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在进行一元二次方程这一章教学时,笔者先让学生用一张长80cm,宽60cm的硬纸板,在四个角上截去相同的小正方形,做成底面积为1500cm2的没盖的长方体盒子,想一想要如何做呢?首先学生要分析计算出小正方形的边长,才能动手制作,于是设小正方形边长为xcm,列出方程(80-2x)(60-2x)=1500,整理得x2-70x+825=0,如何解呢?教师提示:按解一元一次方程的常规思路,应该移项,得:x2-70x=-825,思路再次受阻,教师提醒:左边可以分解因式吗?大部分学生会分解因式把原式变为x(x-70)=-825,教师引导若能把-825分解成两个相差70的两数的乘积,
When conducting the teaching of one-quadratic equation in this chapter, I first asked the students to use a piece of cardboard with a length of 80 cm and a width of 60 cm to cut off the same small square on the four corners and make a cover with an area of 1500 cm 2 First of all, students need to analyze and calculate the side length of a small square, in order to start production, then set the small square side length xcm, list the equation (80-2x) (60-2x) = 1500, finishing x2-70x +825 = 0, how to solve it? Teacher Tip: According to the conventional idea of solving a one dollar equation, should be moved, too: x2-70x = -825, thinking again blocked, the teacher reminds: the left can Decomposition factor? Most students will factor into the original to become x (x-70) = -825, the teacher guide if the -825 can be divided into two products of two different by 70,