基本不等式教学设计(2)

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application preliminary knowleoblem of key is: according to meaniphing, (1) determine standard volume (units \n in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of com measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry prdge (2)--plane gracs review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and arehea combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relatimon units ofonship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和值为4。

以上命题均是根据基本不等式的使用条件中的难点和关键处设置的，目的是利用学生原有的平面几何知识，进一步领悟到不等式ab?a?b成立的条件2a?0,b?0，及当且仅当a?b时，等号成立。这些“陷阱”要让学生自己往里跳，

然后自己再从中爬出来，完全放手让学生自主探究，老师指导，师生归纳总结。

结论：

若两正数的乘积为定值，则当且仅当两数相等时，它们的和有最小值； 若两正数的和为定值，则当且仅当两数相等时，它们的乘积有最大值。 简记为：“一正、二定、三相等”。

五、领悟练习：

公式应用之一：

(1)若x?0,x?1的最小值为________,此时x?_________. x(1) 若a>0,b>0,且a+b=2,则ab的最大值为_______,此时a=_____,b=_____。

公式应用之二：（最优化问题）

设计意图：新颖有趣、简单易懂、贴近生活的问题,不仅极大地增强学生的兴趣，拓宽学生的视野，更重要的是调动学生探究钻研的兴趣，引导学生加强对生活的关注，让学生体会：数学就在我们身边的生活中

(1) 在学农期间，生态园中有一块面积为100m2的矩形茶地，为了保护茶叶的健康生长，学校决定用篱笆围起来，问这个矩形的长、宽各为多少时，所用篱笆最短。最短的篱笆是多少？

(2)现在学校仓库有一段长为36m的篱笆，要围成一个矩形菜园，问这个矩形的长、宽各为多少时，菜园的面积最大。最大面积是多少？

六、反思总结，整合新知：

通过本节课的学习你有什么收获？取得了哪些经验教训?还有哪些问题需要请教？

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units \hen in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和《基本不等式》教学设计

设计意图：通过反思、归纳，培养概括能力；帮助学生总结经验教训，巩固知识技能，提高认知水平.

老师根据情况完善如下：

一个不等式：若a?0,b?0，则有ab?a?b。 2a?b，当且仅当a=b时，2ab?两种思想：数形结合思想、归纳类比思想。

三个注意：基本不等式求函数的最大(小)值是注意：“一正二定三相等”

七、布置作业：P114习题1.2.3

八、课下思考：类比基本不等式，当a,b,c均为正数，猜想会有怎样的不等

式？

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