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2#1-2 Decimals TEACHING TRUE MATHEMATICS, 2018

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  2#1-2 Decimals TEACHING TRUE MATHEMATICS, 2018 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-06-26 21:19 -0700
    Re: Archimedes "just not bolted down too tight in the first place" Plutonium flunked the physics lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-06-27 04:55 +0000

#416505 — 2#1-2 Decimals TEACHING TRUE MATHEMATICS, 2018

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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#416513 — Re: Archimedes "just not bolted down too tight in the first place" Plutonium flunked the physics lifetime-generation test

Did those Russian saboteurs really think that any school in the US would 
*ever* let such crap "True Math" within a mile of their school??

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