Is it sunny today?

In the past, Mr. Sun talked about a series of interesting numbers about the rabbit's reproductive law in the Olympic math class: 1, 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89, 144, 234. Such as:13+21= 34,55+89 =144, etc. After I told my father, my father smiled unhurriedly and said, "Xiaowen, there is still a rule you haven't found." After listening to my father's words, I became suspicious and asked curiously, "What kind of law is this? Tell me quickly! " Dad said, "Starting from the fourth number, the quotient obtained by dividing each number by the next number is close to 0.6 18. The larger the number, the closer the result is to 0.6 18. Give it a try. " "good!" 3÷5=0.6,

8÷13 = 0.615,89÷144 = 0.618, ... Wow, really!

Dad went on to say, "0.6 18 is called magic number, also called golden ratio." Using this ratio in real life can optimize the structure and make the appearance more beautiful. According to architectural archaeologists, the magical number 0.6 18 was once used in the pyramids of ancient Egypt. In addition, the human body structure also embodies the magic of 0.6 18 in many places. For example, the height of each person's stomach divided by its height is about 0.6 18. "

After listening to my father's words, I suddenly realized that nature is really mysterious and wonderful, and also realized the importance of mastering scientific knowledge.

Butterfly counting

Is it sunny today?

Today, my father and I went to the park to catch butterflies. After dad bought the ticket, I took the sea pocket and looked for butterflies happily. Finally, I found many butterflies of different colors. When I was about to catch butterflies with a sea pocket, my father shouted, "Stop catching them and listen to me."

I froze. Dad always wanted to find a good day to catch butterflies with fresh air, but he didn't catch butterflies today. Why? Dad said, "What percentage of all butterflies are black butterflies?" I immediately understood that he wanted to "use" butterflies to test me. I counted all the butterflies: 12. I counted the number of black butterflies again: four. I said, "Black butterflies, well, account for 1/3 of all butterflies. Right? " "By the way," dad said, "you are as lively as before!" Say that finish, we all laughed. Then, the question continued, but the more I asked, the more I wanted to catch a butterfly. Finally, I said impatiently, "Go home! Stop catching butterflies! "

Dad took my hand and dragged me home. Although I didn't catch any butterflies, I learned another math problem.

Fun night orienteering.

Is it sunny today?

Today is Friday, April 7th, 2006. As soon as my mother and I finished dinner, we hurried to the main entrance of Jinan University Gymnasium to participate in the "Jinan Garden Night Orienteering Experience Race" organized by Jinan University Association. Go there and have a look. Wow, all the applicants are college students! I can't help worrying: "I am so young, can I participate?" "Yes," said Mom.

At this time, I heard the president of the Orienteering Association loudly announce: "The rules of the competition are that we arrange 15 points in Jinan Park in advance, and each point has different points, some 10 points, some 20 points, some 30 points, and the total score is 300 points. Limit it to one hour to see who gets the highest total score. One minute late, deduct 10 points. "

At the beginning of the game, my mother and I didn't know how to look at the pictures, and suddenly my mother said; "Fan Jiang, you see someone running ahead, so we just have to follow." After listening to my mother, I ran after her. I first run south from the main entrance of the gymnasium 103, then run 228 steps west, and then run south 15 1. It was like running around in a maze, and finally I shouted, "Found it!" " Mom looked at the map and it turned out to be the third point. After punching a hole in the scorecard, I said to my mother, "We should find it ourselves." My mother looked at me and smiled: "My sail has grown up." We looked at the picture carefully. Mom was going to find the nearest one first. At first, I didn't agree, because those scores were the least, only 10, but I hesitated and agreed.

Watch and watch, we are tired and slowly walk to the last point. It's finally over. At the end, those college students applauded me, and my heart was warm.

I think this game is not only suitable for the direction of learning in math class, but also can exercise. What an interesting game.

My home

Is it sunny today?

My family lives in Building 4 of Jinan Garden 16. I have roughly estimated the housing area of my home.

First, I estimated the area of my room. I walk about 40 centimeters, so I use my steps to measure the area of my room. I took 9 steps and measured the width of the room as 9×40=360(cm). I took the 12 step and measured the length of the room as 12×40=480(cm). So my room area is: 360× 480 =172800 (cm2) ≈17 (m2).

Next, I use the same method to calculate the areas of study, master bedroom, living room, bathroom (2), balcony (2) and kitchen. The total area of these rooms is about 80 square meters.

In this way, the housing area of my family is calculated, which is: 17+80=97(m2).

My parents told me that the shared area of my home is about 2 1㎡, so I can easily calculate that the building area of my home is 97+21=18 (m2).

My parents also told me that the management fee of Jinan Garden Community is 1.2 yuan/square meter/month. Then, the management fee of my family should be: 1 18× 1.2 (yuan/month). Before I learned multiplication with decimal point, my mother taught me a simple method to calculate the monthly management fee:118×1+18× 0.2 =18+23.6 = 60.

Ah! I don't know, but I am shocked. My monthly management fee is really expensive!

Journal of Mathematics and Learning

Harmful automobile exhaust emissions.

Is it sunny today?

Nowadays, the air pollution in cities is becoming more and more serious, mainly because the emission of harmful automobile exhaust pollutes the air. So how much harmful exhaust gas does the car emit?

Assuming that 1 vehicle emits 200g of harmful exhaust gas per hour, it will emit 24? 200=4800 (g) = 4.8 (kg). 4.8 kilograms a day, 4.8 kilograms a month? 30 = 144 (kg). According to this calculation, one year is 144? 12= 1728 (kg), 10 is 1728? 10 = 17280 (kg).

How many cars are there in the world? If you add up all the cars in the world, it won't be the number now. Therefore, it is our responsibility to reduce the emission of harmful automobile exhaust.

Dashan spring water

Is it sunny today?

One spring evening, my parents and I went to Phoenix Mountain to catch spring water. 9 kilometers from home. How many kilometers does it take to go back and forth 9× 2 = 18 (km) Oh! It turned out to be 18 km.

When I got to the water drawing place, my father went to fill the water. I lifted the bucket, it was too heavy! It is estimated that a barrel of water is about 10 kg. No wonder I can't carry it. After drinking water, we went to a nearby farmhouse restaurant for dinner. The area of the restaurant is about 80 square meters.

I'm so happy to use so much math knowledge in one night!

Recently, I learned decimals, areas and so on in math class.

In the past, when I went to the store to buy things, I always didn't know how much to pay or refund, and sometimes I miscalculated. However, after learning decimals, it is very convenient for me to go shopping. For example, 1 yuan 55 points is written as 1.55 yuan, so it is much more convenient to calculate multiplication or addition!

Decimals bring convenience to our shopping. Let's have a look. What did it bring us after learning about this area?

After learning the area, I can use various methods to calculate the area of an object or figure, such as drawing a small square and measuring the side length with a ruler. When I went to my mother's company, there was a floor plan, but I couldn't understand what was drawn on it. Now I know that the floor plan shows the location and area of each department in this big store.

I am more and more aware of the close relationship between mathematics and life. I am more and more interested in mathematics, and I am more and more confident to learn it well.

Interesting measurement

Is it sunny today?

This afternoon, grandpa took me to the small casino downstairs to play. Walking, grandpa suddenly asked, "Xiao Xuan, guess what the circumference of this small casino is?" At first I thought the casino was so big. How should I measure it? So I tilted my head and shook my head and said, "It seems that there is no such long ruler to measure!" " "Grandpa smiled mysteriously again:" As long as you use your math knowledge and use your head, you will definitely think of it! ""So I thought about it again, and after a while, I finally thought of a way. Is to take a natural step first and measure how long this natural step is; Then naturally walk around the small casino and see how many steps you have taken. Finally, the perimeter of the casino can be obtained by multiplying the measured natural step length by the number of steps required to walk a circle.

I told my grandfather this idea, but he was ready and took out a tape measure from his pocket. So, I naturally took a step and measured it to be 53 cm. There are 100 steps around the casino, and 53 × 100 = 5300 (cm) is 53 meters. Therefore, it can be concluded that the circumference of the small casino is about 53 meters.

How interesting! I figured out the circumference of the small casino! Grandpa and I both laughed happily.

Finish this book.

Is it sunny today?

The books on the shelf are in a mess, so I want to tidy them up.

There are three bookshelves on my desk: one is on my desk and two are on it. The one on the desk has 23 books; The second shelf has 27 books; There are 29 books on the third shelf. Which shelf has the most books?

23 & lt27 & lt29

Oh! You can see right away that there are the most books on the third shelf; How much less than the books on the first shelf and the second shelf combined?

23+27=50 (Ben)

50-29 = 2 1 (Ben)

That is, 2 1 this book is missing.

The bookshelf is finally installed! Through this book sorting activity, I realized how important mathematics is!

The pleasure of shopping

Is it sunny today?

Today, my mother and I went shopping in Jusco. As soon as I entered the store, I saw a dazzling array of goods. I pushed the car through the goods in search of what I wanted to buy.

On the right side of the shop are colorful and mouth-watering fruits, and on the left are all kinds of delicious bread and cooked food. Inside the store is the freezer, which contains frozen fish and my favorite yogurt.

I first selected five attractive Sunkist oranges from the fruit counter and one from 3 yuan. Then I took 3 Jin of red apples, each Jin of apples was 3.5 yuan. Later, I pushed the cart to the counter selling fish and yogurt. I bought a box of fish named "skinned cow" and 1 package of cheese and milk. A box of "Piniu" fish 16 yuan, a box of 5 yuan milk, and a pack of 6 boxes. Finally, I bought two packets of biscuits, each of which was 17.5 yuan.

After shopping, I pushed the car full and came to the cashier. While waiting in line, my mother asked me to help me figure out how much it would cost. Let me calculate: 3× 5+3.5+3.5+16+6× 5+17.5+17.5 =106.5 (yuan). So, I asked my mother to prepare 106.5 yuan, and my mother took out 106.5 yuan and gave it to the cashier. I was very happy when I saw the receipt. The above figures are exactly the same as my calculations, and I am right.

Compare the scores by division.

It is sunny today. I was reading Mathematical Olympiad in Primary School at home, and suddenly I found such a problem: compare11111,1 165538. Suddenly, I became interested and took a pen and "brushed" it on the toilet paper. Soon, I found a solution Is to turn these two false scores into fractions and then use the law of fractions. The smaller the denominator, the greater the score. Solve111111

Today, I saw such a problem in the training of Mathematics 1+2. A cubic casting with a bottom area of 648 square centimeters, what is the remaining three-dimensional graphic area after removing the largest cylinder and taking the opposite side as the bottom?

Seeing this topic, I was very confused and thought: just say a bottom area, how to do it? My mother sitting in the chair looked at it and laughed at me and said, "Hum, they all say that the level is high, and they can't even know this problem."

I know my mother used the goad method, in order to irritate my competitive spirit and let me finish this problem. In order to make my mother think that her provocation was successful, I crustily skin of head did it, but I couldn't figure it out. But I'm not discouraged. I persisted and finally succeeded.

According to the drawing (to be drawn), it can be found that when a cylinder is cut off, a hole with the same size as the original cylinder will come out. Although the volume of the hole is the same as that of the cylinder, their surface areas are not the same, but the areas of the two bottoms are smaller than that of the original cylinder.

Therefore, the remaining graphic area should be equal to the area of the six sides of the cube minus the two bottom surfaces of the cylinder+the side surfaces of the cylinder.

The formula is 628× 6-628× 3.14 ÷ 4× 2+628× 3.14.

Today is another sunny day. I was wandering in the street when I suddenly saw a lot of people gathered not far away. I ran for a year, and the result was a prize-winning game. "Hum, what's fun about winning the prize?" I was bored when the person next to me quickly said, "It's not fun to grab the prize, but there is a big prize that can attract people." I asked eagerly, "What is it!" "50 yuan money." The man with big eyes said. I'm very excited to hear that. "I have to try anything for such an attractive prize." Then I asked the shopkeeper how to catch it. The shopkeeper said, "This is 24 Mahjong, and it says 12 5, 12 10. You can only catch 12 mahjong at a time. If the total number of 12 mahjong targets is 60, then you can win the 50 yuan Prize. " Without rolling up my sleeves, I took out 5 yuan money from my pocket and gave it to the shopkeeper.

Although I won 10 times, I still didn't win the grand prize.

When I got home, I thought about it and felt something was wrong. I think, to get 60 points, all 12 mahjong should be marked with 5. In the best case, the first 1 second catch 1 5, the second catch of two 5 s and the third catch of three 5 s will cost at least 6 yuan money. But what if the target number of mahjong is 10 or the sum of the two is the same, how many times will it cost?

Finally, after some consideration, I finally figured it out. I rushed to the street to get even with it, but it had disappeared without a trace.

There is an inscribed circle in a big square, and the area of the big square is 20 square centimeters. Find the area of a circle.

According to common sense, we should first find the side length of a big square, which is D, then R, and finally the area. However, in this problem, how can we find R&D? Unless a prescription is prescribed, it will be troublesome and will certainly be inexhaustible. What should I do? At this time, it is necessary to use the formula flexibly. Since the area formula of a circle is πr2, it is ok to find r2 instead of R! At this time, we can regard it as a whole a, that is, we only need to find aπ. How to ask? The area of a square should be (2r)2, which is 4r2 after simplification, that is, 4a. So we can use 20÷4=5(cm2) to find a, and then use 5×π≈ 15.7(cm2). The area of the circle is about 15.7cm2, so the area of the circle aπ can be solved without roots.

Many formulas can be combined with each other to form a simple and practical new formula.

As long as we innovate, we are actually kneading the steamed bread eaten by the giants into a ball and making new rolls. Is this not good?

Mathematics is difficult to learn because we are often confused by the complicated problem-solving process. Especially when you meet the wrong answer in the book, you will be miserable! It would be better if you accepted it without doubt. If you doubt this answer, it will make you eat badly, sleep badly, and your head swell as big as basketball.

That's what I did when I was studying in the Olympic Mathematics training class. One day when I was solving a problem, I was stumped by a question: 0.99...× 10 =? Let me see, cyclic decimal multiplication! It's too difficult. Let's read the notes. To my surprise, the note actually said: Because 1-0.99 … = 0.00 … = 0, so 0.99 … = 1. What the hell is going on here? I'm confused. On second thought, this seems to be the right way, but look at 0.99 ... and 1. They really don't look alike. How can values be equal? That night, I stared at the ceiling and couldn't sleep. There are always two numbers floating in front of me: 0.99 ... and 1. I didn't fall asleep until midnight.

The next day, I brought this strange phenomenon to the classroom and invited Zhang Yuchen, a math expert in our class, to discuss the answer to this question. This time, even the best Zhang Yuchen was at a loss, only to see him with his chin in his hand, frowning and helpless.

Is there no other proof except subtraction? "Yes!" Zhang Ruoxi said, "0.33 ... =1/3,1/3x3 = 3/3 =1= 0.33x3 = 0.99, 0.99 ... =1".But Teacher Liu is not so. If 0.99... 1, the difference between them must be 0.00... 1, but this number does not exist at all, and there is no result in the end.

Since we couldn't discuss it, we searched the Internet and clicked the mouse, and the result was: 0.99...≠ 1. Their values are different, and no one can tell the difference, because both numbers are irrational. It turns out that the answer in the book is wrong.

Through this problem solving, I learned to discuss, understand irrational numbers and how to deal with mistakes in books. I think, when you find the answer is unreasonable, don't be superstitious about books, otherwise you may never find the right answer. Also, any difficult math problem, as long as you think hard and are not ashamed to ask questions, will always find the correct answer.

The fruit you grow tastes sweet. In fact, mathematics is quite interesting, especially when you get the correct answer through hard work. I will explore and discover in the castle of mathematics in the future, and constantly experience the happiness brought by success.

Failure and mistakes are the foundation of success.

In this long journey of life, failures and mistakes are indispensable, and success can only be achieved through repeated failures.

The ancients said, "Failure is the mother of success". My personal interpretation of this sentence is that after you fail, you should correct your shortcomings. After correcting it again and again, you are the son of failure-success.

There are many examples to show that failure will not make people unsuccessful forever. You must have a strong will and overcome all kinds of difficulties to succeed. For example, during Sun Yat-sen's uprising, after numerous failures, the Republic of China was established and the Qing Dynasty was overthrown.

Of course, mistakes don't necessarily make people bid farewell to success. For example, during the Spring and Autumn Period and the Warring States Period, the King of Qin was in urgent need of talents in order to win state affairs. At that time, a famous philosopher named Han Fei was persuaded by Li Si, the minister, and Han Fei voted for Qin. But the king of Qin did not value him. Instead, he advised the king of Qin and captured Zhao. And Reese is a villain, jealous of Han Fei, and forced Han Fei to death with poisoned wine. The King of Qin knew that he was wrong, and he used villains, so he finally unified China with Han Fei's thoughts in 22 1 BC.

In either case, it is proved that failure and mistakes are the foundation of success.

In our class, there is one thing that makes all our classmates more prepared for mistakes.

That morning, the second class was math. Teacher Liu reviewed the knowledge of cylindrical cones for us to meet the first unit test.

"Bell ... bell" was accompanied by the bell, and we entered the classroom one after another. It seems that Miss Liu has been waiting for us in the class for a long time.

As soon as we sat down, we went straight to the point and began to review the knowledge of cylindrical cones.

"Please turn to page 10. Example 6: Wangcun made 100 uncovered iron drums for farmers to carry water. How much tin do you need at least? Who will solve this problem? " Teacher Liu interacts with her classmates by asking questions.

One of them lifted it up quickly, but she was Fan Anlin, and she didn't like to talk much in class. Not only I was surprised, but also the teachers and other students seemed to be taken aback.

"3. 14 times the diameter, then multiply by the sum of height and radius, and finally multiply by 100." She whipped out a simple formula.

"finished?" Teacher Liu's question

Fan nodded and agreed, but it seemed a bit strange.

She sat down, Zhou Xiao, Zhang Yuchen and others raised their hands again. The teacher shouted, "Zhou Xiao."

"Don't directly calculate the surface area, you must reduce the bottom area." Zhou Xiao corrected it.

"ouch!" Fan Anlin covered her mouth as if she knew the mistake.

Teacher Liu also smiled and said, "Her mistake just reminded everyone. Don't make any mistakes in the future. "

After class, Teacher Liu also said, "The class is wonderful because of mistakes." This sentence seems to contain a great moral.

Life is to have failures and mistakes to add color. Edison said, "Failure is what I need, and it is as valuable to me as success." Kepler said, "Failure is the beginning of a new brilliant fantasy." Dostoevsky said, "If you don't make ten mistakes, you won't get a truth." Hugo also said: "Every step of failure is a step closer to success." ……

Whether it's famous sayings or aphorisms, I always believe that failure and mistakes are the foundation of success.

Skillful mastery and flexible application in mathematics learning.

If the difference between a number and b number is equal to b number, then b number must be a number. On the surface, this is a very simple question, and the answer is 1/2 or 50%, but Zhang Yuchen's answer is different from most people's answer. He thinks that B must be the divisor of A. At first glance, some people may think that this answer is right, and I almost walked into it. When the teacher asked me what this topic had to do, I couldn't remember the names of such topics. It took me a while to answer the teacher's question-the answer was "divisible". After that, Teacher Liu gave us a Chinese fill-in-the-blank question: How to master and apply mathematical knowledge? I soon thought of mastering it skillfully and using it flexibly, and my classmates agreed with this answer. But think about it, have we really achieved these two points? No, we didn't. Just like Zhang Yuchen's mistake today and the time I spent answering questions and thinking, we can see that none of us mastered it skillfully. This sentence is the method and goal of my future study. I must "master it skillfully and use it flexibly."

There are no real problems in the world:

I remember that it was a very funny thing, and I still remember it in retrospect.

In the third grade, Mr. Chen gave us a very simple question: 20 apples, ate 4, how many are left? I quickly worked out the answer in my notebook: 16. But after a while, I didn't see the teacher continue to lecture, so I wondered: Is there any "ambush" on this question? Let's have a look. I snapped my fingers and counted loudly: "I ate seventeen ... ah!" Sure enough, there is an ambush, and there are seventeen left! " I was as happy as if I had discovered a new continent and told this "secret" to Zhang Yuchen.

He also agreed with me and unified the "front". When the teacher began to lecture and asked everyone what the answer was, two voices of seventeen broke the harmony of sixteen, and everyone stared at me and Zhang Yuchen in amazement. After a "war of words", we were finally persuaded. We just found out that this question is so simple.

Although I was wrong that time, I learned not to think of simple problems as complicated. Before seeing every math problem, don't think it is complicated and cause psychological pressure. Secondly, I want to have a good attitude: in fact, there are no problems in the world, only what we can do now and what we won't do for the time being, and the problems we do will be solved as long as we are willing to use our brains.

……

In mathematics learning, there are many interesting or educational things. If we think about it carefully, these things will definitely tell us some learning methods, or let us understand the truth.