توضیحات
احتمال ریاضی پنجم صفحه ی Riazifilm.ir 137
آموزش آمار و احتمال ـ آموزش میانگین ـ آموزش احتمال
نظریهٔ احتمال مطالعهٔ رویدادهای احتمالی از دیدگاه ریاضیات است. بعبارت دیگر، نظریه احتمال به شاخهای از ریاضیات گویند که با تحلیل وقایع تصادفی سروکار دارد. هسته تئوری احتمال را متغیرهای تصادفی و فرایندهای تصادفی و پیشامدها تشکیل میدهند. نظریه احتمال علاوه بر توضیح پدیدههای تصادفی به بررسی پدیدههایی میپردازد که لزوماً تصادفی نیستند ولی با تکرار زیاد دفعات آزمایش نتایج از الگویی مشخص پیروی میکنند، مثلاً در آزمایش پرتاب سکه یا تاس با تکرار آزمایش میتوانیم احتمال وقوع پدیدههای مختلف را حدس بزنیم و مورد بررسی قرار دهیم. نتیجه بررسی این الگوها قانون اعداد بزرگ و قضیه حد مرکزی است.
نخستین کتابها را دو دانشمند ایتالیایی دربارهٔ بازی با تاس نوشتند: جه رولاموکاردان و گالیلئو گالیله. با این همه باید آغاز بحث دقیق دربارهٔ احتمال را سده هفدهم و با کارهای بلز پاسکال و پیر فرما، ریاضیدانان فرانسوی و کریستین هویگنس هلندی دانست. پاسکال و فرما کتابی در این باره ننوشتند و تنها در نامههای خود به دیگران دربارهٔ کاربرد آنالیز ترکیبی در مسئلههای مربوط به شانس صحبت کردهاند، ولی هویگنس کتابی با نام بازی با تاس نوشت که اگر چه با کتاب کاردان هم نام است ولی از نظر تحلیل علمی در سطح بسیار بالاتری است. کار آنان توسط یاکوب برنولی و دموآور در قرن هجدهم میلادی ادامه یافت، برنولی کتاب روش حدس زدن را نوشت و قانون عددهای بزرگ را کشف کرد.
احتمال ریاضی پنجم Riazifilm.ir
اهداف درس احتمال ریاضی پنجم
۱ــ یادآوری مفهوم احتمال و واژههای مرتبط با آن
۲ــ توانایی بیان در امکان رخ دادن یک اتفاق به کمک واژه ها و با توجه به تجربه های قبلی
۳ــ آشنایی با مفهوم آزمایش و مفهوم تکرارهای زیاد یک آزمایش
۴ــ آشنایی با بازی های شانسی عادلانه و ناعادلانه و توانایی تشخیص عادلانه یا ناعادلانه بودن بازی های شانسی ساده
ابزارهای مورد نیاز:
۱ــ تاس
۲ــ سکه
۳ــ چرخنده
۴ــ مهره یا دکمه های رنگی و پاکت
۵ــ کاغذ شطرنجی
در کار در کلاس ۱ درس احتمال ریاضی پنجم چند بازی ساده تر معرفی شده اند.
بازی الف) عادلانه است. بازی ب) عادلانه نیست. در بازی عادلانه (پ) اگر عقربه روی رنگ دیگری بایستد، بازی بدون برنده است. بازی (ت) ناعادالنه است.
کار در کلاس ۲ هم به توسعه به مفهوم پرداخته است. این کار در کلاس پاسخ های مختلفی دارد. (۱۰ آبی، ۱۰ سبز)، اولین پاسخی است که به ذهن می رسد، اما پاسخ (۵ آبی، ۵ سبز، ۱۰ قرمز) هم میتواند یکی از پاسخهای درست باشد.
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