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1、最新北师大版小学数学五年级（上册）知识点第一单元小数除法1、除数是整数的小数除法计算法则：除数是整数的小数除法，按照整数除法的法则去除，商的小数点要和被除数的小数点对齐;如果除到被除数的末尾仍有余数，就在余数后面添0 再继续除。2、除数是小数的小数除法计算法则：除数是小数的除法，先移动除数的小数点，使它变成整数;除数的小数点向右移动几位，被除数的小数点也向右移动几位(位数不够的，在被除数末尾用 0 补足)，然后按照除数是整数的小数除法进行计算。3、在小数除法中的发现：当除数大于 1 时，商小于被除数。如：3.55=0.7 当除数小于 1 时，商大于被除数。如：3.50.5=7 4、小数除法的验
2、算方法：商除数=被除数(通用)被除数商=除数5、商的近似数：根据要求要保留的小数位数，决定商要除出几位小数，再根据“四舍五入”法保留一定的小数位数，求出商的近似数。例如：要求保留一位小数的，商除到第二位小数可停下来;要求保留两位小数的，商除到第三位小数停下来,如此类推。6、循环小数问题：A、小数部分的位数是有限的小数，叫做有限小数。如，0.37、1.4135等。B、小数部分的位数是无限的小数，叫做无限小数。如5.3,7.145145,等。C、一个数的小数部分，从某位起，一个数字或者几个数字依次不断重复出现，这样的小数叫做循环小数。(如 5.3,3.12323,5.7171,)D、一个循环小数的
3、小数部分，依次不断重复的数字，叫做小数的循环节。(如5.333,的循环节是 3，4.6767,的循环节是 67，6.9258258,的循环节是 258)E、用简便方法写循环小数的方法：只写一个循环节，并在这个循环节的首位和末位上面记一个小圆点。例如：只有一个数字循环节的，就在这个数字上面记一个小圆点，5.333,写 作 5.3。有两位小数循环的，就在这两位数字上面，记上小圆点，7.4343,写作 7.4 3。有三位或以上小数循环的，在首位和末位记上小数点，10.732732,写作 10.732。7、除法中的变化规律：商不变性质：被除数和除数同时扩大或缩小相同的倍数(0 除外)，商不变。除数不变
4、，被除数扩大，文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G
5、9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5
6、G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK
7、5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 Z
8、K5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9
9、ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9
10、 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2文档编码:CW6X10W2Q2J3 HH2D9H1A10Z9 ZK5G9P10G9K2商随着扩大。被除数不变，除数缩小，商扩大。被除数不变，除数
11、缩小，商扩大。第二单元轴对称和平移轴对称：1.轴对称图形：如果一个图形沿着一条直线对折，两侧的图形能够完全重合，这个图形就是轴对称图形，那条直线就叫做对称轴。两图形重合时互相重合的点叫做对应点，也叫对称点。2.轴对称图形的性质：对应点到对称轴的距离相等，对应点连线垂直于对称轴。3.轴对称图形具有对称性。4 轴对称图形的法：（1）找出所给图形的关键点，如图形的顶点、相交点、端点等；（2）数出或量出图形关键点到对称轴的距离；（3）在对称轴的另一侧找出关键点的对称点；（4）按照所给图形的顺序连接各点，就画出所给图形的轴对称图形。平移：1.平移的定义：在平面内，将一个图形沿某个方向移动一定的距离，这样
12、的图形运动称为平移。2.平移的基本性质：（1）平移不改变图形的形状和大小，只改变图形的位置。文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档
13、编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ1
14、0X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D
15、2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH
16、1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O
17、10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 Z
18、P1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3（2）经过平移，对应线段，对应角分别相等；对应点所连的线段平行且相等。3.平
19、移图形的画法：（1）确定平移的方向与距离。（2）将关键点按所需方向平移所需距离。（3）按原来图形的连接方式依次连接各对应点并标上相应字母。设计图案的基本方法：平移、对称、旋转。1.运用旋转设计图案的方法：（1）选好基本图案；（2）根据所选的基本图案确定旋转点；（3）确定旋转度数；（4）依次沿每次旋转后的基本图形的边缘画图。2.运用对称设计图案的方法：（1）先选好基本图案；（2）依据基本图案的特点定好对称轴；（3）画出基本图形的对称图形第三单元倍数和因数数的世界知识点：认识自然数和整数，联系乘法认识倍数与因数。像 0，1，2，3，4，5，6，,这样的数是自然数。文档编码:CZ10X6K1D2L9
20、 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5
21、H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O
22、8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J
23、2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K
24、3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:
25、CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6
26、K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3像-3，-2，-1，0，1，2，3，,这样的数是整数。我们只在自然数（零除外）范围内研究倍数和因数。倍数与因数是相互依存的关系，要说清谁是谁的倍数，谁是谁的因数。补充知识点：一个数的倍数的个数是无限的。
27、因数个数是有限的。一个数最小的因数是1，最大的因数是它本身；一个数最小的倍数是它本身，没有最大的倍数。探索活动（一）2，5 的倍数的特征知识点：2 的倍数的特征：个位上是 0，2，4，6，8 的数是 2 的倍数。5 的倍数的特征：个位上是 0 或 5 的数是 5 的倍数。偶数和奇数的定义：是 2 的倍数的数叫偶数，不是2 的倍数的数叫奇数。能判断一个数是不是2 或 5 的倍数。能判断一个非零自然数是奇数或偶数。补充知识点：既是 2 的倍数，又是 5 的倍数的特征：个位上是0 的数既是 2 的倍数，又是 5 3 的倍数。探索活动（二）3 的倍数的特征知识点：3 的倍数的特征：文档编码:CZ10X
28、6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L
29、9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O
30、5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10
31、O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1
32、J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6
33、K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码
34、:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3一个数各个数位上的数字的和是3 的倍数，这个数就是 3 的倍数。同时是 2 和 3 的倍数的特征：个位上的数是 0，2，4，6，8，并且各个数位上的数字的和是3的倍数的数，既是2 的倍数，
35、又是 3 的倍数。同时是 3 和 5 的倍数的特征：个位上的数是 0或 5，并且各个数位上的数字的和是3的倍数的数，既是 3 的倍数，又是 5 的倍数。同时是 2，3 和 5 的倍数的特征：个位上的数是 0，并且各个数位上的数字的和是3 的倍数的数，既是 2 和 5 的倍数，又是 3 的倍数。6 的倍数的特征：既是2 的倍数又是 3 的倍数的数。9 的倍数的特征：一个数各个数位上的数字的和是9 的倍数，这个数就是 9 的倍数。找因数知识点：在 1100的自然数中，找出某个自然数的所有因数。方法：运用乘法算式，思考：哪两个数相乘等于这个自然数。补充知识点：一个数的因数的个数是有限的。其中最小的因
36、数是1，最大的因数是它本身。找质数知识点：理解质数与合数的意义。文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L
37、9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O
38、5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10
39、O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1
40、J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6
41、K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码
42、:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3一个数只有 1 和它本身两个因数，这个数叫作质数。一个数除了 1 和它本身以外还有别的因数，这个数叫作合
43、数。判断一个数是质数还是合数的方法：一般来说，首先可以用“2，5，3 的倍数的特征”判断这个数是否有因数 2，5，3；如果还无法判断，则可以用7，11 等比较小的质数去试除，看有没有因数7，11 等。只要找到一个 1 和它本身以外的因数，就能肯定这个数是合数。如果除了1 和它本身找不到其他因数，这个数就是质数。数的奇偶性知识点：运用“列表”“画示意图”等方法发现规律：小船最初在南岸，从南岸驶向北岸，再从北岸驶回南岸，不断往返。通过“列表”“画示意图”的方法会发现“奇数次在北岸，偶数次在南岸”的规律。能够运用上面发现的数的奇偶性解决生活中的一些简单问题。通过计算发现奇数、偶数相加奇偶性变化的规律
44、：偶数+偶数=偶数 奇数+奇数=偶数 偶数+奇数=奇数偶数-偶数=偶数 奇数-奇数=偶数 偶数-奇数=奇数 奇数-偶数=奇数 偶数偶数=偶数 偶数奇数=偶数 奇数奇数=奇数第四单元多边形面积比较图形的面积知识点：文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O
45、10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 Z
46、P1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4
47、P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档
48、编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ1
49、0X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D
50、2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH1O5H2O10O8 ZP1J2V4P6K3文档编码:CZ10X6K1D2L9 HH