There is an old saying in math diary Grade 6 1 China: "Do the opposite". In fact, we can also use this way of thinking to solve some math problems.
In yesterday's math class, the teacher gave us an interesting math problem: there is a pool of lotus flowers, the growth rate doubles every day, and it takes 20 days to fill the whole pond. What day is half full?
If we think in the traditional way, we should proceed from the conditions, push step by step, and finally draw a conclusion. But this method is not feasible on this issue. At this time, I remembered the sentence "Do the opposite". So, I pushed forward from behind: it takes 20 days to grow a pool, and it is known that the growth rate of lotus doubles every day, so it is 19 days. It used to double daily, but now it doubles daily, so the answer to this question is 19 days.
Conversely, with this idea, this problem can be easily solved.
Math diary Grade Six Grade Two This summer vacation, my mother took me to Hong Kong Disneyland. Compared with the mainland, Hong Kong is very small, with a population of about 6.6 million, with a total area of 1070 square kilometers. The smallest Disneyland in the world is located on Hong Kong Island, with an area of only 65,438+026 hectares (365,438+00 acres). The tour guide said, "If you don't play anything, just walk around for 18 minutes." Let me show you my trip to Disney!
First, we went to Mickey's photo studio and took photos with Mickey and Minnie. When we got there, we saw: Wow! There was a long queue in front of the photo studio, almost 25 meters long, and my mother had a hard time letting me squeeze in. Finally, we went to the Cinderella carousel to play. I got on the merry-go-round and took a closer look. The turntable has three circles, and each circle has 15. I calculated: 15× 3 = 45 (1). Wow, so many! We turned round and round on it, feeling like a happy scene when riding a horse on the grassland. I was deeply impressed by the following fantasy space trip, adventure world, mini world, the performance of the lion king and the Mickey Mouse award party.
Things in Disney are very, very expensive. A bottle of Coke 17 yuan is more than ten yuan more expensive than ours. At lunch, a bowl of noodles 50 yuan. Have you ever eaten a bowl of noodles for 50 yuan? It's really expensive! Before leaving Disney, everyone wants to buy some souvenirs. My mother bought me an umbrella for Princess Disney, which cost 100 Hong Kong dollars. I thought again: We only need 20 yuan for each umbrella here, 100÷20 = 5 (one umbrella). Wow! This is too expensive!
When I got on the bus and left Disney, my mother asked me, "How long did we play from 8 am to 6: 30 pm today?" I thought about it: 6: 30 pm is 18: 30, 18: 30 -8: 00 = 10: 30.
The bus started, and I reluctantly bid farewell to Disney Park: Goodbye, we will come again next time!
Math diary, Grade 6 and Grade 3, this semester, we learned rectangles and cubes. When I first learned, I always felt that these contents were not too difficult, so don't worry about it. As long as you look at the figures and put the formulas of surface area and volume on it, there will be no problem if there is nothing wrong with the calculation. But this morning, I got a new understanding and a better understanding of them.
After getting up in the morning, as usual, my mother asked me to do ten math application problems. Today, I made a new topic about the surface area of a cuboid, and the last one was like this: "The factory makes water pipes, each of which is 2 meters long and the cross section is a square with a circumference of 20 decimeters." How many square meters of iron sheets do you need to make a water pipe like 10? " I see, it's so simple! Brush a few strokes, quickly calculate on the draft paper, copy it to the test paper, and then hand it to mom happily.
Mom looked at the test paper, glanced at me and pointed to the last question: "Read the question and your formula again." I read the title again and found nothing wrong: "Pay attention to the section, not the side length." But I calculated the circumference, and I wrote it correctly, mom! "Mom took a sip of water and shook her head gently:" Read it again! " "I looked up at my mother, as if not kidding me. I read it word for word, but I still found nothing: "Yes! What happened to mom today? " Mom asked, "Don't look at the topic yet. Have you ever seen a water pipe? Think about what the water pipe is for first? " I feel a little puzzled: "Water pipes are used to deliver water." Suddenly, it dawned on me, "Oh-the water pipe is hollow, and neither section needs to be calculated."
When I finished the revision, my mother said earnestly, "Mathematics, like Chinese, is everywhere in life, not just memorizing formulas." Application problem is to use mathematical knowledge and experience to solve problems in real life, which needs to be combined with practice. "
Yes, "a letter is better than no book". The theory in books is limited, but the problems in reality are endless. Only by thinking and connecting with reality can we avoid mistakes as much as possible. There are no simple problems in the world, and the problems that cannot be found are all important problems. Being serious and flexible is the best way to reduce problems.
Math diary uses numbers all the time in her life, from a trivial matter to a huge project. What I describe below is also a short story about numbers.
I made a small scale during the Mid-Autumn Festival. I want to measure the density of eggs with this small scale. I put the egg on the scale and weighed it. The weight of the egg is 0.605 kg, which means that in the process of "mass volume = density", "mass" already exists, so the key is volume.
It's hard to ask what the turnover is. Because the egg is an irregular figure, although it looks like an ellipsoid, it is not a very standard ellipsoid.
"What should I do if I can't use the volume formula of ellipsoid?" I thought hard, "can't Archimedes buoyancy law be used to calculate volume?" "I thought of this method and Mashan started to do it. I take out a bowl from the kitchen first, and then fill it with water, but the water must be full.
I put the bowl under the tap and the water trickled down. I stared at the bowl with my eyes wide open and my hands began to shake, but I told myself, "Hold on, don't shake." Finally, the bowl was filled with water.
I quickly took out a washbasin from the bathroom. There must be no water in this washbasin, otherwise the data will be affected and the error will be too large. Then I wiped the washbasin clean with a dry towel and put the bowl of water into the washbasin trembling. Then, I picked up the eggs, put them on the top of the bowl, and put them into the bowl carefully. At that moment, the water overflowed around the bowl wall.
Water overflows into the basin, and the volume of water in this basin is the volume of eggs. I drop the water in this basin into the measuring cylinder bit by bit and read the numbers. The final result is 10.3 ml.
In this way, we have the mass and volume, and calculate the density of eggs: 0.605 10.3=0.058 (kg/ml). I'm glad that the density of eggs has finally been worked out.
Mathematics is always like this, advancing in constant exploration!
Math diary Grade 6 Grade 5 In our life, numbers are everywhere. In the human world, numbers are indispensable. There are many numbers in life, such as license plate number, house number, page number and mobile phone number. It can be seen how important and indispensable numbers are in our lives!
Yesterday, mother bought some cherries. The sight of cherries makes my mouth water "three thousands of feet". Mother saw me greedy and washed some cherries with a smile. I asked my mother, "Mom, how many cherries did you wash?" ? Who has enough to eat? "My mother saw me like this and couldn't help but want to tease me. Her eyes rolled around as if she were thinking something. After thinking for a moment, I took out a few cherries and said, "I'll give you a debut question." If you answer correctly, the cherries are all yours! " "I couldn't help it, shouting and urging her to ask the question quickly. Mom paused and said, "Two twos leave1; Five figures of five leave two; Seven, seven. There are three left. Do the math yourself. " I took a pen and paper and flew back to my room to sit down, biting my pen and thinking: Find their least common multiple first … No! Is the greatest common divisor! ..... even more ridiculous! I was lost in thought again. Suddenly, I felt that I could "handle" the problem by trying. I tried one by one, and although I tried, I didn't just find a number to put it on. Multiply 2 and add 1. If the other two requirements are met, this is the number. If not, there is no need to add 2× ()+2 ... that would be very troublesome. Just add a 2. So I finally found the number-"17"!
Like an arrow, I ran out of the door and shouted the answer to my mother. My mother smiled and gave me some cherries. I am extremely happy, not only because I have got my favorite cherry, but also because I have gained mathematical knowledge.
Mathematics is wonderful, it is like a kaleidoscope, from which we can see the myriad gestures of the world. Students, let's go to the ocean of mathematics and enjoy it!
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In the sixth grade in math diary, my sister and I attended the Sunshine Youth Summer Camp. My mother gave me 200 yuan pocket money. Don't mention how happy you are. Finally, I can buy my own favorite things. As soon as I got on the train, I started a shopping spree: I bought a bottle of iced black tea and spent 10 yuan; A bag of peanuts spent again 10 yuan; A bag of cumin mutton skewers, 10 yuan; Three sets of playing cards cost 9 yuan money, one * * * cost 39 yuan money, and 200-39= 16 1 (yuan) left 16 1 yuan. As soon as I got off the train, I got on the bus to the Expo site. There are more than 200 national pavilions in the Expo site. We visited the USA Pavilion, pacific alliance Pavilion, Australian Pavilion, Indonesian Pavilion, Danish Pavilion, Petroleum Pavilion and Thailand Pavilion ... We only visited 22 national pavilions once, and the USA Pavilion and pacific alliance Pavilion left the deepest impression on me. The United States Pavilion has three pavilions, and the United Pacific Pavilion has 14 Pacific countries and two countries to participate, showing the beautiful and magical natural landscape, unique human environment and passionate folk customs of Pacific island countries to the people of the world.
Here I bought a Haibao key chain for my mother with 15 yuan. I spent 10 yuan to buy a Kongming fan for my father and 10 yuan to buy myself a bamboo sword. On the train back to Zhengzhou, I bought a massager for my father with 20 yuan money, a toy for my brother with 10 yuan, three boxes of fruit with 30 yuan money, a bag of food with 10 yuan, and the price was 39+ 15+20+ 10 × 4. After listening to my parents' analysis and teaching, I really feel a little extravagant, and some money really shouldn't be spent. This trip gave me a great education.
I understand that the teacher expects a lot of me, but I still didn't do well in the exam. I'm very sorry about that. But since you made a mistake, you have to correct it. So after passing the exam, I also thought a lot about what I must learn in the future.
First of all, I want to get rid of the bad habit of not looking at the questions carefully in the exam. Sometimes I often look at the front of the topic and write the following questions conveniently, but there are many mistakes. This may also have something to do with answering skills. In short, through future practice, I must carefully examine the questions, carefully read the questions, and fill in the information accurately during the exam. If time permits, check it several times more and don't allow yourself to make such mistakes again.
Secondly, I also want to strengthen the practice of Chinese, math, English and physics. Through the exam, I learned about everyone's strength and the truth that there are mountains outside the mountains and there are people outside. On weekdays, everyone gets together to discuss research problems, and there is no obvious difference. But after the exam, it is not difficult to find that there are so many questions that I have never seen before. Well, that's just because I do too little exercise. I can't allow myself to go on like this, I must redouble my efforts. I will learn from the lessons of this exam as a foreshadowing, lay a good foundation for the next exam and get ready.
Practice is the key to exam skills. In life, I should practice more and review myself more, and make a careful review plan before the exam, so I don't have to be in a hurry and have no learning goals. Learn to accumulate and use on weekdays, and Chinese should accumulate some beautiful words and beautiful fragments; Mathematics should practice more difficult problems and recite more key points; Physics should do more experiments, recite theorems and practice the potential of language organization; English is the focus and difficulty of grammar, and practice is also a good way to improve English.
I want to say to the teachers: "I hope the teachers will not lose confidence in me." Although I didn't do well in this exam, I believe in myself and can break through myself. " I will work hard for the next exam! Please believe me. "
Grade six in math diary is sunny on Monday, August and March 10.
Preview is the task assigned by the teacher, and it is our own learning process. However, this notice has already broken my mind. My head is a mess-what a mess! No matter how carefully I look at it and how hard I think, I still can't figure it out. I have to ask my classmates. But everyone doesn't quite understand. I'm still confused after hearing it. The fog seems to be more turbid than before. Looking at the colorful scrolls on the book, I was dazzled. I think I should get a pair of reading glasses. After thinking for a long time, I can only figure out that the scale is a ratio, which is composed of the distance on the map and the actual distance, that is, the distance on the map is greater than the actual distance. I put a question mark on the book, waiting for the teacher to give me a clear picture.
In the evening, I had a dream. I dreamed that I learned the scale, took the test, and got a score of 100. Looking at the red tick on the test paper, I was flattered.
After a few classes, the math class is coming, and I am already excited. One is to solve the mystery in your heart, and the other is to learn new knowledge.
The teacher is coming. He led us to explore the knowledge of "scale", how to find the scale and so on. I'm beginning to understand. The mystery in my heart also fades away like fog. In fact, as long as the unit of distance on the map is unified with the actual distance, and then their proportions are simplified, it is the scale. Of course, we can also calculate the distance on the map by the scale of the map and the actual distance. Or you can find the actual distance according to the distance and scale on the map. The core is three related formulas. Learn math well! So you won't be afraid of all kinds of problems! As long as you master this method, every problem in this respect is not a problem, because the method of solving the problem is very clear, and you can certainly do it if you are willing to use your head. At the same time, the scale has the former and the latter, so we understand the scale as we understand the proportion.
Math diary is in Grade 6 and Grade 9. After studying the first four units, his grades have not improved. The best score is 82, and the worst score is 23. This score came at my most vulnerable time. I am very, very sad. I am sad. Obviously I have worked hard, why can't I improve my grades? I found the mid-term "why" because I didn't insist on doing more, practicing more, watching more and learning more. This is the reason why my grades have not improved. My mother said that I should keep previewing and reviewing every night to improve my grades, but I didn't insist. This achievement is also a great blow to me, and because of this, I am so angry that I insist on doing exercises every night.
The second reason is that I sometimes get distracted in class and don't listen to the teacher carefully, which leads to the teacher's main content not being listened to and I don't want to do more exercises. I was lazy, but the teacher asked me what to do, so most of me didn't do my homework. I copied my classmates directly without asking my parents and teachers. I didn't realize until now that what others say is others' after all. Copy for a while, but not for a lifetime.
The third reason is that I didn't study early in the morning on time, which led to many knowledge points not being firmly grasped. There are many formulas and calculation methods in the gold medal study plan, but I haven't mastered them. Please pay attention to this. The fourth reason is that I don't have enough perseverance. I was hot for three minutes. I said I would study hard and make progress every day. I said I should do exercises tomorrow. I said I should study early every day. But? I didn't do it, which means my perseverance is not enough. I need to persist! The skill of mathematics is to do more, practice more and listen more. If I don't listen carefully and do my homework in class, then I can't play math well and I can't learn math well. I do problems every day, just like a diligent stupid bird, and I insist on doing one page of oral arithmetic problems every day. I believe I can do it as long as I practice more questions, listen more and learn more! For myself, I also want to study hard and learn math well. Study hard and make progress every day! !
Math diary Grade 6 10 Every student has his favorite course, but I like math. The teacher's lectures are sometimes serious and sometimes humorous, which brings us endless happiness.
I deeply remember that time, when the bell rang, we all waited quietly for the teacher and looked forward to the little game in each class. At this time, the teacher said that this is a lesson about' counting to 24 o'clock'. We all interact with teachers with questions and curiosity.
The rules of the game are: randomly draw 3 or 4 cards from A( 1) to (10) with playing cards, and the number calculated by arbitrary addition, subtraction, multiplication and division must be 24. The rules seem simple games. Who will win, me or my opponent?
This is how the game started. The first time I drew three, six, seven and nine cards, I was puzzled and puzzled. I think sadly, but I never have a clue. I have to wait for the next chance. When I saw that all my opponents had calculated 24 points, I was very nervous and encouraged me to calculate 24 points next time.
The game continues. I drew four cards for the second time, 2, 5, 7, 10, and with a nervous mood of winning the prize, I thought that as long as all of them add up, it won't be equal to 24 points!
The competition is getting more and more intense. I began to regain my confidence for the third time and catch up. I drew 2, 5, 6 and 8 cards, thought 2_5+6+8=24, counted 24 points and won.
Although my competition for three chances has ended, as a bystander, I am also very excited to watch other students carefully choose cards. In this intense atmosphere, we have mastered the knowledge of this lesson happily and efficiently, used addition, subtraction, multiplication and division flexibly, and calculated correctly skillfully.
I learned a lesson from it: the first game told me that failure is the mother of success, the second game told me that self-confidence is the first secret of success, and the third game told me that where there is a will, there is a way.
This is my math class and my favorite math class.
Math diary Grade 6 1 1 Today our math exam tested our execution.
Teacher Mo came to invigilate our math. Not invigilating, but not invigilating. Teacher Mo will get some courseware in class. When I got the math test paper, it was not difficult to do it. Computational mathematics is to use draft paper. So, I specially prepared some draft paper. When I encounter uncertain problems or unfinished problems, I can first calculate on the draft paper, which is very easy to do. Soon, I finished one side and moved to the second side. I did it very seriously, and the sound around me was almost zero. "Hua", I wanted to know what the sound was, so I put down my pen and followed the sound to see the sound. It turned out that a classmate's compass accidentally fell to the ground. Out of boredom, I watched it with great interest. Soon, I found that this classmate was not careless, but intentional. She passed it on to another classmate, ready to paddle across the ground! Probably that classmate didn't have a compass, and then she borrowed it from her classmate! After this scene, I began to do the problem seriously again. Suddenly, Deng borrowed my compass, so I lent it to her without saying anything. But gradually, I was stumped by that application question, and that question got four points! Add one point! I can't cross the excellent line. I really thought about it and couldn't help looking around. I glanced at the blackboard and was shocked by the word honesty on the blackboard. I immediately withdrew my horn and thought it over. I dare not move for a long time.
When it was time to collect the test papers, there was a 360-degree change. Teacher Mo didn't ask us to hand in the papers directly, but asked us to put them in the cupboard and not to talk. Like my classmates, I didn't control myself and kept exchanging answers with my classmates. Some students took out their test papers and asked them the answers. Most of them didn't do what the teacher asked. Teacher Mo saw it and said, "Students who failed in execution get up." Only half the students stood up. Teacher Mo said: "There are still some students who have not stood up." Oh, my God! The execution and the examination paper were combined, and our class was almost wiped out! Teacher Mo also asked the team leader to put away the test papers.
This math exam, coupled with the sudden exam, we should make persistent efforts!
Math diary 12, Grade 6, is thoughtful and skillful in buying moon cakes.
In the long history of mathematics, many mathematical geniuses have appeared. That's an example for me to learn. They shine in the night sky like expensive diamonds. With a deep obsession with mathematics, coupled with the love of thinking, learning and expression. Finally, I became a naughty and lovely little star in the starry sky. It is said that the Mid-Autumn Festival is coming, and the unique food of the Mid-Autumn Festival-moon cakes is also coming as scheduled. Moon cakes have many flavors, such as egg yolk, lotus seed paste and beef ... it makes my mouth water. Look at me like this. My mother immediately gave me 100 yuan and said with a smile, "Go and buy some moon cakes to eat." .
I came to the store happily with the money. The boss said, "This pile of moon cakes is big and small, the big one is 500g, and the small one is 300g. The total is 3200 grams. Do you know how many big moon cakes and small moon cakes there are? " If you are right, I will sell you ten moon cakes at a 50% discount. As soon as I saw such a good thing, I used my head to think. After thinking for a while, I sorted out my thoughts and said to my boss, "If they are all big moon cakes, there is still 6.4, but the rest is not as heavy as a small moon cake." So there are no six big moon cakes. We can think from multiples of 5, and the numbers 1 and 2 are too small to be considered. There is no need to consider odd numbers generated by multiples of 3 and 5. Multiplying the number above 6 by 5 is too big. So there are four big moon cakes. The remaining1200g is exactly four times that of 300g. That is, four small moon cakes. " The boss smiled and said, "Keep your word, 10 moon cakes are 50% off, and the original price is 10, which is exactly 100." I immediately said: "Boss, sell it to me as long as 50 yuan!" "The boss happily praised me as" really smart ",and 50 yuan sold me 10 big moon cakes. I said thank you in high spirits and ran home.
There are many secrets hidden in moon cakes! Dear friends, as long as you dare to think and love to think, you will certainly experience endless fun in the palace of mathematics and explore a lot of interesting knowledge in the kingdom of mathematics.
Math diary Grade 6 13 My math is the best of the three, and I get more than 90 points in every exam, so my math teacher has confidence in me and I have confidence. We have a good relationship. Whenever I have difficulties in math, he will appear in front of me to help me solve the problem. I like him very much and he is also my best teacher.
Everything in life is inseparable from mathematics. As long as you are good at observation, you will find that mathematics cannot be separated from you. After studying the knowledge of proportion for six years, I deeply realized that mathematics has brought us many benefits.
It's a sunny afternoon. My brother and I have an appointment to meet at 2 o'clock in the forest park, and then we will go to the zoo to play together. After arriving at our destination, we had to buy a map of the park, because this was our first visit to the zoo in Forest Park. After I got the map, my brother crept up to me and grabbed it. I have no choice but to restrain my unreasonable behavior towards this "little naughty boy" Then my brother solemnly said to me, "Brother, today my guide will take you to see the lion!" " "At this time, I thought to myself: I hope it won't be the opposite! Then my brother took me everywhere like a headless fly. After about an hour, I finally couldn't help it. I shouted, "What are you doing? I'm exhausted. Why haven't I arrived yet "I took the map back directly, and when I saw it, I suddenly realized that it was my pushy brother who made up numbers and interpreted the scale of the map as 1: 5000 on the map as 1 cm representing the actual 5000 cm." Well, learning a skill is really important! If you are as self-righteous as your younger brother and don't study hard, the consequences are often self-defeating! "Then, according to what I learned, soon, we came to the lion. Look at my brother's envy. He's begging me to accept him as an apprentice!
Knowledge is the key to success, students, study hard! Let's create a better tomorrow with our own efforts!
We shouldn't have too much remorse in our hearts, as long as we work hard!
Math diary sixth grade 14 winter and winter, go and make a math test paper! The exam is coming tomorrow, and you are not too slow. You really don't realize it. "Mom nagged again, so I had to listen and do the paper obediently.
I picked up a pen and flew to write the test paper, but when I did a question, my pen stopped. The title of this topic is as follows: Three trucks transport 9 10 tons of cement to a construction site. It is known that the first truck will transport 30 tons more than the second truck, and the third truck will transport 20 tons less than the second truck. How many tons can each of these three trucks hold? This kind of topic is a bit tricky. It is different from the type of problem-solving strategies we have done before. In the past, only two numbers were needed. This time, three numbers are needed. I thought about it for a long time, and finally it dawned on me that I knew what to do. In fact, this kind of problem is done in the same way as before, but in different forms. So, I did it. Because I don't know how many tons of cement was loaded in the first car, I counted the second car first. Using "9 10-30+20=900 (tons)", the first car transported 30 tons more cement than the second car, so I have to subtract 30 tons, and the third car transported 20 tons less cement than the second car, so I have to add 20 tons. If all three cars are, because the title says that the first car has 30 tons more cement than the second car, and the third car has 20 tons less cement than the second car, we can directly use "300+30=330 (tons)" to calculate how many tons of cement the first car has; Use "300-20=280 (ton)" to calculate how many tons of cement are on the third truck. In this way, I worked out the answer to this question easily.
Since I put forward this question, I have summed up a truth-mathematics is alive and changing rapidly, and some new problems are just changing old problems with new forms or statements. Only by following it and solving new problems with the old methods we have learned can we explore more mathematical mysteries and make continuous progress in the mathematical kingdom.
Math diary Grade 6 15 7, 7 is 49. Why did it become 7, 7 miserable for me? Because we are the seventh group, but we are miserable. Sun became the critical eye of the Monkey King.
But we got a "good" result in two long rope competitions, once sixth and once seventh (eight groups in the class, one group counts as one, that is, we are twice, once last and once second last).
Then let me talk about the second long rope competition! During the big break, the teacher announced an exciting news: the second long rope team competition was held in the second math class this morning. Three minutes before the competition, the teacher emphasized the rules: there is no time limit for this long rope competition, only depending on the number of people, and four people must jump in at the same time to start counting. Each group can jump three times, and take the highest one as your final score in this competition. We each let the group leader grab the rope and then walked to the left-hand corridor of Class Five (5). We thought we could practice for a while when we arrived, but the teacher could only dance when he talked about his group. The first group who jumped first was worried, because their group was not very skilled, so they were worried. As a result, their grades are much lower than usual. Our group is seventh, making others laugh while playing. Because Cao Junhao jumped too fast, he stepped on the rope and "0" for the first time. The second time, Cao Junhao was too slow, and the rope hit his foot and didn't jump, so he was "0" for the second time. The third time, we finally jumped to one, but because Tong Wang was so happy, we shook the rope very fast, and the third time was "1". We all hate Tong Wang and Cao Junhao one after another. The eighth group danced seriously, like being criticized by the teacher, with no smile on their faces and a white and bloodless face, and finally won the first place.
Did we get the seventh place again? This time it's because the whole team is not United, so we must work hard next time. Come on, team members, try to beat the eighth group and win the championship.