如果我们能够对课本习题合理地运用变式,提出更深入的新问题,这样能加深对基础知识的理解和掌握.下面笔者对人教版数学教材九年级下册第31页习题7进行变式探究,供学习参考.课本原题:用一段长为30m的篱笆围成一个一边靠墙的矩形菜园,墙长为18m(如图1所示),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?分析:解决本题的关键是把求最大面积问题转化为求二次函数的最大值问题.应建立菜园面积与矩形的长或宽的函数关系式,从而求出使面积最大的长或宽的值.解:设平行于墙的矩形一边的长为xm,菜园面积 If we can make reasonable use of the textbook exercises variants, put forward more in-depth new issues, which can deepen the understanding and mastery of the basic knowledge below the textbook of People’s Education Jiu Xiaobian Volume 31 page 31 exercise 7 variants Explore, for learning reference. Textbook original title: with a length of 30m fence surrounded by a rectangular wall garden, the wall length of 18m (Figure 1), the length and width of the rectangle, Analysis: The key to solve this problem is to transform the problem of seeking the largest area into the problem of finding the maximum of quadratic function.We should establish the function of the length or width of the vegetable garden area and the rectangle, so as to find Out of the maximum length or width of the value. Solution: set parallel to the rectangle on the side of the wall length xm, vegetable garden area