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Öğretmen, 21 Günde Problemler kampının ilk gününde sayı kesir problemlerini adım adım anlatmaktadır.","Video, sayı kesir problemlerinin çözüm yöntemlerini kapsamlı şekilde ele almaktadır. İçerikte matematiksel dile çevirme, basit denklem kurma, tablolaştırma, gruplandırma mantığı, merdiven problemleri, sıralara oturma, orta nokta kayma, bölme ve paylaştırma, kuyruk problemleri, kafa-ayak problemleri, kalem paketleri, şişe-dara problemleri ve meslektaş problemleri gibi çeşitli problem türleri örneklerle açıklanmaktadır.","Öğretmen her problemi detaylı olarak çözerken, öğrencilere görselleştirme teknikleri kullanarak konuyu daha anlaşılır hale getirmekte ve günlük hayattan örnekler üzerinden problem çözme stratejilerini göstermektedir. Video, bir ders serisinin ilk günü olup, ikinci günde devam edileceği belirtilmektedir."]},"endTime":4903,"title":"21 Günde Problemler Kampı: İlk Gün - Sayı Kesir Problemleri","beginTime":0}],"fullResult":[{"index":0,"title":"Problemler Kampı Tanıtımı","list":{"type":"unordered","items":["21 günde problemler kampına başlanıyor ve ilk gün sayı kesir problemleri konusu ele alınacak.","Öğrencilere soruları çözmeye acele etmemeleri, soruları anlamaya çalışmaları tavsiye ediliyor.","Kamp, problemler kitabından ilerleyecek ve her soru tarzı gösterilecek."]},"beginTime":7,"endTime":65,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=7&ask_summarization=1"},{"index":1,"title":"Sayı Kesir Problemlerinde Temel Kavramlar","list":{"type":"unordered","items":["Sayı kesir problemlerinde önemli olan basit denklem kurma ve soruları matematiksel dile çevirme.","Matematiksel dile çevirme için bilinmeyenler (x, y, z, a, b, c) kullanılır.","Türkçe ifadelerin matematiksel karşılıkları: bir sayının iki fazlası (x+2), üç katı (3x), karesi (x²), yarısının iki fazlası (x/2+2)."]},"beginTime":65,"endTime":150,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=65&ask_summarization=1"},{"index":2,"title":"Örnek Problemler","list":{"type":"unordered","items":["Bir sayının dört katının yedi fazlası 43 olduğunda, bilinmeyen x=9 olarak bulunur.","Hangi sayının 1/2 ile 3/5'in toplamı 110 olduğunda, bilinmeyen x=100 olarak hesaplanır.","Hangi sayının iki katının beş fazlası aynı sayının üç katının iki eksiğine eşit olduğunda, bilinmeyen x=7 olarak bulunur.","Üç katının sekiz eksiği, sayının dört fazlasının iki katına eşit olduğunda, bilinmeyen x=16 olarak hesaplanır.","İki duvar arasında duran dikdörtgenler prizması şeklindeki kutunun mavi duvara olan uzaklığı kırmızı duvara olan uzaklığın 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bilet alan kişi sayısı öğrenci bileti alan kişi sayısına eşit ve öğretmen bileti alanların sayısı tam bilet alanların sayısının yarısıdır.","Tam bilet adet sayısına 2x, öğrenci bilet adet sayısına 2x, öğretmen bilet adet sayısına x olarak belirlenir.","Toplam para hesaplanarak denklem kurulur ve x=100 olarak bulunur, yani öğretmen bilet alan kişi sayısı 100'dür."]},"beginTime":914,"endTime":1012,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=914&ask_summarization=1"},{"index":8,"title":"Gruplandırma Mantığı ve Merdiven Problemleri","list":{"type":"unordered","items":["Gruplandırma mantığı öğrenildi ve birçok yerde karşımıza çıkacak.","Merdiven inme çıkma problemlerinde değişmeyen şey merdivenin basamak sayısıdır.","Adım sayısını bulurken merdiven basamak sayısını kaçar kaçar çıktığınıza 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kurularak x/5 - x/2 = 15 denklemi çözülür ve merdivenin 50 basamaklı olduğu bulunur."]},"beginTime":1229,"endTime":1335,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=1229&ask_summarization=1"},{"index":11,"title":"Üçüncü Merdiven Problemi","list":{"type":"unordered","items":["Aslı bir merdivenin basamaklarını dışarı çıkıp üçer üçer iniyor ve inişte ve çıkışta attığı toplam adım sayısı basamak sayısından onbeş eksik.","Denklem kurularak (x/2 + x/3) / 6 = x - 15 denklemi çözülür ve Aslı'nın toplam 90 basamak attığı bulunur."]},"beginTime":1335,"endTime":1442,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=1335&ask_summarization=1"},{"index":12,"title":"Sıralara Oturma Problemleri","list":{"type":"unordered","items":["Sıralara oturma problemlerinde temel mantık, sınıftaki sıra sayısı ve öğrenci sayısının değişmemesidir.","Öğrenciler üçerli oturduğunda iki kişi ayakta kalıyorsa, denklem 3x + 2 şeklinde kurulur.","Öğrenciler ikişerli oturduğunda bir sıra boş kalıyorsa, denklem (x-1) × 2 şeklinde kurulur."]},"beginTime":1447,"endTime":1555,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=1447&ask_summarization=1"},{"index":13,"title":"Farklı Durumlarda Sıralara Oturma","list":{"type":"unordered","items":["Öğrenciler dörderli oturduğunda iki sıra boş kalıyor ve bir sırada üç öğrenci oturuyorsa, denklem (x-2) × 4 + 3 şeklinde kurulur.","Bir sınıfta öğrenciler üçerli otururlarsa beş kişi ayakta kalıyor, dörderli otururlarsa iki sıra boş kalıyorsa, denklem 3x + 5 = 4(x-2) şeklinde kurulur ve sonuç 44 öğrenci 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Kayma Mantığı","list":{"type":"unordered","items":["Homojen bir telin orta noktası, telin her yerinde eşit olduğu bir noktadır.","Bir telin bir ucundan kesildiğinde, orta nokta kesilen kısmın yarısı kadar ters yöne kayar.","Farklı uçlardan kesildiğinde, orta nokta kayma miktarı kesilen kısımların farkının yarısıdır."]},"beginTime":2056,"endTime":2121,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=2056&ask_summarization=1"},{"index":16,"title":"Orta Nokta Kayma Problemleri","list":{"type":"unordered","items":["Bir telin bir ucundan üçte biri kesildiğinde orta noktası eksi eski durumuna göre on santimetre kaydığında, telin ilk boyu altmış santimetredir.","Bir telin bir ucundan iki beş kesildiğinde orta noktası eski durumuna göre sekiz santimetre kaydığında, telin ilk boyu kırk santimetredir.","Bir telin bir ucundan üçte biri, diğer ucundan iki beş kesildiğinde orta noktası beş santimetre kaydığında, telin ilk boyu yüz elli santimetredir."]},"beginTime":2121,"endTime":2326,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=2121&ask_summarization=1"},{"index":17,"title":"Bölme ve Paylaştırma Mantığı","list":{"type":"unordered","items":["Bölme ve paylaştırma problemlerinde, bütün ifade kişi ya da grup sayısına bölünerek bir şey düşen parçalı bir durum oluşur.","Paylaştırma mantığı, bir dağıtım sonrası diğer kişilerin paylarını eşit olarak dağıtmasıdır.","Parçadan bütüne gitme mantığı, parçaların toplam uzunluğunun bütüne eşit olmasıdır."]},"beginTime":2326,"endTime":2441,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=2326&ask_summarization=1"},{"index":18,"title":"Zeytinyağı Problemi","list":{"type":"unordered","items":["Bir miktar zeytinyağı 0,75 litrelik şişelere doldurulduğunda, 1 litrelik şişelere doldurulsaydı 6 şişe daha az kullanılacaktı.","Problemin çözümünde litre ve adet olarak düşünülebilir, toplam zeytinyağı miktarı değişmez.","Denklem kurularak x adet 0,75 litrelik şişe için 0,75x = 1(x-6) şeklinde ifade edilir ve x=24 bulunur.","Toplam zeytinyağı miktarı 1 litre şişelere doldurulduğunda 18 litre olarak hesaplanır."]},"beginTime":2444,"endTime":2587,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=2444&ask_summarization=1"},{"index":19,"title":"Tahta Çubuk Problemi","list":{"type":"unordered","items":["Belirli bir uzunluktaki tahta çubuk, eşit uzunlukta 60 santimetrelik parçalara ayrılıyor.","Aynı tahta çubuk 80 santimetrelik parçalara ayrılsaydı 10 parça daha az olacaktı.","Problemin çözümünde x uzunluğuna sahip çubuğun 60 santimetrelik parçalara ayrıldığında x/60, 80 santimetrelik parçalara ayrıldığında x/80 şeklinde ifade edilir.","Denklem kurularak x=2400 santimetre (24 metre) bulunur."]},"beginTime":2587,"endTime":2796,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=2587&ask_summarization=1"},{"index":20,"title":"Dosya Paylaşımı Problemi","list":{"type":"unordered","items":["Bir işyerinde dosyalar eşit olarak paylaştırıldığında kişi başına 10 dosya düşmektedir.","İşyeri 3 kişide alınırsa kişi başına 9 dosya düşmektedir.","Problemin çözümünde x dosya sayısı ve x kişi sayısı için 10x = 9(x+3) denklemi kurulur.","Denklem çözülerek toplam 27 kişi ve 270 dosya olduğu bulunur."]},"beginTime":2796,"endTime":2969,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=2796&ask_summarization=1"},{"index":21,"title":"Dersin Sonu","list":{"type":"unordered","items":["Birinci günün ilk dersi bitirilmiştir.","İkinci derste kaldığı yerden devam edilecektir.","Sayı kesir problemlerine devam edilecektir."]},"beginTime":2969,"endTime":3003,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=2969&ask_summarization=1"},{"index":22,"title":"Sıra Kuyruk Problemleri","list":{"type":"unordered","items":["Sıra kuyruk problemlerinde kişilerin baştan sondan kaçıncı oldukları belirlendikten sonra arada olan kişilere göre kuyruktaki sayısı hesaplanır.","Kuyruktaki sayısı hesaplanırken \"baştan ve sondan kaç kişi varsa bunları toplayın, ikili sayılanlar çıkartın\" formülü kullanılır.","Kuyruk bir kişi üzerine kurulu ise formül \"baştan ve sondan kaç kişi varsa toplamından bir çıkartın\" şeklinde olur."]},"beginTime":3014,"endTime":3170,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=3014&ask_summarization=1"},{"index":23,"title":"Kuyruk Problemleri Örnekleri","list":{"type":"unordered","items":["Anıl baştan 20. sırada, sondan 12. sırada olduğuna göre kuyrukta toplam 31 kişi vardır.","Eda baştan 3. sırada, Melike sondan 21. sırada ve aralarında 6 kişi olduğuna göre kuyrukta en az 32 kişi vardır.","Ben baştan 4. sırada, sondan 6. sırada olduğuna göre kuyrukta 36 kişi vardır ve Ben baştan 28. sırada yer alır."]},"beginTime":3170,"endTime":3435,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=3170&ask_summarization=1"},{"index":24,"title":"Kafa Ayak Problemleri","list":{"type":"unordered","items":["Kafa ayak problemlerinde hayvanların ayak sayısı hesaplanırken \"hayvan sayısı × ayak sayısı\" formülü kullanılır.","Bir hayvanat bahçesinde 32 hayvanın bir kısmı at, diğerleri ördektir ve toplam ayak sayısı 104 olduğuna göre at sayısı 20'dir.","Tavşan ve tavuklardan oluşan bir kümelikte toplam ayak sayısı 30, kafa sayısı 10 olduğuna göre tavşan sayısı 5'tir."]},"beginTime":3435,"endTime":3639,"href":"/video/preview/13079770838565846500?parent-reqid=1769468608516763-15464531089380958755-balancer-l7leveler-kubr-yp-vla-156-BAL&text=Prob.+LEM&t=3435&ask_summarization=1"},{"index":25,"title":"Denklem Sistemi Çözümü","list":{"type":"unordered","items":["Beşli kalemler 12 TL, onlu kalemler 18 TL'ye satılıyor ve toplam 552 kalem satılıyor.","Toplam gelir 1200 TL olarak verilmiş ve bu durumda iki denklem sistemi kuruluyor.","Denklem sistemi çözülerek beşli paket sayısı 70 olarak 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