2022年工程问题教学设计 .pdf

学习好资料欢迎下载工程问题教学设计教学内容：例 7 教学目的：1.使学生认识工程问题的结构特点，掌握它的数量关系、解题思路和解题方法，并能正确地解答工程问题的基本题。2.培养学生解题的迁移能力，以及数学思维能力。教学准备：课件教学过程：一、导入：今天，老师让每位同学当公司经理，看哪位经理最精明。出示：假如你是某工程队的经理，要修一段路，现有甲、乙两个工程队，甲队单独修10 天完成，乙队单独修15 天完成。你想承包给哪个队？为什么？（学生分组讨论，派代表发言）师：仅考虑时间少行吗？师：有没有更好的方案呢？师：若甲乙两队合做，猜猜看，大约需要几天完工？师：我们不妨计算一下，具体是几天？从实际事例入手，学生成为“经理”，突出了学习的主动性。选择的素材紧密联系本课时的内容，学生在探讨解决问题的同时，兴趣盎然地进入学习新知的准备状态。二、教学例 9 学习好资料欢迎下载1 出示例 9：一段公路长 30千米（60 千米）用黑卡纸盖住，甲队单独修 10 天完成，乙队单独修15 天完成，两队合修几天修完？师：各位“经理”算一算，几天完成呢？谁能当个精明的“经理”呢？学生汇报计算的方法：30（3010+3015）=6（天）师：请你说说每步计算的含义。教师依次对应板书“甲的工效”“乙的工效”“工作总量”“合做时间”并小结数量关系式：工作总量工作效率和=合做时间师：如果把 30 千米改成 60 千米，其他条件不变，合做时间是多少呢？（揭去黑卡纸）生：60（6010+6015）=6（天）师：仔细比较这两道题，你发现了什么？生：无论公路长多少，只要各自单独做的时间不变，合做时间不变。师：是这样吗？同学们用不同的公路长度试一试。学生为了得到证实，即刻得出了结论。学生有了展现自我的机会，同时启发了学生探索数学奥秘的方法。师板书省略号师：为什么会这样呢？生 1：工作总量扩大了，工作效率也在扩大，而且扩大的倍数相同，所以时间不变生 2：无论公路长多少，甲乙两队每天修的各自占总长的几分之几没变，师：（擦去 30 千米和 60 千米）如果没有具体的公路长度，这题还能文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 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部分加一个条件，假如现有三个工程队，丙单独修需12天完成，想一想经理安排合做的方式有几种？每种合做方式各需几天？（只列式，不计算）（有 4 种，分别是甲乙合做，甲丙合做，乙丙合做，三队合做）哪种合做方式时间最少呢？请你把他们从时间少到时间多排列一下。（不计算）本题既巩固了新知，又渗透了简单的排列组合问题，同时让学生领悟工效与所用时间的关系。3 如果仅修这段路的一半，那么这几种合做方式各需几天呢？四、应用工程问题的解题方法，在生活中有着广泛的应用。1有一批布，如果只做西服的上衣可做20 件，只做西服的裤子可做 30 条，请你算一算，这批布可以做几套这样的西服？文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 ZV5P6D6N9V3文档编码:CQ5O1J8K6S8 HY3H5X1F2J6 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