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人教版新课标小学数学五年级下册异分母分数加、减法说课稿2篇

  • 新人教版高中英语必修3Unit 2 Morals and Virtues-Reading and Thinking教学设计

    新人教版高中英语必修3Unit 2 Morals and Virtues-Reading and Thinking教学设计

    The topic of this part is “Learn to make choices in life”.The Listening & Speaking & Talking part aims at the moral dilemmas, and this part is about making choices in life. The heroin is Lin Qiaozhi, a famous medical scientist, made a great contribution to our country’s medical care. Most importantly, her life experience can inspire our students whether in studying or the development of career. she had moral dilemmas and life choices, which are similar to the students who will step into society. Besides, Lin has quite good virtues like kindness, self-improvement, insistence, job-loving , generosity and responsibility, which is worth being learned.Concretely, this article is a biography about Lin Qiaozhi. The article tells her whole life according the timeline, among which the life choices is emphasized. For example, whether married or chased her dream, returned home or stayed abroad, family or public, her choices all reflected her faith, spirit, responsibility and devotion.1. Fast reading to get the detailed information about Lin Qiaozhi; careful reading to do the deductive information.2. Learn the reading skills--deductive judgement according the context.3. Study the structure features and language features. 4. Communicate about Lin’s life choices and reflect their own life choices.1. Learn the reading skills--deductive judgement according the context.2. Study the structure features and language features.3. Communicate about Lin’s life choices and reflect their own life choices.Step 1 Lead in---Small talkWhat are some important life choices?Importance choices: university study, jobs and marriage partners. Because they can determine our future.

  • 新人教版高中英语必修3Unit 2 Morals and Virtues-Reading for Writing教学设计

    新人教版高中英语必修3Unit 2 Morals and Virtues-Reading for Writing教学设计

    1. 这个寓言是一个关于一位国王古寓言。 The fable is an old fable about a king.2.作者用这个故事让读者对于社区的问题负有个人责任的必要印象深刻。The author used the story to impress upon readers with the need to take personal responsibility for problems in the community.3. 这个故事十分成功的实现了它的目的。The story was quite successful in achieving its purpose.Step 7 WritingPlease write a review of the story according the outline above.The fable is an old fable about a king who thought his people are lazy, so he put a large stone in the middle of the road and hides and waited to see if anyone will try to move it.The author used this story to impress upon readers with the need to take personal responsibility for problems in the community. The story was quite successful in achieving its purpose, and I liked it because it had a clear moral.However, while the moral of the story is clear, the actions of the king seemed pointless to me, because none of the characters in the story learnt anything. For this reason, I think there are better stories that can be used to impress upon people with the need for personal responsibility.Step 8 Pair workExchange drafts with a partner. Use this checklist to help your partner revise his/her draft.1. Does the writer give a short description of the story ?2. Does the description include the most important details of the story ?3. Does the writer give his or her opinion about the character or their actions ?4. Is the review well-organised ? 5. Does the writer use the -ing form as the adverbial correctly in the writing ?6. Are there any grammar, spelling, or punctuation errors ?Step 9 HomeworkPut up your revised draft in the classroom or read it to your class.

  • 新人教版高中英语选修2Unit 1 Science and Scientists-Discovering useful structures教学设计

    新人教版高中英语选修2Unit 1 Science and Scientists-Discovering useful structures教学设计

    The grammatical structure of this unit is predicative clause. Like object clause and subject clause, predicative clause is one of Nominal Clauses. The leading words of predicative clauses are that, what, how, what, where, as if, because, etc.The design of teaching activities aims to guide students to perceive the structural features of predicative clauses and think about their ideographic functions. Beyond that, students should be guided to use this grammar in the context apporpriately and flexibly.1. Enable the Ss to master the usage of the predicative clauses in this unit.2. Enable the Ss to use the predicative patterns flexibly.3. Train the Ss to apply some skills by doing the relevant exercises.1.Guide students to perceive the structural features of predicative clauses and think about their ideographic functions.2.Strengthen students' ability of using predicative clauses in context, but also cultivate their ability of text analysis and logical reasoning competence.Step1: Underline all the examples in the reading passage, where noun clauses are used as the predicative. Then state their meaning and functions.1) One theory was that bad air caused the disease.2) Another theory was that cholera was caused by an infection from germs in food or water.3) The truth was that the water from the Broad Street had been infected by waste.Sum up the rules of grammar:1. 以上黑体部分在句中作表语。2. 句1、2、3中的that在从句中不作成分,只起连接作用。 Step2: Review the basic components of predicative clauses1.Definition

  • 新人教版高中英语选修2Unit 4 Journey Across a Vast Land教学设计

    新人教版高中英语选修2Unit 4 Journey Across a Vast Land教学设计

    当孩子们由父母陪同时,他们才被允许进入这个运动场。3.过去分词(短语)作状语时的几种特殊情况(1)过去分词(短语)在句中作时间、条件、原因、让步状语时,相当于对应的时间、条件、原因及让步状语从句。Seen from the top of the mountain (=When it is seen from the top of the mountain), the whole town looks more beautiful.从山顶上看,整个城市看起来更美了。Given ten more minutes (=If we are given ten more minutes), we will finish the work perfectly.如果多给十分钟,我们会完美地完成这项工作。Greatly touched by his words (=Because she was greatly touched by his words), she was full of tears.由于被他的话深深地感动,她满眼泪花。Warned of the storm (=Though they were warned of the storm), the farmers were still working on the farm.尽管被警告了风暴的到来,但农民们仍在农场干活。(2)过去分词(短语)在句中作伴随、方式等状语时,可改为句子的并列谓语或改为并列分句。The teacher came into the room, followed by two students (=and was followed by two students).后面跟着两个学生,老师走进了房间。He spent the whole afternoon, accompanied by his mom(=and was accompanied by his mom).他由母亲陪着度过了一整个下午。

  • 新人教版高中英语选修2Unit 1 Science and Scientists-Learning about Language教学设计

    新人教版高中英语选修2Unit 1 Science and Scientists-Learning about Language教学设计

    Step 7: complete the discourse according to the grammar rules.Cholera used to be one of the most 1.__________ (fear) diseases in the world. In the early 19th century, _2_________ an outbreak of cholera hit Europe, millions of people died. But neither its cause, 3__________ its cure was understood. A British doctor, John Snow, wanted to solve the problem and he knew that cholera would not be controlled _4_________ its cause was found. In general, there were two contradictory theories 5 __________ explained how cholera spread. The first suggested that bad air caused the disease. The second was that cholera was caused by an _6_________(infect) from germs in food or water. John Snow thought that the second theory was correct but he needed proof. So when another outbreak of cholera hit London in 1854, he began to investigate. Later, with all the evidence he _7_________ (gather), John Snow was able to announce that the pump water carried cholera germs. Therefore, he had the handle of the pump _8_________ (remove) so that it couldn't be used. Through his intervention,the disease was stopped in its tracks. What is more, John Snow found that some companies sold water from the River Thames that __9__________________ (pollute) by raw waste. The people who drank this water were much more likely _10_________ (get) cholera than those who drank pure or boiled water. Through John Snow's efforts, the _11_________ (threaten) of cholera around the world saw a substantial increase. Keys: 1.feared 2.when 3. nor 4.unless 5.that/which 6.infection 7.had gathered 8.removed 9.was polluted 10.to get 11. threat

  • 新人教版高中英语选修2Unit 1 Science and Scientists-Reading and thinking教学设计

    新人教版高中英语选修2Unit 1 Science and Scientists-Reading and thinking教学设计

    Step 5: After learning the text, discuss with your peers about the following questions:1.John Snow believed Idea 2 was right. How did he finally prove it?2. Do you think John Snow would have solved this problem without the map?3. Cholera is a 19th century disease. What disease do you think is similar to cholera today?SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.keys:1. John Snow finally proved his idea because he found an outbreak that was clearly related to cholera, collected information and was able to tie cases outside the area to the polluted water.2. No. The map helped John Snow organize his ideas. He was able to identify those households that had had many deaths and check their water-drinking habits. He identified those houses that had had no deaths and surveyed their drinking habits. The evidence clearly pointed to the polluted water being the cause.3. SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.Step 6: Consolidate what you have learned by filling in the blanks:John Snow was a well-known _1___ in London in the _2__ century. He wanted to find the _3_____ of cholera in order to help people ___4_____ it. In 1854 when a cholera __5__ London, he began to gather information. He ___6__ on a map ___7___ all the dead people had lived and he found that many people who had ___8____ (drink) the dirty water from the __9____ died. So he decided that the polluted water ___10____ cholera. He suggested that the ___11__ of all water supplies should be _12______ and new methods of dealing with ____13___ water be found. Finally, “King Cholera” was __14_____.Keys: 1. doctor 2. 19th 3.cause 4.infected with 5.hit 6.marked 7.where 8.drunk 9.pump 10.carried 11.source 12.examined 13.polluted 14.defeatedHomework: Retell the text after class and preview its language points

  • 新人教版高中英语选修2Unit 1 Science and Scientists-Using langauge教学设计

    新人教版高中英语选修2Unit 1 Science and Scientists-Using langauge教学设计

    This happens because the dish soap molecules have a strong negative charge, and the milk molecules have a strong positive charge. Like magnets, these molecules are attracted to each other, and so they appear to move around on the plate, taking the food coloring with them, making it look like the colors are quickly moving to escape from the soap.Listening text:? Judy: Oh, I'm so sorry that you were ill and couldn't come with us on our field trip. How are you feeling now? Better?? Bill: Much better, thanks. But how was it?? Judy: Wonderful! I especially liked an area of the museum called Light Games.it was really cool. They had a hall of mirrors where I could see myself reflected thousands of times!? Bill: A hall of mirrors can be a lot of fun. What else did they have?? Judy: Well, they had an experiment where we looked at a blue screen for a while, and then suddenly we could see tiny bright lights moving around on it. You'll never guess what those bright lights were!? Bill: Come on, tell me!? Judy: They were our own blood cells. For some reason, our eyes play tricks on us when we look at a blue screen, and we can see our own blood cells moving around like little lights! But there was another thing I liked better. I stood in front of a white light, and it cast different shadows of me in every color of the rainbow!? Bill: Oh, I wish I had been there. Tell me more!? Judy: Well, they had another area for sound. They had a giant piano keyboard that you could use your feet to play. But then, instead of playing the sounds of a piano, it played the voices of classical singers! Then they had a giant dish, and when you spoke into it, it reflected the sound back and made it louder. You could use it to speak in a whisper to someone 17 meters away.? Bill: It all sounds so cool. I wish I could have gone with you? Judy: I know, but we can go together this weekend. I'd love to go there again!? Bill: That sounds like a great idea!

  • 新人教版高中英语选修2Unit 3 Food and Culture-Discovering useful structures教学设计

    新人教版高中英语选修2Unit 3 Food and Culture-Discovering useful structures教学设计

    The newspaper reported more than 100 people had been killed in the thunderstorm.报纸报道说有一百多人在暴风雨中丧生。(2)before、when、by the time、until、after、once等引导的时间状语从句的谓语是一般过去时,以及by、before后面接过去的时间时,主句动作发生在从句的动作或过去的时间之前且表示被动时,要用过去完成时的被动语态。By the time my brother was 10, he had been sent to Italy.我弟弟10岁前就已经被送到意大利了。Tons of rice had been produced by the end of last month. 到上月底已生产了好几吨大米。(3) It was the first/second/last ... time that ...句中that引导的定语从句中,主语与谓语构成被动关系时,要用过去完成时的被动语态。It was the first time that I had seen the night fact to face in one and a half years. 这是我一年半以来第一次亲眼目睹夜晚的景色。(4)在虚拟语气中,条件句表示与过去事实相反,且主语与谓语构成被动关系时,要用过去完成时的被动语态。If I had been instructed by him earlier, I would have finished the task.如果我早一点得到他的指示,我早就完成这项任务了。If I had hurried, I wouldn't have missed the train.如果我快点的话,我就不会误了火车。If you had been at the party, you would have met him. 如果你去了晚会,你就会见到他的。

  • 新人教版高中英语选修2Unit 3 Food and Culture-Reading and thinking教学设计

    新人教版高中英语选修2Unit 3 Food and Culture-Reading and thinking教学设计

    The discourse explores the link between food and culture from a foreign’s perspective and it records some authentic Chinese food and illustrates the cultural meaning, gerography features and historic tradition that the food reflects. It is aimed to lead students to understand and think about the connection between food and culture. While teaching, the teacher should instruct students to find out the writing order and the writer’s experieces and feelings towards Chinese food and culture.1.Guide the students to read the text, sort out the information and dig out the topic.2.Understand the cultural connotation, regional characteristics and historical tradition of Chinese cuisine3.Understand and explore the relationship between food and people's personality4.Guide the students to use the cohesive words in the text5.Lead students to accurately grasp the real meaning of the information and improve the overall understanding ability by understanding the implied meaning behind the text.1. Enable the Ss to understand the structure and the writing style of the passage well.2. Lead the Ss to understand and think further about the connection between food and geography and local character traits.Step1: Prediction before reading. Before you read, look at the title, and the picture. What do you think this article is about?keys:It is about various culture and cuisine about a place or some countries.

  • 新人教版高中英语选修2Unit 5 First Aid-Discovering useful structures教学设计

    新人教版高中英语选修2Unit 5 First Aid-Discovering useful structures教学设计

    You have no excuse for not going.你没有理由不去。He was punished for not having finished his homework.他因未完成作业而受到惩罚。2.动词­ing形式复合结构由物主代词或人称代词宾格、名词所有格或普通格加动词­ing,即“sb./sb.'s+doing”构成。动词­ing形式的复合结构实际上是给动词­ing形式加了一个逻辑主语。动词­ing形式的复合结构有四种形式:①形容词性物主代词+动词­ing②名词所有格+动词­ing③代词宾格+动词­ing④名词+动词­ingHer coming to help encouraged all of us.她来帮忙鼓舞了我们所有人。The baby was made awake by the door suddenly shutting.这个婴儿被突然的关门声吵醒了。Can you imagine him/Jack cooking at home?你能想象他/杰克在家做饭的样子吗?无生命名词无论是作主语还是作宾语都不能用第②种形式。Tom's winning first prize last year impressed me a lot.汤姆去年得了一等奖使我印象深刻。Do you mind my/me/Jack's/Jack leaving now?你介意我/杰克现在离开吗?Excuse me for my not coming on time.很抱歉我没能按时来。His father's being ill made him worried.他父亲病了,他很担心。We are looking forward to the singer's/the singer to give us a concert.我们盼望着这位歌手来给我们举办一场演唱会。

  • 大班数学教案:手指计算法

    大班数学教案:手指计算法

    一、手指练习儿歌(伸出右手带动作表示)1122伸伸手,3344点点头,5566弯弯腰,7788扭一扭,9900抬抬腿,动腿,动手和动口。二、 0的认识:0代表什么?0代表什么也没有。顺口溜:0的性格很活跃,自然数离不开0。10离开了0,就变成了1(制作小卡片10 0 1)20离开了0,就变成了2(制作小卡片20 0 2)30离开了0,就变成了3(制作小卡片30 0 3)40离开了0,就变成了4(制作小卡片40 0 4)50离开了0,就变成了5(制作小卡片50 0 5)60离开了0,就变成了6(制作小卡片60 0 6)70离开了0,就变成了7(制作小卡片70 0 7)80离开了0,就变成了8(制作小卡片80 0 8)90离开了0,就变成了9(制作小卡片90 0 9)三、 5的组成图:1 ●○○○○ 4 14=5 1 4 52 ●●○○○ 3 23=5 2 3 5 3 ●●●○○ 2 32=5 3 2 54 ●●●●○ 1 41=5 4 1 5 5 ●●●●● 0 50=5 5 0 5

  • 初中数学人教版二元一次方程组教学设计教案

    初中数学人教版二元一次方程组教学设计教案

    (一)例题引入篮球联赛中,每场比赛都要分出胜负,每队胜1场得2分,负1场得1分。某队在10场比赛中得到16分,那么这个队胜负场数分别是多少?方法一:(利用之前的知识,学生自己列出并求解)解:设剩X场,则负(10-X)场。方程:2X+(10-X)=16方法二:(老师带领学生一起列出方程组)解:设胜X场,负Y场。根据:胜的场数+负的场数=总场数 胜场积分+负场积分=总积分得到:X+Y=10 2X+Y=16

  • 人教版高中语文必修2《氓》教案2篇

    人教版高中语文必修2《氓》教案2篇

    从《诗经》的现实主义到屈原的浪漫主义,是中国诗歌发展的一个里程碑。屈原的骚体诗,依诗取兴,引类譬喻,继承发展了《诗经》的比兴传统。《诗经》的比兴较为单纯,而《楚辞》的比兴具有象征的特质,往往成为一个形象的系统。《离骚》中香草美人的比兴就是范例。楚地本是泽乡山国,其间颇有叠波旷宇、崇山秀岭,这些江山的光怪之气足以摇荡心灵、催发丽辞伟句。但骚体诗已冲破《诗经》四言诗的固定格式,句式加长而灵活,篇章放大而严密,诗采绚丽而贴切,是《诗经》之后的一次诗体大解放。有人说,中国历代诗“莫不同祖风骚”,足见其对后代诗歌的影响。先秦时代,《诗经》与《楚辞》双峰并峙,是中国诗史上现实主义与浪漫主义的两座巍然屹立的坐标。

  • 人教版高中语文必修2《游褒禅山记》教案2篇

    人教版高中语文必修2《游褒禅山记》教案2篇

    1.本文由“不得极夫游之乐”生发出“尽吾志”的观点,又由“仆碑”生发出“深思慎取”的观点,这两个观点彼此有联系吗?作者游褒禅山,本来是一次平常的游历活动,但却从中悟出了人生哲理──从前洞后洞游人的多少悟出“夷以近,则游者众;险以远,则至者少”,从“入之愈深,其进愈难,而其见愈奇”悟出“而世之奇伟、瑰怪、非常之观,常在于险远”;由此再引申一步,就得出了“非有志者不能至”的结论。然后将这次游山而未能“极夫游之乐”的教训升华到理论上来,具体分析了“至”的几个条件,最后得出“尽吾志”的观点──这正是“求思之深而无不在”的结果。由此可见,“尽吾志”的观点跟“深思慎取”的观点是有联系的:“尽吾志”的观点是在“深思慎取”的基础上产生的;有了这个观点,又能反过来促使人们“深思慎取”,二者是相辅相成的。

  • 小学语文三年级上册第6课《小摄影师》优秀教案范例

    小学语文三年级上册第6课《小摄影师》优秀教案范例

    介绍人物,导入新课  1、启发谈话。课前同学们自己已经读过了课文,查阅了有关资料,谁能向大家介绍一下高尔基?  2、学生之间交流收集的有关高尔基的资料。  3、师出示高尔基的画像,并归纳:高尔基(1886年~1936年),是苏联伟大的无产阶级文学家,世界著名的文学家。他写了很多书,发表了《童年》、《在人间》、《我的大学》、《母亲》等多部小说以及著名的散文诗《海燕》和一系列剧本。“书籍是人类进步的阶梯”这句脍炙人口的名言,就出自高尔基的笔下,全世界人民都很敬爱他。他的作品在我国广为流传,得到人们的喜爱。今天,我们来学习高尔基与一位小学生之间的故事:小摄影师。(板书,提示“摄”的读音。)  高尔基与小摄影师之间到底发生了什么事呢?我们下面来看课文

  • 人教版高中历史必修2战后资本主义的新变化教案2篇

    人教版高中历史必修2战后资本主义的新变化教案2篇

    1、知识与能力:(1)识记:20 世纪 50 ~70 年代国家干预经济的政策、 70年代的经济“滞胀”“混合经济”;福利国家;第三产业的蓬勃发展;“新经济”的出现;(2)理解当代资本主义的新变化的实质是资本主义的自我扬弃,是在资本主义内部的自我改善,是资本主义生产关系的自我调整;(3)掌握以美国为代表的主要资本主义国家在战后的经济发展历程,分析各国经济发展的共同原因。2、过程与方法:(1)引导学生利用教材和相关史料,培养归纳、再现历史事件的能力,提高学生的历史思维能力;通过讨论提高学生的思辨能力,培养学生全面客观地分析问题的思维方式。(2)学生通过观察1977年发达国家国有经济比重表,懂得提取有效信息、分析数据的能力;(3)学生通过思考讨论西方福利制度的利弊,培养全面、客观分析和比较历史现象,辩证地观察和分析历史问题的能力。

  • 部编版九年级语文上册第2课我爱这土地教案

    部编版九年级语文上册第2课我爱这土地教案

    整体感知  齐诵诗歌,说说这首诗歌紧扣“土地”,作了哪些形象性的描述。  【交流点拨】点出土地情结。起始两句,诗人对土地的热爱,已到了不知道如何倾诉的地步,于是他舍弃人的思维语言而借用鸟的简单朴素的语言倾泻他的感情。“嘶哑”的歌声正能抒发作者对土地的义无反顾的眷恋和执着,于是土地情结的激越歌声由此响起。  倾吐土地情结。“被暴风雨所打击着的土地”“悲愤的河流”“激怒的风”“无比温柔的黎明”是作者所歌唱的对象,诗人没有沉溺于对“温柔”恬静的“黎明”的欣赏中,为了让自己的爱永远留给土地,他做出了庄严郑重的选择。  升华土地情结。一问一答,诗人由借鸟抒情转入直抒胸臆。太“深沉”太强烈的土地情结,已使人难以诉诸语言,只能凝成晶莹的泪水。“深沉”一词也许达不到与实际感情相适应的强度,于是其后紧跟着沉重的省略号。省略号中似乎涌动着潜流地火一般的激情,更为沉重地叩击着读者的心房,激起读者持续的共鸣。

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    导语在必修第一册中,我们研究了函数的单调性,并利用函数单调性等知识,定性的研究了一次函数、指数函数、对数函数增长速度的差异,知道“对数增长” 是越来越慢的,“指数爆炸” 比“直线上升” 快得多,进一步的能否精确定量的刻画变化速度的快慢呢,下面我们就来研究这个问题。新知探究问题1 高台跳水运动员的速度高台跳水运动中,运动员在运动过程中的重心相对于水面的高度h(单位:m)与起跳后的时间t(单位:s)存在函数关系h(t)=-4.9t2+4.8t+11.如何描述用运动员从起跳到入水的过程中运动的快慢程度呢?直觉告诉我们,运动员从起跳到入水的过程中,在上升阶段运动的越来越慢,在下降阶段运动的越来越快,我们可以把整个运动时间段分成许多小段,用运动员在每段时间内的平均速度v ?近似的描述它的运动状态。

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    3.下结论.依据均值和方差做出结论.跟踪训练2. A、B两个投资项目的利润率分别为随机变量X1和X2,根据市场分析, X1和X2的分布列分别为X1 2% 8% 12% X2 5% 10%P 0.2 0.5 0.3 P 0.8 0.2求:(1)在A、B两个项目上各投资100万元, Y1和Y2分别表示投资项目A和B所获得的利润,求方差D(Y1)和D(Y2);(2)根据得到的结论,对于投资者有什么建议? 解:(1)题目可知,投资项目A和B所获得的利润Y1和Y2的分布列为:Y1 2 8 12 Y2 5 10P 0.2 0.5 0.3 P 0.8 0.2所以 ;; 解:(2) 由(1)可知 ,说明投资A项目比投资B项目期望收益要高;同时 ,说明投资A项目比投资B项目的实际收益相对于期望收益的平均波动要更大.因此,对于追求稳定的投资者,投资B项目更合适;而对于更看重利润并且愿意为了高利润承担风险的投资者,投资A项目更合适.

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    对于离散型随机变量,可以由它的概率分布列确定与该随机变量相关事件的概率。但在实际问题中,有时我们更感兴趣的是随机变量的某些数字特征。例如,要了解某班同学在一次数学测验中的总体水平,很重要的是看平均分;要了解某班同学数学成绩是否“两极分化”则需要考察这个班数学成绩的方差。我们还常常希望直接通过数字来反映随机变量的某个方面的特征,最常用的有期望与方差.二、 探究新知探究1.甲乙两名射箭运动员射中目标靶的环数的分布列如下表所示:如何比较他们射箭水平的高低呢?环数X 7 8 9 10甲射中的概率 0.1 0.2 0.3 0.4乙射中的概率 0.15 0.25 0.4 0.2类似两组数据的比较,首先比较击中的平均环数,如果平均环数相等,再看稳定性.假设甲射箭n次,射中7环、8环、9环和10环的频率分别为:甲n次射箭射中的平均环数当n足够大时,频率稳定于概率,所以x稳定于7×0.1+8×0.2+9×0.3+10×0.4=9.即甲射中平均环数的稳定值(理论平均值)为9,这个平均值的大小可以反映甲运动员的射箭水平.同理,乙射中环数的平均值为7×0.15+8×0.25+9×0.4+10×0.2=8.65.

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