配方法解一元二次方程

配方法解一元二次方程 “配方法解一元二次方程”说课 于晓静:北京市十一学校 中学高级 一、教材的地位和作用 配方法是以配方为手段、以平方根定义为依据解一元二次方程的一种基本方法，其中所涉及的完全平方式、求一个非负数的平方根以及解一元一次方程等都是学生已有的知识与技能，为本节课的学习奠定了知识技能方面的基础。 本节在此基础上，通过经历探索解方程的过程，使学生进一步体会转化、归纳等数学思想，总结配方法的基本步骤。 配方法是初中数学的重要内容，在二次根式、代数式的变形及二次函数中都有广泛应用，也 是进一步完善方程体系的有效载体。 二、教学目标 1 (知识与技能: ( 1)理解配方法的意义，会用配方法解数字系数的一元二次方程; ( 2)在学习的过程，体会配方法的运用， 进一步发展符号感，提高代数运算能力。 2 (过程与方法: 通过探索配方法的过程，让学生体会转化的数学思想方法。 3 (情感与态度: 学生在独立思考中感受探究的兴趣，并体验数学的价值， 促进形成学好数学的自信心。 三、教学重、难点 重点:配方并运用配方法解二次项系数为数字系数的一元二次方程。 难点:发现并理解配方的方法。 因本节课中研究的方程不具备直接开平方法的结构特点，需要合理添加条件进行转化，即 “配方 ”，所以 如何配方就成为本节课的学习重点与难点，如何找到对应的常数项成为解决问题的关键。 弄清楚配方法就是将方程变形为熟悉的能用直接开平方法求解的形式，在这里关键要掌握配方的方法，也就是配方法解一元二次方程的基本步骤，这是基本，也是关键。 四、教学过程 设计 领导形象设计圆作业设计ao工艺污水处理厂设计附属工程施工组织设计清扫机器人结构设计 根据本节课的教学目标，教学过程设计为以下五个环节: 环节一:引出新知; spacing of 100mm. C, line line line nearby. D, spare wire unified terminal strip Terminal (terminal strip at the top of the vertical, horizontal terminal strip from the harness to Terminal Pai end at the beginning), length to ensure as far as Terminal and set aside. After e, form a wire harness, cable, line. When the line should be in the core wire for better identification and marking on the cards will be prepared in advance, alternate core core content for the cable numbering. F, finish line, according to the corresponding terminal locations, wire one by one from the bunch out, pulling line, should be kept parallel to each other and more. Core dark as possible, determined in accordance with specific conditions, it is required that: neat, beautiful, shapely, pleasing to the eye. 7.6.2 wiring technology, out of the core wire according to Terminal position, cut off the excess, with wire stripping pliers or electrician knife stripped of insulation, so that connection. Stripping should not damage the copper core. B, core wire on the oxide and chip-insulated electricians knife scrape. C, core processing has been completed, thread round long nose pliers in a clockwise direction. Circle with the screw in the direction of spin in the same direction, circle should be appropriate, it is best to slightly larger than the screws, bent round the circle and the length of root and appropriate so set screw is screwed on tight. D, when on the crimp-type terminals when wiring, threads do not have to bend. Insulating part should be careful not to press it into a Terminal, and make the loop doesn't make sense and to prevent bad head crimping, fell down, causing an open circuit. After wiring, may be tried. E, crimping Terminal crimping, wire and Terminal contact is good, solid, not subject to mechanical strain, and ensure the insulation level. F, cables, such as when there is a bare copper ground wire, bare copper wire with a plastic pipe should be set. G, when wiring wiring must be in radians. H, terminal screws 环节二:探索与发现; 环节三:归纳与概括; 环节四:巩固与应用; 环节五:回顾与反思。 环节一:引出新知 通过问题 1:具有什么结构特征的一元二次方程能用直接开平方法解,你能举出这样的例子吗, 唤起学生的回忆，明确能用直接开平方法解的方程的特点是:等号左边是一个完全平方式，右边是一个非负常数，即 。这是后面配方转化的目标，也是对比研究的基础。 通过对问题 2中: ( 1) ;( 2) ;( 3) ;( 4) 这四个方程的观察与求解，让学生发现能用直接开平方法求解的方程都可以转化成一般形式，一般形式的方程也能逆向转化为可以直接开平方的形式，所以总结出解一元二次方程的基本思路是将 形式转为 的形式，而怎样转化就成为探索的方向，如何进行合理的转化则是下一步探究活动的核心。 环节二:探索与发现 这个环节是本节课的教学重点，共分为两部分。 第一部分，通过“做一做 ”引发学生思考，在二次项系数为 1的完全平方公式左边，常数项与一次项系数具有怎样的关系。以启发学生进行探究的形式展开，以小组合作探究的方式总结，目的是使学生能够体会并理解完全平方公式的特点，从而达到对配方法的完全理解，实现教学重点的理解和教学难点的突破。学生总结出规律后，然后通过完全平方公式给出证明，体现从特殊到一般的思维过程以及数学的严谨性。 spacing of 100mm. C, line line line nearby. D, spare wire unified terminal strip Terminal (terminal strip at the top of the vertical, horizontal terminal strip from the harness to Terminal Pai end at the beginning), length to ensure as far as Terminal and set aside. After e, form a wire harness, cable, line. When the line should be in the core wire for better identification and marking on the cards will be prepared in advance, alternate core core content for the cable numbering. F, finish line, according to the corresponding terminal locations, wire one by one from the bunch out, pulling line, should be kept parallel to each other and more. Core dark as possible, determined in accordance with specific conditions, it is required that: neat, beautiful, shapely, pleasing to the eye. 7.6.2 wiring technology, out of the core wire according to Terminal position, cut off the excess, with wire stripping pliers or electrician knife stripped of insulation, so that connection. Stripping should not damage the copper core. B, core wire on the oxide and chip-insulated electricians knife scrape. C, core processing has been completed, thread round long nose pliers in a clockwise direction. Circle with the screw in the direction of spin in the same direction, circle should be appropriate, it is best to slightly larger than the screws, bent round the circle and the length of root and appropriate so set screw is screwed on tight. D, when on the crimp-type terminals when wiring, threads do not have to bend. Insulating part should be careful not to press it into a Terminal, and make the loop doesn't make sense and to prevent bad head crimping, fell down, causing an open circuit. After wiring, may be tried. E, crimping Terminal crimping, wire and Terminal contact is good, solid, not subject to mechanical strain, and ensure the insulation level. F, cables, such as when there is a bare copper ground wire, bare copper wire with a plastic pipe should be set. G, when wiring wiring must be in radians. H, terminal screws 第二部分，设计了两道例题，第( 1)是二次项系数为 1的情况，第( 2)题是二次项系数不为 1的情况。通过对例( 1) 的分析，使学生明确对二次项系数是 1的一元二次方程，配方时要注意在方程两边都加上一次项系数一半的平方，同时 规范 编程规范下载gsp规范下载钢格栅规范下载警徽规范下载建设厅规范下载 配方法解方程时的一般步骤。 对于对例( 2)二次项的系数不为 1的一元二次方程的观察与分析，让学生思考解决的 办法 鲁班奖评选办法下载鲁班奖评选办法下载鲁班奖评选办法下载企业年金办法下载企业年金办法下载 ，通过把系数化为 1，将其转化为系数为 1的方程，目的是通过这样的思考让学生把新知识及时纳入到原有的认知结构中，并能认识到新知识可以通过旧知识的转化得到。 在这两道例题的分析过程中，特别注意了每一步的方法及依据是什么，让学生明确是怎样一步步实现配方的，并理解每一步的算理是什么。 例( 1) ;( 2) ( 1) ( 2) 解: spacing of 100mm. C, line line line nearby. D, spare wire unified terminal strip Terminal (terminal strip at the top of the vertical, horizontal terminal strip from the harness to Terminal Pai end at the beginning), length to ensure as far as Terminal and set aside. After e, form a wire harness, cable, line. When the line should be in the core wire for better identification and marking on the cards will be prepared in advance, alternate core core content for the cable numbering. F, finish line, according to the corresponding terminal locations, wire one by one from the bunch out, pulling line, should be kept parallel to each other and more. Core dark as possible, determined in accordance with specific conditions, it is required that: neat, beautiful, shapely, pleasing to the eye. 7.6.2 wiring technology, out of the core wire according to Terminal position, cut off the excess, with wire stripping pliers or electrician knife stripped of insulation, so that connection. Stripping should not damage the copper core. B, core wire on the oxide and chip-insulated electricians knife scrape. C, core processing has been completed, thread round long nose pliers in a clockwise direction. Circle with the screw in the direction of spin in the same direction, circle should be appropriate, it is best to slightly larger than the screws, bent round the circle and the length of root and appropriate so set screw is screwed on tight. D, when on the crimp-type terminals when wiring, threads do not have to bend. Insulating part should be careful not to press it into a Terminal, and make the loop doesn't make sense and to prevent bad head crimping, fell down, causing an open circuit. After wiring, may be tried. E, crimping Terminal crimping, wire and Terminal contact is good, solid, not subject to mechanical strain, and ensure the insulation level. F, cables, such as when there is a bare copper ground wire, bare copper wire with a plastic pipe should be set. G, when wiring wiring must be in radians. H, terminal screws 环节三:归纳与概括 在完成上述探究活动后，提出问题 4、 5，引导学生回顾探究过程，进行阶段性小结。明确配方的目的是通过配成完全平方形式来解方程。对二次项系数不是 1的一元二次方程，配方时要注意首先把二次项系数化 1，然后两边都加上一次项系数一半的平方。 问题 4:配方的目的是什么,配方时应注意什么, 问题 5:通过上述题目，你能归纳出配方法求一元二次方程的步骤吗, ( 1)二次项系数化 1; ( 2)常数项移到方程右侧; ( 3)方程左右两边同时加上一次项系数一半的平方; ( 4)配成完全平方的形式; ( 5)利用直接开平方法求解。 环节四:巩固与应用 在此环节中设计了两个练习，练习 1通过辨析几个一元二次方程的解法，找出出错的原因，加深对配方法过程的理解。 spacing of 100mm. C, line line line nearby. D, spare wire unified terminal strip Terminal (terminal strip at the top of the vertical, horizontal terminal strip from the harness to Terminal Pai end at the beginning), length to ensure as far as Terminal and set aside. After e, form a wire harness, cable, line. When the line should be in the core wire for better identification and marking on the cards will be prepared in advance, alternate core core content for the cable numbering. F, finish line, according to the corresponding terminal locations, wire one by one from the bunch out, pulling line, should be kept parallel to each other and more. Core dark as possible, determined in accordance with specific conditions, it is required that: neat, beautiful, shapely, pleasing to the eye. 7.6.2 wiring technology, out of the core wire according to Terminal position, cut off the excess, with wire stripping pliers or electrician knife stripped of insulation, so that connection. Stripping should not damage the copper core. B, core wire on the oxide and chip-insulated electricians knife scrape. C, core processing has been completed, thread round long nose pliers in a clockwise direction. Circle with the screw in the direction of spin in the same direction, circle should be appropriate, it is best to slightly larger than the screws, bent round the circle and the length of root and appropriate so set screw is screwed on tight. D, when on the crimp-type terminals when wiring, threads do not have to bend. Insulating part should be careful not to press it into a Terminal, and make the loop doesn't make sense and to prevent bad head crimping, fell down, causing an open circuit. After wiring, may be tried. E, crimping Terminal crimping, wire and Terminal contact is good, solid, not subject to mechanical strain, and ensure the insulation level. F, cables, such as when there is a bare copper ground wire, bare copper wire with a plastic pipe should be set. G, when wiring wiring must be in radians. H, terminal screws 练习 2中，师生共同关注一元二次方程中一次项系数不同时，对于配方规律的进一步运用。通过解一次项系数分别是正偶数、负奇数、负分数的一元二次方程，层层深入地加深对配方规律的认识。( 3)( 4)两个题目练习二次项系数不为 1的情况，巩固利用配方法解方程的基本技能。 练习 1:认真观察下面方程的解法是否正确 练习 2:用配方法解方程 (1) ; (2) ; (3) ; (4) ; (5) 环节五:回顾与反思 围绕以下三个问题，让学生展开讨论: 1 (这节课我们学习了什么数学方法, 2 (我们获得这个方法，经历了怎样的过程, 3(通过这个过程，你有什么感受和体会, 这样的小结正是基于对三维教学目标的设计。从知识与技能、过程与方法、情感与态度三个立体的维度对本节课进行系统的回顾。对自身思维过程的反思，是我们获得数学基本活动经验的重要途径。 spacing of 100mm. C, line line line nearby. D, spare wire unified terminal strip Terminal (terminal strip at the top of the vertical, horizontal terminal strip from the harness to Terminal Pai end at the beginning), length to ensure as far as Terminal and set aside. After e, form a wire harness, cable, line. When the line should be in the core wire for better identification and marking on the cards will be prepared in advance, alternate core core content for the cable numbering. F, finish line, according to the corresponding terminal locations, wire one by one from the bunch out, pulling line, should be kept parallel to each other and more. Core dark as possible, determined in accordance with specific conditions, it is required that: neat, beautiful, shapely, pleasing to the eye. 7.6.2 wiring technology, out of the core wire according to Terminal position, cut off the excess, with wire stripping pliers or electrician knife stripped of insulation, so that connection. Stripping should not damage the copper core. B, core wire on the oxide and chip-insulated electricians knife scrape. C, core processing has been completed, thread round long nose pliers in a clockwise direction. Circle with the screw in the direction of spin in the same direction, circle should be appropriate, it is best to slightly larger than the screws, bent round the circle and the length of root and appropriate so set screw is screwed on tight. D, when on the crimp-type terminals when wiring, threads do not have to bend. Insulating part should be careful not to press it into a Terminal, and make the loop doesn't make sense and to prevent bad head crimping, fell down, causing an open circuit. After wiring, may be tried. E, crimping Terminal crimping, wire and Terminal contact is good, solid, not subject to mechanical strain, and ensure the insulation level. F, cables, such as when there is a bare copper ground wire, bare copper wire with a plastic pipe should be set. G, when wiring wiring must be in radians. H, terminal screws