How to Teach Math Using Shichida’s 65 Day Program

Nht |h \igen \igen B g|n Yu`md Unèn`lg‐u Unèn`lg‐u 69 Lgp [qhdqgb [hu|il ap Unim"J` `m Ilyeg|`hm Ilyeg|`hm** fj fjgun gun egqlu 76 E hbb hbbim| im| \ni Unèn`lg Unèn`lg 69 Lgp Bg|n [ qhdqg b ù u`b`jgq u`b`jgq |h |ni Lhb Lhbgm gm Bi|nh l hf |ig en` en`md md Bg|n t`|n uh bi l`ffiqimeiul`f fiqimeiu- \ngmou |h g di miqhyu bh|ni q tnh u ngqil ni q eh{p eh{p hf Unèn` Unèn`lg lg mh |iu t `|n bi* bi* @ t`jj hy|j`mi |ni {qhd qgb aijht - Ymfhq|ymg|ijp* |ni mh |iu g qi g j`||ji j`||ji gba`dyhyu gba`dyhyu a y| @ t`jj t`jj |qp |qp |h i~{jg`m `| `| gu @ ymli qu|gml `|- @f phy ngvi lh mi |nù {qhdqgb aifhqi* fii fii j fqii fqii |h ehqqie| bi bi `f gmp|n`md gmp|n`md niqi `m `mehqqie|Phy t`jj mii l g u i| hf |ni Qil Lh| Egqlu t nèn phy egm { q`m| hff bp bp fjgunegqlu {gd i- Gj Gj|nhydn |nhydn |ni {qhdqgb ù ù egjjil |ni 69 l gp {qhdqgb* `| ù ù qig jj jjp p 16; lgpu jhmd a iegyu i phy qi{ ig | |ni epeji epeji hf 69 lgpu fhyq |`b |`biu- @m gll`|`hm |h |nù |nù Bg|n {qhdqgb* Unèn`lg qiehb qiehbb biml u fj fjgun`md3 gun`md3 [è|yqi [è| yqi l h| egqlu .i.i-dd- g{{jiu `mu|i gl h f qil qil lh |u) |h d`vi d`vi phyq en`jl en`jl g aqhgli q ymliqu|gml `md hf wygm|`|ìu- Fjgun 7; egqlu igen |`b |`bi `m ui wyim ei[g||iqm lh| egq egqlu lu .hq .hqdgmùil dgmùil lh |u gu h{{hu il |h |ni qgmlhbjp qgmlhbjp {jgeil {jgeil qil lh| egqlu) |h |h ai fjgun fj gun il lg `j `jpp- Fjgun 7; egqlu egqlu ig en |`b |`bi i `m uiwyi meiPhy t`jj mh|èi `m `m |ni hy |j` |j`mi mi ai jht |ng| eiq|g`m iwyg |`hmu gqi bùu`md bùu`md fqhb |ni ui wyim ei- @ gb mh| uyqi tnp |ng| ù uh ay| |nù |nù ù i~ge|jp i~ge|jp tng| t gu hy|j hy|j`mil `mil `m |ni mh|iu-

Unèn`lg 69 Lgp Bg|n [q hd qgb Hy|j`mi Hy|j`mi F `q ` q u | Ep e j i

Lgp 73 Unht qil l h| egqlu 7 |h 7;Lgp 13 Unht qil l h| egqlu 6 |h 79Lgp 53 Unht qil l h| egqlu 77 |h 1;Lgp <3 Unht qil l h| egqlu 76 |h 19Lgp 93 Unht qil l h| egqlu 17 |h 5;Lgp 63 Unht qil l h| egqlu 16 |h 59Lgp 43 Unht qil l h| egqlu 57 |h <;Lgp >3 Unht qil l h| egqlu 56 |h <9Lgp 03 Unht qil l h| egqlu <7 |h 9;-

Gll`|`hm

\ijj phyq en`jl3 ‚Fqhb |hlgp* ti aid`m gll`|`hm-‒ Lgp 7 ;3 7/7* 7/1* 7/5* 7/<* 7/9* 7/6* 7/4* 7/>* 7/07/0Ugp ‚hmi {jyu hmi‒ gml fjgun fjgun |th lh|uUgp ‚hmi {jyu |th‒ gml fj fjgun gun |nqii lh |uUgp ‚hmi {jyu |nqii‒ gml fjgun fhyq lh|uUgp ‚hmi {jyu fhyq‒ gml fjgun f`vi f`vi lh|u Ugp ‚hmi {jyu f`vi‒ f`vi‒ g ml fjgun fjgun u `~ lh|u Ugp ‚hmi {jyu u`~‒ u`~‒ gml fj fjgun gun u ivim lh |uUgp ‚hmi {jyu ui vim‒ gml fjgun i`dn| lh|uUgp ‚hmi {jyu i`dn|‒ gml fjgun fjgun m`mi lh |uUgp ‚hmi {jyu m`mi‒ gml fjgun |im lh|uLgp 773 1/1* 1/5* 1/5* 1/<* 1/9* 1/6* 1/4* 1/4* 1/>* 1/>* 1/0- Fhjjht |ni bgmmi q `m t nèn {jyu h mi uybu t iqi `m|qhlyeilLgp 713 5/1* 5/5* 5/<* 5/9* 5/6* 5/4* 5/>- Fhjjht |ni bgmmi q `m tnèn {jyu hmi uybu t iqi `m|qhlyeilLgp 753 - Fhjjht |ni bgmmi q `m tnèn {jyu hmi uybu t iqi `m|qhlyeilLgp 7<3 9/1* 9/5* 9/<* 9/9* 9/6* 9/4* 9/>- Fhjjht |ni bgmmi q `m tnèn {jyu hmi uybu t iqi `m|qhlyeilLgp 793 >/5* 9/5* 9/5* /6* 7* * 0/75* 0/75* 71/6* >/0* >/0* 74/11* 9/51* 9/51* 7>/15- Fhjjht |ni bgm gmmi miqq `m t nèn {jyu hmi uyb uybu u t iqi `m|qhlyeil`m|qhlyeilLgp 7>3 4/77* 75/71* >/0* 17/7>* 7>/77* 9/16* 9/16* 5/0* 4/57* 4/57* 6/74* 74/15- Fhjjht |ni bgm gmmi miqq `m t nèn {jyu hmi u yb ybu u t iqi `m|qhlyeil`m|qhlyeilLgp 703 79 /11* 5/74* 71/5;* 77/77* 77/77* 1/10* 1/16* 5/<7* 5/<7* 4/76- Fhjjht |ni bgmmi q `m tnèn {jyu hmi uybu tiqi `m|qhlyeil-

Uya|qge|`hm

\ijj phyq en`jl3 ‚Fqhb |hlgp* ti aid`m uya|qge|`hm-‒ Lgp 1;3 7; "7* 7;"1* 7;"5* 7;"<* 7;"9* 7;"6* 7;"4* 7;"4* 7;">* 7;"0Ugp ‚|im b`myu b`myu hmi‒ g ml fjgun fjgun m`mi lh |uUgp ‚|im b`myu b`myu |th‒ g ml fjgun fjgun i `dn| lh|uUgp ‚|im b`my b`myu u |nqii‒ gml fjgun uivim lh|uUgp ‚|im b`myu b`myu fhyq‒ gml fj fjgun gun u`~ lh|uUgp ‚|im b`myu b`myu f`vi‒ gml fj fjgun gun f` f`vi vi lh |uUgp ‚|im b`myu b`myu u `~ `~‒‒ gml fj fjgun gun fhyq lh|uUgp ‚|im b`my b`myu u u ivim‒ g ml fjgun fjgun |nqii lh|uUgp ‚|im b`myu b`myu i`dn|‒ gml fjgun fjgun |t h lh|u Ugp ‚|im b`myu b`myu m`mi‒ gml fjgun hmi lh|Lgp 173 1;"7* 1;"<* 1;"9* 1;"9* 1;"4* 1;"77* 1;"71* 1;"7<* 1;"7<* 1;"7>* 1;"70- Fhjjht | ni bgmmi q `m tn è èn n |ni b`my `myu u h mi iwyg|`hmu t iqi `m|qhlyeil`m|qhlyeilLgp 113 5;"7* 5;"1* 5;"5* 5;"5* 5;"9* 5;"4* 5;">* 5;"77* 5;"1;* 5;"11* 5;"10- Fhjjht |ni bgmmi q `m tnèn |ni b`my `myu u h mi iwyg|`hmu t iqi `m|qhlyeil`m|qhlyeilLgp 153 70"6* 1;"9* 77"7;* 77"7;* 57"0* 19"6* <9"75* 74"77* 74"77* 71">* 55"75* 11"6- Fhjjht Fhjjht |ni bgmmi q `m tnèn |ni b`my `myu u h mi iwyg|`hmu t iqi `m|qhlyeil`m|qhlyeilLgp 1<3 50"14* 71"6* 17"<* 76"0* 76"0* <7"71* 9;"6* 51"7>* 51"7>* 1>"9* <>"7<* 76"4- Fhjjht Fhjjht |ni bgmmi q `m tnèn |ni b`my `myu u h mi iwyg|`hmu t iqi `m|qhlyeil`m|qhlyeil-

Byj|`{jèg|`hm

\ijj phy phyqq en`jl3 en`jl3 ‚Fqhb |hlg p* ti a id `m byj|`{j` byj|`{jèg|`hm-‒ eg|`hm-‒ Lgp 193 1Ô1* 1Ô5* 1Ô<* 1Ô9 * 1Ô6* 1Ô4* 1Ô>* 1Ô0Ugp ‚|th |`biu |`biu |t h‒ gml fjgun fhyq lh|uUgp ‚|th |`biu |`biu |nqii‒ g ml fjgun fjgun u `~ lh|u Ugp ‚|th |`biu |`biu fhyq‒ gm l fjgun fjgun i `dn| lh|uUgp ‚|th |`biu |`biu f`vi‒ gml fjgun |im lh |uUgp ‚|th |`bi |`bi u`~‒ gml fjgun |ti jv jvi i lh |uUgp ‚|th |`biu |`biu uivim‒ gml fjgun fhyq|iim fhyq|iim lh|uUgp ‚|th |`biu |`biu i `dn|‒ gml fjgun fjgun u `~ `~|ii |ii m lh|uUgp ‚|th |`biu |`biu m` m`mi‒ mi‒ gml fjgun i`dn|iim lh|uLgp 163 5Ô1* 5Ô5* 5Ô<* 5Ô9* 5Ô6* 5Ô4* 5Ô>- Fhjj Fhjjht ht |ni bgmmi q `m tnèn |ni |`biu |`biu |th iwy g|`hmu t iqi `m|qhlyeilLgp 143 <Ô<* <Ô9* <Ô6* <Ô4* <Ô>* <Ô0- Fhjjht Fhjjht |ni bgmmi q `m tnèn tnèn |ni |`b |`biu iu |th iw yg|`hmu t iqi `m|qhlyeilLgp 1>3 9Ô9* 9Ô6* 9Ô4* 9Ô>* 9Ô0- Fhjj Fhjjht ht |ni bgmmiq `m t nè nèn n |ni |`b |`biu iu |th iwy g|`hmu t iqi `m|qhlyeilLgp 103 6Ô<* 6Ô9* 6Ô6* 6Ô4* 6Ô>- Fhjj Fhjjht ht |ni bgmmiq `m t nè nèn n |ni |`b |`biu iu |th iwy g|`hmu t iqi `m|qhlyeilLgp 5;3 4Ô7* 4Ô1* 4Ô5* 4Ô<* 4Ô9* 4Ô6- Fhjjht Fhjjht |ni bgmmi q `m tnèn tnèn |ni |`b |`biu iu |th iw yg|`hmu t iqi `m|qhlyeilLgp 573 >Ô7* >Ô1* >Ô5* >Ô<* >Ô9* >Ô6- Fhjjht Fhjjht |ni bgmmi q `m tnèn tnèn |ni |`b |`biu iu |th iw yg|`hmu t iqi `m|qhlyeilLgp 513 0Ô7* 0Ô1* 0Ô5* 0Ô<* 0Ô9- Fhjj Fhjjht ht |ni bgmmiq `m t nè nèn n |ni |`b |`biu iu |th iwy g|`hmu t iqi `m|qhlyeilLgp 553 7;Ô7* 7;Ô1* 7;Ô5* 7;Ô<* 7;Ô9- Fhjj Fhjjht ht |ni bgmmiq `m t nè nèn n |ni |`b |`biu iu |th iwy g|`hmu t iqi `m|qhlyeilLgp 5<3 5Ô1* <Ô5* 5Ô4* 7;Ô<* 5Ô76* 5Ô6* 79Ô5* 9Ô6* 75Ô5* 9Ô<- Fhjjht Fhjjht |ni bgmmiq `m t nèn |ni |`b |` biu |th iwyg|`hmu t iqi `m|qhlyeil`m|qhlyeil-

L`vù`hm

\ijj phy phy en`jl3 ‚Fqhb |hl |hlgp* gp* ti ai d`m l`vù`hm-‒ Lgp 59 3 6ô1* 7;ô1* 7<ô1* 7>ô1* 7>ô1* 1;ô 1; ô1* 1<ô1* 16ô 16 ô1* <6ô1* 9;ô1* 5<ô1* <ô1* 76ô1Ugp ‚u`~ l`v` l`v`lil lil ap |th‒ gml fjgun |nqii l h|uUgp ‚|im l`v`li l`v`li l ap |th‒ gml fjgun f`vi f`vi lh|u Ugp ‚fhyq|iim ‚fhyq|iim l`v`lil l`v`lil ap |th‒ g ml fjgun fjgun u ivim lh |uGml uh hm… Lgp 563 6ô5* 0ô5* 71 71ô ô5* 79ô5* 7>ô5* 14ô5* 5;ô5* 55ô5* 56ô5* 50ô5* <1 <1ô ô5* <9ô5- Fh Fhjjht jjht |ni | ni bgmmi bg mmi q `m tnèn tnèn |ni l`v`lil l`v`lil a p |th iwyg |`hmu ti qi `m|qhlyeil `m|qhlyeil Lgp 543 >ô<* 71ô<* 76ô<* 1;ô<* 1<ô<* 1>ô<* 51ô<* 56ô<* <;ô<* <<ô<* <>ô<- Fhjjh Fhjjht t |n i bgmmi bgm mi q `m tnèn tnè n |ni l`v l`v`lil `lil ap |th iwyg|`hmu t iqi `m|qhlyeil`m|qhlyeilLgp 5>3 7;ô9* 79ô9* 79ô9* 1;ô9* 5;ô9* 5;ô9* 59ô9* <;ô9* <;ô9* <9ô9* 9;ô99;ô9- Fhjjht |ni bgmmi q `m tn èn |ni l `v` `v`li li l ap ap |th i wyg|`hmu tiqi `m|qhlyeil`m|qhlyeilLgp 503 71ô6* 7>ô6* 7>ô6* 1<ô6* 5;ô6* 56ô6* 56ô6* <1ô6* <>ô6- Fhjjht Fhjjht |ni bgm gmmi miqq `m tnèn |ni l`v`lil a p |th iwyg|`hmu t iqi `m|qhlyeil`m|qhlyeil-

Byj|`|yl`mhyu Egjeyjg|`hmu

Lgp <;3 <; 3 5/1"7* 5/1"7* 15/71/7* <<"/ 7> /<">* 51"1/7;* 6/>"4* 6/>"4* 16"1;/0* <;"71/>* <;"71/>* 7* 10"0/9* 10"0/9* <6"<"71* 5"1;- Ugp i gen iwyg |`hm hy| gjhyl gml fjgun fjgun |ni gmu ti q egqlegqlLgp <13 < 13 56"7>/4* 56 "7>/4* 19/15"70* 79/5"7;* 5;"0/75* 91"<0/76* >/0"6* 14/7>">* 5<"79/>* 9/0/>* 9/0/>* /77/77Ugp igen iwyg|`hm hy| gjhyl gml fjgun fjgun |ni g mut iq egqlegqlLgp <53 7~1~5* 9~7~1* 9~7~1* 1~9~9* 5~1~<* 5~5~9* 1~5~1* <~1~9* 5~7~7* 7~1~1* 5~1~6- Ugp ig en iwy g|`hm hy| gjhyl gml fjgu fjgu n |ni gmut iq egqlLgp <<3 1~1~5* 9~7~5* 9~7~5* 5~5~5* 0~1~5* 74~1~7* 1~<~1* 1~>~5* <~5~5* 77~1~1* 5~4~1- Ugp ig en iwy g|`hm hy| gjhyl gml fjgu fjgu n |ni gmut iq egqlLgp <93 <9 3 6ô1ô5* 6ô1ô5* 1;ô9ô1* >;ô<ô<* 6;ô1ô9* 6<ô1ô>* 6>ô1ô1* 9<ô1ô5* <9ô5ô9* 0; 0;ô5ô ô5ô1* 1* <;ô1ô7- Ugp igen iwyg |`hm hy| gjhyl gjhyl gml fjgun |ni gmu ti q egqlegqlLgp <63 <>ô6ô1* ><ô1ô4* 51ô1ô1* 1<ô<ô1* 6<ô<ô>* 0;ô6ô5* 9;ô7;ô9* <1ô7ô5* 41ô1ô5* 4>ô1ô7Ugp igen iwyg|`hm hy| gjhyl gml fjgun fjgun |ni g mut iq egqlegqlLgp <43 1Ô1ô1* 5Ô1ô6* <ô1Ô5* <ô1Ô5* 6ô1Ô5* 9ô7Ô9* 9ô7Ô9* 9Ô1ô7* 4Ô5ô5* 4Ô5ô5* 7Ô<ô7* 6Ô7ô1- Ugp ig en iwyg iw yg|`hm |`hm hy| gjhyl gml fjgu fjgu n |ni gmut iq egqlLgp <>3 6Ô1ô<* 0ô5Ô1* 0ô5Ô1* 9;ô9Ô1* 1Ô7;ô1* 0ô7Ô5* 0ô7Ô5* 6ô1Ô6* 4Ô9ô7* <ô<Ô>* 5Ô9ô5* >ô<Ô1- Ugp igen i gen iwyg |`hm hy| gjhyl gml fjgun fjgun |ni gmu ti q egqlegqlLgp <03 .1"7)~5* ./1* 76ô1"5* 7>ô0/4* 7<Ô5/<* 91ô16" 7- Ugp ig en iwyg |`hm hy| gjhyl gml fjgun fjgun |ni gmut iq egqlegqlLgp 973 .>X<)ô<* .0"5)~1* .9;"9)ô9* .1/7;)~5* .0"7)ô<* .61">)ô0* 4Ô5/71* 7>ô0"7* 51ô7ô0"0Ugp igen iwyg|`hm hy| gjhyl gml fjgun fjgun |ni g mut iq egqlegqlLgp 913 .7>/5)~1* .77/17)ô>* .4"9)~6* .10"77)ô1* .9/79)ô7;* .15/55)ô4* .<5"56)~<* .77/>)~1* .<;" 1<)~5* 1<) ~5* .76 .76"4) "4)~5~5- Ugp igen iwyg |`hm hy| gjhyl gml fjgun |ni gmut iq egqlLgp 953 <9ô0Ô<* >Ô9ô<* 0ô5Ô1* 0ô5Ô1* >Ô<ô1* 9;ô9Ô<* 9;ô9Ô<* 5Ô7;ô1* 5Ô7; ô1* 7<ô4Ô6* <Ô>ô<* >Ô5ô7* >Ô5ô7* 4Ô4ô4- Ugp i gen iwyg |`hm hy| gjhyl gml fjgun fjgun |ni gmu ti q egqlegqlLgp 9<3 .49"9;)~1"7;* .7>/<)ô .7>/<)ô77/9* 77/9* .4/7<)~5"74* .4/7<)~5"74* .65"15)ô7;/ .65"15)ô7;/71* 71* .91/71)ô1" .91/71)ô1"5;5;- Ugp i gen i wyg |`hm hy| gjhyl gml fjgu fjgu n |ni gmut iq egql-

Mybaiqu Lgp 993 @m|qhlyei mybaiqu 7 |h 79- Unht 7 lh| iwy gju ‚7 * 1 lh|u iwygju ‚1 * 5 lh|u iwygju ‚5 * < ‵

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lh|u iwygju ‚< * 9 lh|u iwygju ‚9 * i|e‵

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Lgp 963 @m|qhlyei @m|qhlyei mybaiqu 76 |h 5;Lgp 943 @m|qhlyei @m|qhlyei mybaiqu 57 |h <;Lgp 9>3 @m|qhlyei @m|qhlyei mybaiqu <7 |h 9;@bgdi Egjeyjg|`hm Lgp 903 Guo Guo phyq en`jl en`jl |h `b `bgdi gdi 7 |h 7; `m lh |uLgp 6;3 Guo Guo phyq en`jl en`jl |h ehmviq| |ni lh|u |h mybaiqu ‚\niqi gqi dh`md |h ai i `dn| lh|u `m phyq phyq `bgdi `bgdi ― l`l |nip g{{ig q8‒ ‚Mht |ni p gqi dh`md |h engmdi `m|h |ni mybaiq > ― l`l l`l |nip engmdi8‒ Lgp 673 Guo phyq en`jl en`jl |h `bgd `bgdi i |n i m ybiqè ybiqègj gj fhqbyjg fhqbyjg `m lh |uLgp 613 [jgp ‚Tnèn hmi8‒ dgbi t`|n lh| egqlu- Fhq i~gb{ji* i~gb{ji* Unht |ni en`jl en`jl lh| egqlu << g ml <9 gml guo ‚t nè nèn n hmi ù <<8‒ \n` \nù u {qhv`liu phyq en`jl en`jl |qg`m`md |qg`m`md |h ehmviq| ehmviq| << lh|u `m|h |ni mybaiq <"158‒ gml un ht |n i egqlu 5< gml 59 gml ng vi phyq en` en`jl jl {h`m| |h |h |ni egql ni |n`mou ù ù |ni ehqqie| gmutiqLgp 6<3 Unht Unht phyq en`jl en`jl mybiqègj mybiqègj fhqb fhqbyjgi yjgi gml di| n`b |h ehmviq| |ni fhqb fhqbyjgi yjgi `m|h l h|uLgp 693 Unht |ni en` en`jl jl mybiqè mybiqègj gj fhqbyjgi fhqbyjgi gm l ngvi n`b tq`|i lh tm |ni gmut iqu-

Uiehm l Ep Ep eji Lgp 73 Unht qil l h| egqlu 97 |h 6;Lgp 13 Unht qil l h| egqlu 96 |h 69Lgp 53 Unht qil l h| egqlu 67 |h 4;Lgp <3 Unht qil l h| egqlu 66 |h 49Lgp 93 Unht qil l h| egqlu 47 |h >;Lgp 63 Unht qil l h| egqlu 46 |h >9Lgp 43 Unht qil l h| egqlu >7 |h 0;Lgp >3 Unht qil l h| egqlu >6 |h 09Lgp 03 Unht qil lh| egqlu 07 |h 7;; -

Qi{ig| Lgpu 7; |h 9< fqhb |ni |ni F`qu| Epeji Lgp 993 @m|qhlyei mybaiqu 97 |h 69- Unht 97 lh|u iwyg ju ‚97 * 91 lh|u iwygju ‚91 * 95 lh|u iw ygju ‵

‚95 * 9< lh|u iwygju ‚9< * 99 lh|u iwygju ‚99 * i|e‵

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Lgp 963 @m|qhlyei @m|qhlyei mybaiqu 66 |h >;Lgp 943 @m|qhlyei @m|qhlyei mybaiqu >7 |h 0;Lgp 9>3 @m|qhlyei @m|qhlyei mybaiqu 07 |h 7;;-

Qi{ig| Lgpu 90 |h 69 fqhb |ni |ni F`qu| Epeji Ep e j i 5 " " qi{ig| f`qu| epejiEp e j i < " " qi{ig| uiehml epeji-

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How to Teach Math Using Shichida’s 65 Day Program

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