{"id":37119,"date":"2023-03-29T11:51:21","date_gmt":"2023-03-29T06:51:21","guid":{"rendered":"https:\/\/jdpu.uz\/?p=37119"},"modified":"2023-05-06T11:52:04","modified_gmt":"2023-05-06T06:52:04","slug":"english-kasrlar-haqida-tushuncha-va-ularni-orgatishning-zamonaviy-usullari","status":"publish","type":"post","link":"https:\/\/jdpu.uz\/en\/english-kasrlar-haqida-tushuncha-va-ularni-orgatishning-zamonaviy-usullari\/","title":{"rendered":"KASRLAR HAQIDA TUSHUNCHA VA ULARNI \u00a0O\u2019RGATISHNING ZAMONAVIY USULLARI"},"content":{"rendered":"

\u00a0Sh.Eshonqulova\u00a0 Jizzax davlat pedagogika universiteti (PhD) o\u2019qituvchisi<\/strong><\/p>\n

M.Sapaboyeva Jizzax davlat pedagogika universiteti talabasi<\/strong><\/p>\n

Annotatsiya:<\/strong> Ushbu maqolada kasr tushunchasi nima ekanligi, hayotimizda qanday vaziyatlarda kerak bo`lishi, boshlang\u2019ich sinf o\u2019quvchilariga kasrlarni qanday o\u2019rgatish haqida gap boradi.<\/p>\n

Kalit so\u2019zlar: <\/strong>kasr, kasr sonlar, surat, maxraj, kasr chizig\u2019i, ratsional sonlar, yarim, chorak, nimchorak, to\u2019g\u2019ri kasr, noto\u2019g\u2019ri kasr, o\u2019nli kasr.<\/p>\n

Matematika fani oddiydan murakkablikka qarab tuzilgan bo\u2019lib, asta sekin mavzular ham murakkablashib boradi. Matematika asosini sonlar tashkil qiladi. Biz ko\u2019rishimiz mumkinki dastavval inson ehtiyojlari tufayli sonlar paydo bo\u2019la boshlagan. Bu sonlar boshlab narsalarni sanash uchun kerak bo\u2019gan. Lekin vaqt o\u2019tishi bilan \u201cQancha\u201d, \u201cQanchadan\u201d, \u201cNecha\u201d savollariga bu sonlar orqali javob berish yetarli bo\u2019lmagan.<\/p>\n

Qadimda 5 ta ovchi bir o\u2019ljani tutganlaridan so\u2019ng teng bo\u2019laklarga bo\u2019lib o\u2019ljani teng taqsimlaganlar. Lekin ovchilar o\u2019zlariga qanchadan tegganlarini aniq sonlarda ifodalay olishmagan. Va shu tafayli kasr sonlarga ehtiyoj tug\u2019ila boshlagan.<\/p>\n

Biz yana shunga e\u2019tibor qaratishimiz kerakki, butun sonlar to\u2019plamida har doim qo\u2019shish, ayirish, ko\u2019paytirish amallarini bajarishimiz va natija butun son chiqishi o\u2019rinlidir. Lekin butun sonlar ustida bo\u2019lish amalini bajarganda natija har doim ham butun son chiqavermaydi.<\/p>\n

Masalan, 5:2=2,5\u00a0 \u00a08:3=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 bu hosil bo\u2019lgan natijalar butun sonlar to\u2019plamida yo\u2019q.<\/p>\n

Shunda kars sonlar nima degan savolga to\u2019xtaladigan bo\u2019lsak , \u00a0\u00a0<\/strong>,\u00a0 m<\/strong>, n<\/strong><\/p>\n

ko\u2019rinishida yozilgan sonlar karslar deyiladi. Istalgan butun asonni kasr ko`rinishida yozish mumkin. Masalan , 4 ni\u00a0 ,\u00a0 5 ni \u00a0 kabi.<\/p>\n

Kasrlarning tarixiga kelib chiqishiga to`xtaladigan bo`lsak kasr-arabcha \u201cbo`lak\u201d , \u201cparcha\u201d ,rus tilida \u201cezish\u201d, \u201csindirish\u201d degan ma\u2019nolarni bildirgan. Kasrlarning zamonaviy belgilanishi qadimgi Hindistonda paydo bo\u2019lgan. Miqdorlarni aniq o\u2019lchashga bo\u2019lgan talab o\u2019lchov birligini bir nechta teng qismga bo\u2019lishga olib kelgan. Har bir qisim alohida nomga ega bo\u2019lgan. Masalan, Qadimgi Rusiyada \u00a0\u2013 yarimi \u201cpoltinik\u201d,\u00a0 to`rtdan biri \u2013\u201cchet\u201d,\u00a0 sakkizdan biri-\u201cpolchet\u201d, o`n oltidan biri-\u201cpolpolcho`t\u201d, o\u2019lchovning teng qisimlari ulush deb ataganlar. \u00a0O\u2019zimizda ham -\u201cyarim\u201d,\u00a0\u00a0 \u00a0-\u201cchorak\u201d,\u00a0 \u00a0– \u201cnimchorak\u201d deb ataladi.<\/p>\n

Kasrlarni o\u2019rgatish matematika o\u2019quv dasturining muhim qismidir. Lekin, ko\u2019p hollarda kasrlarni tushunish bolalar uchun katta qiyinchilik tug\u2019diradi. Bularning sabablarini ko`rsatadigan bo\u2019lsak birinchidan bu tushunchalarni o\u2019rgatishda ularning yoshini, aqliy rivojlanishini hisobga olmaganligimizdan, ikkinchidan kasr haqida noto\u2019g\u2019ri tushunchaga ega ekanliklari.<\/p>\n

Kasr tushunchasini bolalarga o\u2019rgatishda bir qancha qulay usullardan foydalanib tushuntirgan maqul. Masalan, O\u2019quvchilarni kasrlar bilan tanishtirish o\u2019quv dasturiga binoan 4-sinfdan boshlab o\u2019rgatiladi. Lekin bundan oldin ham bolalarga maktabgacha ta\u2019limda kasrning boshlang\u2019ich tushunchalari o\u2019rgatiladi. Ya\u2019ni bolalar har xil mevalarni, sabzavotlarni shu qatorda non, tort va boshqa shu kabi narsalarni o\u2019zlari bo\u2019laklarga bo\u2019lish orqali boshlang\u2019ich tushunchalarga ega bo\u2019ladilar. Kasr tushunchasini bolalarga singdirishda biz asosan ko`rgazmalilikka katta e\u2019tibor qaratishimiz lozim. Shu oqali narsalarni teng bo\u2019laklarga ajratish, kesish, bo\u2019lish, sindirish orqali kasr tushunchasi kelib chiqqanligini uqtirishimiz kerak.<\/p>\n

Kasr tushunchasini bolalarga o\u2019rgatishning bir qancha zamonaviy usullarini ko\u2019rib chiqadigan bo\u2019lsak:<\/p>\n

-o\u2019yin faoliyati bilan birga olib borish ( LEGO g\u2019ishtlaridan foydalanib)<\/p>\n

-narsalarni teng qisimlarga ajratish orqali<\/p>\n

-kasr piknikini o\u2019tkazish ( oziq-ovqatlar bilan)<\/p>\n

-domino kasrlari bilan hisob kitobni amalga oshirish<\/p>\n

-kasrlarni bolalar sevadigan narsalarga bog\u2019lash ( musiqa )<\/p>\n

-mavzuga oid rasmlarni rangli qalamlar bilan bo\u2019yash orqali<\/p>\n

-texnikaga murojat qilish orqali ( kompyuterda har xil ilovalar orqali)<\/p>\n

-shakllar, diagrammalardan foydalanish va boshqa qiziqarli metod va usullar bilan tushuntirsak yanada tushunishlari oson va darslar qiziqarli bo\u2019ladi. Bu bolalarning mavzuni yaxshi o\u2019zlashtirib olishlariga katta yordam beradi.<\/p>\n

Endi kasr tushunchasini kiritish uchun foydalaniladigan misollarni ko\u2019rib o\u2019tsak, masalan. 1 metr uzunlikdagi arqon o\u2019zaro teng ikki bo\u2019lakka bo\u2019linsa, u holda bo\u2019laklarning har birining uzunligi ana shu arqon uzunligining yarmiga teng bo\u2019ladi va uni \u00a0kabi yozib olishimiz mumkin. Agar shu uzunlikdagi arqonni teng uch bo\u2019lakka bo\u2019lsak, har bir bo\u2019lak uzunligi shu arqonning uchdan biriga teng bo\u2019ladi va uni \u00a0\u00a0kabi yozishimiz mumkin.<\/p>\n

Bir metr uzunlikdagi yog\u2019ochni teng uch bo\u2019lakka bo\u2019lib, undan ikki qismini oladigan bo\u2019lsak, olingan uzunligi \u00a0kabi yoziladi.\u00a0 Ya\u2019ni butun sonning o\u2019zaro teng bo\u2019lgan ma\u2019lum bir ulushi, shu sonning kasri deyiladi.<\/p>\n

Biz yuqorida \u00a0\u00a0\u00a0<\/strong>\u00a0<\/strong>\u00a0ko`rinishidagi sonni kasr son dedik. Bunda \u00a0\u00a0m-<\/strong> kasrning surati n-<\/strong> kasrning maxraji\u00a0 surat va maxraj o\u2019rtasidagi chiziq kasr chizig\u2019i deb yuritiladi.<\/p>\n

Berilgan narsalarni yoki butun sonni qancha teng qisimga bo`linganligini ko`rsatuvchi son kasrning maxraji<\/em>, shunday qismdan nechtasi olinganligini ko`rsatuvchi son kasrning surati<\/em> deyiladi. \u00a0\u00a0<\/strong>\u00a0<\/strong>ko\u2019rinishidagi kasrlarga qarama-qarshi kasrlar\u00a0 – \u00a0<\/strong>ko`rinishda ifodalanadi.\u00a0 ( –<\/strong>, 0, <\/strong>\u00a0<\/strong>) shu ko\u2019rinishdagi to\u2019plam ratsional sonlar to\u2019plami deb yuritiladi.<\/p>\n

Kasrlar 3 xil bo\u2019ladi:<\/p>\n

1.To\u2019g\u2019ri kasrlar<\/p>\n

2.Noto\u2019g\u2019ri kasrlar<\/p>\n

3.O\u2019nli kasrlar.<\/p>\n

Agar kasrning surati uning majrajidan kichik bo\u2019lsa, bunday kasrlarni to\u2019g\u2019ri kasrlar <\/strong>deymiz.<\/p>\n

Masalan:\u00a0 \u00a0, \u00a0, \u00a0\u2026<\/p>\n

Agar kasrning surati uning maxrajidan katta bo\u2019lsa, bunday kasrlarni noto\u2019g\u2019ri kasrlar <\/strong>deymiz.<\/p>\n

Masalan: , , \u00a0\u2026<\/p>\n

Agar kasrning maxraji bir va nol sonlaridan ya\u2019ni o\u2019nning darajalaridan iborat bo\u2019lsa, bunday kasrlarni o\u2019nli kasrlar <\/strong>deymiz.<\/p>\n

Masalan: =0.1 ,\u00a0 =0.01, =0.001<\/p>\n

Xulosa qilib aytganda, kasr tushunchasi o\u2019quvchilarga qulay, oson usullar bilan yaxshi o\u2019rgatilsa bolalar o\u2019zlashtirib olishlari oson bo\u2019ladi, dars samaradorligi yanada yaxshilanadi.O\u2019quvchilar ulushning teng qismlarga bo\u2019linsagina ulush bo\u2019lishi haqidagi tushunchalarga ham ega buladilar. O\u2019quvchilarga keyin ulush bilan kasrning o\u2019zaro bog\u2019lab tushuntiriladi.O\u2019quvchilarga qancha soda qilib tushuntirilsa o\u2019quvchilarning o\u2019zlashtirishi shuncha oson buladi.<\/p>\n

\u00a0\u00a0 <\/strong><\/p>\n

Foydalanilgan adabiyotlar ro\u2019yxati<\/strong><\/p>\n

    \n
  1. E.E.Jumayev. \u201c Boshlang\u2019ich matematika nazariyasi va metodikasi\u201d , \u201cTuron-Iqbol\u201d, Toshkent-2010 yil.<\/li>\n<\/ol>\n

    2.S.Alixonov \u201c Matematika o\u2019qitish metodikasi\u201d, Cho\u2019lpon nomidagi nashriyot-matbaa ijodiy uyi, Toshkent- 2011 yil .<\/p>\n

    3.D.Nusratova , A.Shamsiyev \u201c Boshlang\u2019ich matematika kursi nazariyasi\u201d, \u201cVNESHINVESTPROM\u201d Toshkent- 2021 yil.<\/p>\n

    4.N.U.Bikbayeva, E.Yangabayeva, K.M.Girfanova \u201c\u00a0 Matematika 4-sinf uchun darslik\u201d, \u201cO\u2019qituvchi\u201d nashriyot-matbaa ijodiy uyi ,Toshkent-2017.<\/p>\n

    5.N.U.Bikbayeva,R.I.Sidel\u2019nikova,G.A.Adambekova \u201cBoshlang\u2019ich sinflarda matematika o\u2019qitish metodikasi\u201d Toshkent.O\u2019qituvchi 1996 yil<\/p>","protected":false},"excerpt":{"rendered":"

    \u00a0Sh.Eshonqulova\u00a0 Jizzax davlat pedagogika universiteti (PhD) o\u2019qituvchisi M.Sapaboyeva Jizzax davlat pedagogika universiteti talabasi<\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[145],"tags":[],"sdg_goal":[],"class_list":["post-37119","post","type-post","status-publish","format-standard","hentry","category-ommaviy_maqolalar"],"acf":[],"views":957,"_links":{"self":[{"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/posts\/37119","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/comments?post=37119"}],"version-history":[{"count":1,"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/posts\/37119\/revisions"}],"predecessor-version":[{"id":37120,"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/posts\/37119\/revisions\/37120"}],"wp:attachment":[{"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/media?parent=37119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/categories?post=37119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/tags?post=37119"},{"taxonomy":"sdg_goal","embeddable":true,"href":"https:\/\/jdpu.uz\/en\/wp-json\/wp\/v2\/sdg_goal?post=37119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}