北师大版小学数学五年级下册知识点整理.doc

conferences, learned superiors policies; reports, you can learn to deal with problems, art, just wanted to learn, to learn at any time. To continuously expand the scope of the study. The complexity and comprehensiveness of our work, decided to not only do we want to be "professionals", or if "generalists", to dabble in different areas of knowledge. Mastery of knowledge not only to have knowledge to rational analysis. This on requirements we, not only to learning national of route, and approach, and policy, also to learning national of legal, and regulations; not only to with political theory armed mind, also to with economic theory guide work; not only to read history, also to read history; not only to absorption SM of mirror, also to gets is of road; not only to from local learn, also to to outside learn; not only to to books learn, also to field study learn. Therefore, I would encourage you, and more to the outside world when I have time to take a look at, take a stroll, outside developments, learn other people's development approach, and then come back to guide our work. Second, we must think. "Learning without thought to overshadow, thinking without learning is perilous." We want to foster the character of advancing with the times, forge ahead, often reflect themselves in adapting to the new situation on whether there are delays, have anything to fear in the reform and innovation, whether in terms of accelerating the development of a relaxation, keep promising State of mind. In order to do investigations, investigations is the road to heaven, God disposes of the base. To wants to real heard truth, and justice to truth, and get truth, received effectiveness, on must in-depth actual, and outreach, and in-depth masses, worship masses for Division, and masses heart, with masses with discussion everyone care of problem, listening they of calls, understand they of mood, feel they of suffering, summary they of experience, concentrated they of wisdom, especially on masses most hope, and most urgent, and most worries, and most complained of hot, and difficulties and focus problem, more to active research, caught not put. Dare to innovate, in our work, often remain "the old way doesn't work, the new approach would not" situation, the reason, the key is that many people know that copying other people's ideas, mechanically, using someone else's old ways. To change this predicament, requires us to break the shackles of traditional concepts to overcome conservative, conformist, good at finding new problems and to accept new things, summarize new experience, new ideas, developing new programmes and Maverick, a new approach to solve problems, speed up development. Especially in implement superior policy spirit of process in the, both implementation, and cannot mechanically, to to extraordinary of courage and develop enterprising of spirit, put flexibility and principle combined up, put superior of spirit and local reality combined up, Yong conspiracy to breakthrough of policy, and exercise innovation of lift, developed out development works of, and grass-roots welcomes of, and北师大版小学数学五年级（下册）知识点第一单元：分数乘法1、分数乘整数的意义：分数乘整数的意义同整数乘法的意义相同，就是求几个相同加数的和的简便运算。2、求一个数的几分之几是多少用乘法计算。如：甲数是20，乙数是甲的，乙数是多少？ 20×= 16 答：乙数是163、分数乘整数的计算方法：分母不变，分子和整数相乘的积作分子。能约分的要约成最简分数。计算时，可以先约分再计算。4、理解打折的含义。例如：九折，是指现价是原价的十分之九。5、分数乘分数的计算方法：分子相乘做分子，分母相乘做分母，能约分的可以先约分。计算结果要求约成最简分数。           6、比较分数相乘的积与每一个乘数的大小。乘数乘以小于1的数，积小于乘数；乘数乘以等于1的数，积等于乘数；乘数乘以大于1的数，积大于乘数；真分数相乘积小于任何一个乘数；真分数与假分数相乘积大于真分数小于假分数。长方体和正方体物体顶点面棱个数个数形   状大小关系条数长度关系长方体86都是长方形，特殊的有两个相对的面是正方形，其余四个面是完全一样的长方形。相对的面是完全一样的长方形。12可以分为三组，分别叫做长、宽、高。相对的棱平行且相等。正方体86都是正方形。每个面都是相等的正方形。12长度都相等。 长方体或正方体6个面的面积之和叫做它的表面积。 露在外面的面的面积 = 露在外面的面的面积×每个面的面积正方体的拼组：每拼组一次就少2个黏合面的面积。长方体的切割：每切割一次就多2个切割面的面积。1、体积：物体所占空间的大小叫作物体的体积。（从外部测量） 容积：容器所能容纳物体的体积叫做容器的容积。（从内部测量）注意：同一个容器，体积大于容积；当容器壁很薄时，容积近等于体积。如果容器壁忽略不计时，容积等于体积。几个物体拼在一起时，它们的体积不发生改变（它们占空间的大小没有发生变化）2、常用的体积单位有：立方厘米cm³、立方分米dm³、立方米m³。棱长是1厘米的正方体体积是1立方厘米，记作1cm³。如半个大拇指的体积大约是1立方厘米。棱长是1分米的正方体体积是1立方分米，记作1dm³。如粉笔盒的体积你大约是1立方分米。棱长是1米的正方体体积是1立方米，记作1m³。如1张讲台桌的体积大约是1立方厘米。3、 常用的容积单位有：毫升ml、升L 手指头、苹果、火柴盒体积较小，可用作单位西瓜、粉笔盒体积稍大，可以用作单位矿泉水瓶、墨水瓶可以用毫升作单位热水瓶等较大盛液体容器、冰箱可用升作单位我们饮用的自来水、集装箱用“立方米”作单位。4、 相邻两个体积单位之间的进率是1000 。 高级单位变低级单位=进率×高级单位的数低级单位变高级单位=低级单位的数÷进率1立方米=1000立方分米 1立方分米=1000立方厘米 1升=1000毫升 1升=1立方分米 1毫升=1立方厘米长方体的棱长总和 =（长+宽+高）×4 = 长×4 + 宽×4 + 高×4 C=（a+b+h）×4或C=a×4+b×4+h×4长方体的表面积 =（长×宽 + 长×高 + 宽×高）×2 S = ( ab + ah + bh )×2长方体的体积 = 长×宽×高 V = abh正方体的棱长总和 = 棱长×12 C = a×12正方体的表面积 = 棱长×棱长×6 S = 6a²正方体的体积 = 棱长×棱长×棱长 V = a³长方体的体积=横截面面积×长能利用长方体（正方体）的体积及其他两个条件求出问题。如：长方体的高=体积÷长÷宽 长=体积÷高÷宽 宽=体积÷高÷长注意：计算体积时，单位要统一；表面积与体积表示的意义不一样，单位不同，无法比较大小1、 不规则物体体积的测量方法：一般都是用溢水法、升水法、降水法等方法把不规则物体的体积转化成可通过测量计算的水的体积（注意液面是“升高了”还是“升高到”）注意：在测量体积较小的不规则物体的体积时，要先测量出一定数量物体的体积，再算出一个物体的体积。 2、不规则物体体积的计算方法 = 现在液体的体积 - 原来液体的体积第三单元：分数除法1、 倒数：如果两个数的乘积是1，那么我们称其中一个数是另一个数的倒数。倒数是对两个数来说的，并不是孤立存在的。2、 求一个数的倒数只要将这个数的分子、分母调换位置。求小数的倒数要先把小数化成分数再求倒数。3、1的倒数仍是1；0没有倒数。因为在分数中，0不能做分母。4、 分数除以整数，就是求这个数的几分之几是多少。分数除以整数（0除外）等于乘这个数的倒数。5、分数除法的计算方法：除以一个数（0除外）等于乘这个数的倒数。6、比较商与被除数的大小。 除数小于1，商大于被除数；除数等于1，商等于被除数；除数大于1，商小于被除数。1、 “已知一个数的几分之几是多少，求这个数”一般采用列方程 （1）、找到分率句，找出单位“1”，列出等量关系式。 这里的单位“1”未知，所以设单位“1”为x，再根据等量关系式列出并解这个方程。 （2）、算术方法：用部分量除以它所占整体的几分之几（对应量÷对应分率=标准量）2、判断单位“1”： 一般来说，某个数的几分之几，“某个数”就是单位“1”数比谁多几分之几或少几分之几，“比”字后面的数量就是单位“1”谁是谁的几分之几，“是”字后面的数量就是单位“1”第五单元：分数混合运算1、分数混合运算顺序与整数混合运算顺序相同。2、整数运算定律在分数运算中同样适用。3、一般的分数混合应用题，计算时，要一步一步地认真分析，在分析每一步时，关键是要找好单位“1”，看单位“1”是否已知，如果已知，一般用乘法计算，如果未知，便用除法计算。在计算时，要注意约分。第六单元：百分数1、 百分数的意义：表示一个数另一个数的百分之几。百分数也叫百分比、百分率。2、 百分数与分数的联系和区别：分数既可以表示一个数是另一个数的几分之几，也可以表示一个具体数量，当表示具体数量时可以带单位名称。百分数只表示一个数是另一个数的百分之几，是一个比率，百分数不能表示具体的数量，后面不能带单位名称。3、解决一个数是另一个数的百分之几的实际问题。这部分知识同分数除法中求一个数是另一个数的几分之几相同。4、小数、分数化成百分数的方法：把小数化成百分数，只要把小数点向右移动两位，同时在后面添上百分号；把分数化成百分数，可以先把分数化成小数（除不尽时，通常保留三位小数），再写成百分数；也可以把分子分母同时乘一个数将其化成一百分之几的数，再写成百分数。5、求一个数的百分之几是多少。方法同求一个数的几分之几是多少。6、 百分数化成分数、小数：百分数化成小数：只要把小数点向左移动两位，同时去掉百分号；百分数化成分数：先把百分数改写成分数，能约分的要约成最简分数。第七单元：统计条形统计图折线统计图扇形统计图特点用一个单位长度表示一定的数量用整个圆面积表示总数，用圆内的扇形面积表示各部分占总数的百分数。用直条的长短表示数量的多少。用折线的起伏表示数量增减变化。作用 （优点）从图中能清楚地看出各数量的多少，便于相互比较。从图中能清楚地看出数量增减变化的情况，也能看出数量的多少。从图中能清楚地看出各部分与总数的百分比，以及部分与部分之间的关系。1、中位数：将一组数据从小到大（或从大到小）排列，中间的数称为这组数据的中位数。当一组数据的个数是偶数时，中位数取中间两个数的平均数。2、众数，就是一组数据中出现次数最多的数。在一组数据中，众数可能是1个，也可能是多个，还可能是没有。百分数应用题知识点归纳1、求一个数的百分之几是多少 一个数（单位“1”） ×百分率2、已知一个数的百分之几是多少，求这个数 部分量÷百分率=一个数（单位“1”）3、求常见的百分率 如：达标率、及格率、成活率、发芽率、出勤率等 a率=a的数量÷总量×100%4、比多比少的第一种类型：求一个数比另一个数多（或少）百分之几（未知数） 实际生活中，人们常用增加了百分之几、减少了百分之几、节约了百分之几等来表示增加、或减少的幅度。口诀：“一减一除”（大的减小的除以比后面的）求甲比乙多百分之几 （甲乙）÷乙×100%求乙比甲少百分之几 （甲乙）÷甲×100%5、比多比少的第二种类型：已知一个数比另一个数多或少百分之几（已知数），和其中一个数，求另一个数公式：a÷（1±b%）只需判断两点：一，已知a乘法，未知a除法。二，比多（或提高、增加.）括号内就“”，比少（降低、减少.）括号内就“”6、 折扣 几折就是十分之几也就是百分之几十 现价=原价×折扣 原价=现价÷折扣 折扣=现价÷原价×100% 埋地部分整根敷设不允许有接头。地上一层至四层为低区，由小区室外给水管网直接供水，地上五层至十六层为中区，由小区中区变频调速泵组供水，地上十七层至三十三层为高区，由小区高区变频调速泵组供水。According to Office Party of mass line education practice activities led group of unified arrangements, units main led to for cadres workers Shang a times party lecture, due to himself level limited, only put this stage concentrated learning of experience today and everyone common with learning exchange, purpose is let we further deep understanding mass line of connotation, insisted party of mass line, do masses work, following main from four a aspects told: a, and full awareness party of mass line education practice activities of major meaning Party's 18 major distinct proposed to focus on the party's advanced nature and purity, in the party, with "pragmatic and clean for the people" as the main content of the party's mass line and educational practice. This is comrade XI Jinping as party General Secretary and adhere to strictly administering the party, strengthen the party's major decision is in line with the public expectations and strengthening the construction of learning-oriented service innovation of Marxist party's major deployment, is the important measure to advance the great cause of socialism with Chinese characteristics. First, carry out the party's mass line in education practice, was carrying 18 of the party spirit, summon a powerful force for realizing the great rejuvenation of the Chinese nation the Chinese dream of urgent needs. Party's 18 to promote strategic deployment to building socialism with Chinese characteristics, presents two 100-year goal, namely, by 2020 China's gross domestic product and per capita income of urban and rural residents in 2010 on the basis of double complete the building of a well-off society; the middle of this century into a prosperous, democratic, civilized and harmonious Socialist modern country, and on this basis, the Chinese dream of realizing the great rejuvenation of the Chinese nation. 18 Congress of the party, Comrade XI Jinping repeatedly expounded the Chinese dream. The basic connotation of the Chinese dream, is the national prosperity, national revitalization, the happiness of the people, China important to follow is to keep China Road, carry forward the spirit and cohesion strength of China, dream dreams of the people of China, but determined confidence, enhance self-awareness, achieve self-reliance, to build a stronger China, civilization, harmony, beauty, China, China, China. Strategic conception of China was 18 the spirit of the enrichment and development of the party, conscientiously study the Chinese dream, leading people to hard to realize the Chinese dream, mass education activities in depth the fundamental starting point and ending point. Strengthen the education of the party's mass line, helps to train the collective consciousness of the unity of the party and the people, playing the Chinese dream ideological bases. Comrade Mao Zedong stressed that parties should have "common language" socialist countries must have "unity of will". History has