Last class, we talked about the "whole transformation method", the core idea of which is to take a certain condition in a math problem as a whole, then transform this into that, and then use the attributes of that to solve the problem. To put it bluntly, it is the combination of "mathematical transformation thought" and "mathematical whole thought"
I won't go into details here. Interested friends can pay attention to the account of "strategic research" first, and then go to my homepage to see the complete course!
Overall design method So, what is the "overall design method"?
Before solving this problem, let's first understand what "yuan" is.
In mathematics, the so-called "yuan" actually means "unknown", and children who have studied equations should be familiar with "yuan".
So what is "unknown"?
Quite simply, in fact, any letter can be used to represent "unknown", not just the familiar "X".
Well, after we understand the concept of "element", the "all-element method" is easy to understand.
The so-called "total element method" is to regard a condition in a math problem as a whole, express it with an unknown number, and then substitute this unknown number into the problem to carry out related "movement", so as to achieve the effect of solving the problem!
Here, it is estimated that many children still don't understand and look confused. Never mind, let's take our time and slowly unveil the mystery of "the whole design method".
As we know, the whole idea is actually a condition as a whole, but this "whole" is often a huge "relational expression". If used directly, all kinds of mathematical knowledge points will be dazzling and complicated to apply. At this time, the method of setting elements was introduced.
Imagine, if such a huge whole is set as a letter, and then the letter is used to solve the problem, isn't it much easier?
To put it bluntly, if this "whole" is not defined, it can actually solve the problem, but in the process of solving the problem, because of the huge data, it is not only very tired to write, but also inconvenient to apply various mathematical knowledge points, prone to mistakes and complicated. But if you use a "yuan" and a "letter" instead of that "huge data", the problem will be much simpler.
Having said so much, I believe everyone understands.
Yes, the fundamental purpose of setting elements is actually to make "complex things" simple and not easy to make mistakes in solving problems.
Careful children can easily find that, in fact, regardless of this method or that kind of thinking, the ultimate goal is to make the problem "from difficult to easy" and simplify the "complex problem" so as to find a "breakthrough" and solve the problem easily!
If we only explain the "holistic meta-method" at the text level, it is obviously vague and difficult to understand. If you practice this method in actual combat, the effect will be completely different and the understanding will be much easier.
For example, this problem, at first glance, is impossible to start, but if we take it as a whole, then "determine the elements", "multiply" and finally "subtract", the problem will be solved!
The solution is as follows:
By solving this problem, it actually embodies the wonderful use of "integral method". The idea of solving the problem is to set a "relationship" as "yuan" and "t", so that the original "formula" becomes an "equation", and then use the nature of "equation", that is, "both sides of the equation are multiplied or divided at the same time, and the two sides are still equal"! So the problem is solved.
Obviously, the purpose of this problem is to change the original "formula" into "equation" and then solve the problem with "equation"!
Let's give another example, and then understand another wonderful use of "Dingyuan":
Hardware decoding can also solve this problem, but it is a bit complicated and laborious. If you use the "overall design method", the problem will be easy to handle and it will be much easier to solve it!
We found that there are two problems.
Let's take it as a whole and set it as a.
We also found that there are two other problems.
Let's take it as another "whole" and set it as b,
Obviously, if you use the "holistic meta-method", the problem will be much simpler at once, and the original problem can be written as:
( 1+a) x b - ( 1+b) x a
Applying the mathematical knowledge point of "multiplication and division", we can get
=b + ab - a - ab
=b - a
= 1/5
Using the "integral element method", the problem is much easier to solve. At the same time, it also embodies another wonderful use of the "total element method", that is, "replace a formula with a letter and then substitute it for solution, and the complex structure will be simplified"
Course summary Through the above two vivid examples, it is not difficult to find the wonderful use of "holistic design method" in mathematical problems.
Obviously, the "total element method" is actually a clever use of letters, so that even the most difficult problems can have a "turning point", thus solving problems will be much easier!
From the above two examples, we find that the "integral element method" plays two roles in solving problems:
First, "use a letter to turn a formula into an equation and use the properties of the equation to solve the problem"; One is "setting a complex formula as a letter, then substituting it into the problem and applying various mathematical knowledge points to solve the problem".
Ok, that's all for today. Next class will talk about "integral filling method", so be there or be square!