/r/n9/r/n一元一次不等式與一次函數(shù)（/r/n1/r/n）》教案/r/n一、/r/n教學(xué)內(nèi)容分析/r/n本節(jié)內(nèi)容是在學(xué)生已有對(duì)一元一次方程、一元一次不等式和二元一次方程組等的認(rèn)識(shí)之后，從變化和對(duì)應(yīng)關(guān)系的角度，對(duì)一元一次不等式的運(yùn)算進(jìn)行更深入的討論，是站在更高起點(diǎn)上的動(dòng)態(tài)分析。通過(guò)討論一次函數(shù)與方程（組）及不等式的關(guān)系，用函數(shù)的觀(guān)點(diǎn)加深對(duì)這些已經(jīng)學(xué)習(xí)過(guò)的內(nèi)容的認(rèn)識(shí)，加強(qiáng)知識(shí)間的橫向和縱向聯(lián)系，發(fā)揮函數(shù)的統(tǒng)領(lǐng)作用，構(gòu)建和發(fā)展相互聯(lián)系的知識(shí)體系。/r/n二、/r/n教學(xué)目的/r/n1/r/n、知識(shí)與技能目標(biāo)：（/r/n1/r/n）通過(guò)觀(guān)察函數(shù)圖象、求方程的解和不等式的解集，體會(huì)一元一次方程、一元一次不等式與一次函數(shù)的聯(lián)系；（/r/n2/r/n）會(huì)用圖象法解一元一次不等式。/r/n2/r/n、數(shù)學(xué)思考目標(biāo)：通過(guò)對(duì)一次函數(shù)與一元一次不等式關(guān)系的探究及相關(guān)實(shí)際問(wèn)題的解決/r/n,/r/n體會(huì)數(shù)形結(jié)合的思想。/r/n3/r/n、問(wèn)題解決目標(biāo)：能利用一次函數(shù)與一元一次不等式的內(nèi)在關(guān)系，解決實(shí)際問(wèn)題。/r/n4/r/n、情感態(tài)度目標(biāo)：培養(yǎng)學(xué)生的探究精神，體會(huì)事物之間的相互聯(lián)系，進(jìn)一步感受數(shù)學(xué)的價(jià)值。/r/n三、/r/n教學(xué)重點(diǎn)/r/n重點(diǎn)：通過(guò)觀(guān)察函數(shù)圖象解一元一次不等式。/r/n四、/r/n教學(xué)難點(diǎn)/r/n難點(diǎn)：一元一次方程、一元一次不等式與一次函數(shù)的內(nèi)在聯(lián)系。/r/n五、/r/n教學(xué)準(zhǔn)備/r/n學(xué)情分析：學(xué)生學(xué)習(xí)了一次函數(shù)、一元一次方程和二元一次方程組，已能初步理解函數(shù)與方程的聯(lián)系，同時(shí)也具備了一定的數(shù)形結(jié)合的意識(shí)和能力，積累了利用一元一次不等式解決簡(jiǎn)單實(shí)際問(wèn)題的經(jīng)驗(yàn)。/r/n教法分析：基于本節(jié)課的內(nèi)容特點(diǎn)和初二年級(jí)學(xué)生的年齡特征，遵循/r/n“/r/n讓學(xué)生主動(dòng)積極參與學(xué)習(xí)，發(fā)揮其學(xué)習(xí)的主體性/r/n”/r/n的教學(xué)理念，我決定采用/r/n“/r/n啟發(fā)引導(dǎo)、自主學(xué)習(xí)、合作探究/r/n”/r/n的教學(xué)模式，充分發(fā)揮教師的主導(dǎo)作用和學(xué)生的主體作用。/r/n六、/r/n教學(xué)流程框圖/r/n七、/r/n教學(xué)過(guò)程設(shè)計(jì)/r/n預(yù)計(jì)時(shí)/r/n間(分)/r/n5/r/n分鐘/r/n教學(xué)/r/n內(nèi)容/r/n1/r/n、/r/n創(chuàng)設(shè)情境、引入新知/r/n教師活動(dòng)/r/n深圳市寶安中學(xué)在全市率先開(kāi)展了/r/n“/r/n學(xué)會(huì)生存/r/n”/r/n的必修課，目前/r/n“/r/n中學(xué)生生存教育的理論與實(shí)踐研究/r/n”/r/n已成為學(xué)校獨(dú)立承擔(dān)的全國(guó)教育科學(xué)/r/n“/r/n十一五/r/n”/r/n規(guī)劃教育部重點(diǎn)資助課題。/r/n在周一的/r/n“/r/n防止踩踏/r/n”/r/n疏散課上，初一(/r/n4/r/n)班的同/r/n學(xué)在警報(bào)響起/r/n3/r/n秒后疏散距離(米)與時(shí)間(秒)滿(mǎn)足關(guān)系式是/r/ny=2x-5/r/n。/r/n1/r/n.作函數(shù)/r/ny/r/n=/r/n2/r/nx/r/n-/r/n5/r/n的圖象/r/n：/r/nx/r/ny/r/n=/r/n2/r/nx/r/n-/r/n5/r/n解：列表；描點(diǎn)，連線(xiàn)；/r/n-/r/n■-i/r/nJ/r/n—/r/n!—/r/nJ/r/nJ/r/n1/r/n2/r/n3/r/n11/r/nX/r/n-1/r/n-2/r/n—5/r/n4/r/n-/r/n-1/r/n2/r/n.觀(guān)察圖象回答問(wèn)題：/r/nx/r/n取何值時(shí)，/r/ny=0/r/n?/r/nx/r/n取何值時(shí)，/r/ny/r/n>/r/n0/r/n?/r/nx/r/n取何值時(shí)，/r/ny/r/n</r/n0/r/n?/r/n10/r/n分鐘/r/n2/r/n、/r/n思考討論、探索新知/r/n問(wèn)題一：觀(guān)察你畫(huà)出/r/ny/r/n=/r/n2/r/nx/r/n-/r/n5/r/n的圖象，回答下列問(wèn)題。/r/nx/r/n取何值時(shí)，/r/n2x/r/n-/r/n5=0/r/n?/r/nx/r/n取何值時(shí)，/r/n2x/r/n-/r/n5/r/n>/r/n0/r/n?/r/nx/r/n取何值時(shí)，/r/n2x/r/n—/r/n5</r/n0/r/n?/r/n練習(xí)/r/n1/r/n、如圖/r/n,/r/n是函數(shù)/r/ny=/r/n-/r/n2x/r/n-/r/n6/r/n的圖象/r/n，/r/n看圖回答下列問(wèn)題：/r/n當(dāng)/r/nx/r/n時(shí)/r/n,/r/n一/r/n2x/r/n—/r/n6/r/n>0/r/n；/r/n當(dāng)/r/nx/r/n時(shí)/r/n,/r/n一/r/n2x/r/n—/r/n6/r/n<0/r/n；/r/n學(xué)生活動(dòng)/r/n學(xué)生作出函數(shù)圖象后觀(guān)察，發(fā)現(xiàn)：/r/n以/r/n(/r/n2.5/r/n,/r/n0/r/n)為界,右邊函數(shù)圖象在/r/nx/r/n軸的上方，所以當(dāng)/r/nx>2.5/r/n時(shí)，/r/ny>0，/r/n左邊函數(shù)圖象在/r/nx/r/n軸的下方，所以當(dāng)/r/nx<2.5/r/n時(shí)，/r/ny<0/r/n。/r/n學(xué)生求解一元一次方程和不等式，發(fā)現(xiàn)/r/nx/r/n的取值范圍相同，更有的同學(xué)直接發(fā)現(xiàn)兩/r/n教學(xué)評(píng)/r/n價(jià)/r/n以/r/n“/r/n舊/r/n”/r/n弓/r/n1“/r/n新/r/n”/r/n，由原有的知識(shí)為基礎(chǔ),探討新的內(nèi)容。/r/n通過(guò)作函數(shù)圖象、觀(guān)察函數(shù)圖象,進(jìn)一步理解函數(shù)概念,并從中體會(huì)一元一次/r/n練習(xí)/r/n2/r/n、觀(guān)察你畫(huà)出/r/ny/r/n=/r/n2/r/nx/r/n-/r/n5/r/n的圖象，回答下列問(wèn)題：/r/nx/r/n取何值時(shí)/r/n,/r/ny>3/r/n?/r/n變式：/r/nx/r/n取何值時(shí)/r/n，/r/ny/r/n</r/n-2/r/n?/r/n種情況只是問(wèn)法不同。/r/n學(xué)生初步體會(huì)一元一次不等式與一次函數(shù)的關(guān)系：/r/n一元一次不等式的解集可通過(guò)觀(guān)察相應(yīng)一次函數(shù)圖象獲得。/r/n不等式與一次函數(shù)的內(nèi)在聯(lián)系。/r/n學(xué)生由討論可見(jiàn)，一次函數(shù)與一元一次方程、一元一次不等式之間有密切關(guān)系，當(dāng)函數(shù)值等于/r/n0/r/n時(shí)即為方程，當(dāng)函數(shù)值大于或小于/r/n0/r/n時(shí)即為不等式。/r/n通過(guò)具體問(wèn)題初步體會(huì)一次函數(shù)的變化規(guī)律與一元一次不等式解集的聯(lián)系。通過(guò)完成這題進(jìn)一步培養(yǎng)了學(xué)生的數(shù)形結(jié)合意/r/n識(shí)。/r/n10/r/n分鐘/r/n15/r/n分鐘/r/n3/r/n、/r/n深入探究、多維理/r/n4/r/n、/r/n展用、決題/r/n問(wèn)題二：/r/n如下圖，在/r/n“/r/n問(wèn)題/r/n1”/r/n中的平面直角坐標(biāo)系/r/n、、/r/n1—/r/n中添加一條直線(xiàn)/r/ny/r/n2/r/n=/r/ny/r/nx/r/n+/r/n1/r/n，即：已知/r/ny/r/n1/r/n=2/r/nx/r/n—/r/n5/r/n1/r/n—、/r/n

/r/n與/r/ny/r/n2/r/n=/r/n2/r/nx/r/n+/r/n1/r/n，請(qǐng)你回答下列問(wèn)題。/r/nx/r/n取何值時(shí)，/r/ny/r/n1/r/n=/r/ny/r/n2/r/n?/r/nx/r/n取何值時(shí)，/r/ny/r/n>/r/ny/r/n?/r/nx/r/n取何值時(shí)，/r/ny/r/n</r/ny/r/n?/r/n你是怎樣做的？與同伴交流/r/n./r/n問(wèn)題三：在疏散演習(xí)的過(guò)程中，老師將初一(/r/n4/r/n)班的同學(xué)分成/r/nA/r/n、/r/nB/r/n兩組，/r/nA/r/n組出發(fā)時(shí)/r/nB/r/n組已跑/r/n9/r/n米。已知/r/nB/r/n組每秒跑/r/n3/r/n米，/r/nA/r/n組每秒跑/r/n4/r/n米。/r/n1./r/nA/r/n組疏散的時(shí)間為/r/nx/r/n(秒)/r/n，/r/nA/r/n組與/r/nB/r/n組同學(xué)疏散的路程分別為丁廣/r/ny/r/n2/r/n(/r/n米/r/n)/r/n，列出丁廣/r/ny/r/n2/r/n與/r/nx/r/n的函數(shù)關(guān)系式。/r/nf/r/n1/r/n3D/r/n■TH/r/nz/r/nZ/r/nrU/r/nfin/r/nZ/r/n■rn./r/nJ/r/n■1/r/n—/r/nJU/r/n』/r/n-U/r/non/r/n//r/nJU/r/n20/r/nin/r/n-/r/n2/r/n2/r/n6/r/n8/r/n10/r/n12/r/n14/r/n16/r/n2/r/n./r/n如圖，在同一平面直角坐標(biāo)系內(nèi)分別作出函數(shù)/r/ny/r/ni/r/n=4x,y/r/n2/r/n=3x+9/r/n的圖象。/r/n觀(guān)察圖象，小組活動(dòng)：我問(wèn)問(wèn)題你來(lái)答！/r/n練習(xí)/r/n3/r/n、如圖是一次函數(shù)/r/ny=kx+b(k/r/n#O/r/n的圖象，則關(guān)于/r/nx/r/n的方程/r/nkx+b=0/r/n的解為/r/n；關(guān)于/r/nx/r/n的不等式/r/nkx+b>0/r/n的解集為/r/n;關(guān)于/r/nx/r/n觀(guān)察圖象找到當(dāng)/r/ny/r/n產(chǎn)『/r/n2/r/n、/r/ny/r/n1/r/n<y/r/n2/r/n和/r/n心/r/n2/r/n時(shí)/r/nx/r/n的取值范圍，發(fā)現(xiàn)/r/nyr/r/n即找交點(diǎn)/r/n，兒/r/n<y/r/n2/r/n即/r/ny/r/n1/r/n的圖象在/r/ny/r/n2/r/n的圖象下方，/r/ny/r/n1/r/n>y/r/n2/r/n即/r/ny/r/n1/r/n的圖象在/r/ny/r/n2/r/n的圖象上方。/r/n小組活動(dòng)：我問(wèn)問(wèn)題你來(lái)答！學(xué)生根據(jù)函數(shù)圖象出題，小組互換進(jìn)行解答。有的同學(xué)問(wèn):/r/nA/r/n組、/r/nB/r/n組什么時(shí)候相遇，相遇時(shí)距離出發(fā)地多少米？什么時(shí)候/r/nA/r/n組在/r/nB/r/n組的前面，什么/r/n通過(guò)學(xué)生觀(guān)察、自主思考，然后小組討論，培養(yǎng)學(xué)生合作交流的學(xué)習(xí)意識(shí),完成這題進(jìn)一步培養(yǎng)了學(xué)生的/r/n數(shù)形結(jié)合/r/n意識(shí)。/r/n感知不等式、函數(shù)、方程的不同作用與內(nèi)在聯(lián)系。絕大部分學(xué)生都能畫(huà)出函數(shù)圖象,并能借助函數(shù)圖象完成上述問(wèn)題。/r/n對(duì)/r/n

/r/n上環(huán)節(jié)/r/n

/r/n中解決/r/n

/r/n此類(lèi)問(wèn)/r/n

/r/n題的方/r/n

/r/n法進(jìn)行/r/n5/r/n分鐘/r/n5/r/n、/r/n反思小結(jié)、培養(yǎng)能力/r/n練習(xí)/r/n4/r/n、如圖，直線(xiàn)/r/n1/r/n1/r/n與/r/n1/r/n2/r/n交于/r/nP/r/n點(diǎn)，當(dāng)/r/nx/r/n在什么范圍內(nèi)取值時(shí)/r/ny/r/n1/r/n>y/r/n2/r/n?/r/n1/r/n、/r/n通過(guò)本節(jié)課，你學(xué)到了什么知識(shí)?/r/n2/r/n、/r/n你體會(huì)到了什么數(shù)學(xué)思想/r/n？/r/n板書(shū)：/r/n§/r/n2.5/r/n一無(wú)-'衣.不茅式專(zhuān)一&毎數(shù)/r/nfl/r/n」/r/n任意一元一次不等式/r/n(/r/n4數(shù)"/r/nt/r/n當(dāng)/r/n-歡函數(shù)尸/r/nkx+b/r/n的函數(shù)值人于/r/n0/r/n(小干/r/n0/r/n)/r/n時(shí),/r/nkv+b>0/r/n求自變竝盟和應(yīng)的取伯范卿./r/n?/r/n或彳/r/nkv+b<0]/r/n“/r/n羽”；求/r/nli^-=kr+b/r/n軸/r/n的上方/r/n(下方｝部/r/n分所有/r/n點(diǎn)的械坐標(biāo)/r/n的収值/r/n范圍./r/nK/r/n權(quán)看圖方法：找交/r/n點(diǎn)一定/r/n圖魚(yú)一取范圍/r/n課本/r/nP/r/n51/r/n習(xí)題/r/n2.6/r/n如下圖是函數(shù)/r/ny/r/n./r/n=2x/r/n—/r/n4/r/n與/r/ny/r/n2/r/n=/r/n—/r/n2x+8/r/n時(shí)候在/r/nB/r/n組的后面?/r/nA/r/n組和/r/nB/r/n組誰(shuí)先跑過(guò)/r/n20/r/n米,誰(shuí)先跑過(guò)/r/n80/r/n米?等/r/n對(duì)本節(jié)課的知識(shí)和思想方法進(jìn)行系統(tǒng)性地總結(jié)。/r/n分層設(shè)/r/n計(jì)，讓學(xué)/r/n鞏固，建立解決此類(lèi)問(wèn)題的數(shù)學(xué)模型;讓學(xué)生在合作學(xué)習(xí)的過(guò)程中進(jìn)一步體驗(yàn)一元一次不等式與一次函數(shù)的圖象之間的關(guān)系。/r/n通過(guò)師生共同反思，優(yōu)化學(xué)生的認(rèn)知結(jié)構(gòu)，培養(yǎng)學(xué)生的歸納能力/r/n,/r/n把課堂教學(xué)傳授的知識(shí)較快轉(zhuǎn)化為學(xué)生的素質(zhì)。結(jié)合板書(shū)，對(duì)本節(jié)課的知識(shí)和思想方法進(jìn)行系統(tǒng)性地總結(jié)。/r/n業(yè)、自主學(xué)習(xí)/r/n有余力的同學(xué)加深對(duì)所學(xué)理解/r/n業(yè)、自主學(xué)習(xí)/r/n有余力的同學(xué)加深對(duì)所學(xué)理解/r/n的圖象，觀(guān)察圖象回答下列問(wèn)題：/r/nx/r/n取何值時(shí)，/r/ny/r/ni/r/n>/r/n0/r/n?/r/nx/r/n取何值時(shí)，