(新教材)【人教版】20版《高中全程学习方略》必修三Unit 1 Reading and Thinking(英语)

课时素养评价一角的推广(20分钟·40分)一、选择题(每小题4分,共16分,多选题全部选对的得4分,选对但不全的得2分,有选错的得0分)1.-215°是第________象限的角. ( )A.一B.二C.三D.四【解析】选B.由于-215°=-360°+145°,而145°是第二象限角,则-215°也是第二象限角.【加练·固】在①160°;②480°;③-960°;④1530°这四个角中,属于第二象限角的是 ( )A.①B.①②C.①②③D.①②③④【解析】选C.②480°=120°+360°是第二象限角;③-960°=-3×360°+120°是第二象限的角;④1530°=4×360°+90°不是第二象限的角.2.(多选题)下列说法中,不正确的是( )A.第二象限的角都是钝角B.第二象限角大于第一象限的角C.若角α与角β不相等,则α与β的终边不可能重合D.若角α与角β的终边在一条直线上,则α-β=k·180°(k∈Z)【解析】选ABC.A错,例如495°=135°+360°是第二象限的角,但不是钝角;B 错,α=135°是第二象限角,β=360°+45°是第一象限的角,但α<β;C错,α=360°,β=720°,则α≠β,但二者终边重合;D正确,α与β的终边在一条直线上,则二者的终边相差180°的整数倍,故α-β=k·180°(k∈Z).3.将-885°化为α+k·360°(0°≤α<360°,k∈Z)的形式是( )A.-165°+(-2)×360°B.195°+(-3)×360°C.195°+(-2)×360°D.165°+(-3)×360°【解析】选B.-885°=195°+(-3)×360°,0°≤195°<360°.4.若α是第四象限角,则180°-α是( )A.第一象限角B.第二象限角C.第三象限角D.第四象限角【解析】选C.可以给α赋一特殊值-60°,则180°-α=240°,故180°-α是第三象限角.二、填空题(每小题4分,共8分)5.已知-990°<α<-630°,且α与120°角的终边相同,则α=________.【解析】因为α与120°角终边相同,故有α=k·360°+120°,k∈Z.又-990°<α<-630°,所以-990°<k·360°+120°<-630°,即-1 110°<k·360°<-750°,所以-<k<-,又因为k∈Z,所以k=-3.当k=-3时,α=(-3)·360°+120°=-960°.答案:-960°6.如果将钟表拨快10分钟,则时针所转成的角度是________度,分针所转成的角度是________度.【解析】由题意结合任意角的定义可知,钟表拨快10分钟,则时针所转成的角度是-×=-5°,分针所转成的角度是-×360°=-60°.答案:-5 -60三、解答题7.(16分)写出与75°角终边相同的角β的集合,并求在360°≤β<1080°范围内与75°角终边相同的角.【解析】与75°角终边相同的角的集合为S={β|β=k·360°+75°,k∈Z}.当360°≤β<1 080°时,即360°≤k·360°+75°<1 080°,解得≤k<2.又k∈Z,所以k=1或k=2.当k=1时β=435°;当k=2时,β=795°.综上所述与75°角终边相同且在360°≤β<1 080°范围内的角为435°角和795°角.(15分钟·30分)1.(4分)若α与β终边相同,则α-β的终边落在( )A.x轴的正半轴上B.x轴的负半轴上C.y轴的正半轴上D.y轴的负半轴上【解析】选A.因为α=β+k·360°,k∈Z,所以α-β=k·360°,k∈Z,所以其终边在x轴的正半轴上.2.(4分)设集合M={α|α=45°+k·90°,k∈Z},N={α|α=90°+k·45°,k∈Z},则集合M与N的关系是 ( )【解析】选B.对于集合M,α=45°+k·90°=45°+2k·45°=(2k+1)·45°,即M={α|α=(2k+1)·45°,k∈Z};对于集合N,α=90°+k·45°=2×45°+k·45°=(k+2)·45°,即N={α|α=(k+2)·45°, k∈Z}={α|α=n·45°,n∈Z}.因为2k+1表示所有的奇数,而n表示所有的整数,所以3.(4分)若角α=2020°,则与角α具有相同终边的最小正角为________,最大负角为________.【解析】因为2 020°=5×360°+220°,所以与角α终边相同的角的集合为{α|α=220°+k·360°,k∈Z},所以最小正角是220°,最大负角是-140°.答案:220°-140°4.(4分)角α,β的终边关于y=x对称,若α=30°,则β=【解析】因为30°与60°的终边关于y=x对称,所以β的终边与60°角的终边相同.所以β=60°+k·360°,k∈Z.答案:60°+k·360°,k∈Z【加练·固】α满足180°<α<360°,5α与α有相同的始边,且又有相同的终边,那么α=________.【解析】因为5α=α+k·360°,k∈Z,所以α=k·90°,k∈Z.又因为180°<α<360°,所以α=270°.答案:270°5.(14分)已知角β的终边在直线x-y=0上.(1)写出角β的集合S.(2)写出集合S中适合不等式-360°<β<720°的元素.【解析】(1)如图,直线x-y=0过原点,倾斜角为60°,在0°到360°范围内,终边落在射线OA上的角是60°,终边落在射线OB上的角是240°,所以以射线OA,OB为终边的角的集合分别为S1={β|β=60°+k·360°,k∈Z},S2={β|β=240°+k·360°,k∈Z},所以角β的集合S=S1∪S2={β|β=60°+k·360°,k∈Z}∪{β|β=60°+180°+k·360°,k∈Z}={β|β=60°+2k·180°,k∈Z}∪{β|β=60°+(2k+1)·180°,k∈Z}={β|β=60°+n·180°,n∈Z}.(2)由于-360°<β<720°,即-360°<60°+n·180°<720°,n∈Z.解得-<n<,n∈Z,所以n=-2,-1,0,1,2,3.所以集合S中适合不等式-360°<β<720°的元素为60°-2×180°=-300°;60°-1×180°=-120°;60°+0×180°=60°; 60°+1×180°=240°;60°+2×180°=420°;60°+3×180°=600°.。

2020学年人教版高中英语必修三Unit1 Festivals around the worldGood morning, ladies and gentlemen, it’s my great pleasure to be here sharing my teaching plan with you. The topic of the lesson is from Senior English for China Student’s Book 3 Unit 1: Festivals around world. I’ll talk about the lesson from six main parts: the teaching material, teaching objectives, teaching key and difficult points, teaching methods, studying methods and teaching procedures. Firstly，I’ll introduce the teaching material.This unit is mainly about festivals and celebrations around the whole globe. The first reading passage“festivals and celebrations” is the center of this unit, which is also what my teaching plan based on. In this passage, it introduces the four different kinds of traditional festivals, their origins and celebrations. From this passage, students will know more about festivals around the world. Secondly, I’d like to talk about my teaching objectives.Knowledge objectives:Enable students to master the words, phrases and understand what this passage is about.Ability objectives:1: Improve students’ reading ability, especially skimming and scanning.2: Improve students’ spoken English and cooperative ability by group work. Emotional objectives:Help students know more about festivals and celebrations, enhance their culture awareness and their respect to tradition.Thirdly, teaching key points, difficult points.Teaching key points1:Enable students get a main idea of the passage, make students understand the different customs of different festivals.Teaching difficult points1: Make sure students can describe some major festivals with their own words, Fourthly, Teaching methods.1: Task-based TeachingBy using TBT method, students can be given opportunities to practice and use a language in daily life activities, which help them to master the language naturally and better.3: Computer Assisted TeachingBy using CAT method, teachers can provide more attractive teaching material, and create an interesting and vivid learning environment.Fifthly, studying methods.1: Task-based learning.2: Cooperative learningSixthly, Teaching procedures.1: Lead-inShow students a short video some traditional festivals’ celebrations. After watching that, ask students questions like “have you ever had these festivals?” “what do you do at these festivals?” “how do you know about these festivals?”Justification: in the beginning of the class, I want to use online video to create a lively environment in which students can get involved in more quickly, and also activate students interest and background knowledge of the topic.2: While-reading.Task 1 SkimmingDivide students into 8 groups, give them 3 minutes to glance over the title and each paragraph, then try to discuss and sum up the main idea of each and the theme of the whole passage.Justification: practice students’ ability of reading for the general idea, moreover, by group disc ussion, turn passive study to active study, and enhance students’ spoken English and the consciousness of cooperative learning.Task 2 ScanningGive students 8 minutes to read the passage carefully, then ask them questions like:1, what festivals are held to honour the dead and ancestors?2, who is honoured in India in October 2?3, what do European people do to celebrate harvest?4, what festivals are celebrated in Spring?Justification: practice students’ ability of reading for specific information. And also, by answering those questions students can have a better understanding of festivals around the world.3: Post-reading.Divide students into 8 groups, ask students to find out and discuss all the festivals and celebrations mentioned in the passage. After that, each group sends a representative to describe two festivals in front of the whole class. Justification: deepen students’ knowledge of today’s class. Make sure students can talk about festivals and celebrations by using their own words. Encourage students to express themselves in the face of people and to cooperate with others.4: Consolidation.Ask students to review the passage very quickly then complete the exercise below.Justification: review and consolidate the knowledge we’ve just learnt.5: Homework.Write an essay to introduce a festival and how it is celebrated.Justification: this activity does not only strengthen students’ understanding of different kinds of festivals and celebrations, but also improve students’ interculture awareness.。