Super top students: the most efficient learning method for top students

Chapter 7 Quick Calculation - Brain Gymnastics (2)
Learning quick calculation is the same as learning other knowledge, and you have to work hard to learn it, so you can definitely learn it well.

"If you want to succeed, you have to work hard." This is a truth.The famous composer Mozart said it well: "Whoever works as hard as me will be as successful as me."

There are several aspects to pay attention to when learning quick calculation:
First, we must improve our understanding of learning.We must realize that as long as we study hard, study hard, and have the courage to overcome difficulties in learning, we can learn quick calculation well.

Second, we must grasp the characteristics of various quick calculations.Grasping the characteristics is the key to mastering the law.

Third, it is necessary to memorize quick calculation skills and methods. Only by mastering quick calculation skills can they be applied to actual mathematical operations and improve the calculation speed of mathematics.

Fourth, practice more.You can't give up all your previous efforts, you must persevere and practice more. Only in this way can you master the quick calculation skills proficiently.

Fifth, when doing quick calculations, you should use your brains, think more, and use the knowledge you have learned flexibly, especially for variable oral calculation questions, which require more than one quick calculation method you have learned to answer.

Sixth, one should be good at identifying the characteristics and solving methods of special quick calculation questions, and be good at using special algorithms for quick calculation.

Quick calculation makes mathematics beautiful.

If you think that mathematics is all dull formulas and theorems, then you are wrong.There is a lot of beautiful mathematics in this world.

For example: using regular lines to make beautiful patterns, this is mathematics.

The Arabs brought numbers from India to Europe, and used the regular patterns of numbers to make beautiful wool blankets.Because Arabs have always been very close to numbers, they can make beautiful patterns.

In the process of learning mathematics, we often encounter arithmetic problems, which are cumbersome, time-consuming, and nerve-wracking, so we must not see the beauty of mathematics, so we have a sense of fear and boredom towards mathematics.

In fact, mathematics is not so scary. Mathematics contains a lot of order and laws. If you don’t want to use a pen to calculate, then use your brain to master the laws and order in mathematics, that is, the methods and techniques of quick calculation.

Once you learn the method, mathematics will become easier and easier, you can calculate faster than a calculator, and in the long run, you will be a "winner" in learning mathematics.

British scholar Bernard said it well: "A good method can enable us to make better use of our natural talents, while a poor method may hinder the use of talents."

Through the learning of quick calculation methods and skills, you will fall in love with mathematics, cultivate a smart and wise mind, and improve your thinking ability and innovation ability as a whole.

Whether it is divisible or not, you can easily "recognize" it

There are some secrets that allow you to quickly "recognize" whether it is integer division.Knowing these secrets, division will become very interesting, and finding divisors and multiples will become very easy.

Let us observe the multiplication formula first. The numbers with no remainder in the quotient in division are all in the multiplication formula.

比如：3、6、9、12、15、18、21、24、27都是能被3整除的数字。

The numbers in paragraph 4 of the multiplication formula are all divisible by 4.By analogy, all the paragraphs in the multiplication formula are the same.

So, what about the numbers after the other numbers?Here are some tips:

(1) Numbers divisible by 2: All even numbers are divisible by 2.

(2) Numbers divisible by 3: Numbers whose sum of digits is a multiple of 3 are all divisible by 3.

比如153，1+5+3=9，9是3的倍数，那么153就可被3整除。

(3) Numbers divisible by 4: Numbers whose last two digits are divisible by 4.

For example, 13416, the last two digits of this number are 16, 16 is a multiple of 4, so 13416 is divisible.

（4）可被5整除的数：尾数为0或5的数，都可以被5整除。

(5) A number divisible by 6: first of all, it must be an even number and divisible by 3, so it must be divisible by 6.

(6) Numbers divisible by 7:

The following method can be used to find the number divisible by 7 in the three-digit or four-digit number:
First separate the tens and hundreds digits.

For example, 539, separate 5 from 39.Multiply the number in the hundreds place by 2, here is 5×2=10.Then, add the product of the hundreds digit × 2 to the ones and tens digits, here is 10+39=49, if their sum is a multiple of 7, then the original number can be divisible by 7 .

Here 49 is divisible by 7, so 539 is divisible by 7.

（7）可被8整除的数：最后的三位数可除尽8的数，就可以被8整除。比如17328，其最后的三位数328可以被8整除，那么17328也可以被8整除。

（8）可被9整除的数：各位数之和可被9整除的数。比如3456，3+4+5+6=18，18能被9整除，那么3456也就能被9整除。

(9) Numbers divisible by 10: All numbers with mantissa 0 are divisible by 10.

Several clever ways

1. "Recognition", the benefits of recognition
Recognize some simple calculation formulas as a character, in this way, the calculation speed and accuracy will be greatly improved.

Especially for primary school students in grades [-] to [-], they always feel that arithmetic homework is difficult and they always make mistakes. If you teach children to "recognize arithmetic formulas", those formulas will come out as soon as they are recognized. Fast and accurate.

Some children form the habit of relying on pen calculations. If they don’t do pen calculations, they feel unsure whether they are right or not. This will make their learning efficiency too low. If this continues, the pressure of studying in junior high school and high school will become even greater.

On the surface, there is not much to learn in primary school mathematics, especially many female students, who earnestly calculate with a pen and have enough time, often get 100 points in mathematics, and many parents often sigh: "My daughter is pretty good at primary school mathematics. , I often get full marks in math exams, why can’t I fail in math when I get to junior high school?”

These girls are not without problems in elementary school mathematics, but their parents and teachers have neglected and never noticed that their speed is too slow.

From a technical point of view, it is also a serious hidden "mistake" to do math problems with high accuracy but not high speed. However, this kind of hidden error cannot be detected from the test paper, and is almost all teachers and parents ignored.

This question is very important.Many students, especially many female students, lose at the starting line, so in elementary school, we must firmly grasp the "recognition" and really pay attention to it. As our age and school age increase, our academic performance will also follow. promote.

2. "Addition formula" uses "eye" to see the number

Clever use of residual difference method.

When doing addition calculations, you can first regard the numbers that are close to the whole ten, the whole hundred, the whole thousand... The added fractions plus the "principle for processing.We usually call the "fraction" here "residual difference".

3. The addition of the same numerator and different denominator can be blurted out
The way to get the answer by adding the same numerator and different denominator without common denominator is: use the product of the two denominators as the denominator, and use the sum of the two denominators and the product of the numerator as the numerator.Note: If the numerators of two fractions with different denominators are both 1, just use the product of the denominators as the denominator, and the sum of the denominators as the numerator.

4. Addition and calculation are getting higher and higher

You may like to add two numbers because it is easier, but what if you encounter several or even dozens of numbers?One question is enough to make your head spin.

Breaking the rules and finding shortcuts is the best way to add quickly.To achieve the effect of fast calculation, mastering the arithmetic of addition is the most important thing.

Perseverance will make your calculations flourish
Quick calculation skills can only be achieved through practice, and only by doing more practice can "practice make perfect", but if you want to become a quick calculation genius, in addition to doing more exercises and focusing on your heart, you must persevere and don't give up halfway. "Frozen three feet is not a cold day "A real master of quick calculations is built on the basis of accumulated practice.

Meals need to be eaten one bite at a time, and roads must be taken step by step. You must proceed step by step and persevere. Don’t fish for three days and hang the net for two days, otherwise you will never be a quick calculation genius.

Some students said: "I just can't persevere in doing some things. It may be because I am not interested in these things by nature, or I feel more and more boring about these things, so I give up before I know it."

How to be persistent?Here are some suggestions, I hope you will try them out.

First, set a clear goal for yourself.

Before you study or do other things, think about what you want to do now, what kind of goal you want to achieve, and encourage yourself not to give up until you reach your goal.

Second, eliminate all possible interference.

If you insist on doing one thing, there are other people or other things that interfere with you, or eliminate the interference, or continue to stick to the original thing after doing these things, do not divert your attention and give up the original thoughts and behaviors .

Third, ask yourself every day: "Did I do it today?"

Strengthen a kind of consciousness every day, let yourself always point to the established goal, so as to ensure the focus on the goal, avoid distraction and useless work, you can ask yourself every day: "Did I do it today?" Remind yourself every day , Let yourself settle down and persevere.

To truly become a master of learning and a genius in quick calculation, persistence is the way you must go, because you have no choice.

At the same time, avoid half-heartedness, half-heartedness is the enemy of quick calculation

The focus of energy has two meanings: one means that when studying or doing something, the energy (attention) is highly concentrated and not half-hearted;

The second means that in the long-term learning career, the direction of attention is consistent, dedicated to learning, and has a certain focus.The reason why the laser can cut the steel plate and the reason why the solar cooker can cook the beef is the result of focusing.

The ancients said: "Thinking for a long time will give birth to wisdom." "Only after doing something can you do something." If you can choose the right goal and concentrate on it, your energy will shine brightly.

You must concentrate on everything you do, and don't be half-hearted, especially for quick calculations.

If you do quick calculation half-heartedly, thinking about going out to play early while doing the problem, all the quick calculation knowledge and skills you have learned will fly out of your mind at that time.

Speed ​​calculation is a thinking exercise that requires concentration.Half-hearted and half-hearted means that you put your heart into many places, and as a result, you can't do anything well.If you want to become smart and improve your learning efficiency, you must concentrate on quick calculations.

In addition, when you have confidence, use your brain instead of a pen

I started to have some confidence in mathematics, but I still often fail.As soon as you see the numbers, you don’t care about 21, [-], and you have to start calculating with a pen, only to find out that you made a mistake later. This is not a good way to learn.

First put down the pen and read the title carefully.Even if it is a question that you think is easy to do, put down your pen and read the question a few times first.Calculating blindly is sometimes not a good thing.

Quick calculations are accompanied by joyful details.

How to train yourself to become a quick calculation master?In fact, the details of normal study are crucial:

1. Change mindset
When doing a problem, don't follow the rules, but have a quick calculation concept, and see if the problem can be solved by a quick calculation method. You can't pick up a pen and start calculating on paper, you must first think with your brain.

2. Familiar with algorithms, laws, etc.
Because calculation rules, laws, and properties are the basis of calculation, if you can't master these regular things, it will be more difficult to learn quick calculation skills, and it is not solid.

3. Do more practice

The "many" mentioned here refers to the "many" of high quality, not just the "many" in quantity.Do more questions, see more questions to be knowledgeable, practice makes perfect, and perseverance can improve computing ability.

4. Cultivate the habit of quick calculation and clever calculation
能速算、巧算是一个学生能综合运用计算知识、计算能力强的突出表现。比如计算855÷45的商应比900÷45的商小1，应是19。

5. Focus on quick calculations

When performing quick calculation training, the attention should be highly concentrated, and you should not look left and right.Otherwise, even if you do too much training, you will not be able to achieve the effect of quick calculation.

(End of this chapter)