Njira Yachangu Yothetsera Mavuto Otsatizana
Mafunso otsatirana (mafunso otsatirana) ndi mtundu wa mafunso ofala kwambiri pamayeso olowera kusukulu, mayeso osankha ntchito, komanso mayeso oyambira aluso. Lingaliro ndi losavuta: mumafunsidwa kuti mupeze chitsanzo mu manambala angapo, kenako dziwani nambala yotsatira (kapena nambala yomwe ikusowa). Ngakhale zingawoneke zovuta, mndandanda ukhoza kuthetsedwa mwachangu ngati muli ndi "mapu" omveka bwino a masitepe. Nkhaniyi ikufotokoza momwe mungathetsere mwachangu mavuto otsatirana pogwiritsa ntchito njira zothandiza, mitundu yodziwika bwino ya mapangidwe, ndi malangizo opewera mapangidwe abodza.
1. Kumvetsetsa cholinga cha vuto la mndandanda
Kwenikweni, mafunso otsatizana amayesa luso lanu lozindikira ubale pakati pa manambala. Maubwenzi amenewa angaphatikizepo kuwonjezera, kuchotsa, kuchulukitsa, kugawa, kuphatikiza magwiridwe antchito, komanso ngakhale mapangidwe kapena magulu ozikidwa pa malo.
Kawirikawiri mafunso amakhala mu mawonekedwe awa:
- Dziwani nambala yotsatira: 2, 4, 8, 16, ...
- Dziwani manambala omwe akusowa: 3, 6, __, 24, 48
- Sankhani yankho loyenera kwambiri kuchokera ku mayankho omwe alipo.
Chinsinsi chachidule ndi ichi: musaganize mwachisawawa. Gwiritsani ntchito njira zotsatirazi mwadongosolo.
2. Njira zachangu (njira yapadziko lonse) zothetsera mndandandawu
Zotsatirazi ndi njira zogwirira ntchito zoganizira zomwe nthawi zambiri zimagwiritsidwa ntchito poyesa:
1) Chongani kusiyana (kusiyana) pakati pa manambala
Werengerani kusiyana kotsatizana: a2–a1, a3–a2, ndi zina zotero. Magulu ambiri osavuta amagwiritsa ntchito kusiyana kosasintha (masamu) kapena kusiyana komwe kumapanga chitsanzo.
2) Chongani chiŵerengero (gawo)
Ngati kusiyana sikuli bwino, yesani kugawa: a2/a1, a3/a2, ndi zina zotero. Izi zimathandiza kupeza njira zowerengera kapena njira zochulukitsa.
3) Chongani mawonekedwe osakanikirana (masitepe awiri/kusinthana)
Mndandanda nthawi zambiri umagwiritsa ntchito njira yosinthirana: onjezerani, chulukitsani, onjezerani, chulukitsani. Kapena mndandanda iwiri yosinthirana (manambala osadziwika amapanga njira imodzi, ngakhale manambala amapanga ina).
4) Chongani chitsanzo cha mulingo wachiwiri (kusiyana kwa kusiyana)
Ngati kusiyana kumasintha nthawi zonse, werengani kusiyana kwa kusiyana. Izi nthawi zambiri zimachitika mu quadratic series kapena stepwise increasing patterns.
5) Chongani mapatani apadera: sikweya, kiyubiki, prime, Fibonacci, factorial
Mayeso ambiri amasonyeza mapangidwe "odziwika bwino". Ngati manambala akuoneka odziwika bwino (1, 4, 9, 16…) ndiye kuti mwina ndi sikweya.
6) Chongani mapangidwe ozikidwa pa manambala
Nthawi zina chitsanzo sichili mu mtengo, koma mu manambala: chiwerengero cha manambala, kutembenuka, kuwonjezera manambala, kapena kuchulukitsa kwa 9/11.
Ndi ndondomekoyi, simudzataya nthawi. Muyenera kungoyeserera mpaka itakhala yokha.
3. Mapangidwe a mndandanda omwe amapezeka kawirikawiri komanso njira yachangu yochitira izi
A. Mndandanda wa masamu (kusiyana kosalekeza)
Chitsanzo: 5, 9, 13, 17, …
Kusiyana: +4, +4, +4.
Kotero nambala yotsatira: 21.
Njira yofulumira: Mukapeza kusiyana komweko kawiri motsatizana, pitirizani ndi kachitidweko.
B. Mndandanda wa geometric (chiŵerengero chokhazikika)
Chitsanzo: 3, 6, 12, 24, …
Chiŵerengero: ×2, ×2, ×2.
Chotsatira: 48.
Langizo lachidule: ngati manambala akuwonjezeka kapena kuchepa mofulumira, ganizirani kuchulukitsa/kugawa.
C. Mndandanda wa kusiyana kwa magiredi (kusiyana kowonjezeka nthawi zonse)
Chitsanzo: 2, 5, 9, 14, 20, …
Kusiyana: +3, +4, +5, +6.
Kusiyana kotsatira +7 → 27.
Langizo lachidule: ngati kusiyana "kukwera kamodzi ndi kamodzi", ndi chizindikiro cha kapangidwe ka tiers.
D. Mndandanda wa Quadratic ndi cubic
– Mabwalo: 1, 4, 9, 16, 25, … (n²)
– Chikoka: 1, 8, 27, 64, … (n³)
Njira yofulumira: lowezani mabwalo 1–15 ndi ma cubes 1–10. Izi zimathandizira kuzindikira mwachangu ndi masekondi.
Mndandanda wa E. Fibonacci ndi mitundu yake
Fibonacci Yakale: 1, 1, 2, 3, 5, 8, 13, …
Nambala iliyonse = chiwerengero cha manambala awiri am'mbuyomu.
Zosiyanasiyana zomwe zimachitika kawirikawiri:
2, 3, 5, 8, 13, 21, … (kuyambira pa 2 ndi 3).
Njira yofulumira: onani ngati a(n) = a(n-1) + a(n-2). Ngati ikugwirizana m'magawo awiri mpaka atatu, nthawi zambiri yankho lake ndi limenelo.
F. Mndandanda wa manambala akuluakulu
2, 3, 5, 7, 11, 13, 17, …
Njira yofulumira: sungani ma prime mpaka 50. Mavuto ambiri amathera pamenepo.
Mndandanda wa G. Factorial
1, 2, 6, 24, 120, … (1!, 2!, 3!, 4!, 5!)
Njira yofulumira: onani ngati kuchulukitsa kukukwanira: ×2, ×3, ×4, ×5.
H. Kachitidwe kosinthana (ntchito ziwiri)
Chitsanzo: 2, 6, 7, 21, 22, 66, …
Chitsanzo: ×3, +1, ×3, +1, ×3 …
Chotsatira: 67.
Njira yofulumira: ngati palibe njira imodzi, yesani kulekanitsa ntchito za "kuchulukitsa ndi kuwonjezera" mosinthana.
I. Mndandanda wa manambala awiri osinthana (manambala osamveka bwino ndi ofanana ali ndi mapatani osiyanasiyana)
Chitsanzo: 1, 4, 2, 8, 3, 12, 4, …
Manambala a malo osamvetseka: 1, 2, 3, 4 (kuwonjezera +1)
Manambala a malo ofanana: 4, 8, 12 (kuwonjezeka +4)
Lotsatira (malo ofanana): 16.
Njira yofulumira: gawani m'mizere iwiri: (1st, 3rd, 5th,…) ndi (2nd, 4th, 6th,…).
Mapangidwe ozikidwa pa digito a J.
Chitsanzo: 10, 11, 13, 17, 25, …
Nthawi zina chitsanzocho chimakhala chiwonkhetso cha manambala, kapena "nambala yotsatira = nambala yapitayi + chiwonkhetso cha manambala ake".
Mwachitsanzo, lamulo: a(n+1) = a(n) + (chiwerengero cha manambala a a(n)).
Njira yofulumira: ngati manambala akuoneka "osamveka" ndipo sakugwirizana ndi kusiyana/chiŵerengero, yang'anani manambala.
4. Njira zopewera misampha yabodza
Mu mayeso, olemba mayeso nthawi zambiri amapereka njira zomwe "zimawoneka" kuti zikugwirizana ndi njira zosiyanasiyana. Momwe mungapewere izi:
1) Yesani chitsanzocho pa kusintha kosachepera katatu
Musakhutire ndi chinthu chimodzi chokha chofanana. Onetsetsani kuti mwagwirizanitsa manambala angapo.
2) Sankhani chitsanzo chosavuta komanso chogwirizana kwambiri.
Ngati pali njira ziwiri, nthawi zambiri chomwe chimasankhidwa ndi chitsanzo chomwe sichili chovuta kwambiri ndipo chimagwira ntchito pa manambala onse.
3) Samalani mayankho omwe alipo
Mu mafunso osankha mayankho angapo, nthawi zina mutha kuyesa imodzi mwa njirazo kenako ndikuwona ngati zotsatira zake zikuwonekera mu njirazo. Ngati sizikuwoneka, njirazo sizolondola.
5. Zitsanzo zazifupi zochitira (njira yachangu)
1) 7, 14, 28, 56, …
Chongani chiŵerengero: ×2 kenako → lotsatira 112.
2) 3, 8, 15, 24, 35, …
Kusiyana: +5, +7, +9, +11 (mpaka 2) → lotsatira +13 = 48.
3) 1, 3, 6, 10, 15, …
Kusiyana: +2, +3, +4, +5 → lotsatira +6 = 21 (iyi ndi mndandanda wa katatu).
6. Malangizo ophunzirira mwachangu
- Lembani mndandanda wa mapangidwe oyenera kukumbukira: sikweya, kiyubiki, prime, factorial, Fibonacci.
- Yesetsani mafunso 10–20 patsiku: bwino nthawi zonse kuposa mafunso ambiri koma kawirikawiri.
- Gwiritsani ntchito wotchi yoyimitsa: yesetsani masekondi 20-40 pa funso lililonse pamlingo woyambira.
- Lembani njira zomwe nthawi zambiri mumaganiza kuti sizolondola: zidzakhala "banki yolakwika" yomwe idzafulumizitsa kusintha.
Kutseka
Kuthetsa mavuto a sequence mwachangu sikukhudza luso, koma njira ndi chizolowezi. Yambani ndi masitepe ofala kwambiri (kusiyana ndi chiŵerengero), pitirizani ku mapatani osinthasintha kapena olumikizana, kenako yang'anani mapatani enaake monga masikweya, ma prime, manambala a Fibonacci, kapena ma factorial. Mukamachita masewera olimbitsa thupi kwambiri, mudzazolowera kuwona mapatani m'masekondi ochepa chabe. Ngati mumakhala okhazikika, mavuto a sequence omwe poyamba ankaoneka osokoneza adzakhala osavuta komanso ofulumira kuthetsa.
Ngati mukufuna, nditumizireni zitsanzo 5-10 za mavuto omwe muli nawo, ndipo ndikuthandizani kukambirana limodzi ndi limodzi pogwiritsa ntchito njira yachangu kwambiri.
