Modeling and Problem Solving——函数模型及其应用教案中澳课程部王晓叶学情分析：澳方MathB每次的Paper Test都分为两部分，其中Knowledge and Procedures（知识与过程）这个和普通高中数学相似，学生A/B率比较高，但是另外一部分Modeling and Problem Solving（建模与实际问题的解决）学生的A／B率不高。
这一部分内容题目普遍很长、生词量较多，并且都是将数学知识应用于实际生活中，所以大多数学生遇到此类题目都是放弃不做。
MathB这门课又特别注重实际生活问题的解决，而我们的学生这方面意识比较薄弱，抽象概括能力较弱。
所以，我们的教学任务是提高学生的考试成绩等级，提高OP成绩。
但是另一方面，12年级的学生大多数能灵活的使用图形计算器，具有一定的英语语言基础。
教学目标：1.了解函数模型在现实生活中的运用。
2.能够建立恰当的函数模型，并对函数模型进行简单的分析。
3.利用所得函数模型解释有关现象，对某些发展趋势进行预测。
教学重难点：1.建立合适的函数模型2.利用得到的函数模型解决实际问题教学过程一、引入案例、探索新知（如何确定最合适的函数模型）（18分钟）案例：根据《Daily Mail》报道，上个月一名中国留学生将自己车速飙到180公里／小时的录像传到了Instagram个人网页上，并以配以中文：“从Albany开回Perth，一路180公里／小时，将4.5小时的车程缩短到3.5小时。
”目前，他正在接受警方调查。
警察表示，视频显示这名男子在限速110公里／小时的高速公路开到了180公里／小时，他将面临巨额罚款、吊销驾照以及拘留。
Example1:The table below shows the relationship between the velocity of a car and theVelocity 10 20 30 40 50 60 70 80 90 Distance 2 10 15 20 27 38 47 60 75a. Use the calculator to find the relationship between the velocity of a car and the distance after it braking.b. What’s the minimum safe following distance for a car travelling at 110 km/h on the motor way?项目罚款扣分超速少于10km/h 163澳元扣2分超速10km/h－20km/h 357澳元扣3分超速20km/h－30km/h 726澳元扣5分超速30km/h－40km/h 866澳元扣7分未系安全带341澳元扣3分闯红灯437澳元扣3分开车使用手机315澳元扣3分（设计意图：从生活案例引入新知，激发学生的学习兴趣。
从简单题目入手，目的是让学生掌握图形计算器的使用，能够利用图形计算器建立合适的函数模型，为解决函数模型的应用做铺垫。
同时在课堂中渗透德育内容，让学生知法懂法守法。
）小结：如何建立合适的函数模型？•Solve the practical problemExercise．Some Chemistry students measured the concentration of chlorine remaining in a swimming pool over a period of 8 hours on a hot summer day. Chlorine had been placed in theMorning AfternoonTime 9 10 11 12 1 2 3 4 Chlorine concentration(ppm) 5.0 3.8 2.9 2.2 1.6 1.2 0.9 0.7a. Develop a model for the data。
b. What’s the concentration of chlorine at 8 am?（设计意图：通过练习，巩固加强掌握图形计算器的使用，为下一个例题的讲解做好铺垫。
）二、例题精讲(函数模型的应用)（12分钟）A/B Standard-Modeling and Problem SolvingExample2．Some Chemistry students measured the concentration of chlorine remaining in a swimming pool over a period of 8 hours on a hot summer day. Chlorine had been placed in theMorning AfternoonTime 9 10 11 12 1 2 3 4 Chlorine concentration(ppm) 5.0 3.8 2.9 2.2 1.6 1.2 0.9 0.7e the calculator to find the relationship between the chlorine concentration and the timeelapsed since the chlorine was placed in the pool.e the results to find the concentration that would be needed at 8 am on a similar day toensure that the chlorine concentration did not fall below 1.5ppm(parts per million) before 3 pm.3.If two chlorine doses were used , one at 8 am and another at 12 noon, what concentrationswould be needed at these times to ensure that the concentration did not fall below 1.5 ppm before 3 pm.4.What are the implication of your answers for the effective chlorination of poolsat lowest cost?(设计意图：例题为11年级MathB一次大考中的一道原题，是一道A/B等级的题目，大多数学生遇到此类型的题目都是放弃不做，原因是题目太长，生词太多，难度较大。
针对这些问题，所以通过前面的练习让学生看懂题目，拟合出合适的函数模型。
精解函数模型的应用。
首先是引导学生审题，找关键词，读懂题目。
又将题目分解成多个小题，层层递进，由易到难，引导学生学会解决此类问题的方法。
遇到大的困难时，先一个一个小困难的解决。
)三、课堂检测（14分钟）1. An oscilloscope is used by students to measure the voltage across a capacitor as it discharges through a large resistance. Observations made by the students were as follows.Time(s) 4 8 12 20 30 40V oltage 49 40 33 22 13 8b. Use yours results to predict the voltage after 2 min.2.The removal of some substances from the blood by the kidneys depends on the concentration in the blood. The following measurements of the concentration of an antibiotic were taken after theTime (hours) 0.5 1 1.5 2 2.5 3 Concentration(ppm) 18 16 14 13 11 10a. Develop a model for the data。
b. For the drug to be effective, it is known that the concentration must be between 5 and 20ppm. How often must a follow-up dose be given?（设计意图：由于澳方核心能力考试强调学科间的结合，所以例题涉及化学，课堂练习两道题目涉及分别涉及物理、生物医药。
目的是为了检测本节课学习成果，检测学生的掌握程度。
题目难度比例题要低一些，确保大多数同学都能完成，增强信心，第二题的第二个小问稍微有些难度，题目由易到难。
）四：总结（1分钟）五、课后练习：1.People from the country say that the pace of city is too fast. They claim that people in the bigcities walk faster than those in smaller towns. Marc and Helen Bornstern collected data on theLocation Population Speed(m/s)Brooklyn,USA 2602000 1.54Munich,Germany 1340000 1.91Prague Czechoslovakia 1092759 1.79Jerusalem,Israel 304500 1.35New Haven,USA 138000 1.34Iraklion,Greece 78200 1.17Netanya,Israel 70700 1.31Bastia,France 49375 1.49Dimona,Israel 23700 1.00Safed,Israel 14000 1.13Corte,Corsica 5491 1.01Itea,Greece 2500 0.69Psychro,Crete 365 0.84Athens,Greece 867023 1.59Brno,Czechoslovakia 341948 1.47a. Develop a model for the datab. Use your results to predict the speed of walkers in Toowoomba, which has a population of about100000.2. In 1798,Thomas Malthus suggested that exponential growth of the human population musteventually outstrip the possible food supply and lead to wars and disease.a.Investigate the records of word population given above to find whether you agree with theYear 1000 1200 1400 1500 1600 1700 1750 1800 1850 1900 1950 2000Population 350 435 465 475 490 630 800 900 1300 1600 2500 6000 idea that it does grow exponentially.b.Malthus originally suggested that the world’s food supply would have been outstripped longbefore the present day. Suggest some reasons to explain the fact that his dire predictions haveat least been delayed.。