimedes Plutonium 

Calculus is based upon there being Grid points in geometry, no 
continuum, but actually, empty space between two neighboring points. 
This is called Discrete geometry, and in physics, this is called 
Quantum Mechanics. In 10 Grid, the first few numbers are 0, .1, .2, 
.3, etc. That means there does not exist any number between 0 and .1, 
no number exists between .1 and .2. Now if you want more precise 
numbers, you go to a higher Grid like that of 100 Grid where the first 
few numbers are 0, .01, .02, .03, etc. 

Calculus in order to exist at all, needs this empty space between 
consecutive numbers or successor numbers. It needs that empty space so 
that the integral of calculus is actually small rectangles whose 
interior area is not zero. So in 10 Grid, the smallest width of any 
Calculus rectangle is of width .1. In 100 Grid the smallest width is 
.01. 

But, this revolutionary understanding of Calculus does not stop with 
the Integral, for having empty space between numbers, means no curves 
in math exist, but are ever tinier straight-line segments. 

It also means, that the Derivative in Calculus is part and parcel of 
the function graph itself. So that in a function such as y = x^2, the 
function graph is the derivative at a point. In Old Math, they had the 
folly and idiocy of a foreign, alien tangent line to a function graph 
as derivative. In New Math, the derivative is the same as the function 
graph itself. And, this makes commonsense, utter commonsense, for the 
derivative is a prediction of the future of the function in question, 
and no way in the world can a foreign tangent line to a point on the 
function be able to predict, be able to tell where the future point of 
that function be. The only predictor of a future point of a function, 
is the function graph itself. 

If the Calculus was done correctly, conceived correctly, then a 
minimal diagram explains all of Calculus. Old Math never had such a 
diagram, because Old Math was in total error of what Calculus is, and 
what Calculus does. 

The fundamental picture of all of Calculus are these two of a 
trapezoid and rectangle. In fact, call the picture, the 

FUNDAMENTAL THEOREM OF CALCULUS, Picture 

Trapezoid for derivative as the roof-top of 
the trapezoid, which must be a straight-line segment. If it is curved, 
you cannot fold it down to form a integral rectangle. And the 
rectangle for integral as area. 

From this: 
        B 
        /| 
      /  | 
 A /----| 
  /      | 
|        | 
|____| 


The trapezoid roof has to be a straight-line segment (the derivative) 
so that it can be hinged at A, and swiveled down to form rectangle for 
integral. 

To this: 

______ 
|         | 
|         | 
|         | 
--------- 

And the derivative of x= A, above is merely the dy/dx involving points 
A and B. Thus, it can never be a curve in Calculus. And the AB is part 
of the function graph itself. No curves exist in mathematics and no 
continuum exists in mathematics. 

In the above we see that CALCULUS needs and requires a diagram in 
which you can go from derivative to integral, or go from integral to 
derivative, by simply a hinge down to form a rectangle for area, or a 
hinge up to form the derivative from a given rectangle. 

Why in Old Math could no professor of math ever do the Calculus 
Diagram? Why? The answer is simple, no-one in Old Math pays attention 
to Logic, and that no-one in Old Math was required to take formal 
Logic when they attended school. So a person bereft of Logic, is never 
going to find mistakes of Logic and think clear and think straight. 

by Archimedes Plutonium 
------------------ 
------------------- 

Proofs that the Real Electron=muon, Real Proton=840MeV, and that the .5MeV particle was the magnetic monopole, afterall 

12 PROOFS that Real-Electron = muon 
by Archimedes Plutonium 

Proofs that the Real Electron=muon and that the .5MeV particle was the magnetic monopole, afterall 
> 
PROOFS that Real-Electron = muon 

1st proof is chemical bonding cannot exist with momentum of 938 versus .5MeV 
Chemical Bonds are covalent, ionic, metallic. You simply cannot get atoms to bond if the electron is thought of as the .5MeV particle, only with a muon at 105 MeV and the proton at 840 MeV with neutron at 945 MeV do you have the physics of angular momentum that allows bonding in Chemistry. The .5MeV particle was, all along a magnetic monopole of a photon with .5 MeV charge energy, not rest mass energy. 

AP

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#413833 — Re: Archimedes Plutonium flunked the Math Test of a lifetime-generation test

Cone? Did you say cone? Here's a real cool proof about the cone!

Below you will find a simple *proof* that shows that certain conic 
sections are ellipses.

Some preliminaries:

Top view of the conic section and depiction of the coordinate system used 
in the proof:

              ^ x
              |
             -+- <= x=h
         .'   |   `.
        .     |     .
        |     |     |
        '     |     '      
         `.   |   .'
 y <----------+ <= x=0
             
Cone (side view):
                 .
                /|\
               / | \
              /b |  \
             /---+---' <= x = h
            /    |'   \
           /   ' |     \
          / '    |      \
x = 0 => '-------+-------\
        /    a   |        \

Proof:

r(x) = a - ((a-b)/h)x  and  d(x) = a - ((a+b)/h)x,  hence

y(x)^2 = r(x)^2 - d(x)^2 = ab - ab(2x/h - 1)^2 = ab(1 - 4(x - h/2)^2/h^2.

Hence (1/ab)y(x)^2 + (4/h^2)(x - h/2)^2 = 1  ...equation of an ellipse

qed

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#413836 — Moroney calls MIT Harvard coneheads// Bernard Burke, George Clark , Jeffrey Goldstone//never realizing the Real Electron = muon, proton=840MeV, .5MeV = Dirac's monopole

On Friday, May 25, 2018 at 1:48:23 PM UTC-5, Michael Moroney wrote:
> Cone? Did you say cone? Here's a real cool proof about the cone!
> 

Bernard Burke, George Clark , Jeffrey Goldstone//never
 realizing the Real Electron = muon, proton=840MeV, .5MeV = Dirac's monopole

percentage for Moroney, 938 is what percent short of 945 


On Wednesday, December 6, 2017 at 12:30:22 AM UTC-6, Michael Moroney wrote: 
> 
> Silly boy, that's off by more than 12.6 MeV, or 12% of the mass of a muon. 
> Hardly "exactly" 9 muons. 

Wednesday, December 6, 2017 at 9:52:21 AM UTC-6, Michael Moroney wrote: 

> 
> Or, 938.2720813/105.6583745 = 8.88024338572.  A proton is about the mass 
> of 8.88 muons, not 9. About 12% short. 

AP writes: 
Does the state of Massachusetts ever have education reviews. For here is a stalker of Moroney for 25 years-- obsessive stalker of AP, and only AP, says he is a electrical engineer yet never admits to mistakes that 938 is not 12% short of 945, but only .7% short, less than 1% short. So what kind of engineer is it from Barry Shein's std.com, that cannot even do a percentage correctly and never admits to mistakes, only stalks and harasses other people who do know math and science. 

Why is std.com so hateful of the tv program THIS OLD HOUSE, when I have learned so much from that show. 

Why is std.com such a antiscience ISP, with Moroney hating percentage problem, hating geothermal-- is std.com the worst isp for science in Boston, or is Barry Shein topped by someone else? 


President: L. Reif (electrical engineer) 

MIT physics dept 
William Bertozzi, Robert Birgeneau, Hale Bradt*, Bernard Burke, George Clark , Jeffrey Goldstone*, Thomas Greytak, Lee Grodzins , Paul Joss, Vera Kistiakowsky, Earle Lomon, Irwin Pless, Paul Schechter, James Young 

   /\-------/\ 
   \::O:::O::/ 
  (::_  ^  _::) 
   \_`-----'_/ 
You mean the classroom is the world, not just my cubbyhole in Boston? 
And, even though you-- professors of physics, want to remain stupid in Real Electron=105MeV, Real Proton = 840MeV, and .5MeV was Dirac's magnetic monopole, your students deserve better. 

Drs.Larry Summers, Sheldon Glashow, Lisa Randall of Harvard, teach percentages correctly-- Moroney//never realizing the Real Electron = muon, proton=840MeV, .5MeV = Dirac's monopole 

President Larry Summers 

Harvard Physics dept 
Jacob Barandes, Howard Berg, Michael Brenner, Adam Cohen, Eugene Demler, Michael Desai * 
Louis Deslauriers, John Doyle, Cora Dvorkin, Gary Feldman, Douglas Finkbeiner, Melissa Franklin, Gerald Gabrielse, Howard Georgi, Sheldon Glashow, Roy Glauber, Jene Golovchenko, Markus Greiner, Roxanne Guenette, Girma Hailu, Bertrand Halperin, Lene Hau 
Thomas Hayes, Eric Heller, Jason Hoffman, Jenny Hoffman, Gerald Holton, Paul Horowitz, John Huth, Arthur Jaffe, Daniel Jafferis, Efthimios Kaxiras, Philip Kim, John Kovac, Erel Levine 
Mikhail Lukin, Logan McCarty, L. Mahadevan, Vinothan Manoharan, Eric Mazur, Masahiro Morii 
David Morin, Julia Mundy, Cherry Murray, David Nelson, Kang Ni, Hongkun Park, William Paul 
Peter Pershan, Mara Prentiss, Lisa Randall, Matthew Reece, Subir Sachdev, Aravinthan Samuel, Matthew Schwartz, Irwin Shapiro, Isaac Silvera, Andrew Strominger, Christopher Stubbs, Cumrun Vafa, Ronald Walsworth, David Weitz, Robert Westervelt, Richard Wilson 
Tai Wu, Amir Yacoby, Susanne Yelin, Xi Yin 


Can someone in the Boston area make sure this numbskull is never a science teacher in Boston-- and the damage he can do to a classroom 

Mike Moroney, science failure-- on geothermal 


(1) 
On Monday, May 9, 2016 at 12:15:22 AM UTC-5, Michael Moroney wrote: 

> 
> There are some places here that use "geothermal" for heating and cooling 
> but even these are solar power in disguise.  They pump water from wells 
> from where the temperature is the average over many years and extract heat 
> from it (in the winter) and dump heat into it (in the summer) and pump the 
> water back into the ground.  The water is about 55F out of the ground. 



(2) 
On Monday, June 6, 2016 at 1:31:27 PM UTC-5, Michael Moroney wrote:   

> 
> >Just as a point of order, what you described is not geothermal. What 
> >you've just described is thermal balancing with water, using water 
> >cooler than air from the water table to cool a building in the summer, 
> >and using water warmer than air from the water table to warm a building 
> >in the winter. 
> 
> In other words, glorified solar energy.  Solar energy stored and averaged 
> out over many, many years. 
> 

(3) 
On Friday, December 23, 2016 at 8:44:12 PM UTC-6, Michael Moroney wrote: 

> 
> Admit it, you were fooled by a "This Old House" type show where they 
> use a high-tech sounding buzzword to impress people who don't know any 
> better. 
> 
> Just answer one question, if you can.  If it's really geothermal, why 
> is the temperature only 51 degrees, but in Iceland, where there's real 
> geothermal, they're accessing temperatures of hundreds of degrees? 


(4) 
> On Friday, December 23, 2016 at 10:40:09 AM UTC-6, Michael Moroney wrote: 

> > 
> > Pretty cool, fossil solar energy! 51 degrees, the average of summer and 
> > winter temperatures for hundreds or even thousands of years, depending 
> > on how deep they go. 
> > 
> > Too bad you do have to use real energy to run the heat pump, although it 
> > is much better than simply using that energy to make heat. 
> 

(5) 
On Tuesday, September 19, 2017 at 12:30:56 PM UTC-5, Michael Moroney wrote: 

> 
> It's amusing how he can't handle that at all. Just like he can't 
> handle the concept of permafrost when he goes off on geothermal 
> energy.  All he can do is attack. 

(6) 


On Saturday, October 14, 2017 at 12:21:15 AM UTC-5, Michael Moroney wrote: 

> geothermal heat energy is 99% from the sun where he was (unsure where, 
> Mass. I think) 
> 
> Now tell us where Permafrost comes from. 
> 
> p.p.s. I was searching because I am actually looking into getting 
> geothermal heat. Fossil solar energy is a great resource! 


Proofs that the Real Electron=muon, Real Proton=840MeV, and that the .5MeV particle was the magnetic monopole, afterall 

12 PROOFS that Real-Electron = muon 
by Archimedes Plutonium 

Proofs that the Real Electron=muon and that the .5MeV particle was the magnetic monopole, afterall 
> 
PROOFS that Real-Electron = muon 

1st proof is chemical bonding cannot exist with momentum of 938 versus .5MeV 
Chemical Bonds are covalent, ionic, metallic. You simply cannot get atoms to bond if the electron is thought of as the .5MeV particle, only with a muon at 105 MeV and the proton at 840 MeV with neutron at 945 MeV do you have the physics of angular momentum that allows bonding in Chemistry. The .5MeV particle was, all along a magnetic monopole of a photon with .5 MeV charge energy, not rest mass energy. 


On Friday, February 23, 2018 at 5:07:26 PM UTC-6, Archimedes Plutonium wrote in sci.physics:
Kjaergaard's famous Danish experiment of 2014 Re: Chemists are smarter than Physicists-- 2018 textbook of Experiment-- Real Electron = 105MeV
13) Proof came in February 2018 for AP's ion theory, that ions are monopoles .5MeV either +1 or -1 charge, attached to a 840MeV proton and 105MeV muon as hydrogen.
Newsgroups: sci.physics
Date: Tue, 6 Feb 2018 19:37:37 -0800 (PST)

Subject: H+1 bonds to P+1 Re: EXPERIMENTAL PROOF Re: Hydrogen is the very best
 way to prove AP's ION theory Re: proving AP's ion theory
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Wed, 07 Feb 2018 03:37:37 +0000

H+1 bonds to P+1 Re: EXPERIMENTAL PROOF Re: Hydrogen is the very best way to prove AP's ION theory Re: proving AP's ion theory

The below is a famous experiment of 2014, very famous because it opens a flood gate of new understanding of both Physics and of Chemistry for it proves these 5 points of issue:: 

1) That in Electricity Magnetism there is only a force of attraction, and all scientists were confused because what they thought was "repel" is merely a "denial of same space occupancy-- Pauli Exclusion" for exclusion is not the same as repel. 

2) The real electron of atoms is a 105 MeV particle called the muon and the Real-proton is 840 MeV 

3) The particle that is .5MeV we always thought was the electron way back since JJ Thomson in 1897, turns out, that this .5MeV particle is Dirac's magnetic monopole, which is a photon or neutrino with a .5MeV charge energy, not rest mass energy. 

4) The Real Electron and Real Proton rarely ever escape a atom, but what does escape and what is in almost all transactions of atoms is the monopole which can be either +1 or -1 of .5MeV. 

5) The Real Electron is firmly bonded to the proton as 105 MeV with 840 MeV, for which the proton itself is composed of 8 muons. The neutron is actually 945 MeV and is a proton + muon + some other particles. 

Kjaergaard's experiment is the first of what will become a cascade of chemistry experiments that all will prove the above 5 points of interest. 

On Friday, February 23, 2018 at 5:07:26 PM UTC-6, Archimedes Plutonium wrote in sci.physics: 
 Kjaergaard's famous Danish experiment of 2014 Re: Chemists are smarter than Physicists-- 2018 textbook of Experiment-- Real Electron = 105MeV 
13) Proof came in February 2018 for AP's ion theory, that ions are monopoles .5MeV either +1 or -1 charge, attached to a 840MeV proton and 105MeV muon as hydrogen. 
Newsgroups: sci.physics 
Date: Tue, 6 Feb 2018 19:37:37 -0800 (PST) 

Subject: H+1 bonds to P+1 Re: EXPERIMENTAL PROOF Re: Hydrogen is the very best 
 way to prove AP's ION theory Re: proving AP's ion theory 
From: Archimedes Plutonium <plutonium....@gmail.com> 
Injection-Date: Wed, 07 Feb 2018 03:37:37 +0000 


H+1 bonds to P+1 Re: EXPERIMENTAL PROOF Re: Hydrogen is the very best way to prove AP's ION theory Re: proving AP's ion theory 

Below is an experiment done in Denmark where it is shown that H+1 bonds to P+1 ions, proving not only that the Muon is the real-electron and that ions are magnetic monopoles, but, in addition, proving that like charges attract, for in Nature, attraction force is the only force existing and that what appears to be repel is merely-- denial of same space occupancy. 

Positively Charged Phosphorus as a Hydrogen Bond Acceptor 

Anne S. Hansen, Lin Du and Henrik G. Kjaergaard* 

Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark 
The Journal of Physical Chemistry Letters 

Vol. 5: , Issue. 23, : Pages. 4225-4231 
Publication Date (Web): November 19, 2014 

https://doi.org/10.1021/jz502150d   


Scientists discover impossible hydrogen bond | ScienceNordic 
sciencenordic.com/scientists-discover-impossible-hydrogen-bond‎ 
Mar 25, 2015 ... Scientists have discovered a new type of hydrogen bond which was previously considered impossible or at least highly improbable. "The discovery is significant because hydrogen bonds are such a fundamental part of both chemistry and biology," says Professor Henrik Kjærgaard from the Department of ... 

ScienceNordic 
Scientists discover impossible hydrogen bond 
March 25, 2015 - 06:25 
By: Lise Brix 

Professor Henrik Kjærgaard and his colleagues have demonstrated that a new kind of hydrogen bond can occur between a hydrogen atom and a phosphorous atom. Pictured here is Kjærgaard in his lab at the University of Copenhagen. (Photo: University of Copenhagen)Scientists have discovered a new type of hydrogen bond which was previously considered impossible or at least highly improbable. 
"The discovery is significant because hydrogen bonds are such a fundamental part of both chemistry and biology," says Professor Henrik Kjærgaard from the Department of Chemistry at the University of Copenhagen. "They form the basis of biological molecules and it’s for instance hydrogen bonds that determine the boiling point of water." 
He led the new study, which has been published in the Journal of Physical Chemistry Letters. 

At Aarhus University, chemistry professor Jeppe Olsen is surprised.... 

(snipped) 
Olsen points out that not only have Kjærgaard and his colleagues found the new hydrogen bond in experiments -- they have also provided "an excellent explanation" of the discovery. 
The theory behind the discovery is that the atoms' charge is not uniformly distributed around their surface -- which is how simplified models say they do. 
“Our discovery emphasises that the charge around the surface of an atom is not uniform. If there was a positive charge all the way around the phosphorous atom this hydrogen bond wouldn't be possible. But it is. This must mean that the charge is not uniformly distributed around the atom -- you might say that there are tiny pockets of negative charge around the phosphorus atom," says Kjærgaard. 
The discovery of the special hydrogen bonds was made in experiments with infrared spectroscopy -- a method used by scientists to obtain knowledge about molecules and their vibrations by irradiating them with infrared light. 

AP writes:: Sorry, but the explanation of why this bonding exists is because there is no force of repulsion in Electricity Magnetism, only attraction. There is denial of same space occupancy which is known as the Pauli Exclusion Principle. 

But what will really force everyone in science to accept the idea that the real electron = 105MeV is when you break apart the hydrogen proton into a 840 MeV particle plus a 105 MeV muon. 

I suspect this has already happened in Poland-- 


Quoting 

Indication For A Broad J(pc) = 2++ Meson At 840-mev Produced In The Reaction Pi- P ---> Pi+ Pi- N At High |t| 
K. Rybicki, I. Sakrejda (Cracow, INP) 
1985 - 10 pages 

Z.Phys. C28 (1985) 65-74 
DOI: 10.1007/BF01550250 
Abstract (Springer) 
The reaction π−p→π+π−n has been studied at 17.2 GeV/c and 63 GeV/c. A partial wave analysis shows a fairly broad (∼250 MeV) resonance at about 840 MeV. This object, already visible in moments of the angular distribution, is produced in theD wave with helicitym=2 via unnatural exchange. The cross section for the reaction π−p→D2U(840)n is only by an order of magnitude lower than that of ϱ(770) and falls likepLAB−2.1±0.3. We have not been able to explain this object by systematic experimental effects like acceptance and/orN* reflections; neither is the nature of the resonance (if real) clear to us. 
--- end quote --- 

AP 

  __ 
/^,,)__/ 

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#413828 — page3&4 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

#1-3 Decimals 

Alright, it is important that students of age 8 onwards get the correct view and understanding of "What are Numbers" This book starts with age 8, because it is about here, where fake and corrupt Old Math sets hold. I do not want education where in one year you learn something and a few years later, be told, forget what you learned and this is the true math. 

In the past history of math education, the students were misled and then when they reach College, they have such an error filled view of numbers, and geometry. For this reason, I needed to start this book for age 8, to catch the student before corruption of math can set in. 

Now in the Core Curriculum too much time is spent on Fractions. So, what I want to see here, is cut that time in half, or a third, and with that extra time, spend it on teaching Decimals better. We still teach fractions but regard them as incidental to math. We teach them what fractions are-- ---unfinished division problems---- for some reason or other, the person is too lazy too dumb to put into a decimal number, and we teach them the operators on fractions 1/2 + 1/3, or 1/2 - 1/3, or 1/2 x 1/3, or 1/2 divided by 1/3. But we do not do what happened to me in school, spend almost two years on just fractions. It is reasons like this, that I must start this textbook for 8 year olds. To guide them and the teachers away from phony math.

I want the 8 year old to be able to do these decimals without much trouble. 

  34.23 
+23.11 
----------- 


  9.08 
+1.32 
---------- 


     4.56 
-    1.13 
---------- 

  9.11 
-9.08   This one maybe more trouble since it has a carryover and deals with 0
------- 

  7.1 
x7.3 
------ 

   6.2 
x  5.4 
-------- 

So, teacher, please assemble long lists of exercises with these easy decimals of add, subtract, multiply. Spend weeks on this. If the above is too hard do only one digit to the right of decimal point and one digit to the left. Getting acquainted with numbers is half the battle of learning, once acquainted, when the young minds of students sees it again in the future, they learn it even faster than before.

Now, on to division of decimals in next lesson. 

AP


Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 




On Sunday, March 25, 2018 at 10:46:37 PM UTC-5, Archimedes Plutonium wrote:
#1-4 dividing Decimals 

Review of Decimals, division, for teacher and student:: 

Now, let us start teaching division of decimals to 8 year olds. Start them with the easiest of divisions, and do not worry too much that it is difficult for them to grasp, it is more of an introduction, so that when they are 9 year olds, they can repeat this lesson easily. 

Alright, still in Grade School with 8 year olds. We just taught them decimals but every year, here-after, we teach them more about decimals, for that was just a starting point of decimal teaching. The lesson of mathematics for all students, for they all need to know what numbers are, to count, to manage money. Not only for future scientists, engineers, those in medicine have to master decimals, but all people who never go on in science or engineering need numbers and those numbers are decimals. 

Alright, well, I want logical flow. 

I started this book with memorization of the Multiplication Table. 

Now, we do division, short division at first, slowly we get to long division and for students for the first time in their life, to divide in math. These are 8 year olds, and if taught this in prior years, well, all the better. And parents, if you want to help your child in math, especially math, encourage your daughter or son, encourage them in division. If you as a parent emphasize division at home, the student is doubly interested and can learn faster. Long Division is the toughest your child will do in Grade School at age 8.

So, Teacher have a list of the multipliers in lesson #1 

2x2 =4 
2x3 =6 
2x4 =8 
2x5 =10 
2x6 =12 
2x7 =14 
2x8 = 16 
2x9 =18 

3x3 = 9 
3x4 = 12 
3x5 = 15 
3x6 = 18 
3x7 = 21 
3x8 = 24 
3x9 = 27 

4x4 = 16 
4x5 = 20 
4x6 = 24 
4x7 =28 
4x8 = 32 
4x9 = 36 

5x5 = 25 
5x6 = 30 
5x7 = 35 
5x8 = 40 
5x9 = 45 

6x6 = 36 
6x7 = 42 
6x8 = 48 
6x9 = 54 

7x7 = 49 
7x8 = 56 
7x9 = 63 

8x8 = 64 
8x9 = 72 

9x9 = 81 


And introduce the division symbols of / such as 4/2, or as 
  ____ 
2| 4 

Move to the next one 

6/3 and 6/2 

  ____ 
3| 6 

  ____ 
2| 6 

So the 8 year old student first introduction to long division is short division and a recall of the Multiplication Table, and that is very very fitting, because, well multiplication and division are linked together. So we memorized multiplication, so that we can do division. You see why we memorized multiplication.

Say to the class about multiplication and division, the word "reverse" and the word "inverse". Tell them they mean about the same thing in that multiply 2x3 = 6 is the reverse of 6/3 = 2. So drill that idea that multiply is the reverse of divide, and divide is the reverse of multiply. 

Now it is important for me to get the first 10 lessons covering decimals, logic, graphing and sigma-error as near to perfect as I can get for 8 year olds, because I do not want to write 10 lessons for every year age increase until High School. I do not want to micro-tune each lesson for each year. That is the responsibility of the teachers using the textbook. So once I get the 8 year olds 10 lessons to perfection, I will just use that as a template, a mold, a die cast for the next 5 years of school teaching, the 9,10,11,12, and 13 year olds. 

So here, we should make good use of the 8 year olds having memorized multiplication table. 

Now my own memory of when I was taught long division has long escaped my mind. I do not know how old I was and how it was taught. So I leave much of that to teacher discretion. 

Also, I am somewhat worried of my English for these young ages, that many of the words I use are over the heads of 8 year olds, and so the teacher should step in and teach those words, what they mean if any student asks, and make any sentence I write that is difficult, make them easier to understand. 

Now introduce the division symbols of / such as 6/3, or as 
  ____ 
3| 6 

So we have two symbols that mean divide /, 
______ 
| 

Some computers still have the old symbol of -:- and I do not like it for it confuses, for one does not remember if 6 -:- 7 means 6/7 or 7/6. And so we never bother with -:- as division anymore. Just stick with the two symbols of

/
_____
|

Now the answer of 6/3, is 2 and that answer is called a quotient. For we call the answer a quotient. Where 4/2 = 2, and 2 is the quotient,--- the answer.

6/3 and here the answer is 2, a quotient is the answer 2. And 6/2 is an answer of 3, the quotient is 3. Quotient means answer. The divisor is what you divide into the dividend and the quotient is the answer. So in 6/2 the divisor is 2, the dividend is 6 and the answer or quotient is 3.

In multiplication such as 3x2, the multipliers are 3 and 2 and the product is the answer, so 3x2, we have a product of 6.

  ____ 
3| 6 
  
  ____ 
2| 6 


Move to the next one of 

8/4 and 8/2 

  ____ 
4| 8 

then 
  ____ 
2| 8 


So the 8 year old student first introduction to long division is a recall of the Multiplication Table, and that is very very fitting, because, well multiplication and division are linked together. Repeat the words "reverse and inverse", for multiplication is the reverse or inverse of division and division is the reverse or inverse of multiplication.

And we see why we have to memorize multiplication table, because we need that memorization to know how to divide.

     ___ 
6  | 36 

    _____ 
10| 100 


Now, teacher, here we go with division that is not even and has a remainder, so now we are getting into long division. And so divide and with carryover and that of a remainder. So in the first case we have this 
   ___
6 | 8


       1 remainder 2 
     ___ 
6  | 8
      ^
      6 a little 6 below the 8 and on the 8 but above the arrow-- computer will not allow me to write the 6 small and resting upon the larger 8.

Now subtract 6 from 8 and we have a 2,  and we carry that 2 up and have our answer, 1 remainder 2.

And here we see where Computer Technology needs to go next-- it needs to be able for the person to write onto the screen in long hand, to write not print type from a keyboard, but to actually write and draw on the screen and be able to send that writing off as a post. In other words, computers and iphones of the future do not need a keyboard, for they can write on the screen as if it were a blank sheet of paper.

Now let us do a more challenging division
   _____
6 | 879
     ^       So 6 into 8 is 1 and place a 1 above the 8 like so

   _1____
6 | 879
     ^  
Now write a tiny 6 into the 8 but above the arrow, a 6 that is smaller than the 8. Now subtract and that is a 2 and with the 2 we carryover the 2 where the " is located.

   _1____
6 | 8"79
     
Now write that 2 next to the 7 only write it smaller, much smaller than the 7 for the 2 is a carryover and written small and now we have to divide 6 into 27 and remember from the multiplication table what is close to 27 by 6? It is 4 for 4x6 = 24 and write a 4 above the 7, so now write the 24 in small script below the 27 and above the arrow


   _14___
6 | 8"79
        ^
Now we have 27 and immediately below it a 24 and subtract, and we have 3, so again we carryover the 3 in small script next to the 9.


   _14___
6 | 87"9

and we have 39 with the 3 in small script as the carryover and now we ask again how many 6 can go into 39? From our multiplication table we remember 6x6=36 and we write the 6 above the 9, so in small script we write 36 below 39 but above the arrow.

   _14 6___
6 | 87"9
          ^

And now subtract 36 from 39 we get 3 and so our final answer is 146 remainder 3.


We do Long Division this way so there is no waste of space by writing a small 6 below yet on top of the 8. Impossible to do with keyboard. So let us call all computers of the world at this moment in time-- April 2018, call them KEYBOARD based computers. That includes my iphone.

What I am asking the world of electrical and electronic engineering to do, is build the first WRITING based computer. Where the screen of the iphone acts like a blank sheet of paper and with a common pencil as I write anything on that screen, I can post my complete writing-- as is -- post it and be seen by others as my writing. 

Now, this technology is not totally unknown, because just yesterday at the grocery store I signed my name to a credit card signature at the end of the cashier stand. Although the electronic signature is a bit awkward looking, still, it is writing not keyboard.

So, the next revolution in computers, is get them to write instead of keyboard based, and, well combine the two.

Now teacher give the students, the 8 year olds loads and loads of division with carryover and with remainder. Here is a starting list of exercises, even homework, and perhaps parents can help their child on the most basic and troubling math problems they face. Long Division is the hardest they are going to experience at age 8.
   ____
5 | 89
   _____
7 | 374
   ______
9 | 2112
   _____
2 | 1101

In the next lesson we go even deeper into Long Division


Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 

[toc] | [prev] | [next] | [standalone]

#413868 — page5&6 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

#1-5 Long Division

Alright, now we do long division, no holds barred. Previously we did division with remainders, now we do them with no remainders.

Now on second thought, perhaps it is better not to have parents help their child because most of them probably divided with the extravagant use of the paper as they went down and down filling up the paper with just one or two divisions. Our Long Division is such that we hardly use up any paper. So better not have parents help unless the parents can change for the better.

First we have a rule, for whenever we have a number without a decimal point we include the decimal point and we tack on three zeroes to the right of the decimal point. Say we had the number 3456 then we include the decimal point 3456.000 and tack on three zeroes. Every number without a decimal point we include the decimal point and tack on three zeroes. Teacher, teach them that tacking on zeroes makes no change in the number itself, for 3456 is the same as 3456.000.

So, let us do this problem in long division
   _____
3 | 100

First we tack on the decimal point and then three zeroes
   ________
3 | 100.000

now we proceed to long divide

 
  __3_____
3| 100.000
      ^
so, 3 into 1 will not go so we go, 3 into 10, and what is our multiplication table tell us the closest number to 10 with a number 3? Remember that 3x3 = 9. So we write a 3 above that first 0 of 10, and we write a small script 9 between 0 of 10 and above the arrow, it is alright to write the 9 into the 0, a small 9. Now we subtract 9 from 10 and we get a 1.


 
  __3_____
3| 10'0.000
      
Now we move that 1 as a carryover, move it to where you see the ' and so we have another 10 with the moved 1 and the next 0

 
  __3_____
3| 10'0.000
         ^
Now what is 3 into 10? Again another 3 and we place a 3 above the 10 and a 9 below the 10 but higher than the arrow

  __33____
3| 10'0.000
         ^
Now we subtract again and get another 1 and we carryover that 1 as before only we cross the decimal point

  __33. 3____
3| 100.'000
           ^
now we raise the decimal point exactly above as below, and subtract the 9 from 10, equals 1 carryover again until we have no more zeroes to work with

Our final answer is this:

  __33. 333__
3| 100.'000

So now, try these out, see if the students grasp it, carryover and remainder. If not well, wait for another year.


1/6 or written as
   _____
6 |1.000
            
       _ .166___ 
6    | 1.000
     

Answer 1/6 = .166

    _____ 
4 | 5.000

     ______
6  | 37.000 


Teacher, plan out your own quizzes and tests to see if the student has mastered Decimals at 8 years of age, and I include some of the simple long division above, but if the 8 year olds are not ready for long division, then skip it for another year.

Lecture to the teacher--
We do not call 1/6 a number, nor 
       _____ 
6    | 1.00   

a number, but rather it is a division that will lead to a number. And, likewise 1/6 is not a number but a call to divide. This is one of the reasons I am starting with 8 year olds. For I do not want the 8 year old or younger be taught the phony notion that 1/6 is a number. It is not a number, but a division, a long division. And although after you divide you get a number--- a decimal number. The symbol of 1/6 is not a number. Now the 8 year olds need not know that now, in this book, even though they can easily read my words. But, before they get into the last 3 years of High School, they must know by then, that fractions are not numbers, but long-division exercises. The division ends up being a number, but before the number is reached, it is not a number. 


You cannot order, place in an order, nor can you count fractions, and that is the reason they are not numbers. You can order and count Decimals and it is for this reason that Decimals are the Only Numbers. 

So cut the teaching of fractions by half, and that half devote to teaching better, decimals. The history of this problem stretches back centuries, and the major part of the problem was in writing division. 

We easily can see that 

5 -:-  3 is not mistaken for a number but is a division process that will lead to a decimal number answer. 

And, I have asked that the symbol -:- be removed out of all of mathematics for it is just too confusing as to what is being divided into what. Explain whether above you divide 5 by 3 or whether you divide 5 into 3. So, delete the symbol altogether out of math. 

Math can get by with the symbols of 
 ____ 
| 

and the symbol / for division 

Likewise we do not mistake 
   ______ 
3 | 5.000   is not a number but a plea to divide. Once we have divided then the end result is a decimal number.
  


Let the student try this one out, remember to put the decimal point exactly straight above

5/3
    _______ 
3 | 5.000 


Fraction 10/5 becomes 

        
    _______ 
5 | 10.000 


Now do the fraction 1/2 


    _______ 
2 | 1.000 


Now the answer is when you carry up the decimal point is .5, so we have 1/2 = .5 

Before we had 10/2 = 5. Now we have 1/2 =.5 

Spend some considerable time on this with the students and do 3/1, and then 1/3. 

Do 3/2, then do 2/3. 

Let us do 5/4. 


  
    _______ 
4 | 5.000 



Note: Teacher and Student, some like to put commas after every 3 digits such as 1000 is 1,000. I myself prefer no commas. The commas are not a part of mathematics, but just for people with eye strain can read 1,000 faster than without commas. And, commas get in the way of the decimal point in that some are confused if you write a comma thinking it is a decimal point. So try avoiding commas.

So, Teacher and Students, you decide if you want to use commas or not, it is totally up to you. But in computers, with banks, my bank wants no commas. 

Now should i do this, maybe not 

Maybe i should 

Maybe not. 

Send the 8 year home on a homework assignment to survey their parents and other family members. Get them privately alone and as each parent or family member ask what the fraction 1/2 is in decimal. All parents should immediately say .5. But other family members, depending on their age should be slower in responding that 1/2 as decimal is .5. 

And, see if the student can teach the parents the new way of Long Division where you do not take up much space on the paper.


Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 





Newsgroups: sci.math
Date: Sun, 11 Mar 2018 19:09:16 -0700 (PDT)

Subject: TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Mon, 12 Mar 2018 02:09:16 +0000


#1-6  Logic of AND, OR// TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium 

Now, today in this lesson we do Logic. We start Logic, we start a new topic, which is a relief to some 8 year olds who spent the last 3 or 4 months learning decimals. Ask the students if they ever watched Star Trek and Dr. Spock. Well, logic is what Dr. Spock was proud of, and it was his specialty. Even though it was science fiction, we see what logic is about-- thinking cool, thinking straight, thinking clear, thinking correctly. 

Now there are two types of Logic, one is called Algebra Logic and the other is called Geometry Logic. We will hear and see more about Geometry Logic later on, but for now we do Algebraic Logic. Ask the class if anyone knows what "Algebra" means. Well, Algebra means analysis of parts of a whole. Algebra means we  look at and examine parts of a whole. To examine and inspect parts of a whole. In this case-- to examine and inspect grammar and words as parts of a whole sentence in Language. Here are two sentences.

(1) The Earth goes around the Sun and the Moon goes around Earth.

(2) Either the refrigerator is working because it is plugged into the electric outlet, or, the refrigerator is not working because it is not plugged in to the electric outlet.

And today we learn two connectors of Algebraic Logic, the AND, and the OR. Do you see those two sentences of Language and do you see the "and" in sentence (1)? Do you see the "either,, or" in sentence (2) ?

So, teacher, do about a page full of AND statements and a page full of OR statements. 

Something like this: 

The boy with the ball and the girl with the bat went to the backyard field to play. 

That can be broken down into 

The boy with the ball went to the backyard field to play. 

The girl with the bat went to the backyard field to play. 

So we stick an AND in those two sentences to produce our original sentence. Ask the class what is And like? Is it like add, like subtract, like multiply, like divide? 

A OR example. 

Either it rains at noon time today or it is sunshine at noon today. 

So, ask the class what that OR is like, is it add, subtract, multiply, divide? 

Show them it is subtract, for at Noon time, if it is raining it is not sunny and you subtracted sunshine. But if it is sunny, it is not raining and so you subtracted out the rain. 

Now many examples come from math itself. 

2 AND 3 is what? It is 5 

7 OR 10 is what? Well if you have 7 not 10 you subtracted 10, and if you have 10 not 7 you subtracted 7. OR is one of two items but never both. OR is subtraction. 

AND is the joining together of items. AND is add, OR is subtract, remove. 

So have a sheet full of AND examples and another sheet full of OR examples. 

Warning to Teacher: please spend considerable time on composing AND, OR statements, especially OR statements, for although we may think this is easy material, in fact, it is difficult to do nice pure logical statements. So prepare the night before especially well and cautiously. 

So go over the above exercises with about several days of new examples of AND and of OR.  I want to go over again AND of Logic and OR of Logic. Here again, give the students a whole page of AND statements. Another whole page of OR statements and let them figure out how the AND is adding, and then, how the OR is subtracting by choosing one item and dismissing the other item. 

Summary:: We learned what Algebra means-- a examination of parts of a whole and we learned Algebra Logic is the examination of sentences and words of Language, a look at grammar of language and words in sentences.

You be surprised at how well students at this young age of 8 years, pickup on knowledge. When I was a teacher, my favorite classes were these young students for their sole interest in life at that age was learning. A little older and then body hormones kick in and the students are interested in other things also and easily distracted. 

So the lessons on Decimals took about 4 months. The lessons on Logic, And with Or, is only going to take a week or two, not much. 


Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 

[toc] | [prev] | [next] | [standalone]

#413994 — page7&8 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

#1-7  Graphing // TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

Now we move on to Graphing, and the graphing is going to bring back the Decimal numbers again. And is going to cost the School in graph paper. So, either the School provides graph paper, or the students bring their own graph paper. But bring a good pencil with erasure so we can use the same graph paper over and over again.

There was an example of Either Or. Either the School provides the graph paper, or, the student brings their own graph paper. 

Now in addition to Graph paper, have them bring a pencil with good eraser, or even a gummy eraser that does not tear up the graph paper so they can use the graph paper over and over. If careful, a student can use one graph paper that lasts for weeks even a month. Erase gently, and do not write the numbers or lines too dark or too thick. 

Also, now the student needs a ruler. 

For Grade School into start of High School I want a theme package of four major topics-- Numbers, decimals mostly, Logic, Graphing and Sigma error. 

Those four form the basis of a good education in math, what all students need, even if they do not take math ever again after High School. 

The Decimals are the numbers, the algebra of mathematics. The Logic is to think clear, correct and straight. The Graphing is geometry, a geometry with numbers. The sigma error in math is an intrinsic error and when doing math we must consider the error involved such as when using geometry and many measurements. So those four are the essential four of mathematics. 

Now the first 10 lessons are for students age 8. I need to teach those at 8 years old the true math, so their minds are not polluted and have to re-teach them. Education is always horrendous if a teacher one year tells the students-- forget what your past teachers told you-- this is the straight up true. That is horror education. And trouble is, today in 2018, more than 75% of what is taught in schools is outright fakery, mind numbing propaganda, much of it reminding me of Soviet education when Stalin was in USSR, where the State teaches not what is true, but what pleases some people in power. About 75% of the math education in the USA today in my opinion, is not true math, but math that pleases those math professors and their publishing presses making them rich and filling their pockets with money and fame. 

So, I need to catch the student at an age in school, where money-math is totally cut out. And only True Math is taught.

And I suspect age 8 is a good year to start so the student does not encounter the con math money machine and pollute their understanding of math, rather than enhance their math. 

So, today, Lesson7, starts Graphing. 

Now either the teacher supplies each student with graph paper, or the student's parents supply their student with these materials. I prefer the white graph paper where all the blocks are uniform the same. Some graph paper is green tinted and where they make bold lines and non-bold lines. The thing I hate about these green tinted, is they make the bold lines after every 5 blocks. Why could they not be more logical. Since numbers are all Decimals, make the bold lines after every 10 blocks. Did any graph paper publishing company ever produce such? 

So here, is an example for students 8 years old, to see that Logic is so very very important. Because if you make bold lines on graph paper, why in the world would you chose every 5 small blocks. Decimals are 10 not 5. 

So, furnish the student with Graph paper and with pencil and gummy erasure that does not tear up the paper, and pencil sharpener-- those small plastic thumb size sharpeners, and with ruler. Tell the kids that they will use the eraser many times and not to make too dark of spots on the graph paper so they can reuse the paper over and over again. 

Now, for first Graphing, teacher, have the students write as many numbers as possible for each block on the bottom and going up the side. 

On my white all uniform blocks Graph Paper, no bold lines but all the same, I can go out to 42 along the bottom and 32 along the side, looking like this: 

32 
31 
30 
29 
28 
. 
. 
. 
. 
. 
4 
3 
2 
1 
0 1, 2, 3, 4, 5, 6, . . .                  38, 39, 40, 41, 42 

Teacher, spend a nice full day just teaching graphs for the first time to these students. 

Make sure they write numbers small, for there is little room. Go around to each student helping them 
do this clean and properly. There are no commas, for I only wrote them since the above is not a graph paper. 

And have the students write them lightly because there is going to be many erasing and you need to save on graph paper. 

Now I wish we had paper that was 100 blocks high and 100 blocks long, but our paper is too small to have that. 

I prefer the Decimal representation even in graphing. So, teacher, try to get a overhead projector with a graph of 100 blocks to supplement this teaching, and tell the students, even though their paper goes from 32 to 42, what we really wanted was 100 by 100. 


Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 




On Tuesday, March 27, 2018 at 3:00:51 PM UTC-5, Archimedes Plutonium wrote:
#1-8  Graphing // TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium


Alright, so my graph paper is 42 along the bottom and 32 blocks high. Now the students graph paper may be different so the teacher is going to have to take an inspection of each students graph paper so that they can cope with the x-axis number line and the y-axis number line. 

So, teach which is the x-axis and which is the y-axis. The x-axis runs along the bottom. The y-axis runs from bottom to top. 

Teacher, teach the bottom row is called the x-axis and draw a arrow  ---->. Teach the column that goes up 32 blocks is called the y-axis and draw a arrow 

^ 
| 
| 
| 

Now, teach the meaning of a coordinate point. (x, y) 

For example, do these coordinate points and plot them. 

(1,1) 

(2,3) 

(5, 10) 

(6, 20) 

(0, 0) 

Notice I deliberately did (0,0) last, thinking that this may stump some young 8 year olds. 

By plotting them, let them make an "x" mark on the graph where the coordinate point lies. Or, if they write it small, just write the point such as (6,20). 

Now have the teacher, make pictures of things such as triangle, square, rectangle, parallelogram, rhombus, trapezoid connect by a straightline from one point to the next point. The teacher has to do this on the blackboard so the students themselves connect the correct points. 

The prime lesson here is Coordinate Points and x-axis, y-axis. 

Spend several days on plotting points. Always reviewing the key concepts, of x-axis, y-axis, coordinate points (x,y) like (1,2). 

Summary:: Learn what x-axis is, what y-axis is. Learn what coordinate point is, such as (1, 3). Learn how to plot those points given, then connect points with a ruler. 

Graphing: figures of geometry, right angle
 
Alright in the Common Core, I do not know when they teach right-angle or angles for the first time. So I am going to presume 8 year olds are taught angles for the first time. And here we introduce students to the most common figures in geometry. 

Such things as a triangle, square, a rectangle, a parallelogram, a rhombus, a trapezoid. 

Find out the coordinate points of figures, then have the students plot them, then connect points with a ruler to find out what the coordinate points formed. 

Now my graph paper allows for 42 blocks by 32 blocks and I have plotted some of these figures. However, if your students have smaller graph paper, then the teacher is going to have to assign different points for the below exercises. 

Right triangle  (1,1) (1,4) (5,1) plot the points and have the students connect with a ruler, but have the teacher show each of these on the blackboard first. And here introduce what a Right-Angle is, a 90 degree angle, introduce the term perpendicular, means right-angle. 

Right Angle: teach where two line rays, call it a "line ray", where you have two line rays and they meet at a vertex point |__ and the angle is the amount of space between the two line rays. 

Not a Right triangle: (7,3) (10,6) (12,3) and show the students that the angles are less than 90 degrees 

Square: (2,6) (6,6) (6,10) (2,10), teacher show this on the blackboard first and show them how to connect with ruler. Discuss the four angles. 

Rectangle: (13,4) (17,4) (17,11) (13,11). Discuss the angles and then discuss what is different from the square and rectangle-- the square sides are all four of them equal to each other. Whereas the rectangle has two of the four equal to each other, the opposite sides are equal to each other. 

Trapezoid: (13,15) (17,15) (17,20) (13,17) discuss what is different about a trapezoid from a rectangle 

Parallelogram: (19,14) (25,14) (28,17) (22,17) discuss what is different between a rectangle and parallelogram, note especially there is no right angle. 

Rhombus: (21,4) (26,4) (30,7) (25,7) discuss what is different between a rhombus and square and what is different between a rhombus and parallelogram. 

Now this lesson is to practice in plotting points, then connecting points with a straightline segment. We learn a right-angle and we just eyeball in what is not a right angle, for these are 8 year olds and we need not go into depth about angles. 


Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 

[toc] | [prev] | [next] | [standalone]

#414009 — page9&10 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

On Tuesday, March 27, 2018 at 5:35:35 PM UTC-5, Archimedes Plutonium wrote:
#1-9  Graphing // TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium 

Alright in the Common Core, I do not know when they teach circle for the first time. So I am going to presume 8 year olds are taught circles for the first time. The students are going to need their graph paper, pencil and eraser, and a compass (teacher be wary since a compass has a needle like end, and do not want anyone getting hurt). 

Now do a x-axis from 0 to 15, and do a y-axis from 0 to 15. Remind students of the x and y axis. The x-axis is horizontal, going across the bottom and the y-axis is vertical going upwards. 

Now, find the point (8,7) and measure a distance of 7 units for the compass, radius. From the point (8,7) with the compass, make a circle that is radius 7, diameter 14. 

Teacher: show the students this construction on the blackboard, before they do it on their graph paper. 

Now, for the rest of the class period, have the students write out the coordinate points of the circle. 

And, we are going to teach Sigma Error here. 

(1,7) is the first point I get off the circle, and moving on to 2 on the x-axis we have two new points. 

(2, 3.4) now, here, teacher, explain how we get the .4 in 3.4 

and we must not forget the other point (2, 10.6) 

Explanation: 

Say we have a block of the graph as this where the circle curve passes through that block 
 __ 
|__| 

And our circle curve goes through that block 

We divide the block into 10 fine marks evenly spaced on side and on bottom of block and we guess where the curve lands or passes through. 

  __ 
|-__| 

To, me, it looks like it landed .4, but some may say .3, others may say .5. 

The next two points is when we have a 3 on the x-axis. 

And eyeballing the two points in, I get 

(3, 2) and (3, 12) 

The next two points is when we have a 4 on x-axis. 

(4, 1.3) and (4, 12.7) 

Teacher, have the students go all the way out to 15 on the x-axis and while they are doing that, walk around the classroom seeing if each student is coping with the job at hand. 


Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 




On Thursday, March 29, 2018 at 1:36:14 PM UTC-5, Archimedes Plutonium wrote in sci.math:
#1-10 Sigma-error in math TEACHING TRUE MATHEMATICS, 2018  

Alright, this is new to mathematics, totally new, for it teaches that math is internally having error. We always thought math was perfectly error free, but here we teach that math, like physics has uncertainty, internal error. And math even has a whole subject on error, but never realized that the error was a part of mathematics itself. It is called Statistics. And much of science deals with statistics, even physics is inundated with statistical mechanics. 

So, it is best to start teaching the error of math, rather than have young people, with 8 year olds, thinking math is perfect, when far from it, math has internal errors. 

And I cannot think of a better "first lesson of sigma-error" than in reading the coordinate points of a circle. In the last lesson of #9 we learned how to write the coordinate points of a circle drawn by a compass (teacher watch the students carefully for a compass has a sharp pointed end). 


> 
> Alright in the Common Core, I do not know when they teach circle for the first time. So I am going to presume 8 year olds are taught circles for the first time. The students are going to need their graph paper, pencil and eraser, and a compass (teacher be wary since a compass has a needle like end, and do not want anyone getting hurt). 
> 
> Now do a x-axis from 0 to 15, and do a y-axis from 0 to 15. Remind students of the x and y axis. The x-axis is horizontal, going across the bottom and the y-axis is vertical going upwards. 
> 

Teacher, review the circle drawn last time. 

> Now, find the point (8,7) and measure a distance of 7 units for the compass, radius. From the point (8,7) with the compass, make a circle that is radius 7, diameter 14. 
> 

Review that circle again with radius 7. 

> Teacher: show the students this construction on the blackboard, before they do it on their graph paper. 
> 
> Now, for the rest of the class period, have the students write out the coordinate points of the circle. 
> 
> And, we are going to teach Sigma Error here. 
> 
> (1,7) is the first point I get off the circle, and moving on to 2 on the x-axis we have two new points. 
> 
> (2, 3.4) now, here, teacher, explain how we get the .4 in 3.4 
> 

So, teacher, here we teach Sigma error. Because the point (2, 3.4) the ".4" we had to eyeball in, and some students are going to guess .5 not .4, some will guess .3 and not .4 

So, teacher, draw on the blackboard a magnified unit block and hatch mark in so you have 10 equal spaces below and above, like this 

-- 
-- 
-- 
-- 
-- 
-- 
-- 
-- 
-- 
-- |  |  |  |  |  |  |  |  |  | 

Pretend that is a Magnified block that the graph curve goes through of the circle 
4 
-- 
-- 
-- 
-- 
-- 
-- 
--X 
-- 
-- 
-- |  |  |  |  |  |  |  |  |  | 
3 

And our circle curve went through that block from 3 to 4 at about .4 


and we must not forget the other point (2, 10.6) 

Explanation: 

Say we have a block of the graph as this where the circle curve passes through that block 
    __ 
   |__| 

And our circle curve goes through that block 


So teacher, here, what you are teaching is how math can be imprecise, imperfect and that it depends on your eyeballing in what is the point, is it (2, 3.4) or some would say it was (2, 3.3) 


We divide the block into 10 fine marks evenly spaced on side and on bottom of block and we guess where the curve lands or passes through. 
 
     __ 
   |-__| 
 
To, me, it looks like it landed .4, but some may say .3, others may say .5. 


Teacher, now go around and list on the blackboard what each student eyeballed that point in as. 

Make a list of who got 3.2, who got 3.3, who got 3.4, who got 3.5 


The next two points is when we have a 3 on the x-axis. 

And eyeballing the two points in, I get 

 (3, 2) and (3, 12) 
 
 The next two points is when we have a 4 on x-axis. 

 (4, 1.3) and (4, 12.7) 

Teacher, have the students go all the way out to 15 on the x-axis and while they are doing that, walk around the classroom seeing if each student is coping with the job at hand. 
 

Now, as exercise, the teacher can do a new circle, with a new radius, say radius 8 with a new center, say center (8,8) and see how the students figure out what the coordinate points are, and check out the Sigma error. 

Now these are 8 year olds, so we only want to teach them SIGMA ERROR to get acquainted with the idea of error in math. We do not want to go into any detail or depth of error, just an error because we had to judge or decide where a point was, in-between 10 hatch marks. Remember, decimals are ten, so we have ten hatch marks to decide. 

It is important to teach Sigma Error early in math, because it removes that flawed perception that mathematics is always "perfect with no error". But, even numbers multiplied have a sigma error. For the square root of 2 has a Sigma error. And have your students of 8 years old, do this exercise. The square root of a number, teach them, the square root of a number, is what number when multiplied by itself equals that given number. In our case we want the square root of 2. Which means, what number when multiplied by itself is equal to 2. Teacher, show the students that the square root of 9 is what? Is 3 because 3x3=9. The square root of 4 is what, the square root of 16 is what? The square root of 25 is what? The square root of 36, of 49, of 64, of 81, of 100 is what? 

So, to the class, say that we are going to find the square root of 2, and see what Sigma Error exists for the square root of 2. 

So, to the class, say, is 1 multiplied by itself, is that 2? Is 2, multiplied by itself equal to 2? No, so it must be in between 1 and 2, lies the square root of 2. So, now, anyone guess? Let us guess 1.5 is the square root of 2. 

  1.5 
x1.5 
-------- 
  75 
15 
_____ 
2.25 

Check to see if all the students remember how to multiply decimals 

So, is 1.5 the square root of 2? No, it is too large, so let us try 1.4 

   1.4 
x 1.4 
-------- 
   56 
 14 
------- 
1.96 

So, is 1.4, the square root of 2? No, it is too small and needs a tiny bit more. So we try 1.41 

   1.41 
x 1.41 
--------- 
    141 
  564 
141 
------ 
1.9881 

So, is 1.41, the square root of 2? No, it is too small and needs a tiny bit more. So we try 1.42 

Now, teacher this is a pretty way of ending a year of teaching math to 8 year olds for it ends by reviewing multiplication of Decimals, and decimals understanding is of prime major concern for youngsters of this age. Hopefully the 8 year olds have a running start with decimal Long Division, and if not, well, 9 and 10 year olds will be taught more and more of Long Division, until they are fluent in it. But, back to this square root of 2. 

   1.42 
x 1.42 
--------- 
    284 
  568 
142 
------ 
2.0164 

Now, here the teacher is going to have to review the fact that we are in 10 Grid, and in 10 Grid, 1.42 is the square root of 2 because the only numbers that exist in 10 Grid have one digit to the right of the decimal point so the digits of "164" are Sigma Error of math, for in 10 Grid, the square root of 2 is precisely 1.42. 

--- END, end of a one year teaching of 8 year olds --- 



Very crude dot picture of 5f6, 94TH 
ELECTRON=muon DOT CLOUD of 231Pu 


                ::\ ::|:: /:: 
                 ::\::|::/:: 
                     _ _ 
                    (:Y:) 
                     - - 
                 ::/::|::\:: 
                ::/ ::|:: \:: 
One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
            . \ .  . | .   /. 
           . . \. . .|. . /. . 
              ..\....|.../... 
               ::\:::|::/:: 
---------------      ------------- 
--------------- (Y) ------------- 
---------------      -------------- 
               ::/:::|::\:: 
              ../....|...\... 
           . . /. . .|. . \. . 
            . / .  . | .   \ . 

  
http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 

I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      

Read my recent posts in peace and quiet.

https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
Archimedes Plutonium 

[toc] | [prev] | [next] | [standalone]

#414015 — page11&12 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

On Thursday, March 29, 2018 at 6:46:55 PM UTC-5, Archimedes Plutonium wrote:
Chapter#2 For 9, 10, 11, 12, 13 year olds-- Decimals, Logic, Graphing, Sigma-error TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

#2-1 teaching decimals Decimals // TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium

Chapter#2 For 9, 10, 11, 12, 13 year olds-- Decimals, Graphing, Logic, Sigma-error 

#2.1 teaching decimals TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium 

Alright, from the age of 8 years through 13, mathematics is concentrated on having all students learn very well what Decimal numbers are and how to add, subtract, multiply, divide decimals. The concept of percentage will be taught in one of those years and carried forward to age 13. The two key performance achievements for Decimals is the definition and the Long Division. Now, some teachers are going to complain that I focus too much on decimals. But, they are wrong, for I myself and my entire generation who studied math in college will attest to the fact that Numbers in those days was a helter skelter bag of what I would eventually find out is nonsense. Where in Freshman Calculus in college the first chapters are about Real-Numbers. Then as sophomore in college we had to take Real-Numbers with Peano Axioms. Yet, what this textbook is going to teach, is that you need none of those College courses on numbers for most of those numbers in college were fake math. The Irrational numbers are fake numbers, that do not exist at all, so why waste some two years in college over numbers that do not exist. So, that is why it is so important that I started this book with 8 year olds, so they are not polluted in mind over numbers of mathematics. And so the focus is on Decimals for which the student never again needs to learn any other kind of "so called numbers". Decimal Grid Numbers do it all. 

Now I taught this below Common Core to 8 year olds, and we are going to return and return to this definition of decimal so the students are extremely comfortable with the definition. If the 9 year olds have a tough time-- teacher, you be the judge, then go back to 8 year old lesson and do the definition to one place to the right and one place to the left side of the decimal point, such as 9.4, or 6.2, or 2.5 etc etc. And then go into two place values to right and left such as 34.87, 21.03, 55.66, etc etc. Every year, from 8, 9, 10, 11, 12, 13 year olds, we patiently do decimals, everyone gets it then move on to a bit harder. By the time they reach an age where they are comfortable with three place values, our work is mostly done. So they can do 821.092, 125.127, 999.999, etc etc. Now in 12 and 13 year olds, I want the teacher to extend the decimals out to four place values to right and left and that will be the end of Decimals. So they can do the definition and Long Division to four place values, 7523.9801, 2211.3355, 1001.0001. 

teaching decimals without calling on fractions TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium 

On Tuesday, March 20, 2018 at 4:45:15 PM UTC-5, Archimedes Plutonium wrote: 
(snipped) 
For the teacher-- SCALE NUMBERS: are defined as being a part of the axioms that build the Counting Numbers. We are given an axiom in Peano as there exists a 0 and 1. We need two numbers to exist in order to get a metric distance or unit measure between them. The Incorrect Peano axioms say-- let there exist 1 and all goes from that. But that is wrong, for you need to say-- let there exist 0 and 1 which defines a unit distance between them. Then you can take off. 

So, you have the existence of 0 and 1 and the Scale Numbers are all those numbers involving a single 1 and nothing but 0s. 

For the student, this is a list of Perfect Numbers 
the etc,.001,.01,.1, 0, 1, 10, 100, 1000, etc 

Now we revisit the Definition of Decimal found in Common Core and remove the fractions 

Google Internet search: 
        1.        Number & Operations in Base Ten - Common Core State Standards ...www.corestandards.org/Math/Content/5/NBT/‎
Read, write, and compare decimals to thousandths. CCSS.Math.Content.5.NBT.A .3.a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 ...‎CCSS.Math.Content.5.NBT.B.7 - ‎CCSS.Math.Content.5.NBT.B.5 

So, now, we use the definition of DECIMAL NUMBER without fractions but with Scale Numbers, the etc,.001,.01,.1, 0, 1, 10, 100, 1000, etc 

Definition of Decimal:: a number such as 347.392 = (3 × 100) + (4 × 10) + (7 × 1)  .  + (3 × (.1)) + (9 × (.01)) + (2 x (.001)) 

And I would be content if they, the 8,9,10,11 year olds, only learned to the thousandths place value in decimals. By age 12, 13, push the students to four place values. The above number 347.392 is good for 8,9,10,11 year olds. At age 12, 13, try out 7213.9456 

Now, here Teacher, you decide which is appropriate for your classroom. Whether they can learn this, shown below or if that is too much for 9, 10 year olds: 

Definition of Decimal:: a number such as 347.392 = (3 × 100) + (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) + (2 x (.001)) 

Now further on down the road in the education of students, they will learn fractions, or may already know fractions well enough to know what 1/10 as fraction is and 1/100 and 1/1000 as fractions by 10 years of age. For 8 year olds, 1/10 is .1 is known because in that graph of numbers .1 is a dime or 10 cents or 10 cents out of a dollar, is good enough. For8 or 9 year olds they must also learn 1/100 as fraction for in that graph on numbers that .01 was 1 cent out of 100 cents which is 1 dollar, so 1/100 is .01. Next years they learn 1/1000 and then 1/10,000. Remember about commas, teach they can go either way, with commas or without, for it is only an eye-strain issue, whether we want to count zeroes. 

Definition of Decimal:: a number such as 347.392 = (3 × 100) + (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) + (2 x (.001)) 

And here, in the definition, the student practices multiplication of decimals such as 3x.1 and then 9x.01 and then 2x.001. 

You see, I am trying to figure out logically, how to fit together teaching Decimals, fractions, the most logical and best way. If we are going to de-emphasize fractions as lazy-boy-girl division, then there really is no need to have fractions in a definition of decimals. And, decimals should not be dependent on fractions, for fractions are division. 

Teacher-- many exercises like this -- write out what 2.4 = ( 2x(1)) . +(4x(.1)) 

what 1.7 = 

what 9.8 = 

what 5.3 = 

etc, a lot of practice exercises 

Then at 9 of age we come back and do a little more this time 

47.39 = (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) 

write out what 21.48 = 

what 33.25 = 

what 19.17 = 

etc 

Finally by age 10 we come back for more on the definition of decimal 

Definition of Decimal:: a number such as 347.392 = (3 × 100) + (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) + (2 x (.001)) 

Make sure you point out the parenthesis marks as that you want to operate inside those parenthesis-- take some time to teach parenthesis and order of doing math operations. 

So, teacher, give the students many numbers and let them write that number according to the definition. Check up closely on their parenthesis marks. 

By the time they are 10 year olds they should easily do these and much more. 

135.687 written out is (1x(100)) + (3x(10)) + (5x(1))  . + (6x(.1)) + (8x(.01)) + (7x(.001)) 

980.002 written out is (9x(100)) + (8x(10)) + (0x(1)) . + (0x(.1)) + (0x(.01)) + (2x(1/.001)) 

So, do many exercises of writing out decimals, and point out the Place Values. The "ones" place value, the tens place value, the hundreds place value. Point out the decimal point then the .1 place value, etc etc. Review fractions so that they know 1/10, 1/100, 1/1000. 


Exercises:: 

1.01 

231.94 

444.555 

980.002 written out is 9x(100) + 8x(10) + 0x(1) . + 0x(.1) + 0x(.01) + 2x(1/.001) 

Have them do 6980.003, then 7773.112 then 5453.011 then 8889.999 

So, do many exercises of writing out decimals, and point out the Place Values. The "ones" place value, the tens place value, the hundreds place value. Point out the decimal point then the .1, the .01 and the .001 place value, etc etc. 

If all of this is easy for them, then push them to the 10,000 and .0001 place value such as 18923.0809 

Never frustrate students, but slowly get them to be masters at Decimals. 

AP 





On Thursday, March 29, 2018 at 9:38:29 PM UTC-5, Archimedes Plutonium wrote:

#2-2 teaching decimals; operations, add, subtract, multiply for ages 8-13

With add and subtract, it is pretty much the same as if we dealt with numbers without a decimal point, just make sure you ___line up the decimal point___ before adding or subtracting. 



  34.23 
+23.11 
----------- 


  9.08 
+1.32 
---------- 


2.9 +3.7 

5.1 + 4.9 + .2 


16.45 
45.39 
78.02 
----- 

77.65 + 33.92 + 5.01 

80.02 + 79.03 + 60.99 



534.232 
+234.119 
----------- 


109.008 
+111.32 
---------- 

333.333 + 666.667 

100.003 + 2.7 + 1.002 

Teacher, make many many exercises on addition as well as subtraction. The decimal point needs to be lined up. 




     4.56 
-    1.13 
---------- 

  9.11 
-9.08 
------- 

8.2 - 7.1 

9.3 - 4.2 

10 - 9.1 

28.99 - 17.55 

23.19 - 19.27 




324.567 
-177.122 
---------- 

444.11 
-9.08 
------- 



888.999 - 777.666 

701.972 - 402.863 

187233.32 
-67894.56 
---------- 

Again, teacher make many exercise lists of subtraction. 


  7.1 
x7.3 
------ 

   6.2 
x  5.4 
-------- 



1.5 x 1.5 

.9 x .3 

8.2 x 1.9 

.23 x .45 

5.102 x 3.002 

11.11 x 9.55 

87 x .01 

1.2 x 2.8 


12.89 
x7.38 
------ 

772.953 
x265.5 
-------- 


892.755 x 125.328 



Now teach the students a key idea of multiplication, one item that gave me trouble when I was a 8-14 year old. The idea in multiplication that if you multiply two small numbers, and, what I mean by small numbers are, numbers less than 1, that the product is smaller than either of the two numbers you started with. But, any multiplication of two large numbers, numbers bigger than 1, the product is always larger than either one of its multipliers. 

For example, two large numbers 1.1 x 1.9, that the product 2.09 is bigger than either 1.1 or 1.9 

Example, .1 x .93 that the product .093 is smaller than either .1 and .93. 

It takes time for young minds to understand when you multiply little things, numbers between 0 and 1, you get smaller but when you multiply big things (numbers bigger than 1) you get larger. 

History Note:: So in covering Decimals, the key thing that students are going to slowly learn over the next seven years of teaching decimals every year, is that Numbers are things that you can count. You cannot count fractions, because fractions are not orderly, they pop up everywhere, but you can count decimals. That is a key idea in math and science-- numbers that exist, like Decimals cover all numbers that exist because you can count them. If it is a number, it is a decimal because you can count decimals. And, in the history of mathematics, math was poorly sputtering along until about 1202 when an Italian mathematician named Fibonacci wrote a book called Liber Abaci (book of calculations) using Decimals, it was only after 1202 that mathematics exploded in growth because finally the True Numbers of mathematics were discovered. This is now 2018, so approximately 800 years since the first numbers were widely used. 

Decimals are to math what the microscope is to the biologist. 

Decimals are to math, what the telescope is to the astronomer. 

Decimals are to math, what electricity and magnetism is to the physicist. 

Decimals are to math, what the table of atomic elements is to chemistry. 

AP 

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#414016 — Re: Archimedes Plutonium flunked the Math Test of a lifetime-generation test

Archimedes Plutonium <plutonium.archimedes@gmail.com> writes:

>On Sunday, May 27, 2018 at 3:24:16 PM UTC-5, Michael Moroney wrote:
>>What about your own manners?

And once again, what about your own manners? You complain that Jan had
poor manners, yet again you show poor manners as you attack me for
pointing out your poor manners. And what's this with stalker posts
refering to MIT staff? I already told you I have nothing to do with MIT.
How illogical is it to post stalker posts of staff I have nothing to do
with? How illogical is that? What happened to your so-called "Logical
Mind"? Logical people would not do that!

[toc] | [prev] | [next] | [standalone]

#414012 — Re: _Burse calls 25 years crazy-- Manfred Einsiedler, Paul Embrechts, Giovanni Felder of ETH, no picture diagram of Calculus proof// still believing proton is 938MeV electron .5MeV when they are 840MeV, 105MeV

Archimedes Plutonium <plutonium.archimedes@gmail.com> writes:

>One would have thought Switzerland had plenty of time to teach its young 
>some manners and morals, and not be a screaming crazy like Burse to the 
>world.

What about your own manners?

Jan comments on the absurdity of Apple high level managers mucking with
your phone (why would they care about you?) and why you are unable to cut
out an ellipse, and you attack him? And what's this with the stalker lists
again? Does Jan have anything to do whatsoever with ETH Zurich other than
being in the same country? That's completely illogical! I thought you had
a logical mind?

[toc] | [prev] | [next] | [standalone]

#414005

Maybe there is something wrong with your kitchen.
First all conic sections were oval, but not ellipses.

Now, the air gets disconnected from your phone.
Possibly a wormhole or something, no wonder you

got crazy. 25 years spamming, and not a single
line of math... 

Am Donnerstag, 24. Mai 2018 18:48:38 UTC+2 schrieb Archimedes Plutonium:
> Newsgroups: sci.math
> Date: Sat, 24 Mar 2018 11:16:31 -0700 (PDT)
> 
> Subject: *TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Sat, 24 Mar 2018 18:16:31 +0000
> 
> TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium
> 
> Chapter 1 TEACHING TRUE MATHEMATICS, 2018, by Archimedes Plutonium 
> 
> Preface: 
> 
> Alright I devote the entire years 2018-19 to doing this textbook on math. A textbook like none other for it takes the student from age 8 through to age 26 for all their math studies, throughout the subject of mathematics. The one book for all of mathematics. Of course we supplement with some outside sources like the common core curriculum, although I have found most math books are full of error. 
> 
> This book is historic in the sense that it cleans out all the errors of Old Math, and believe you me, the errors in Old Math were vast. So vast, that the best thing is to rewrite all the math textbooks, throw out the old-- so to speak. 
> 
> And historic in the sense the book is used from ages 8 to 26 as a single math text, where teachers supplement blank pages to tailor fit their class. I write this textbook with the Common Core Curriculum in the USA, in mind. So I know what Grade level students are taught specific topics. But here the teachers have to help this book along as to what is most appropriate for their classrooms, and have to tailor-make many lessons. 
> 
> I write this textbook in a style never seen before in science textbooks, for I am talking most often to the student, but also, talking very much to the teacher. So both the student and teacher are addressed in this textbook. 
> 
> This book is unique, in that you need only this text of math for all school needs. None of this buying a new book for each course. And it requires work by the teacher to fill in blanks. I cover only the very basic. But the beauty of that, is many students bored with the lessons under study at the moment, will keep on looking further ahead in the pages, at more advanced math-- for it is available and open to their eyes to wander on into what their future math lessons are going to be-- what we now call surfing the book in our age of computers. 
> 
> I am a pragmatist teacher myself, and know that if math is available, only more advanced, that the students will often exceed expectations and learn what was meant for them years into the future. I see it the case that some very bright High School students will have mastered the College level math from this textbook before they even get to college, just because it is in plain sight starting at age 8. 
> 
> Now in writing this text I need commentary along with lessons. So the structure of the book is lessons and then commentary. Arranged in chapters, and arranged for age level of students. The 8 year old starts at the beginning. Then 9 through 13 year olds has a chapter. Then 14 year olds have their own chapter. Then the High School students starts have their chapters on geometry, algebra, trigonometry and precalculus. The college student starts near the middle and takes up over half the book. The need of the College student is all the math that can take them through physics. Any other math a college student can read on their own time. But all ages can wander through this textbook learning more and more about math. And I myself remember that the worst nightmare for me, often in College, was that I could not remember a past year's teaching to understand what was before me at present. So in this textbook, if a student has trouble in later pages, well, just flip backwards to a earlier section and pick up what is needed. 
> 
> And this textbook is unique in another way, it is written Logically, a logical minded author, am I. Logic means clarity and order. So few, so very very few books of science and math are written by authors who possess a logical mind. 
> 
> But, I was a teacher myself, and know the key number one element of being a teacher, a good teacher, is that a good teacher teaches students at a level of age, that the student can readily comprehend and understand the material. If a student cannot understand what is being taught, cannot understand the teacher, cannot understand the book, gets frustrated and is turned off by math. It is not the student's fault, but the teachers and book fault. The teacher or book is not at the level where the student can learn. The teacher and book is "over the heads of the students". And that is the worse kind of education situation. Over the heads of the student and makes the student fear math, and forever turned off by math. Math, never needs to be feared. 
> 
> But another sign of a excellent teacher, is he/she comes to class every day, prepared, not ad-lib an hour, but prepared the night before. 
> 
> So, teacher, to young students, tell them this book is used by them throughout their life, but for the classroom at a certain age, only this part of the book are they going to learn. Tell them the rest of the book they will learn in later classes in later years, not your class. Your class only is responsible for this part of the textbook. And of course, well, the brightest students will be bored with what they are responsible for, and will peek ahead into future lessons. And, let them do that. 
> 
> But, in all my lessons of this textbook, I strive for CLARITY, strive for Understanding, and strive for Logic and Order. A text on math written by a logical author. 
> 
> Bon voyage 
> 
> 
> #1-1 Decimals  Counting, and "What are Numbers" TEACHING TRUE MATHEMATICS, 2018 
> 
> Now we start mathematics with the students memorizing multiplication tables. Sad to say, that is how math should start for 8 year olds. Memorization. They learned some math in prior years, but now starts their formal education of math. And it starts with memorizing a table: 
> 
> 2x2 =4 
> 2x3 =6 
> 2x4 =8 
> 2x5 =10 
> 2x6 =12 
> 2x7 =14 
> 2x8 = 16 
> 2x9 =18 
> 
> 3x3 = 9 
> 3x4 = 12 
> 3x5 = 15 
> 3x6 = 18 
> 3x7 = 21 
> 3x8 = 24 
> 3x9 = 27 
> 
> 4x4 = 16 
> 4x5 = 20 
> 4x6 = 24 
> 4x7 =28 
> 4x8 = 32 
> 4x9 = 36 
> 
> 5x5 = 25 
> 5x6 = 30 
> 5x7 = 35 
> 5x8 = 40 
> 5x9 = 45 
> 
> 6x6 = 36 
> 6x7 = 42 
> 6x8 = 48 
> 6x9 = 54 
> 
> 7x7 = 49 
> 7x8 = 56 
> 7x9 = 63 
> 
> 8x8 = 64 
> 8x9 = 72 
> 
> 9x9 = 81 
> 
> Now, some students would benefit by seeing rectangles on graph paper such as 7x8, of 7 rows of 8, or 8 rows of 7 and count the smaller blocks as 56. Show pictures as often as you can.
> 
> Teach them the word "commutative" in this Multiplication Table, by saying commutative is switching around is the same as not switching around and do the table all over again. Switching around does not change the answer for 2x3 is the same as 3x2. That 9x6 is the same as 6x9.
> 
> 3x2 =6 
> 4x2 =8 
> 5x2 =10 
> 6x2 =12 
> 7x2 =14 
> 8x2 = 16 
> 9x2 =18 
> 
> 4x3 = 12 
> 5x3 = 15 
> 6x3 = 18 
> 7x3 = 21 
> 8x3 = 24 
> 9x3 = 27 
>   
> 5x4 = 20 
> 6x4 = 24 
> 7x4 =28 
> 8x4 = 32 
> 9x4 = 36 
> 
> 6x5 = 30 
> 7x5 = 35 
> 8x5 = 40 
> 9x5 = 45 
> 
> 7x6 = 42 
> 8x6 = 48 
> 9x6 = 54 
>   
> 8x7 = 56 
> 9x7 = 63 
> 
> 9x8 = 72 
> 
> Now, teacher, make sure all the 8 year olds have that table memorized, to where they say the answer from rote memory. A few of the above are tricky for youngsters-- such as the 54, 56. And teach the students that you have the same answer (commutative) going in either direction. I mean that 5x7 = 35 is the same as 7x5 = 35. 
> 
> Now I do not recall how I learned this table, and teachers probably know better than I on how to teach this table rote memory. Whether daily out loud questions where all the students answer, so the teacher says 7x3 is what? Then 8x6 is what? so on and so forth. 
> 
> Students have to memorize the multiplication table because when you do division, you have to have memorized multiplication to do division.
> 
> Now, teacher, stay with that table of memorizing multiplication, until you feel that the students have it rote memorized. It is important to have it memorized because division depends on the students memorizing multiplication. If they do not memorize it, and go to division, they are frustrated. 
> 
> Sad to say, the most important use of mathematics by every person alive is to be able to know how much money, count money and know numbers to count money correctly. But, then again, that is why everyone needs to learn math-- to be able to handle money. Very difficult to live in modern society and not be able to handle money because you have no math. 
> 
> We start this book for 8 year old students and to Count and then from Counting learn "What is a number". 
> 
> Have the students write out all the numbers from 0 to 100. They are Counting 
> 
> Something like this:: 
> 
> 90, 91, 92, 93, 94, 95 96, 97, 98, 99, 100 
> 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 
> 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 
> 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 
> 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 
> 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 
> 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 
> 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
> 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 
> 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 
> 
> Now, teacher, warn the students that writing 1 as 01 or 2 as 02, etc, does not affect the number. Teach them a 0 in front of a number does not affect the value, but a 0 after does affect the value. Such as 1 is 01 but 10 is ten, and 02 is 2 but 20 is twenty. So, teacher, spend a good deal of time teaching when 0 affects the value of a number. Tell the students that the reason they are writing a 0 in front of 1 or in front of 0 itself is so there are two digits, yes two digits for all these numbers, except for 100. 
> 
> Now, ask the students to Count those numbers as if they were whole dollars (in other countries, they may not or may have a currency- a money in decimal, if they do not, well, just use USA dollar with cents). 
> 
> So, zero dollars, 1 dollar is 01, 2 dollars is 02, etc, etc. Have the entire class count up to 100 dollars. 
> 
> 90, 91, 92, 93, 94, 95 96, 97, 98, 99, 100 
> 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 
> 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 
> 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 
> 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 
> 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 
> 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 
> 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 
> 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 
> 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 
> 
> 
> Now I am a firm believer in repetition by students, for they memorize and it boosts their confidence-- that they can do this, do math. They understand it and do it easily. 
> 
> Now, we take our chart and place a decimal point "." between digits. We just took our above table of numbers 00 to 100 and added a decimal point. Teacher, it is not far away where we teach Decimals, but let the students do mostly counting for now, and the decimal explanation will come soon enough. 
> 
> 9.0, 9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0 
> 8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 
> 7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 
> 6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 
> 5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 
> 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 
> 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 
> 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 
> 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 
> 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 
> 
> Now, have the students count these numbers. 
> Zero point zero, zero point 1, zero point 2, zero point 3, zero point 4, etc etc. Count all the way to nine point nine, ten point zero. 
> 
> Now, teacher, have them count that same table as if they were dollars and cents. Zero cents, ten cents is .1, twenty cents is .2, thirty cents is point .3, forty cents is .4, on up to 9 dollars and ninety cents is 9.9, ten dollars is 10.0. 
> 
>   
> 
> Very crude dot picture of 5f6, 94TH 
> ELECTRON=muon DOT CLOUD of 231Pu 
> 
> 
>                 ::\ ::|:: /:: 
>                  ::\::|::/:: 
>                      _ _ 
>                     (:Y:) 
>                      - - 
>                  ::/::|::\:: 
>                 ::/ ::|:: \:: 
> One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
>             . \ .  . | .   /. 
>            . . \. . .|. . /. . 
>               ..\....|.../... 
>                ::\:::|::/:: 
> ---------------      ------------- 
> --------------- (Y) ------------- 
> ---------------      -------------- 
>                ::/:::|::\:: 
>               ../....|...\... 
>            . . /. . .|. . \. . 
>             . / .  . | .   \ . 
> 
>   
> http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 
> 
> I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      
> 
> Read my recent posts in peace and quiet.
> 
> https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
> Archimedes Plutonium 
> 
> 
> 
> On Saturday, March 24, 2018 at 9:35:18 PM UTC-5, Archimedes Plutonium wrote:
> #1-2 Decimals TEACHING TRUE MATHEMATICS, 2018 
> 
> Picking up where we left off the last time. Only this time we move the decimal point over one more time. 
> 
> .90, .91, .92, .93, .94, .95, .96, .97, .98, .99, 1.0 
> .80, .81, .82, .83, .84, .85, .86, .87, .88, .89, 
> .70, .71, .72, .73, .74, .75, .76, .77, .78, .79, 
> .60, .61, .62, .63, .64, .65, .66, .67, .68, .69, 
> .50, .51, .52, .53, .54, .55, .56, .57, .58, .59, 
> .40, .41, .42, .43, .44, .45, .46, .47, .48, .49, 
> .30, .31, .32, .33, .34, .35, .36, .37, .38, .39, 
> .20, .21, .22, .23, .24, .25, .26, .27, .28, .29, 
> .10, .11, .12, .13, .14, .15, .16, .17, .18, .19, 
> .00, .01, .02, .03, .04, .05, .06, .07, .08, .09, 
>   
> 
> Now teacher, prepare for class the night before, for students deserve to have a teacher that prepares, and does not walk into the class just ad-libing, just winging it. Come prepared for each lesson. The difference between a excellent teacher and those beneath, is preparedness. Although Grade schoolers may not recognize a prepared teacher from not prepared, by High School, the students do recognize. 
> 
> That is why I like to blend in one lesson with the next, so that the blend shows the preparedness. 
> 
> Now, have the students make the above table where we moved that decimal point over once more. Now count these numbers. 
> 
> Point zero zero is 0 cents. Point zero 1 is 1 cent, point zero 2 is 2 cents, point zero 3 is 3 cents. Count all the way to point nine nine is 99 cents, one point zero is 1 dollar. 
> 
> Bring some coins to class, for students always deserve visuals to go along with learning. Bring a penny, nickel, dime quarter, half dollar, even a dollar (Susan B coins).
> 
> Now, teacher, if the class is not fluent in these tables, repeat them until they are fluent and do other exercises, until they are very good at this. In fact do exercises focused on decimals. 
> 
> Now the next exercise once the students are fluent in the above tables-- homework, quizzes, tests, and make them easy quiz and test, build confidence. Is the teaching of Decimal Numbers themselves. From a look at the Common Core Curriculum, either the students of 8 years age has seen the decimals before, or they have not. So the teacher here has to determine if the students have been already taught the decimal numbers or not, and with that determination the teacher must supplement my teaching with a  good chapter of common core on decimals. I do not know how the Common Core teaches decimals. And my own personal memory can no longer pull that experience up and what age I was. I vaguely recall doing fractions, multiply, add, subtract even divide fractions. And here is where I argue with Common Core. That more time needs be spent on Decimals for decimals are the True Numbers in mathematics, whereas Fractions are a bit of exotica, for fractions are just Long Division without actually doing the division. So, what I propose is that Fractions be cut deeply from the curriculum and with that extra time, devote it to Decimals. Do not eliminate fractions altogether, just pare away about 1/2 the time spent on fractions and give it to decimals.
> 
> One memory does stick out in my youth, of around the age of 8 or 9. I would go across the street to the neighbors and play with their kids of my age. And one day, the father was home and wanted to see me especially. He wanted to see if I could Long Divide a number he wrote down on a pad of paper. Sorry to say, I could not do it, and being a kind father, he went ahead and showed me how to Long Divide. So, that scene stuck in my mind through my life. What the father was testing, was not whether I was smart enough, but seeing whether his own sons of my age should be able to do it. For if I could do it, he would be angry that his own sons could not. And, well, that scene perhaps in some manner, made me think, math was special, and I had to be better in math than I was.
> 
> Now this is just my gut instinct, but I think, Decimals as a concept are far more difficult to learn than is fractions, because of the definition of Decimals, with its place values. Place values for 8 year olds seems too difficult. So, what I propose is teaching Decimals every year, just gradually a bit more and more, so that by High School, they surely will have comprehended the Decimals, and its tough definition. For me, I vaguely just vaguely remember that the definition I would gloss over, sort of like surf the definition-- only the word "surf" was never around when I was in Grade School in 1958 an 8 year old. And the first time I used the word surf was from some songs out of California in the 1960s. But now we have surfing the web and internet. So, why not surf the definition of Decimal. By surfing Decimal definition at age 8 and for the next 6 years reinforce that understanding of the Decimal number. 
> 
> I must emphasize that Decimals are a key crucial part of mathematics, a essential part. So the teacher must have Decimals taught long and hard. 
> 
> So here is a juncture point for the teacher and me as author. I am not going to write long lessons on teaching decimals or long division. But at this moment of this textbook, what the teacher has to evaluate and accomplish, and the student has to learn well and hard. First Decimals and then Long Division. 
> 
> Google Internet search: 
>         1.        Number & Operations in Base Ten - Common Core State Standards ...www.corestandards.org/Math/Content/5/NBT/‎
Read, write, and compare decimals to thousandths. CCSS.Math.Content.5.NBT.A .3.a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 ...‎CCSS.Math.Content.5.NBT.B.7 - ‎CCSS.Math.Content.5.NBT.B.5 
> 
> 
> Now the above Google Search hit of common core on decimals is fine except it is written in fractions. Here we want to eliminate fractions as much as possible, because they are not numbers but division of numbers.
> 
> And I would be content if they, the 8,9,10 year olds, only learned to the thousandths place value in decimals. The above number 347.392 is good for 8,9,10 year olds. 
> 
> Now, here Teacher, you decide which is appropriate for your classroom. Whether they can learn this, shown below or if that is too hard for 8 year olds: 
> 
> Definition of Decimal:: a number such as 347.392 = (3 × 100) + (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) + (2 x (.001)) 
> 
> Obviously the students are going to need to know what .1 is, and remember our number graph that .1 was a dime or ten cents out of 1 dollar, as fraction .1 is 10/100 = 1/10, and then 1/100 is 1 cent out of a dollar as .01,  and .001 is 1/1000 as a fraction, but this is all probably too hard for 8 year olds. You, the teacher find out where you can teach to 8 year olds, whether they can understand 7.3, one decimal place. If 8 year olds can understand one decimal place to left and right of decimal point, then teach that and no more on place value. Save the harder for another year. Never frustrate students. 
> 
> I do not know if that is too much for 8 year olds? If they have seen this before, and if not, well, we never want to frustrate, so start the 8 year old on this. 
> 
> Definition of Decimal:: a number such as 7.3 =  (7 × 1) . + (3 × (.1)) 
> 
> With exercises like this -- write out what 2.4 = 
> 
> what 1.7 = 
> 
> what 9.8 = 
> 
> what 5.3 = 
> 
> etc, a lot of practice exercises 
> 
> Then at 9 years of age we come back and do a little more this time 
> 
> 47.39 = (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) 
> 
> write out what 21.48 = 
> 
> what 33.25 = 
> 
> what 19.17 = 
> 
> etc 
> 
> Finally by age 9, 10 we come back for more on the definition of decimal 
> 
> Definition of Decimal:: a number such as 347.392 = (3 × 100) + (4 × 10) + (7 × 1) . + (3 × (.1)) + (9 × (.01)) + (2 x (.001)) 
> 
> Make sure you point out the parenthesis marks as that you want to operate inside those parenthesis-- take some time to teach parenthesis and order of doing math operations. 
> 
> So, teacher, give the students many numbers and let them write that number according to the definition. 
> 
> By the time they are 12, 13 year olds they should easily do these two and much more. 
> 
> 135.687 written out is (1x(100)) + (3x(10)) + (5x(1)) . + (6x(.1)) + (8x(.01)) + (7x(.001)) 
> 
> 980.002 written out is (9x(100)) + (8x(10)) + (0x(1)) . + (0x(.1)) + (0x(.01)) + (2x(.001)) 
> 
> So, do many exercises of writing out decimals, and point out the Place Values. The "ones" place value, the tens place value, the hundreds place value. Point out the decimal point then the .1 place value, etc etc. Review fractions so that they know 1/10, 1/100, 1/1000 are division problems. 
> 
> And use the Common Core, a proven teaching guidelines. Find out what old books used as teaching the Decimals.
> 
> Now out of curiosity I had to see what age is Long Division taught, and apparently in 5th grade, ages 10-11. So here the teacher has to decide whether 8 year olds can handle Long Division. If not, well, wait for 10 years of age. So here I need guidance by teachers who teach 8, 9, 10, 11, 12, 13 year olds. When does Long division start and how is it best taught? So let the teacher decide on this. 
> 
> But in the meantime. I wonder if we can add, subtract, multiply decimals, keeping it very simple for 8 year olds. 
> 
> So here I ask the teacher to determine how much the students know of decimals and know how to add, subtract, multiply. If weak, then months go by with the teacher using Common Core materials to ground the students well in Decimals. Use other books for the teacher to do the lessons. That means the teacher has to well prepare these month long lessons. 
> 
> DECIMALS: 
> 
> So here, let us focus on Decimals. And according to Core Curriculum, the 8 to 14 year old students learned what Decimals are, and how to add, subtract, multiply and divide with them. 
> 
> It would be nice, very nice to repeat lessons on Decimals in all the age groups from 8 to 14, giving them refreshment exercises each year. Unless they learn decimals well, they cannot go into science or engineering or medicine. 
> 
> So, first, let me repeat the meaning of a decimal with an example using the number 321.987. 
> 
> Decimals are place values and that number represents (3x100) + (2x10) + (1 x 1) . + (9x .1) + (8 x .01) + (7x .001) 
> 
> Teacher, show the students the progression leftward of the decimal point starting with 1 then 10 then 100 according to the place value. Then show them the progression of place value going rightward. 
> 
> I think the Common Core even shows diagrams and pictures of place value. 
> 
> So let me get a list of practice exercises, and the teacher preparing each day for months on end with practice on decimals, and add, subtract, multiply with decimals. 
> 
> With add and subtract, it is pretty much the same as if we dealt with numbers without a decimal point, just make sure you ___line up the decimal point___ before adding or subtracting. 
> 
> 1.6 
> 4.5 
> 7.8 
> ----- 
> 
>  7.9 
> -6.7 
> ---- 
> 
> 5.3 x 4 
> 
> 1.2 x 2.8 
> 
> 87 x .1 
> 
> Here the idea is to introduce Decimals by age 8, make it extremely simple, and then build on that introduction in ages 9 to 14. Never do we want to frustrate students. 
> 
> 
> Very crude dot picture of 5f6, 94TH 
> ELECTRON=muon DOT CLOUD of 231Pu 
> 
> 
>                 ::\ ::|:: /:: 
>                  ::\::|::/:: 
>                      _ _ 
>                     (:Y:) 
>                      - - 
>                  ::/::|::\:: 
>                 ::/ ::|:: \:: 
> One of those dots is the Milky Way galaxy. And each dot represents another galaxy. 
>             . \ .  . | .   /. 
>            . . \. . .|. . /. . 
>               ..\....|.../... 
>                ::\:::|::/:: 
> ---------------      ------------- 
> --------------- (Y) ------------- 
> ---------------      -------------- 
>                ::/:::|::\:: 
>               ../....|...\... 
>            . . /. . .|. . \. . 
>             . / .  . | .   \ . 
> 
>   
> http://www.iw.net/~a_plutonium/ 
whole entire Universe is just one big atom 
where dots of the electron-dot-cloud are galaxies 
> 
> I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.      
> 
> Read my recent posts in peace and quiet.
> 
> https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe         
> Archimedes Plutonium

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