2022年2018春人教版数学九年级下册26.2《实际问题与反比例函数》教案 .pdf

名师精编优秀教案262实际问题与反比例函数教学目标知识技能1能根据实际问题确定变量之间的反比例关系，并求出反比例函数解析式2能灵活运用反比例函数的意义和性质解决相关的实际问题3能综合运用几何、方程、不等式、反比例函数的知识以及物理等跨学科知识解决相关的实际问题数学思考与问题解决1经历观察、分析实际问题中变量之间的关系，建立反比例函数模型，进一步体会数学建模思想2体会数学与现实生活(包括物理世界)的紧密联系，能从现实情境中提出问题，增强学生应用数学解决实际问题的意识3经历“实际问题 建立模型 求解模型 拓展应用”的过程，增强学生发现和提出问题、分析和解决问题的能力情感态度1体验反比例函数是有效地描述现实世界的重要手段，认识到数学是解决实际问题和进行交流的重要工具2体验数学的实用性，提高学习数学的兴趣重点难点重点：从实际问题中构建反比例函数模型，运用反比例函数的意义和性质解决实际问题难点：从实际问题中寻找变量之间的关系，建立函数模型教学设计一、复习引入1反比例函数y12x的图象形状、位置、增减性是怎样的？当x3 时，y _；当 y3 时，x_.2结合一个反比例函数实例，说说反比例函数两个变量之间的关系设计意图：进一步熟悉反比例函数的图象和性质，理解反比例函数两个变量之间的依存名师精编优秀教案关系，为例题学习做好准备二、例题评析师：生活中存在着大量的反比例函数的现实问题这节课我们学习“实际问题与反比例函数”，你会发现有了反比例函数，很多实际问题解决起来会很方便例 1(教材第 12 页例 1)教师重点关注：(1)能否从实际问题中抽象出反比例函数模型；(2)能否利用函数模型解释实际问题中的现象；(3)能否积极主动阐述自己的见解例 2(教材第 13 页例 2)分析：(1)根据“货物的总量平均卸货速度卸货时间”，可以求出货物总量k；再根据“平均卸货速度货物的总量 卸货时间”，求出v 和 t 之间的函数解析式为v240t.(2)根据关键词“不超过”“至少”，可用多种方法解答方法 1：由 v240t得 t240v，因为 t 5，所以240v5，又因为 v0，所以 2405v，解得 v48.方法 2：画出函数 v240t(t0)的图象，如图，当 t 5时，v48.根据反比例函数的性质，在第一象限内，v 随 t 的增大而减小，所以当0t 5 时，v 48.方法 3：把 t5 代入 v240t，得 v240548.若全部货物恰好5 天卸完，则平均每天要卸货 48 吨因此，若货物在不超过5 天内卸完，则平均每天至少要卸货48 吨设计意图：鼓励学生从不等式、函数图象、方程等多个角度思考问题，渗透数形结合思想，进一步理解不等式、函数、方程之间的联系 教师重点关注学生能否自己建构函数模型，能否把关键词“不超过”“至少”正确转化为“符号”，进而将函数、方程、不等式的知识联系起来，学会多策略解决问题例 3(教材第 15 页例 4)文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 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ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3名师精编优秀教案提问 1：电学知识告诉我们，用电器的功率P(单位：W)、电阻 R(单位：)、两端的电压 U(单位：V)有如下关系：PR_，也可写为P_，或 R_.提问 2：结合例3，想一想为什么收音机的音量、台灯的亮度、风扇的转速可以调节？音量、亮度、转速随_的减小而增大，随_的增大而减小提问 3：“给我一个支点，我可以把地球撬动”这是哪一位科学家的名言？蕴涵着什么样的原理？提问 4：你能利用“杠杆原理”解决问题吗？出示例4(课件展示教材第14 页例 3)提问 5：用反比例函数知识解释：在我们使用撬棍时，为什么动力臂越长就越省力？设计意图：通过物理学科中已学过的电学公式，建立公式与反比例函数的联系，解决生活中熟悉的有关问题，进而解释音量、亮度、转速大小变化的原因由于八年级物理已经学习了“杠杆原理”，且原理本身学生容易掌握，所求问题与例2 类似，因此把教材例3置于例 4 之后，并做“提问 3、4”处理，避免例题的重复，同时让学生进一步领会反比例函数在物理学中的综合应用，感受用数学的视角解释生活中的物理现象，体现跨学科知识的魅力三、课堂练习1教材第15 页练习2你还能举出生活中可以用反比例关系解释的例子吗？四、反思小结这节课你有什么收获？用反比例函数解决实际问题一般有哪些程序？用反比例函数解决实际问题的一般程序：审题：弄清题意，分清条件和结论，理顺数量关系；建模：将文字语言转化为数学语言，利用反比例函数等知识，建立数学模型；解模：求解数学模型，得出数学结论；还原：将用数学知识和数学方法求解得出的结论，还原为实际问题的结果五、布置作业1必做题：教材第16 至 17 页第 5，6，7 题2选做题：教材第17 页第 8，9 题板书设计文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 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阻力阻力臂动力动力臂小结：用反比例函数解决实际问题的一般程序文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 HW7I1S2Z5J9 ZQ5C5U8I4V3文档编码:CD10C6V4M3O5 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