加法的意义和运算定律

    The Reflexive and Associative Property of Addition

教学内容：人教版第八册P47——48页例1

教学目的：Teaching Aims:

1.学生理解加法的意义；

   Understand the essence of addition.

2.掌握加法交换律和加法结合律，培养学生初步的归纳推理能力。

Grasp the Reflexive Property and the Associative Property of Addition.

Develop the students’ ability to conclude and reason.

教学重点：理解加法的意义和掌握加法交换律和结合律。

Teaching Important Points:

 Understand the essence of addition and grasp the Reflexive Property and the Associative Property of Addition.

教学难点：让学生学会归纳推理的方法。

Teaching Difficult Points: Develop the students’ ability to conclude and reason.

教学过程：Teaching Procedures:

一复习 Revision:

1         口算  7+0     0+7    0+0

      Please solve these problems in your mind.

   师：0和一个自然数相加有什么规律？

     The problems are additions of 0 and natural numbers. Are there any common laws of them?

   生：一个数加上0，还得原数。（板书结论）

     Any number plus 0 remains the same.

2         在（  ）里填上>  < 或=

Please fill in the blanks with  the signs >greater than,  < less than      =equal

26+35（   ）35+26         300+410（   ）410+300

师：这两道题有什么规律？

What can you find from these two problems?

生：交换两个加数的位置，和不变。

Switch the two addends and the sum remains the same.

3         电脑显示：（40个苹果，50个香蕉，求和）

二  新课

    大家对加法的计算方法掌握得很好，现在我们要进一步明确什么是加法？以及加法各部 

    分名称，掌握加法的运算定律。

        You can do the addition problems very well. But what does addition really mean? And are there 

        any calculating laws for addition? Now we’re going to talk about it.

(一)          加法交换律 The Reflexive Property of Addition

1                   出示例1的线段图 

师:谁能说一说这图的意思?

Look at the line segment. What does it mean?

生:北京到天津的铁路长137千米,天津到济南的铁路长357千米.北京到济南的铁路长多少千米?

The Beijing-Tianjin railway is 137km and Tianjin-Jinan railway is 357km. How long is the Beijing-Jinan railway?

教师整理出示例1的应用题提名读一次。

      师：谁能列出式子？为什么要用加法？

           Who can solve this problem? Why do you use addition?

生：从图上可以看出，北京到济南的铁路长，就是把北京到天津的铁路长和天津到济南的铁路长合起来，所以要用加法。

From the picture we know the Beijing-Jinan railway is the sum of two parts: The Beijing-Tianjin railway and the Tianjin-Jinan railway.

师：把两个数合并成一个数的运算叫做加法。（出示结论）

The way to combine two numbers into one is called “ Addition”.

2                   加法各部分的名称

师：137和357在加法算式中叫什么数？他们相加的得数494 叫做什么数？

What do you call the three numbers 137, 357 and 494 in this addition problem?

生：137和357在加法算式中叫做加数。他们相加的得数494 叫做和。

137 and 357 are the addends. The answer 494 is the sum.

3                   电脑出示结论：相加的两个数叫做加数，加的数叫做和。

The two numbers being added are the addends. The answer is the sum.

4                   教学加法交换律

师：看例1，这道题还可以怎样列式计算？

Look at the addition again. Any other ways to solve it?

生：357+137

师：请同学们观察讨论：137+357和357+137比较，有什么特点？

Compare 137+357 with 357+137. Are they the same? Discuss in pairs.

生：两个数相加，交换加数的位置，他们的和不变。

In addition, switch the two addends and the sum remains the same.

5                   师：看卡片，比较下列每组数的两个得数有什么关系。

18+117     117+18       73+26     26+73  

Look at the cards. What can yu find from the answers?

7     生：两个数相加，交换加数的位置，他们的和不变。

           Switch the two addends and the sum remains the same.

      师：用字母a 和  b分别表示两个加数，你能写出一个等式，表示他们的关系吗？                              

      If a and b are the two addends, can you write an equation to show their  relationship?

      生：a+b=b+a

8           练习 Excerises:

            Fill in the blanks:  

          48+（  ）=72+（     ）

          726+35=（     ）+729

          a+38=(    )+(       )

         (     )+55=55+42

（二）加法结合律 The Associative Property

1           师：请做下面两组题。（分组做）

Please do the two groups of problems. Team 1-3 do Group A. Team 4-6 do Group B.

    A                               B

27+36+14                       27+(36+14)

(23+44)+56                     23+(44+56)

(19+37)+163                    19+(37+163)

 654+(46+ a)                   (654+46)+a

  把结果相同的式子用等号连接起来。

    Please match the two problems with the same answer.

  通过这几个等式的比较，发现了什么规律？请讨论。

   What can you find from these problems? Please discuss in pairs first.

  生：三个数相加，先把前两个数相加，再和第三个数相加；或先把后两个数相加，再和

  第一个数相加，它们的和不变。

   In addition, add the addends in any order and the sum remains the same.

     师：这就是加法结合律。利用加法结合律，可以进行简便运算。请做下列题。

     Yes. This is the Associative Property of Additin. We can use this law to solve the problems in

          an easier way. Please try the following problems.

2           例1： 480+325+75        例2   325+480+75

师：讨论先做什么，再做什么。

Look at the two problems. Which two numbers should we add first? Why? Discuss with your partner.

生：…

师：比较这两题，它们分别应用了哪些运算定律？

What law do you use to solve these two problems?

生：加法结合律和加法交换律经常结合使用

Ex 1 we use the Reflexive Property. Ex 2 we use the Reflexive Property and Associative Property together.

三   练习  Excercises:

         Say “ True” or “ False”

        1.  28+56 means to combine 28 and 56 into one number.

        2.  In addition, add the numbers in any order and the sum remains the same.

        3.  Only the Associative Property is used in this problem: 38+95+62=95+（38+62）

        4.  The Reflexive Property and the Associative Property are used in the problem:

       64+87=(60+80)+(4+7)

四小结（略）Summary (omitted)

重点词汇: Key Phrases and Expressions:

the Reflexive Property    交换律              the Associative Property    结合律

addend                 加数                     sum                 和

greater than             大于                   less than               小于

equal                    等于                   line segment             线段

广东碧桂园学校英语高小部双语教学课题组