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#2-2 through 2-4 Division TEACHING TRUE MATHEMATICS, 2018

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  #2-2 through 2-4 Division  TEACHING TRUE MATHEMATICS, 2018 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-29 17:16 -0700
    #2-5 through 2-6 Division  TEACHING TRUE MATHEMATICS, 2018 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-30 12:04 -0700
      Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-10-31 03:49 +0000

#426387 — #2-2 through 2-4 Division TEACHING TRUE MATHEMATICS, 2018

#2-2 Division  TEACHING TRUE MATHEMATICS, 2018 

Now I cannot remember myself in school at ages 7-9 and when I learned division and long division and how it was taught to me. Whether wood cube blocks were used in classroom. Whether there was a continuity of thought, of logic that division is the reverse of multiplication, for we have 2 x 5 = 10 and we have 10/5 = 2. Did we use wood cube blocks? I cannot remember, but here, we are going to use them a lot, all because it is a good idea to always link math with physical objects.

So now, we already know that add is increasing with more blocks.

2 + 3 is

HH + HHH = HHHHH = 5

And we know that Rapid Add is multiply

2 x 3 is


HH
HH
HH

And that is equal to 6

But let us spend a moment in analyzing that picture of 6 wooden cube blocks where the 2 in 2x3 is the number in the Row

And the 3 in 2x3 is the number of cubes in the height of the row.

So in 2x3

we have 2 in a row

HH

and the 3 is the height, or how tall is the row and the height is 3

H
H
H

So now we can count the cubes if we never knew what multiplication ever was

HH
HH
HH

And by counting we get 6, so we know that 2x3 = 6

But, is there a faster way than counting cubes? Yes, and it is called multiplication.

The row is the length, and is the first number in multiplication. The height is just the height or some like to call it width, for multiplication is rectangle area length x width or length x height.

Here is another rectangle

3 x 5

What is the row number? It is 3

HHH

What is the height number? It is 5

HHH
HHH
HHH
HHH
HHH

What is that rectangle area? It is 3 x 5 = 15 and we can count the blocks counting 1 to 15.

Now we learned subtraction was remove. So what is 15 subtract 5, 15 - 5 = ?

Well let us take our rectangle of 15


HHH
HHH
HHH
HHH
HHH

And subtract or remove 5. We like to remove the 5 as cleanly as possible so we leave behind a new rectangle if possible.


HHH
HHH
HHH
HHH
HHH  subtract 

H
H
H
H
H

And that would leave us with 


HH
HH
HH
HH
HH

Or 10 remaining when we do 15 - 5

But we learned that Division is Rapid Subtract.

We learned multiplication is Rapid Add, so we can expect division to be rapid subtract.

So let us do division on 15 and see how that is rapid subtract or rapid remove.

Multiplication was 3 x 5 = 15 and with wooden cubes that forms


HHH
HHH
HHH
HHH
HHH

But if we write it as 5 x 3 = 15, here our row is 5 or length is 5 and our height is 3 and looks like this

HHHHH
HHHHH
HHHHH

And both add up to 15

So now what is divide 15 with 15/3 is equal to 5 for here you Removed, subtracted the rows, and leave behind one height, there are 5 in a height

H
H
H
H
H

What is 15/5 is equal to 3 for here you removed, subtracted height and leave behind 1 row which has 3

HHH

So division is the reverse of multiplication, and division is rapid remove, rapid subtraction.

Now in class show wooden cubes of the rectangles made by these multiplications.

2x3
2x4
2x5
2x6
2x7
2x8
2x9
2x10
3x3
3x4
3x5
3x6
3x7
3x8
3x9
3x10
4x4
4x5
4x6
4x7
4x8
4x9
4x10
5x5
5x6
5x7
5x8
5x9
5x10
6x6
6x7
6x8
6x9
6x10
7x7
7x8
7x9
7x10
8x8
8x9
8x10
9x9
9x10
10x10


Ask the class to see if there are bright students, why we did not include 1 in multiplication?

And, ask the class, why we did not do the reverse of each multiplication such as 2x3, why not 3x2 (see if they remember commutative).

AP



#2-3 teaching decimals; operations, Long Division for ages 8&9

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. 

  
AP


On Saturday, March 24, 2018 at 9:35:18 PM UTC-5, Archimedes Plutonium wrote:
#2-4 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 improvising, 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.


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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#426447 — #2-5 through 2-6 Division TEACHING TRUE MATHEMATICS, 2018

On Friday, March 30, 2018 at 5:46:21 PM UTC-5, Archimedes Plutonium wrote:
#2-5 teaching decimals; operations, Long Division for ages 8 & 9


Review of Decimals, for teacher and student:: 

Alright, we are in Grade School teaching 8 year and 9 year olds. 

When you say math, the first thing to come to mind is numbers, and that means decimals. 

So, start them at age 8 and continue into age 9 with decimals. If anything in math that has to be learned as mathematics is numbers. What are the numbers, and the answer is decimals. And this book will further review decimals for years after 8 and 9 year olds. 

Now I do not mind the students doing the math of decimal operations and having a calculator handy. Only when doing quizzes and tests, they cannot have a calculator. And remind the students that they cannot cheat because they have to show work, not just a answer. And on tests, they must show their work, such as in multiplication or long division, so tell them, calculators will not help on tests or quizzes. 

Now I gave some problems in last lesson. I do not know whether those are too hard or just right for your class of 9 year olds. So the teacher may want to adjust. I reckon it will take 4 months focused on Decimals, so the teacher has his/her work cut out. Use the best Common Core on teaching decimals. 

I did say, let us cut back severely on Fractions. Fractions are not numbers but a division exercise. If you must and want to teach fractions, then show how fractions are converted to decimals, because, really, fractions are just -uncompleted divisions. Fractions are just decimals that have not been divided out. 

We do not call 
       _____ 
6    | 1.00   

a number. 

And that division is the fraction 1/6. 

For 1/6, is not a number, but rather it is a division that will lead to a number. 

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, to be polluted in mind. 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 to 13 year olds need not know that with any sort of expertise, 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, and that fractions are 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 any order all the fractions, nor can you count all the 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. 

To help make this clear, suppose cars that run are numbers, well we have all kinds of cars running on roads. But now, suppose someone drops off a large box containing car parts, disassembled. Now, maybe a good mechanic can put the parts all together to make a running car. But in the box it is not a car for it cannot run. Same thing in mathematics. Fractions are not numbers but a invitation to divide numbers. And although a number after the division is produced, it is not a number until the division ends. So fractions are not numbers, but decimals are numbers. And it is for this reason I start this book at age 8. I do not want the student's mind polluted with bad math, with wrong math at such an early age. 

So cut the teaching of fractions by half, and when you teach fractions, teach them as a long division exercise. And spend more time devoted to teaching 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. So, delete the symbol altogether out of math. For in the above, do we mean 5 divided by 3 or do we mean 3 divided by 5. 

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. And we are never confused that 3 is dividing into 5, just as 5/3 is that 3 is dividing into 5. 

Likewise 

5/3 is not a number but a plea to divide. 

Unfortunately, because we see just a line drawn between 5 and 3, that some thought 5/3 is a number, all itself, before anyone divided it. So the convenience, the sheer brevity, the sheer simple design of a slanted line / 

The / between two numbers, that illogical people thought 5/3 is a number itself. It is not; it is only a plea to do the operation of divide. What comes out of the division is a number. 

So, fractions are not numbers. Fractions are division. Decimals are numbers and we will learn, decimals are the only numbers in all of mathematics. That is why these first lessons are about Decimals, for if you want to go straight, true clear in math, you must learn Decimals. 

Now, let us start teaching division of decimals to 9 year olds, a little bit harder than for 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 a building on from last year, so that when they are 10, 11, 12, 13 year olds, they can repeat these lessons and master division. 
Alright start the 9 year olds out on fractions and long division, start with say 1/6. 


          .16 
       _____ 
6    | 1.00 
           ^
Remember how to long-divide, the tiny script of 6 and the carryover of the tiny script 4.

Review Long Division again, where we have economy of space saving by small script. We do not go down but go across when dividing. And parents probably are no help because they learned how to waste a whole sheet of paper on just a few long divisions.
              
Answer 1/6 = .16 

Teacher, note especially where the decimal point belongs. 

Fraction 10/5 becomes 

       2.000
    _______ 
5 | 10.000 
      ^
Teacher, if any student has trouble with the extra zeroes in the answer 2.000, remind them about zeroes to the right of the decimal point is 2. is the same as 2.0, same as 2.00, same as 2.000. Some students at this age are scared of zeroes and need refreshing.


Now do the fraction 1/2 

       .5 
    _______ 
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 with 1/2 being .5. For many people, this is a difficult concept for them to grasp, because they have in mind that 1/2 shows no digit of "5", yet here they are shown that .5 is 1/2. 

Now do 3/1, and then 1/3. 

Do 3/2, then do 2/3. 

Let us do 5/3 again. 


     1.666
    _______ 
3 | 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 especially in fractions and decimals since they may confuse with the decimal point. Keep commas with whole large numbers, because commas are confusing with decimals, so that above 1.666 is not 1,666 and so teach the students that commas are really only for whole numbers that are large whole numbers.

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. 

But I say, teach them commas for large whole numbers, for it is a comfortable read. 

AP 


#2-6 teaching decimals; operations, Long Division for ages 8 & 9//TEACHING TRUE MATHEMATICS


So, Long Division, for many years in ages of 8 to 13, we drill drill drill until the students master the division of decimals. They can use calculators to see if their work is correct, only not on tests or quizzes. For they have to show their work. Here the teacher must hand walk the students through the key mechanics of Long Division 

1) use of the multiplication table to know what number divides 

2) proper placement of decimal point

3) subtraction

4) remainder that is carryover to next digits 


Now probably for centuries, the tried and true method of teaching Long Division in classroom across the US and around the world works well. However, it consumes up too much Space of paper or writing surface. So in this book we teach Long Division that is economy of Space.

     ___ 
6  | 8 

  _____ 
3| 100 

Now, teacher, in those two above divisions, teach them carryover and small script. But first, tack on the decimal point for often it is not shown, and then tack on three zero digits.
       
     _____
6  | 8.000 

  ________
3| 100.000 

Now proceed to divide long division using carryover and small script so that you use up just a little of the Space on the paper.

      1.333
6  | 8.000 
      ^
Have the first 6 above the arrow and into part of the 8 but in small script, subtract and carryover the 2 in small script to be with the next 0 digit. Now 6 into 20 is 3, and repeat.


  __33.333_
3| 100.000 

See if the students can do this one without any help.


I want the students by the time they are 13 year olds to be able to do these decimals without any trouble. 

     _________ 
6.3| 829.200 

       _________
137| 1.000000 

Teacher, plan out your own quizzes and tests to see if the student has mastered Decimals by 13 years of age. 

So spend less time on Fractions and more time on Decimals. 

Teacher's Story Note:: Now one story about Decimals that is telling. Is that many people who never had Decimals in school, come to believe that 1/2 is not that of 0.5, that 

  ______ 
2| 1.00 

is not .5. Why? Is it because they were not formally taught in classroom? Perhaps they cannot understand how 1/2 has a 2 involved and they see no "2" in .5. So the same kind of a "mental block" is here, as is in the situation of .9999... equaling something. If we teach students the correct and true numbers of mathematics as Decimals, we avoid that crazy silly thought that .999...=1 for it is not equal to 1. I remember myself in High School, that the issue of what is .9999... never came up. It came up for, the first time was a freshman in college, studying Calculus. But more on that in High School when I cover the issue of .9999...., for this issue if far over the heads of Grade School, and I bring it up, only, because, to show how important it is to teach decimals young and early, rather than fractions because that issue of .9999.... has its roots in the problem of 1/3, what is it? Is 1/3, that of .3333.....  So, so, save these problems for later years. 

Summary of Decimals: 
So I had to catch the students of age 8, so as to avoid teaching these students falsehoods and later having to tell them-- what you learned is phony and here is the real truth. 

So, by this lesson at the age of 13 years old students, I want the teacher to see if all his/her students can do Decimals with a fairly good of accuracy, maybe a few mistakes but not many; at least add, subtract, multiply and long division. 

The Long Division is the most difficult one, so here, get what the Common Core has found to work well in teaching add, subtract, multiply, divide of decimals. Make sure the 13 year old is totally comfortable with Long Division. 

Now, the students are going to see decimals come up and come up again and again, not just in daily life of money counting, but also in science, if the students want to go on in science or engineering. You have to master decimals. 

AP 

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#426480 — Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test

Math Failure Archimedes Plutonium <plutonium.archimedes@gmail.com> fails:

>Michael Moroney writes:
>Sep 30 (17 hours ago)
>Re: Archimedes "Failure" Plutonium,

>>Subject: Re: Racist-Physicists, Weinberg,Witten,Glashow,Gell-Mann,Higgs
>>who refuse to admit proton=840MeV, electron=105MeV, Dirac monopole
>>.5MeV, proofs by AP, because they never respect the source

>** because they never respect the source **

>Respect must be earned, Archie. You will NEVER earn any respect,

You need to read that over and over aqgain until you understand it.
You will NEVER get any respect by attacking anyone and everyone who
points out a flaw in one of your claims. NEVER EVER. Keep it up,
Failure Plutonium, and you will remain a failure, until one day
you go to that Nuclear Waste Dump in the Sky, and you'll be quickly
forgotten.  You post stalker lists of professors, apparently in a vain
attempt at getting their attention. But what if one of them actually does
see your posts? What would he think? He sees you attacking others
for correcting you, he sees you accuse everyone of being homosexual, and
you misusing/abusing the word 'failure'. He sees you post stalker lists
of other professors. What would he do? He'll sneer "What a complete
nutcase!" and lrave, and never give you or your ideas another thought.

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