"Any number divided by 0 is meaningless." This is a "conclusion" about 0 that teachers from primary school to middle school are still talking about. At that time, division (primary school) was to divide a copy into several parts and figure out how many there were in each part. A whole cannot be divided into 0 parts, which is "meaningless". Later, I learned that 0 in a/0 can represent a variable with zero as the limit (the absolute value of a variable is always smaller than an arbitrarily small positive number in the process of change) and should be equal to infinity (the absolute value of a variable is always larger than an arbitrarily large positive number in the process of change). From this, another theorem about 0 is obtained: "A variable whose limit is zero is called infinitesimal".
"Room 203 105 in 2003", although all of them are zeros, they are roughly similar in appearance; They have different meanings. 0 indicator vacancy of 105 and 2003 cannot be deleted. 0 in Room 203 separates "Building (2)" from "House Number". (3) "(that is, Room 8 on the second floor) can be deleted. 0 also means that ...
Einstein once said: "I always think it is absurd to explore the meaning and purpose of a person or all living things." I want to study all the numbers of "existence", so I'd better know the number of "non-existence" first, so as not to become what Einstein called "absurd". As a middle school student, my ability is limited after all, and my understanding of 0 is not thorough enough. In the future, I hope (including action) to find "my new continent" in the "ocean of knowledge".
Mathematical problems in RMB
One day, my mother and I went shopping. Mom went into the supermarket to buy things and let me stand at the place where I paid. I have nothing to do, just watch the assistant aunt collect money. After reading it, I suddenly found that the money collected by the assistant aunt was 1 yuan, 2 yuan, 5 yuan, 10 yuan, 20 yuan and 50 yuan. I feel very strange: Why isn't RMB from 3 yuan, 4 yuan, 6 yuan, 7 yuan, 8 yuan, 9 yuan or 30 yuan, 40 yuan or 60 yuan? I ran to ask my mother, and my mother encouraged me to say, "Think hard and calculate well. My mother believes you can figure out the reason." I calmed down and thought it over. After a while, I jumped up happily: "I know, because as long as you have 1 yuan, 2 yuan and 5 yuan, you can form 3 yuan, 4 yuan, 6 yuan, 7 yuan, 8 yuan and 9 yuan at will, and as long as you have 10 yuan, 20 yuan and 50 yuan, you can also form 30 yuan and 40 yuan." Why 2 yuan and 5 yuan? "I said," it is not convenient to use 1 yuan to form a larger number. "Now my mother showed a satisfied smile and praised me for observing more and thinking more. I am really more comfortable than eating my favorite ice cream.
Hua, a famous mathematician, said: "The universe is big, the particles are tiny, the speed of rockets, the cleverness of chemical engineering, the change of the earth, the mystery of biology, and the complexity of the sun and the moon require mathematics everywhere." Especially in 2 1 century, the application of mathematics is everywhere. Then, how do we lay a good foundation for mathematics from childhood, and what kind of classroom teaching is suitable for the new generation of students? I think that in class, we want students to play a leading role in learning. Then, math activity class is a teaching method that allows us to fully embody autonomous learning.
In the activity class, under the guidance of the teacher, we divide into groups, measure ourselves, piece together ourselves, cut ourselves, calculate ourselves, explore and discover laws, and master mathematical knowledge. This not only cultivates the practical ability, but also improves the thinking ability, which gives us a preliminary taste of the success of mathematicians in studying problems and doubles our interest in mathematics.
For example, in our "Calculation of parallelogram area" class, the teacher asked us to divide into several groups and hand out some small pieces of parallelogram paper for the students to discuss with each other. How to make a parallelogram into a figure whose area we have calculated? Everyone had a heated discussion. Some students found that parallelogram can be cut into right triangle and right trapezoid along its height with scissors, and then it can be spliced into rectangle. Some students also found that two right-angled trapezoids can be cut from any height of a parallelogram, and they can still be combined into a rectangle of the same size. Through observation and thinking, students realize that the "length" and "width" of the assembled rectangle are the "bottom" and "height" of the original parallelogram respectively. From this, we finally found the parallelogram area formula: S=ah. For another example, in the division class with remainder, the teacher uses the game of playing cards to let students quickly understand and master the calculation law of division with remainder, so that they can learn knowledge in relaxed and happy activities.
Every time I do math olympiad, I always pick up a problem to do it, because I think it will be done quickly. However, when I was doing math olympiad today, a question changed my view. It is not necessarily right to do it quickly, but mainly to do it right.
Today, I made a question that puzzled me. I struggled for hours and couldn't figure it out, so I had to look at the basic refining and let it help me analyze it. The question is this: How many odd numbers are there in the square of 333333333? The analysis is as follows: the square of 33333333333 is 333333× 3333333. Because there are too many numbers, this multiplication formula is very complicated. We can simplify it by transformation, that is, one factor is enlarged by three times and the other factor is reduced by three times, and the product remains unchanged. The problem is transformed into finding 99999999999999×1111111= (1. That is, 3×3=9→ product 1 odd number. 33×33= 1089→ There are two odd numbers in the product. 333×333= 1 10889→ There are three odd numbers in the product. There are four odd numbers in the product of 3333× 3333 =1108889 → ……
From the previous calculation, it is easy to find that the product is composed of 1, 0, 8 and 9. The number of 1 and 8 is the same, which is less than the number of 3 in a factor 1, and 0 and 9 are after 1 and 8 respectively. The number of odd numbers in the product is the same as the number of 3 in the factor. It can be deduced that the product of the original problem is:111111110888889, and.
After finishing this problem, I know I can't do math olympiad quickly. I need to know how to do it. In a word, I think it is very popular for us primary school students to have math classes in the form of activity classes. In class, every student is curious about the process of knowledge exploration, and they are eager to find a solution to the problem through their own experimental activities. In learning, we fully realize the happiness and pride of being the master of learning. I hope the teacher will take more activity classes and math classes. In this way, we will learn more solidly, more easily, more flexibly and better.