女儿作业有如下这样一道题，如何解答才能让孩子对这种题目理解得更容易，答题更顺手。 它是属于什么题型。求方法。
The average height of 38 children is 161cm.
The 38 children consist of 20 boys and 18 girls.
The difference between the average height of the boys and that of the girls is 17.1cm.
What is the average height of the girls?
38*161=6118
17.1*20=342
6118-342=5776
5776/38=152
女生平均身高152厘米
如果还没学代数就用model，不会上传图，只能大概描述下
女孩18个unit,男孩是20个大点的unit，比女孩一个unit多17.1,然后就是经常的题型，为了同一unit，把20个男孩unit多出的20×17.1从总数38×161里减掉，结果再除以38。
女孩子的高度=X
18X+(17.1+X)*20 = 161*38
18X+342+20X=6118
38X=5776
X=152
女孩子的高度=152CM
有点像带小数点的鸡兔同笼。平均身高=〉腿的数量。加腿变成加身高。
把女孩身高加17.1MM 就变成男孩。
如果都是男孩，总身高变成：161×38+17.1×18=6425.8
男孩身高：6425.8/38=169.1
女孩身高：169.1-17.1=152.0
应该是四年级的功课吧？
为啥男孩高？小学一般是女孩高吧
综上， 大致都属于同一种方法, 理解起来很轻松。
可孩子的数学老师在课堂上否认了这种方法，说虽然结果正确，但method不对。
老师通过列表格做的解释，孩子理解不透， 涉及DIFF 1.9, 3.8….17.1/1.9=9， 161-9=152.
等作业纸发下来，再琢磨老师讲述的方法吧。。。
小六会考有限制不许用方程式来解题吗
没有。教育部曾明确地澄清过此事：
Different Approaches Taught for Mathematics Techniques
http://www.moe.gov.sg/media/forum/2007/20070217.htm
Mr Lim Boon Tong had sought clarification on whether mathematics techniques like algebra, other than the model drawing method, could be used in the Primary School Leaving Examination (PSLE) Mathematics. (“Can algebra be used to solve PSLE maths problems”, The Straits Times, 12/2).The model drawing method is a powerful approach for problem solving and learning mathematical concepts. By drawing models, pupils can represent the mathematical relationships in a problem pictorially. This helps them understand the problem and plan the steps for the solution.The pictorial form also helps pupils visualise what could otherwise be abstract concepts. In this way, model drawing supports the learning of fractions, ratio and percentages. Pupils will find model drawing useful when they solve problems involving these concepts in Primary Five and Six.The model drawing method is thus a developmentally sound approach for young children. It is recognised internationally as an effective way for young children to learn problem solving and to have early exposure to algebraic concepts. At Primary Six and Secondary One, pupils can draw upon their earlier experience of using models to help them understand algebraic relationships in problems.Other than the model drawing approach, pupils are also taught different problem solving methods. They are encouraged to try different approaches and have the flexibility to choose the method that works best for them in solving the problems. They are also encouraged to present their solutions clearly so that these can be understood.While pupils are not required to use algebra to solve word problems in the PSLE Mathematics, they are also not restricted to the use of any one particular method. In the marking of PSLE Mathematics, all mathematically correct solutions are acceptable and there is no loss of marks if a correct algebraic method is used.We thank Mr Lim for his feedback.
Ho Peng (Ms)
Director, Curriculum Planning and Development
Ministry of Education
Tan Yap Kwang
Chief Executive
Singapore Examinations and Assessment Board
—————————————————————–
小学老师是这样告诉孩子的: 可以用方程式，但不提倡。用方程式解题，如果步骤正确但答案错误，将得不到“method mark”。
你太专业了，谢谢，早知道我早点上网跟你多聊聊，有时候看孩子做不出来时间又赶，我就让他用方程，看来我不能再瞎说了，新加坡的国情跟中国不一样
还有一点，想跟您聊一下，我的孩子算三角形面积这种图形题的时候从来不写公式，造成很多粗心错误，比如光是底乘以高，忘记再乘以1/2，然后扣分，这样我们简单的题目都保不住，圆的面积也一样，由于不写公式，有时候把半径的平方错带入成直径的平方，导致一些本不该有的错误，他还跟我说，如果写公式，老师和同学会笑话，孩子是不是在新加坡学傻了？每次考试简单的题目都错很多，难题也不保，所以我们的数学成绩一直上不来，现在最后两个月了，我也挺急的，和孩子在学习上产生很多类似的矛盾，想听一下您的意见，谢谢
首先，方程式是一定要学的，通常小学会教小六学生一些简单的一元一次方程式，解题时可以使用。
事实上现在小学的数学题越来越难，有些题不用方程式是很难解出的。尤其是PSLE考试时，时间紧迫，碰到难题时很多孩子还是选择用方程式来解题。用方程式解题的好处是简单明了快速，运用熟练的话出错的可能性也比较少。
运用方程式时应该尽量打一些“擦边球”，不要使用X, Y之类的符号，不要用二元一次方程。应该尽量让解题方法看起来比较像“普通方法”。下面是一个例子：
莱佛士女小的一道小六试题：
Beaker A and Beaker B contain some water. If 46.5ml of water is drained from Beaker A, the volume of the water in beaker A will be 60% that of the water in Beaker B.
If 35.2 ml of water is drained out from Beaker B, the volume of the water in Beaker B will be 85% that of the water in Beaker A.
What is the tota volume of water in Beaker and Beaker B?
解答：
1 u —> 1 unit
Before draining out water fram Beaker A，
Beaker A : Beaker B –> (3u + 46.5) : 5u
If 35.2ml drained from Beaker B，
Beaker A : Beaker B –> 3u + 46.5 : 5u – 35.2 = 100 : 85
(3u + 46.5) : (5u – 35.2) = 20 : 17
Equalize/cross-multiply:
(3u + 46.5)x17=(5u – 35.2)x20
51u + 790.5 = 100u – 704
49u=1494.5
1u –> 30.5
Beaker A –> 3 x 30.5 + 46.5 = 138 ml
Beaker B –> 5 x 30.5 = 152.5 ml
Total –> 138+152.5 = 290.5ml
有些数学题，用“普通方法”解题反而更加简单，此时就不要使用方程式了。
比如下面这道南洋小学2011年Prelim的试题：
In a cinema, the ratio of the number of girls to the number of boys was 3:2. The ratio of the number of woman to the number of boys was 5:4.The ratio of the number of men was 2:5. During the movie, 6 women and 27 men left the cinema. The ratio of the number of woman to the number of men then became 1:2.
a) Express the number of women as a fraction of the number of men at first. Leave your answer in its simplest form.
b) How many children were there in the cinema?
解答：
(a) Boy: Girl —> 2:3 —> 4:6
Boy: Women —> 4:5
Men :Girl —> 5:2 —>15:6
Men: Women —> 15:5 —> 3:1
(b) Men: Women —> 3:1 —> 45:15
after less 6 women and 27 men —> (45-27) ：(15-6)=2:1
I unit —> 15/5=3
nos of children —> 3x(4+6) = 30
还有一些题，如果用二元一次方程的话很容易解开。但是二元一次方程对于多数孩子的来说太难，很容易出错，因此应该把它转化为一元一次方程来解答。比如下面这道万慈小学的数学题：
Laura and Ahmad have some stamps. If Laura gives 80 stamps to Ahmad, he will have five times the number of stamps as she has. If Ahmad gives 120 stamps to Laura, she will have 1/3 as many stamps as Ahmad. How many stamps does Laura have at first?
用二元一次方程：
L — > nos of Laura’s stamp
A — > nos of Ahmad’s stamp
5x(L-80) = A+80 ……(1)
3x(L+120) = A-120 …. (2)
5L-400=A+80 ……(1)
3L+360=A-120 ……(2)
(1)-(2) —> 2L-760=200
2L=960
L = 480
用一元一次方程：
u — >unit
If Laura gives 80 stamps to Ahmad
L —> 1u
A —> 5u
At first,
L —> 1u+80
A —> 5u-80
If Ahmad gives 120 stamps to Laura
L —> 1u+80+120
A —> 5u-80-120
3x(1u+80+120) = 5u-80-120
3u + 600 = 5u – 200
2u = 800
1u = 400
400+80=480
谢谢！想请问你，新加坡老师为什么不让学生写公式？
以前新加坡的小学数学和中国差不多，后来教学改革后就变成这样了。现在的方法应该是考虑到多数孩子在小学阶段较难理解和应用方程和代数的概念，因而采用图形和符号的方式以便让孩子更容易理解和找出数学运算中的逻辑关系和集体方法。另外，如果孩子过早学习方程式，可能就会对其产生一定的依赖性，结果是限制了孩子其它方面的思维发展。
对于理解能力较强的孩子，运用方程式解题没有什么不妥之处。但是孩子接触方程式不宜过早，最好是在完全掌握Model Drawing， 比较法、假设法、找不变量等方法以后。
非常感谢！