人教版高中数学《二项式定理》教案.doc

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1、人教版高中数学二项式定理教案113 二项式定理（第1课时）教学目标：1、掌握二项式定理及二项展开式的通项公式，并能熟练地进行二项式的展开及求解某些指定的项.2、通过探索二项式定理，培养学生观察问题、发现问题、归纳推理问题的能力.3、激发学生学习兴趣，培养学生不断发现、探索新知的精神，渗透事物相互转化和理论联系实际的辩证唯物主义观点，并通过数学的对称美，培养学生的审美意识.重点：二项式定理的推导及运用难点：二项式定理及通项公式的运用教学过程：（一）创设情境，激发兴趣提出问题：“今天是星期六，你能很快知道再过810天的那一天是星期几吗？”（二）问题初探请同学们运用多项式的乘法法则写出（a+b）2、

2、（a+b）3、（a+b）4的展开式：(a+b)2= ;(a+b)3= ;(a+b)4= ;用这种方法写出（a+b）10的展开式容易吗？（a+b）100、（a+b）n呢？对于这个问题，我们如何解决？（三）理性探究通过对（a+b）2、（a+b）3、（a+b）4的展开式的观察，进行下列四个方面的探究： 项数； 各项次数； 字母a、b指数的变化规律； 各项系数（四）归纳、猜想通过对（a+b）2、（a+b）3、（a+b）4三个展开式探究，归纳得出（a+b）n展开式有如下特性：（1）共有 项；（2）各项的次数都等于 ；（3）字母a的指数由 递减到 ；同时字母b的指数由 递增到 ；（4）各项的系数依次为 。

3、猜想：（五）几个概念、通项；、二项式系数与项的系数；（六）尝试应用、回到引例：今天是星期六，你能很快知道再过810天的那一天是星期几吗？、例题展示例1：（1）展开； （2）展开思考：两个展开式有什么不同？例2：化简：。例3：求的展开式的第5项。变式： （1）求展开式的常数项；（2）求展开式的有理项；（3）求展开式中含项；例4: 求（x+3y-z）8展开式中含x2y3z3的项的系数。（七）课堂练习1、课本：1、2、3、42、求 的展开式的第3项。（八）课堂小结（由学生自己归纳总结，教师补充）（九）作业布置1、必做题：习题1.3：2、3、42、选做题：在的展开式中，的系数是什么？结束语！祝大家学到

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