The world is full of wonders, and there are many interesting things in our mathematics kingdom. For example, in my ninth exercise book, there is a thinking question that reads: "A bus goes from Dongcheng to Xicheng at a speed of 45 kilometers per hour and stops after 2.5 hours. At this time, it is just 18 km away from the center of the east and west cities. How many kilometers is it between East and West? When Wang Xing and Xiaoying solve the above problems, their calculation methods and results are different. Wang Xing's mileage is less than Xiao Ying's, but xu teacher said that both of them were right. Why is this? Have you figured it out? You can also calculate the calculation results of both of them. " In fact, we can quickly work out a method for this problem, which is: 45× 2.5 = 1 12.5 (km),112.5+18 =130.5 (. In fact, we have neglected a very important condition here, that is, the word "Li" mentioned in the condition is "just 18 km from the center of the east and west cities", and it does not say whether it has not yet reached the midpoint or exceeded the midpoint. If the distance from the midpoint is less than 18km, the formula is the previous one; If it is greater than 18km, the formula should be 45× 2.5 = 1 12.5 (km), 1 12.5-65448. Therefore, the correct answer should be: 45 × 2.5 = 1 12.5 (km),12.5+18 =130.5 (km),/kloc-. Two answers, that is to say, Wang Xing's answer and Xiaoying's answer are comprehensive.

In daily study, there are often many math problems with multiple solutions, which are easily overlooked in practice or examination. This requires us to carefully examine the problem, awaken our own life experience, scrutinize it carefully, and fully and correctly understand the meaning of the problem. Otherwise, it is easy to ignore other answers and make a mistake of generalizing.

Mathematical paper

Today, in our math club, the teacher gave us an interesting topic, which is actually a somewhat complicated topic to find the law. The title is like this: "There is a column number: 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3. What is the sum of the top 240 numbers in this column? " As soon as I got the topic, it suddenly occurred to me that this topic must be done according to law! ! !

Idea 1: First, I will try to sum in groups of three, 6, 5, 10, 9, 12, 15, 14. In this way, these figures have their own characteristics, and the key is that they can't find a suitable law. So, I found a group of four to sum, 8, 10, 12,16,20. After a careful look, it seems that there is no rule, so I have to try to find a group of five to sum, 9, 14, 19, 24 ..., so obviously they are equal series, I am very happy, and then 240÷5=48 (group), a group of five, (6544. (4, 5, 6, 5, 4) ... Then we can find the sum of the last term, 9+47×5=244, and divide the sum of the first term and the last term by 2, (9+244)×48÷2=6072. That's it!

Idea 2: I also found that the first number at the beginning of each group is exactly 1, 2, 3, 4...48, so I came up with another method, (1+48) × 48× 2+(2+49 )× 48× 2. It is reasonable to think so, and it is also a clear and practical method!

Idea 3: I also find that when there are n groups, his sum is also the sum of (1+2+3+4+n) × 5+4n = the number of n groups you need, for example, (1+2+3+4+...+48. Although this rule is somewhat abstract, it is simpler than the other two methods if you understand it yourself.

All I did was three of them. In fact, there are many ways, but I have to find the rules myself and solve the mystery myself!