伤城文章网 > 其它课程 > 2010年第五届卡西欧杯全国高中青年教师优秀课观摩与评比活动教案-《正弦、余弦函数的周期性》教案(广东彭

2010年第五届卡西欧杯全国高中青年教师优秀课观摩与评比活动教案-《正弦、余弦函数的周期性》教案(广东彭


Learn G eneral Se cretary on "two t o learn a" strengt heni ng "four Cons cious nesse s" important spee ch caused a str ong reacti on i n the country. T ime, watching "red treasure", the origi n of buildi ng the party back t o power, how to strengthe n servi ces for the masses, im prove party cohesion, fig hting to be come t he grass -root s party members a nd mas ses hot topi c. Gras s-r oots party organizati ons "two" is to strengthen the service of party members a nd cadres, t he pi one er spirit . Distribution of grass -root s party organi zations in all wa lks of pe ople , clot hing , she lter, w hich bel ongs t o the ner ve endi ngs of the party organizati on a nd comments re putation ha s a dire ct perception of the mas ses. Strengthen the party ahe ad of the "pe dal" spirit; strengt hen the party members a nd cadres "s uccess doe s not have to be me" and "the first to bear hards hips, the la st to" service spirit to s e t the party's positive im age among the people is important. Gras s-r oots party organizati ons "two" is to clea nse all people not happy not to see "stere otypes", esta blis h the hone st faithful, dilige nt faith for the pe opl e. No nee d to avoi d mentioning t hat, some members of our party ca n not sta nd t he "mone y," corrosion of temptation, thin, Xu Z hou, s uch abuse and corrupt bribery, malfeasa nce borers , and ra ts. Two, is to cl ean up, thi n, Xu, Zhou' s sol ution to restore t he party's fresh a nd natural, s oli d and honest w ork style. Cleansing "take, eat, card," undes irable a nd behavi our, "cros s, har d and col d, pus h" attitude. Gras s-r oots party organizati ons "two" is to strengt hen the sense of or dinary party members, parti cipati ng in consci ous nes s, unity cons ciousne ss. For rea sons known, mem bers of grass -roots party bra nches les s mobile, les s resource s, and the constructi on of party organizati ons have s ome lag. Two st udie s, is to focus on the grass -roots party branche s "loose, s oft, loos e" problem, advance the party members a nd ca dres, "a gang w orking", "Hong Kong report." Strong cleanup acti ons, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" r eal unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

正弦、余弦函数的周期性教案
广东省东莞中学松山湖学校 彭 科

一、教材分析: 《正弦、 余弦函数的周期性》 是普通高中课程标准实验教科书必修四第一章第四节第二 节课,其主要内容是周期函数的概念及正弦、余弦函数的周期性.本节课是学生学习了诱导 公式和正弦、余弦函数的图象之后,对三角函数知识的又一深入探讨.正弦、余弦函数的周 期性是三角函数的一个重要性质,是研究三角函数其它性质的基础,是函数性质的重要补 充.通过本课的学习不仅能进一步培养学生的数形结合能力、推理论证能力、分析问题和解 决问题的能力, 而且能使学生把这些认识迁移到后续的知识学习中去, 为以后研究三角函数 的其它性质打下基础.所以本课既是前期知识的发展,又是后续有关知识研究的前驱,起着 承前启后的作用. 二、教学目标: 学情分析: 学生在知识上已经掌握了诱导公式、正弦、余弦函数图象及五点作图的方法;在能力上 已经具备了一定的形象思维与抽象思维能力; 在思想方法上已经具有一定的数形结合、 类比、 特殊到一般等数学思想. 本课的教学目标: (一)知识与技能 1.理解周期函数的概念及正弦、余弦函数的周期性. 2.会求一些简单三角函数的周期. (二)过程与方法 从学生生活实际的周期现象出发,提供丰富的实际背景,通过对实际背景的分析与 y=sinx 图形的比较、概括抽象出周期函数的概念.运用数形结合方法研究正弦函数 y=sinx 的 周期性,通过类比研究余弦函数 y=cosx 的周期性. (三)情感、态度与价值观 让学生体会数学来源于生活,体会从感性到理性的思维过程,体会数形结合思想;让学 生亲身经历数学研究的过程,享受成功的喜悦,感受数学的魅力. 三、教学重点:周期函数的定义和正弦、余弦函数的周期性. 四、教学难点:周期函数定义及运用定义求函数的周期. 五、教学准备:三角板、多媒体课件 六、教学流程: 创设问题 情境引入 复习回顾 引入新知 构建周期 函数定义

正弦函数 的周期

巩固周期 函数定义

余弦函数 的周期

课堂 小结

课堂 反馈

知识 应用

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n t he "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely diff erent, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "d o" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, p ut for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long -term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvem ent. T he same, only party members and

Learn G eneral Se cretary on "two t o learn a" strengt heni ng "four Cons cious nesse s" important spee ch caused a str ong reacti on i n the country. T ime, watching "red treasure", the origi n of buildi ng the party back t o power, how to strengthe n servi ces for the masses, im prove party cohesion, fig hting to be come t he grass -root s party members a nd mas ses hot topi c. Gras s-r oots party organizati ons "two" is to strengthen the service of party members a nd cadres, t he pi one er spirit . Distribution of grass -root s party organi zations in all wa lks of pe ople , clot hing , she lter, w hich bel ongs t o the ner ve endi ngs of the party organiza ti on a nd comments re putation ha s a dire ct perception of the mas ses. Strengthen the party ahe ad of the "pe dal" spirit; strengt hen the party members a nd cadres "s uccess doe s not have to be me" an d "the first to bear hards hips, the la st to" service spirit to s e t the party's positive image among the people is important. Gras s-r oots party organizati ons "two" is to clea nse all people not happy not to see "stere otypes", esta blis h the hone st faithful, dilige nt faith for the pe opl e. No nee d to avoi d mentioning t hat, some members of our party ca n not sta nd t he "mone y," corrosion of temptation, thin, Xu Z hou, s uch abuse and corrupt bribery, mal feasa nce borers , and rats. Two, is to cl ean up, thi n, Xu, Zhou' s sol ution to restore t he party's fresh a nd natural, s oli d and honest w ork style. Cleansing "take, eat, card," undes irable a nd behavi our, "cros s, har d and col d, pus h" attitude. Gras s-r oots party organizati ons "two" is to strengt hen the sense of or dinary party members, parti cipati ng in consci ous nes s, unity cons ciousne ss. For rea sons known, members of grass -roots party bra nches les s mobile, les s resource s, and the constructi on of party organizati ons have s ome lag. Two st udie s, is to focus on the grass -roots party branche s "loose, s oft, loos e" problem, advance the party mem bers a nd ca dres, "a gang w orking", "Hong Kong report." Strong cleanup acti ons, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

七、教学过程: 预 计 时 间 教学程序 (分) 创设问题 情境引入

教师活动 问 : 生活中有哪些周而复始 现象? 问:数学中有哪些周期现象?

学生活动

备注 从生活中的 周期现象引 入, 激发学生 的学习兴趣.

学生举例

1 分钟

2 分钟

复习回顾

引导学生回顾: 1.诱导公式(一) 2.正弦线 3.利用正弦线画正弦函数 图象(动画演示).

引导学生回 学生回顾诱导公式 (一) 顾旧 知为本课 做准备. 学生观察动画演示 通过动画演 示让 学生直观 感知 周而复始 的变化规律.

问:正弦函数 y=sinx 图象有 什么特征? 问: 图象呈周期性变化怎样
10 分钟

构建周期 函数定义

用数学表达式表示? (让学生再次观察动画演示) 正弦函数图象的周而复始 的变化实际上就是函数值 的周而复始的变化. sin(2π +x)=sinx 这个结论可 由图象观察分析得到,也可 由诱导公式得到. 问: 对于 sin(2π +x)=sinx, 若记 f(x)=sinx,则对于任意 x∈R,都有 f( )=f( ) 给 出 周期 函数 及 周期 的定义.

通过对正弦 函数 y=sinx 图 得:正弦函数图象具有 象观察、分析, 周而复始的变化规律 结合诱导公 式, 构建出周 答:即 sin(2π +x)=sinx, 期函数的定 由诱导公式也可得: 义, 主要是立 sin(2π +x)=sinx, 足于 从学生的 最近 思维区入 手, 着力于知 抽象概括: 识建 构,培养 设 f(x)=sinx,则对于任意 学生 观察、分 x∈R,都有 f(x+2π )=f(x). 析和 抽象概括 周期函数定义: 能力 , 并进一步 一般地,对于函 渗透 数形结合 数 f(x),如果存在 思想方法. 一个非零的常数 T, 使得定义域内的每一 个 x 值,都满足 f(x+T)=f(x), 那么函 数 f(x)就叫做周期 函数,非零常数 T 叫 做这个函数的周期. 答:由动画演示观察可

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo-w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir v alue. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long -term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the countr y, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the gr ass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members and

Learn G eneral Se cretary on "two t o learn a" strengt heni ng "four Cons cious nesse s" important spee ch caused a str ong reacti on i n the country. T ime, watching "red treasure", the origi n of buildi ng the party back t o power, how to strengthe n servi ces for the masses, im prove party cohesion, fig hting to be come t he grass -root s party members a nd mas ses hot topi c. Gras s-r oots party organizati ons "two" is to strengthen the service of party members a nd cadres, t he pi one er spirit . Distribution of grass -root s party organi zations in all wa lks of pe ople , clot hing , she lter, w hich bel ongs t o the ner ve endi ngs of the party organiza ti on a nd comments re putation ha s a dire ct perception of the mas ses. Strengthen the party ahe ad of the "pe dal" spirit; strengt hen the party members a nd cadres "s uccess doe s not have to be me" and "the first to bear hards hips, the la st to" service spirit to s e t the party's positive image among the people is important. Gras s-r oots party organizati ons "two" is to clea nse all people not happy not to see "stere otypes", esta blis h the hone st faithful, dilige nt faith for the pe opl e. No nee d to avoi d mentioning t hat, some members of our party ca n not sta nd t he "mone y," corrosion of temptation, thin, Xu Z hou, s uch abuse and corrupt bribery, malfeasa nce borers , and rats. Two, is to cl ean up, thi n, Xu, Zhou' s sol ution to restore t he party's fresh a nd natural, s oli d and honest w ork style. Cleansing "take, eat, card," undes irable a nd behavi our, "cros s, har d and col d, pus h" attitude. Gras s-r oots party organizati ons "two" is to strengt hen the sense of or dinary party members, parti cipati ng in consci ous nes s, unity cons ciousne ss. For rea sons known, members of grass -roots party bra nches les s mobile, les s resource s, and the constructi on of party organizati ons have s ome lag. Two st udie s, is to focus on the grass -roots party branche s "loose, s oft, loos e" problem, advance the party members a nd ca dres, "a gang w orking", "Hong Kong report." Strong cleanup acti ons, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

预 计 时 间 教学程序 (分) 正弦函数 的周期和 最小正周 期 的 定 义.

教师活动 问: 正弦函数的周期为多少? 答:

学生活动

备注

…… 2? 、4? 、6? 、

2 分钟

2kπ (k∈Z 且 k≠0)都是 它的周期. 问: 在正弦函数的周期中, 最小正数是多少? 给出最小正周期的定义. 判断题: 1. 因 为 sin(? ? ? ) ? sin ? , 4 2 4 所以 ? 是 y ? sin x 的周期.
2

答:

2?

让学 生理解最 小正 周期的定 义. 培养学生的 数形结合能力

答:1.错 举反例:
sin(

?
3

?

?
2

) ? sin

?
3

9 分钟

巩固周期 函数定义

2.周期函数的周期唯一. 3.常数函数 f(x)=5 是周期函 数. (分四人一组进行讨论 ,再 由学生发表看法.)

引导学生做完判断题后谈 一谈体会.

2. 错(结合正弦函数周 期分析) 3.对(结合定义分析) 学生谈体会: 1. 周期的定义是对定 义域中的每一个 x 值来 说的. 2.周期函数的周期不唯 一. 3.周期函数不一定存在 最小正周期. 说明 : 今后不加特殊说 明,涉及的周期都是最 小正周期.

为了帮助 学生 正确理解 周期函数概 念, 防止学生 以偏 概全,让 学生 学会怎样 学习 概念;培 养学 生透过现 象看 本质的能 力, 使学生养 成细 致、全面 地考 虑问题的 思维品质.让 学生 在讨论交 流中 不断完善 自己 的认知结 构, 充分感受 成功 与失败的 情感体验. 通过对定 义的 理解、余 弦函 数图象以 及类 比正弦函 数, 可以得到 余弦 函数是周 期函 数,这样 使学 生加深对 定义 的理解, 培养 学生类比 思想 和数形结 合能力.

问题: 探究余弦 函数的周 期 余弦函数 y=cosx 是周期函 数吗?即能否找到非零常 数 T,使 cos(T+x)= cosx 成 立?若是,请找出它的周 期,若不是,请说明理由.

学生回答: 余弦函数 y=cosx 是周 期函数,2kπ (k∈Z 且 k≠0)都是它的周期. 最小正周期为 2?

2 分钟

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo-w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into si m ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long -term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n t he country, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wi t h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of huma n thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members and

Learn G eneral Se cretary on "two t o learn a" strengt heni ng "four Cons cious nesse s" important spee ch caused a str ong reacti on i n the country. T ime, watching "red treasure", the origi n of buildi ng the party back t o power, how to strengthe n servi ces for the masses, im prove party cohesion, fig hting to be come t he grass -root s party members a nd mas ses hot topi c. Gras s-r oots party organizati ons "two" is to strengthen the service of party members a nd cadres, t he pi one er spirit . Distribution of grass -root s party organi zations in all wa lks of pe ople , clot hing , she lter, w hich bel ongs t o the ner ve endi ngs of the party organiza ti on a nd comments re putation ha s a dire ct perception of the mas ses. Strengthen the party ahe ad of the "pe dal" spirit; strengt hen the party members a nd cadres "s uccess doe s not have to be me" an d "the first to bear hards hips, the la st to" service spirit to s e t the party's positive image among the people is important. Gras s-r oots party organizati ons "two" is to clea nse all people not happy not to see "stere otypes", esta blis h the hone st faithful, dilige nt faith for the pe opl e. No nee d to avoi d mentioning t hat, some members of our party ca n not sta nd t he "mone y," corrosion of temptation, thin, Xu Z hou, s uch abuse and corrupt bribery, mal feasa nce borers , and rats. Two, is to cl ean up, thi n, Xu, Zhou' s sol ution to restore t he party's fresh a nd natural, s oli d and honest w ork style. Cleansing "take, eat, card," undes irable a nd behavi our, "cros s, har d and col d, pus h" attitude. Gras s-r oots party organizati ons "two" is to strengt hen the sense of or dinary party members, parti cipati ng in consci ous nes s, unity cons ciousne ss. For rea sons known, members of grass -roots party bra nches les s mobile, les s resource s, and the constructi on of party organizati ons have s ome lag. Two st udie s, is to focus on the grass -roots party branche s "loose, s oft, loos e" problem, advance the party mem bers a nd ca dres, "a gang w orking", "Hong Kong report." Strong cleanup acti ons, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

预 计 时 间 教学程序 (分)

教师活动

学生活动

备注

例 1.求下列函数的最小正 周期 T. 1. f ( x) ? 3 sin x , x ? R ; 两名学生板演,其余学 生在下面独立完成, 2. f ( x) ? sin 2 x , x ? R ; 完成后由学生点评. 3. f ( x) ? 2 sin( 1 x ? ? ) , 学生可能的方法: 2 4 1.周期函数定义 x? R; 2.函数图象观察得到周 第 1 题师生共同完成 期 第 2、3 题学生独立完成 预设:利用课件中的图象引 导学生发现最小正周期 练习: 1. 等式 sin(300 ? 1200 ) ? sin 300 是否成立? 如果这个等式成 立,能否说1200 是正弦函数
4 分钟

9 分钟

知识应用

观察学生 对周 期函数定 义的掌握情 况. 培养学生 的数 形结合能 力.

答: 1. 成立

不能

课堂反馈

y ? sin x 的一个周期?
2.求下列函数的周期: 2.(1)

(1) y ? cos 4 x, x ? R 1 (2) y ? cos x, x ? R 2

? 2

(2) 4?

通过课堂反 馈能 准确、及 时地 了解学生 对周 期函数定 义和 函数周期 求法 的掌握情 况,做到及时 反馈、评价,及 时查漏补缺, 达到堂堂清.

1 分钟

课堂小结

1.回顾周期函数的定义. 2.函数 y=sinx 和函数 y=cosx 周期为多少?. 3.函数周期有多少种求法?

1.周期函数定义: 一般地,对于函数 f(x),如果存在一个 非零的常数 T,使得定 义域内的每一个 x 值, 都满足 f(x+T)=f(x), 那么函数 f(x)就叫做 周期函数,非零常数 T 叫做这个函数的周期. 2. 函 数 y=sinx 和 函 数 y=cosx 周期均为 2π . 3.周期的求法: ①定义法 ②图象法

引导学生 对所 学知识进 行小结,有利 于学 生对已有 的知 识结构进 行编码处理, 加强记忆.

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo-w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir v alue. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long -term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the countr y, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the gr ass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members and

Learn G eneral Se cretary on "two t o learn a" strengt heni ng "four Cons cious nesse s" important spee ch caused a str ong reacti on i n the country. T ime, watching "red treasure", the origi n of buildi ng the party back t o power, how to strengthe n servi ces for the masses, im prove party cohesion, fig hting to be come t he grass -root s party members a nd mas ses hot topi c. Gras s-r oots party organizati ons "two" is to strengthen the service of party members a nd cadres, t he pi one er spirit . Distribution of grass -root s party organi zations in all wa lks of pe ople , clot hing , she lter, w hich bel ongs t o the ner ve endi ngs of the party organiza ti on a nd comments re putation ha s a dire ct perception of the mas ses. Strengthen the party ahe ad of the "pe dal" spirit; strengt hen the party members a nd cadres "s uccess doe s not have to be me" and "the first to bear hards hips, the la st to" service spirit to s e t the party's positive image among the people is important. Gras s-r oots party organizati ons "two" is to clea nse all people not happy not to see "stere otypes", esta blis h the hone st faithful, dilige nt faith for the pe opl e. No nee d to avoi d mentioning t hat, some members of our party ca n not sta nd t he "mone y," corrosion of temptation, thin, Xu Z hou, s uch abuse and corrupt bribery, malfeasa nce borers , and rats. Two, is to cl ean up, thi n, Xu, Zhou' s sol ution to restore t he party's fresh a nd natural, s oli d and honest w ork style. Cleansing "take, eat, card," undes irable a nd behavi our, "cros s, har d and col d, pus h" attitude. Gras s-r oots party organizati ons "two" is to strengt hen the sense of or dinary party members, parti cipati ng in consci ous nes s, unity cons ciousne ss. For rea sons known, members of grass -roots party bra nches les s mobile, les s resource s, and the constructi on of party organizati ons have s ome lag. Two st udie s, is to focus on the grass -roots party branche s "loose, s oft, loos e" problem, advance the party members a nd ca dres, "a gang w orking", "Hong Kong report." Strong cleanup acti ons, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

课外作业: 求下列函数的周期: (1) y ? 3sin

(3) y ? cos(2 x ? ) , 3

x ? , x ? R ;(2) y ? sin( x ? ) , x ? R ; 4 10 1 ? ? x?R x?R
(4) y ? 3 sin( x ? ) , 2 4

课外思考: 1. 求 函 数 f ( x) ? A sin(? x ? ? ) 和 f ( x) ? A cos(? x ? ? ) ( 其 中 A, ? , ? 为 常 数 , 且

A ? 0, ? ? 0 )的周期.
2.求下列函数的周期: (1) y ?| sin x | , x ? R ; (2) y ?| cos 2 x | , x ? R

附:板书设计 课题:正弦、余弦函数的周期性 1. 周期函数定义 2. 正弦函数 y=sinx 的周期为 2? 余弦函数 y=cosx 的周期为 2? . 例 1 板演及学生演示区 为了使学生全面 系统地了解本节内容 的知识结构 , 达到突 出重点 , 简洁明了的 目的. 设计意图

附:
1.本节课预计学生建构周期函数概念时有困难,特别是“正弦函数图象的周而复始变化 实际上是函数值的周而复始变化” 的本质学生理解有一定困难.为了突破这个难点,借助了 几何画板来帮助学生从形象思维过渡到抽象思维. 2. 预计部分学生对周期函数定义的自变量的任意性的理解有困难, 为了突破这个难点, 设计了三道判断题让学生分组讨论交流, 通过学生思维碰撞来体会数学概念的严谨, 通过学 生互动建构自己对周期函数概念的认识. 3.预计部分学生运用周期函数定义求函数周期有一定困难,为了解决这个困难,在设 计中,例1第1问由师生共同完成,完成后小结解题的思路方法.再由学生完成第2问和第 3问,再由师生共同点评.

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo-w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into si m ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long -term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n t he country, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wi t h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of huma n thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members and

Learn G eneral Se cretary on "two t o learn a" strengt heni ng "four Cons cious nesse s" important spee ch caused a str ong reacti on i n the country. T ime, watching "red treasure", the origi n of buildi ng the party back t o power, how to strengthe n servi ces for the masses, im prove party cohesion, fig hting to be come t he grass -root s party members a nd mas ses hot topi c. Gras s-r oots party organizati ons "two" is to strengthen the service of party members a nd cadres, t he pi one er spirit . Distribution of grass -root s party organi zations in all wa lks of pe ople , clot hing , she lter, w hich bel ongs t o the ner ve endi ngs of the party organiza ti on a nd comments re putation ha s a dire ct perception of the mas ses. Strengthen the party ahe ad of the "pe dal" spirit; strengt hen the party members a nd cadres "s uccess doe s not have to be me" an d "the first to bear hards hips, the la st to" service spirit to s e t the party's positive image among the people is important. Gras s-r oots party organizati ons "two" is to clea nse all people not happy not to see "stere otypes", esta blis h the hone st faithful, dilige nt faith for the pe opl e. No nee d to avoi d mentioning t hat, some members of our party ca n not sta nd t he "mone y," corrosion of temptation, thin, Xu Z hou, s uch abuse and corrupt bribery, mal feasa nce borers , and rats. Two, is to cl ean up, thi n, Xu, Zhou' s sol ution to restore t he party's fresh a nd natural, s oli d and honest w ork style. Cleansing "take, eat, card," undes irable a nd behavi our, "cros s, har d and col d, pus h" attitude. Gras s-r oots party organizati ons "two" is to strengt hen the sense of or dinary party members, parti cipati ng in consci ous nes s, unity cons ciousne ss. For rea sons known, members of grass -roots party bra nches les s mobile, les s resource s, and the constructi on of party organizati ons have s ome lag. Two st udie s, is to focus on the grass -roots party branche s "loose, s oft, loos e" problem, advance the party mem bers a nd ca dres, "a gang w orking", "Hong Kong report." Strong cleanup acti ons, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

教案设计说明
广东省东莞中学松山湖学校 彭 科

《正弦、余弦函数的周期性》是普通高中课程标准实验教科书必修四第一章第四节第二 节课,其主要内容是周期函数的概念及正弦、余弦函数的周期性.正弦、余弦函数的周期性 是三角函数的一个重要性质,是研究三角函数其它性质的基础,是函数性质的重要补充.本 课的重点为周期函数的定义和正弦、 余弦函数的周期性, 难点为周期函数定义及运用定义求 函数的周期.本课的教学设计分为六个部分,包括:教材分析,目标分析(含学情分析), 教学重难点,教学准备,教学流程,教学过程.设计反映了由学生熟悉的生活的周期现象出 发,通过概括、抽象,并结合正弦函数的图象引导学生感受周期函数概念的形成过程,这是 设计的数学本质基础;设计中结合本班学生的学习的实际情况,从而确定了教学活动的环 节. 以这些分析为基础从而确定教学目标, 而过程设计则针对目标从九个环节进行具体的设 计.教学过程设计自始至终贯穿数形结合思想.下面从如下几个方面进行详细说明.

一、教学内容的数学本质及教学目标定位
本节课主要内容是周期函数的概念及正弦、 余弦函数的周期性. 通过对正弦函数图象 “周 而复始”的变化规律特征的感知,使学生建立比较牢固的理解周期性的认知基础,然后再引 导学生了解用代数表达式刻画图象“周而复始”的变化规律.本节课要探究的周期函数的概 念的数学本质是从形和数两个方面去刻画 “周而复始”的变化规律. 学生在知识上已经学习了函数概念与基本初等函数等知识, 已经掌握了三角函数图象的 画法及五点法作图; 在能力上已经具备了一定的形象思维与抽象思维能力; 在思想方法上已 经接触过数形结合、类比、特殊到一般等数学思想. 另外,我还对我班学生的具体情况做 了如下分析:我班学生基础知识比较扎实、思维较活跃,学生层次差异不大,能够很好的掌 握教材上的内容,能较好地做到数形结合,善于发现问题,深入研究问题,但是部分学生处 理抽象问题的能力还有待进一步提高. 于是,结合以上的学情分析,我从 “知识与技能”、“过程与方法”和“情感态度与 价值观”设定目标.其中知识与技能目标为:理解周期函数的概念及正弦、余弦函数的周期 性,会求一些简单三角函数的周期.过程与方法则是:从学生实际中的周期现象出发,提供
learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo-w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir v alue. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写 "Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long -term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the countr y, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the gr ass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members and

Learn G eneral Se cretary on "two t o learn a" strengt heni ng "four Cons cious nesse s" important spee ch caused a str ong reacti on i n the country. T ime, watching "red treasure", the origi n of buildi ng the party back t o power, how to strengthe n servi ces for the masses, im prove party cohesion, fig hting to be come t he grass -root s party members a nd mas ses hot topi c. Gras s-r oots party organizati ons "two" is to strengthen the service of party members a nd cadres, t he pi one er spirit . Distribution of grass -root s party organi zations in all wa lks of pe ople , clot hing , she lter, w hich bel ongs t o the ner ve endi ngs of the party organiza ti on a nd comments re putation ha s a dire ct perception of the mas ses. Strengthen the party ahe ad of the "pe dal" spirit; strengt hen the party members a nd cadres "s uccess doe s not have to be me" and "the first to bear hards hips, the la st to" service spirit to s e t the party's positive image among the people is important. Gras s-r oots party organizati ons "two" is to clea nse all people not happy not to see "stere otypes", esta blis h the hone st faithful, dilige nt faith for the pe opl e. No nee d to avoi d mentioning t hat, some members of our party ca n not sta nd t he "mone y," corrosion of temptation, thin, Xu Z hou, s uch abuse and corrupt bribery, malfeasa nce borers , and rats. Two, is to cl ean up, thi n, Xu, Zhou' s sol ution to restore t he party's fresh a nd natural, s oli d and honest w ork style. Cleansing "take, eat, card," undes irable a nd behavi our, "cros s, har d and col d, pus h" attitude. Gras s-r oots party organizati ons "two" is to strengt hen the sense of or dinary party members, parti cipati ng in consci ous nes s, unity cons ciousne ss. For rea sons known, members of grass -roots party bra nches les s mobile, les s resource s, and the constructi on of party organizati ons have s ome lag. Two st udie s, is to focus on the grass -roots party branche s "loose, s oft, loos e" problem, advance the party members a nd ca dres, "a gang w orking", "Hong Kong report." Strong cleanup acti ons, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

丰富的实际背景,通过对实际背景的分析与 y=sinx 图形的比较、概括抽象出周期函数的概 念. 运用数形结合方法研究正弦函数 y=sinx 的周期性,通过类比研究余弦函数 y=cosx 的周 期性.并且在过程中渗透了本课的情感态度目标: 让学生体会数学来源于生活,体会从感 性到理性的思维过程,体会数形结合思想;让学生亲身经历数学研究的过程,享受成功的喜 悦,感受数学的魅力.以上是对教学目标定位的说明. 二、教学流程 复习回顾 引入新知 构建周期 函数定义

创设问题 情境引入

正弦函数 的周期

巩固周期 函数定义

余弦函数 的周期

课堂 小结

课堂 反馈

知识 应用

三、学习基础及作用
本节课是学生学习了诱导公式和正弦、 余弦函数的图象之后, 对三角函数知识的又一深 入探讨.正弦、余弦函数的周期性是三角函数的一个重要性质,是研究三角函数其它性质的 基础,是函数性质的重要补充.通过本课的学习不仅能进一步培养学生的数形结合能力,分 析问题和解决问题的能力, 而且能使学生把这些认识迁移到后续的知识学习中去, 为以后研 究三角函数的其它性质打下基础. 正弦函数、 余弦函数的周期性, 与后面高中物理研究的 《单 摆运动》 、 《简谐运动》 、 《机械波》等知识有着密切相关的联系.在数学和其它领域(物理学、 生物学、医学等)中具有重要的作用,所以,该内容在教材中具有非常重要的意义,是连接 理论知识和实际问题的一个桥梁.

四、教学诊断分析
1.学习正弦、余弦函数的周期性时,用图象法求周期学生容易理解;建构周期函数概 念时学生有困难, 特别是“正弦函数图象的周而复始的变化实际上是函数值的周而复始的变

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo-w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into si m ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long -term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n t he country, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wi t h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of huma n thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members and

Learn G eneral Se cretary on "two t o learn a" strengt heni ng "four Cons cious nesse s" important spee ch caused a str ong reacti on i n the country. T ime, watching "red treasure", the origi n of buildi ng the party back t o power, how to strengthe n servi ces for the masses, im prove party cohesion, fig hting to be come t he grass -root s party members a nd mas ses hot topi c. Gras s-r oots party organizati ons "two" is to strengthen the service of party members a nd cadres, t he pi one er spirit . Distribution of grass -root s party organi zations in all wa lks of pe ople , clot hing , she lter, w hich bel ongs t o the ner ve endi ngs of the party organiza ti on a nd comments re putation ha s a dire ct perception of the mas ses. Strengthen the party ahe ad of the "pe dal" spirit; strengt hen the party members a nd cadres "s uccess doe s not have to be me" an d "the first to bear hards hips, the la st to" service spirit to s e t the party's positive image among the people is important. Gras s-r oots party organizati ons "two" is to clea nse all people not happy not to see "stere otypes", esta blis h the hone st faithful, dilige nt faith for the pe opl e. No nee d to avoi d mentioning t hat, some members of our party ca n not sta nd t he "mone y," corrosion of temptation, thin, Xu Z hou, s uch abuse and corrupt bribery, mal feasa nce borers , and rats. Two, is to cl ean up, thi n, Xu, Zhou' s sol ution to restore t he party's fresh a nd natural, s oli d and honest w ork style. Cleansing "take, eat, card," undes irable a nd behavi our, "cros s, har d and col d, pus h" attitude. Gras s-r oots party organizati ons "two" is to strengt hen the sense of or dinary party members, parti cipati ng in consci ous nes s, unity cons ciousne ss. For rea sons known, members of grass -roots party bra nches les s mobile, les s resource s, and the constructi on of party organizati ons have s ome lag. Two st udie s, is to focus on the grass -roots party branche s "loose, s oft, loos e" problem, advance the party mem bers a nd ca dres, "a gang w orking", "Hong Kong report." Strong cleanup acti ons, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

化”的本质学生感到有一定困难. 我首先让学生回顾如何利用正弦线画正弦函数 y=sinx 图 象(动画演示),通过动画演示,让学生感知正弦函数图象“周而复始”的变化规律,再引 导学生用代数表达式刻画图象“周而复始”的变化规律. 2.部分学生对周期函数定义中的任意性理解容易出现错误,需要在教学中反复强调. 3.本节课充分利用了多媒体技术的强大功能,把现代信息技术作为学生学习数学和解 决问题的强有力工具,使学生乐意投入到现实的、探索性的教学活动中去.

五、教法特点及预期效果分析
结合教学目标以及学生的实际情况, 我采用了启发引导与小组合作交流相结合的教学方 式,而在知识构建过程中,在教师引导下,使学生经历了直观感知、观察发现、抽象概括等 思维活动,提高数学思维能力;注重信息技术与数学课程的整合,提倡利用信息技术呈现以 往教学中难以呈现的课程内容, 鼓励学生运用信息技术进行探索和发现. 本节课遵循学生的 认知规律,通过典型具体例子的分析和学生自主地观察、探索活动,使学生理解周期概念的 形成过程, 体会蕴含在其中的数形结合的思想方法, 把数学的学术形态通过适当的方式转化 为学生易于接受的教育形态, 教学内容利用生活中的问题和课本上已有的知识创设情境, 使 教学内容不仅贴近生活,并且来源于旧知识,设计内容一环扣一环,使学生对周期函数的概 念理解和应用步步深入.在教学方法上运用多种方法,如观察、分析、归纳、讨论;在知识 的学习过程中,重视知识的形成过程和概括过程.在解决问题中,引导学生分析、归纳方法, 注意优化学生的思维品质;在教学手段上采用多媒体和黑板重点板书结合的教学方法. 通过本节课学习,我力求达到:1 、形成学生主动参与,自主探究,合作交流的课堂 气氛.2、学生进一步了解数学来源于生活,理解周期函数和周期的定义.3、让学生体会从感 性到理性的思维过程,体会数形结合思想,让学生领悟问题探究的学习方法.由于本课内容 不多,难度不大,相信大多数学生都能掌握本课知识,实现预期的目标.

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo-w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir v alue. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long -term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the countr y, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the gr ass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members and


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