教學指標(1)

易算盤教數學   教學指標

(1)自然法則即原本
算盤歸零如同水往低處流的原本,
重力使上翻往下,下翻往上皆歸零,
0 1 2 3 4 5 6 7 8 9 連續數是加法,
9 8 7 6 5 4 3 2 1 0 倒數就是減法,
加減相反,即 + - 互逆,
加往上則減往下,加往下則減往上,
充分且必要,展現原本即自然。
如圖:九珠十進算盤的二種歸零法,
面對面的對打教學盤。

Computing math
Mathematics Teaching Index
(1) the natural law that the original
Abacus as water to the low flow of the original,
Gravity to turn down,
the next turn up to zero,
0 1 2 3 4 5 6 7 8 9
Continuous number is added,
9 8 7 6 5 4 3 2 1 0
The countdown is subtraction,
Addition and subtraction is the opposite, that is,
+ - Plus the next is reduced down,
plus the next is reduced to the last,
Full and necessary,
to show the original natural.
Figure: nine beads decathlon two zero method,
Face-to-face teaching.

教學指標(2)

(2)象形示數

寓教於樂親子對打,
數學就是這麼簡單,
生命哲理原本啟發,
悟理解盤算易算盤。
 ■ 1 ,   ■■ 2 ,   ■■■   3  ,  4  ,  5  ,...
☆1 , ☆☆2 , ☆☆☆3  ,  4  ,  5  ,...
算盤構造
取長方形或正方形的幾何對稱性,
圓柱串珠可上可下歸零就是開始,
橫樑分段完成整數特性原理延伸,
任何進位制原理與四則運算相通,
含概所有整數分數小數自然展現,
位數位名位值手腦互動一目了然,
啟蒙教學小中高大案前必備工具。

(2) pictographs

Entertaining play with others,
Mathematics is so simple,
The philosophy of life was originally inspired,
Understand the calculation of easy to calculate disk.
 ■  1,   ■ ■  2,     ■■■    3, 4, 5, ...
☆ 1, ☆ ☆ 2, ☆ ☆ ☆ 3, 4, 5, ...
Abacus construction
Take the geometric symmetry of the rectangle or square,
Cylindrical bead can be on the next zero is the beginning,
The crossbar segment completes the integer characteristic principle extension,
Any carry system principle and four operations connected,
Contains all the integer fraction fractional natural show,
Bit position bit value mind brain interaction at a glance,
Enlightenment teaching small and medium high before the necessary tools.

教學指標(3)

(3)四則運算

手撥眼及腦運算,專注盤算演邏輯,
一個一數曉自然,連加速得推乘法,
續減分完配成商,四則特性知原本,
算式呈現定律通,易位對打樂相長。
   + 1連續數 , -1倒數； +  - 互逆
   1+1+1      = 3 = 1  ×3   , 一有三個
   2+2+2+2 = 8 = 2  ×4   ,  二有四個
☆乘法是加法的速算法
   4  ÷2 = 2  四顆糖平分,每人得二顆
   4 -2 -2 =0 四顆平分減二減二分完
☆除法是減法的速算法
   ∵4+3=7=3+4  ∴4×3=12=3×4
☆∵ 加減互逆 , ∴ 乘除互逆
☆加法適合交換律,乘法也是
   ∵7 -5=2  ≠  5 -7   ∴7÷5  ≠  5÷7
☆減法不適合交換律,除法也相同
☆盤算算盤演證數理邏輯通原本。

(3) four operations

Hand-dial and brain computing, focusing on computing logic,
A number of small nature, and even speed to push the law,
Continued to sub-sub-set into the business, the four characteristics of the original,
The formula is presented with the law.
   + 1 consecutive number, -1 reciprocal; + - reciprocal
   1 + 1 + 1 = 3 = 1 × 3   ,  a three
   2 + 2 + 2 + 2 = 8 = 2 × 4   ,  two have four
☆ multiplication is the addition of the speed algorithm
   4 ÷ 2 = 2 four sugar equal, each person had two
   4 -2 -2 = 0 four cents minus two minus two points finished
☆ division is the speed of the subtraction algorithm
   ∵ 4 + 3 = 7 = 3 + 4 ∴ 4 × 3 = 12 = 3 × 4
☆ ∵ addition and subtraction of each other, ∴ multiplied by the inverse
☆ Addition is suitable for exchange law, multiplication is also
   ∵7 -5 = 2 ≠ 5 -7 ∴ 7 ÷ 5 ≠ 5 ÷ 7
☆ subtraction is not suitable for exchange law, division is also the same
☆ calculate the operator count the logic of the original logic of the original.

(4)地球算盤通行無阻

⑷算盤無國界
易算盤數位分明計算簡單通行地球,
 1500年前印度人發明阿拉伯數字,
 0123456789,"十"進制 統一了地球,
每個位數都有 0~9 共 "十" 個數碼,,,
 10=1+9,     +9=+10-1,     +1=+10-9
 10=2+8,     +8=+10-2,     +2=+10-8
 10=3+7,     +7=+10-3,     +3=+10-7
 10=4+6,     +6=+10-4,     +4=+10-6
 10=5+5,     +5=+10-5,
 -5=-10+5,     -6=-10+4,     -7=-10+3
 -8=-10+2,     -9=-10+1,     -1=-10+9
 -2=-10+8,     -3=-10+7,     -4=-10+6
口訣:各檔滿十, 進位加1及借位減1,
 23+88=23+80  +10-2 =111
聚化速算  20+90 +3-2 =111
 74-36=74 -30 -10+4=38
聚化速算   74  -40+4=38
 51-19=51 -10 -10+1=32
聚化速算    51 -20+1=32
  201- 112 = 101 - 12
速算          = 101 - 20 +8 = 89
每個位數方法相同,依此類推,,,
因為十進數各個位名都有十個數碼,
按九珠十進盤面 : 口訣就是"補十",
( 1,9 ),( 2,8 ),( 3,7 ),( 4,6 ),( 5,5 )。

⑷ abacus without borders
Easyabacus the number of clear calculation of the passage of the Earth,
 1500 years ago the Indian invented the Arabic numerals,
 0123456789, "ten" into the system unified the earth,
Each bit has 0 to 9 a total of "ten" digital ,,,
 10 = 1 + 9, + 9 = + 10-1, + 1 = + 10-9
 10 = 2 + 8, +8 = +10-2, +2 = +10-8
 10 = 3 + 7, + 7 = + 10-3, +3 = +10-7
 10 = 4 + 6, +6 = +10-4, +4 = +10-6
 10 = 5 + 5, +5 = +10-5,
 -5 = -10 + 5, -6 = -10 + 4, -7 = -10 + 3
 -8 = -10 + 2, -9 = -10 + 1, -1 = -10 + 9
 -2 = -10 +8, -3 = -10 +7, -4 = -10 + 6
formulas: the file full of ten, carry plus 1 and borrow by 1,
 23 + 88 = 23 + 80 + 10-2 = 111
Aggregation speed calculation
20 +90 +3-2 = 111
 74-36 = 74 -30 -10 + 4 = 38
Aggregation speed count
 74 -40 + 4 = 38
 51-19 = 51 -10 -10 + 1 = 32
Aggregation speed count
 51-20 + 1 = 32
 201 - 112 = 101 - 12
Express     = 101 - 20 +8 = 89
Each bit of the same method, and so on, and so on ,,,
Because the decimal number of each bit name has ten digital,
According to nine beads into the disk: formula is "make up ten"
(1, 9), (2, 8), (3,7), (4,6), (5,5).



           

(5)乘是加的速算

乘法  智慧的加法
Multiplication is the addition of wisdom
⑸乘法聚化速算
看算式手撥珠,盤面演證邏輯,
推論乘法九九,理解乘即累加,
連加倍乘相通,順暢快速運算。
   1=1×1=1               一個1 , 1有一個
   1+1=1×2=2          二個1 , 1有二個
   2+2+2=2×3=6     三個2 , 2有三個
   2+2+2+2=2×4=8              2有四個
 按圖示方法練習九九乘法,
 盤算推演二位數及 乘10 補 0 法,
 依此類推  乘百 補 二個 0 ,,,,,
    8 連加九次得    8×  9 =     72
    5 連加六次得    5×  6 =     30
    7 連加十次得    7×10 =     70
  16連加20次得  16×20 =  320
  29連加百次得   29×100= 2900
 利用"算式"加減化聚作乘法運算
     24×15 =   (20+4)×15
                  = 20×15 + 4 ×15
                  =    300   +   60  = 360
                  = 24×(10+5)
                  = 24×10  + 5×24
                  =   240    +  120 = 360
     38×29  = (40-2)×29
                   =  40×29 - 2×29
                   =    1160 -   58 = 1102
                   = 38×(30-1)
                   = 38×30 - 38×1
                   =   1140 - 38  =1102
⑸ multiplication polymerization speed calculation
See the dial hand dial,
disk show logic,
Inferred multiplication ninety-nine, to understand the cumulative,
Even doubled multiplication, smooth and fast operation.
   1 = 1 × 1 = 1 a 1, 1 has one
   1 + 1 = 1 × 2 = 2 two 1, 1 there are two
   2 + 2 + 2 = 2 × 3 = 6 three 2, 2 have three
   2 + 2 + 2 + 2 = 2 × 4 = 8 2 There are four
According to the illustrated method of practice ninety multiplication,
Calculate the deduction of two digits and multiplied by 10 to fill 0 method,
And so on by one hundred plus two 0 ,,,,,
    8 plus nine times 8 × 9 = 72
    5 plus six times 5 × 6 = 30
    7 plus 10 times 7 × 10 = 70
  16 plus 20 times 16 × 20 = 320
  29 plus 100 times were 29 × 100 = 2900
Using the "formula" plus and minus multiplication multiplication
     24 × 15 = (20 + 4) x 15
                  = 20 × 15 + 4 × 15
                  = 300 + 60 = 360
                  = 24 × (10 + 5)
                  = 24 × 10 + 5 × 24
                  = 240 + 120 = 360
     38 × 29 = (40-2) × 29
                   = 40 × 29 - 2 × 29
                   = 1160 - 58 = 1102
                   = 38 × (30-1)
                   = 38 × 30 - 38 × 1
                   = 1140 - 38 = 1102

教學指標(6)原本無礙

⑹ + - × ÷ 四則的原本
    ÷ 是 - 的速算法，與 ×  相反,互逆
    ÷ × 互為逆運算，因 + - 是逆運算
             +  ⇆  -
             ↯        ↯
             ×  ⇆  ÷
四則原本通用於數學領域
數論代數幾何延伸全靠它
三大領域推演無限超智慧
   16 + □ = 33   ,  □ = 33  - 16 = 17
   ○  -  28 = 45  ,  ○ = 45 + 28 = 73
   19 × ♢= 57  ,  ♢ = 57 ÷ 19 =  3
   ◇  ÷ 15 =   8  ,  ◇ = 8 × 15 = 120
   除法是減法延伸,減法不適合交換
   除法也不適合交換；加,乘則皆可
   6+6+6=6×3    乘是加的速算
   5+9=9+5         ∵加適合交換律
   9×5=5×9         ∴乘也適合
☆10顆糖分二盤,每盤幾顆糖？
         10  - (  ) - (  ) = 0
     ∵10  ÷ 2 = (  )
     ∴減法的速算是除法
☆65人分座五台車,每車幾人？
         65  -□ -□ -□ -□ -□ = 0
         65 = □ × 5 ,  □ = 65 ÷ 5 =13
   ⑹ + - × ÷ four of the original
÷ is - the speed algorithm,
and × the opposite, the inverse
÷ × mutually inverse operation, because + - is the inverse operation
     +  ⇆  -
     ↯        ↯
     ×  ⇆  ÷
four were originally used in the field of mathematics
The geometric extension of algebra depends on it
three areas to deduce infinite super wisdom
   16 + □ = 33, □ = 33 - 16 = 17
   ○ - 28 = 45, ○ = 45 + 28 = 73
   19 × ♢ = 57, ♢ = 57 ÷ 19 = 3
   ◇ ÷ 15 = 8, ◇ = 8 × 15 = 120
Division is subtraction extension, subtraction is not suitable for exchange
Division is not suitable for exchange; plus, by the can be
   6 + 6 + 6 = 6 × 3
multiplied by the speed of the operator
   5 + 9 = 9 + 5
∵ add the appropriate exchange law
   9 × 5 = 5 × 9
∴ is also suitable
☆ 10 sugar two sets, each few sugar a few?
         10 - () - () = 0
     ∵ 10 ÷ 2 = ()
     ∴ subtraction is the speed of the division
☆ 65 seats five cars, several people per car?
         65 - □ - □ - □ - □ - □ = 0
         65 = □ x 5, □ = 65 ÷ 5 = 13