nomanfiy butun sonlar to’plami

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nomanfiy butun sonlar to’plami nomanfiy butun sonlar to’plami shodiyeva r.s. predstavleniya o chisle u chelovechestva skladivalis postepenno. i dvigatelem vistupala praktika. uje na pervom etape razvitiya cheloveka poyavilas neobxodimost podscheta razlichnix predmetov. skolko chelovek ushli na oxotu i skolko vernulos? skolko zverey dobil oxotnik? chislo matematika poyavilas dlya resheniya prakticheskix zadach, voznikayushix pered chelovekom. prakticheskie zadachi vinujdali ee razvivatsya. i xotya vam, navernoe, kajetsya, chto matematika – suxaya i skuchnaya nauka, eto vovse ne tak. nachat nashe obshenie ya xochu s bazovogo matematicheskogo ponyatiya – ponyatiya chisla. kakie chisla sushestvuyut? skolko ix? chto s nimi mojno delat i polni li nashi ponyatiya o mnojestve chisel? rebenok, kotoriy nauchilsya schitat do 10, chuvstvuet sebya velikim matematikom. no vot pered nim otkrivaetsya, chto bivayut chisla bolshe 10, sushestvuet sotnya, tisyacha, million… - a ya umeyu schitat do milliona! – xvastaetsya odin - a ya – do sta tish millionov! – zayavlyaet drugoy …

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da nedostatochno… nujna eshe i matematika. * natural sonlar na koordinatnoy pryamoy naturalnie chisla mojno izobrazit tochkami, raspolojiv ix v poryadke vozrastaniya * natural sonlar ustida amallar qo’shish pervoe deystvie, kotoroe osvoil chelovek – slojenie. esli predstavit naturalnie chisla v vide stupenek, to slojenie napominaet pod'em po lestnitse * natural sonlar ustida amallar qo’shish * natural sonlar ustida amallar qo’shish * natural sonlar to'plamida qo'shish natural sonlar to'plamida har doim qo'shish mumkin, natural sonlar to'plami qo'shish ostida yopiladi slojenie vsegda vipolnimo na mnojestve naturalnix chisel, ili, drugimi slovami, mnojestvo naturalnix chisel zamknuto otnositelno slojeniya. * qo’shish uni amalga oshirish mumkin: kalkulyatorda barmoqlar yordamida aqlda na paltsax – esli umstvennoe razvitie naxoditsya na urovne 5-7 let v ume – esli on est v nalichii na kalkulyatore mogut skladivat vse ostalnie * qo’shish qonunlari kommunikativlik assosiativlik svoystva slojeniya izuchayutsya v pervom klasse. togda vi nazivali ix peremestitelnim i sochetatelnim zakonom. teper prishlo …

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nlar to'plamida ayirish natural sonlar to'plamida ayirish har doim ham mumkin emas. natural sonlar to'plami ayirish paytida yopilmaydi. vichitanie ne vsegda vipolnimo na mnojestve naturalnix chisel * natural sonlar ustida amallar ko’raytirish a raqamini b soniga ko'paytiring, bu har biri a ga teng bo'lgan b hadlarining yig'indisini topishni anglatadi. umnojenie – eto po suti neskolko raz povtorennoe slojenie umnojit chislo a na chislo b, eto znachit nayti summu b slagaemix, kajdoe iz kotorix ravno a * natural sonlar ustida amallar ko’paytirish umnojenie napominaet igru v kubiki * ko’paytirish uni amalga oshirish mumkin: ustun shaklida jadval yordamida kalkulyatorda esli vi ne viuchili tablitsu umnojeniya vo vtorom klasse, nakleyte ee na oblojku tetradi. bez tablitsi umnojenie v stolbik stanovitsya nevozmojnim… vprochem, umnojat mojno i na paltsax. na 9, naprimer. (pokazat priem umnojeniya na 9 na paltsax) * ko’paytirish xossalari kommunikativlik assosiativlik distributivlik umnojenie takje kommutativno i assotsiativno. vo vtorom klasse vam pokazivali …

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elgilari 2 ga nol yoki juft son bilan tugaydigan sonlar 2 ga bo'linadi * sonlarning bo'linish belgilari 2 ga nol yoki juft son bilan tugaydigan sonlar 2 ga bo'linadi 2 ga bo’lish mumkin emas * sonlarning bo'linish belgilari 2 ga nol yoki juft son bilan tugaydigan sonlar 2 ga bo'linadi 2 ga bo’linmaydi chunki, 7 – toq son * sonlarning bo'linish belgilari 5 soniga nol yoki 5 raqami bilan tugagan har qanday son 5 ga bo’linadi * sonlarning bo'linish belgilari 5 soniga nol yoki 5 raqami bilan tugagan har qanday son 5 ga bo’linadi * sonlarning bo'linish belgilari * sonlarning bo'linish belgilari * sonlarning bo'linish belgilari 10 soniga faqat nollar bilan tugagan sonlar 10 ga bo’linadi * sonlarning bo'linish belgilari 4 soniga bo’linadi, 2 ta nol bilan tugasa oxiridagi 2 xonali son 4 ga bo’linsa * sonlarning bo'linish belgilari 25 soniga bo’linadi, 2 ta nol bilan tugasa; oxiridagi 2 xonali …

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( ) abca sbc +×=+ ( ) 21035 +×= 70350420 =+= 1035 ×= 1235 ×= 235 ×+ : ab = xba ×= x 17:3 = ? 5:0 x = 05 x ×= 05 x ×= 5:0 x = 14582698 2 m 1458269 8 3652987 82 m 14582698 365298 7 82 m 14582690 5 m 1458269 0 3652985 1458269 0 365298 5 75312696 1458269 0 365298 5 7531269 6 10 m 365298 5 7531269 6 145826 00 4 m 365826 08 456876 16 145826 45 145826 63 25 m 365826 50 456876 25 145826 45 145826 63 1458369 3 m 145836936 369 ++++++= += 93 m 653127 63 m 65312724 246 +++++= += 69124379 6912437941 415 +++++++= += 2458368 9 m 245836836 369 ++++++= += 99 m 6912437941 +++++++= 2 3 5 11 13 123 4 1 2 4 6 3 6 46 ? 87 141 0

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nomanfiy butun sonlar to’plami nomanfiy butun sonlar to’plami shodiyeva r.s. predstavleniya o chisle u chelovechestva skladivalis postepenno. i dvigatelem vistupala praktika. uje na pervom etape razvitiya cheloveka poyavilas neobxodimost podscheta razlichnix predmetov. skolko chelovek ushli na oxotu i skolko vernulos? skolko zverey dobil oxotnik? chislo matematika poyavilas dlya resheniya prakticheskix zadach, voznikayushix pered chelovekom. prakticheskie zadachi vinujdali ee razvivatsya. i xotya vam, navernoe, kajetsya, chto matematika – suxaya i skuchnaya nauka, eto vovse ne tak. nachat nashe obshenie ya xochu s bazovogo matematicheskogo ponyatiya – ponyatiya chisla. kakie chisla sushestvuyut? skolko ix? chto s nimi mojno delat i polni li nashi ponyatiya o mnojestve chisel? rebenok, koto...

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