There are many mathematical problems around our lives, which run through all aspects of our lives. There are many math games in real life, such as children's quick calculation of 24 when playing poker, math box filling game, and even Zhao Benshan's sketches have many such math games, such as "seven monkeys in the tree, a monkey on the ground, and a few monkeys." And so on. These games constitute a colorful picture in our life. We get together every morning. First of all, we make a relatively simple plan for the day's work, what to do in a day, when to finish it, and what is the budget expenditure and income of this day; After having a preliminary plan, start to implement the work of the day; A day's work is accompanied by various calculations, and the budget is mathematics. After a day's work, the next step is the summary of the day. Summarized by a mathematical operation, the result of the operation is a relatively intuitive number. In our real life, shopping, estimating, calculating time, determining location and buying and selling stocks are all related to mathematics. It can be said that mathematics is everywhere in people's lives. Mathematics is an indispensable tool in daily life. No matter what occupation people are engaged in, they will use mathematical knowledge and skills and mathematical thinking methods to varying degrees. Especially with the popularization and development of computers, this demand is increasing day by day. Whether it is weather forecast, savings, market research and forecast in our daily life, or gene map analysis, engineering design, information coding, quality monitoring and so on. It is inseparable from the support of mathematics. Mathematics, like language, is a tool with international universality. It can be said that there are countless mathematics in nature, such as the honeycomb built by bees, whose surface is composed of wonderful mathematical figures-regular hexagon, which consumes the least material and time; The manhole covers of urban sewers are all round. Do you know why? On the sidewalk, we often see such patterns, which are paved with square or regular hexagonal floor tiles of the same size, so that the floor tiles of this shape can be paved into a flat ground without pores. Is there a mathematical truth of salvation in this? For another example, 100 households need to install telephones, but they don't need 100 telephone lines. As long as they are kept busy for a period of time, the installation cost can be greatly saved, which embodies the role of mathematical statistics. Therefore, life cannot be separated from mathematics, which is the epitome of life. At the end of the year, businessmen said that my new year was coming. Farmers are also talking about how much food they have earned this year; The workers are also discussing whether the income and expenditure of this year are equal and how much savings there are; The soldiers talked about their training achievements this year and how many achievements they improved; Students' academic performance is the standard to measure a teacher's efforts in the past year; The unit is also making such a summary. The end of one year is like this, and the beginning of the next year also needs a budget; People are doing the same thing every day, every month, every quarter and every stage; A person, a family, a unit, an organization, a country, etc. They all use mathematical methods to do certain operations on them in different time, place, space, people and things. And then get an intuitive numerical index as the goal, conclusion, budget, degree, etc. In short, mathematics in life can be said to be everywhere, and mathematics has a serious impact on our lives.
2. Interesting mathematical knowledge in life
1. A garment worker can produce 4 coats or 7 pairs of trousers per person every day, and one coat and one pair of trousers make a suit. At present, 66 workers produce, how many sets of clothes can you produce at most every day?
Xiao Wang has three stamp albums, one fifth of all stamps are in the first one, n divided by 8(N is a non-zero natural number) is in the second one, and the remaining 39 stamps are in the third one. How many stamps does Xiao Wang have?
Xiao Ming looked at his report card and predicted that if the next math test is 100, the total average score will be 9 1. If he gets 80 points in the next exam, the overall average score will be 86 points. How many times did Xiao Ming take the math statistics exam?
1
To set up X workers to produce coats, you must
4x=7*(66-x)
Then x=42.
So you can produce 4*42= 168 sets of clothes a day.
2
Suppose it has x stamps.
x/5+N/8+39=x
Simplified to 4x/5-N/8=39.
According to the meaning of the question, n is the ending of 8, 4x/5 is an even number, and 39 is an odd number. Then n is the odd tail of 8. Let N=(2t+ 1)*8 get 4x/5-(2t+ 1)=39.
x=( 100+5t)/2
Then 5t is an even number, let t=2w, x=( 100+5*2w)/2=50+5w.
It can be seen that * * * has 50+5w stamps, where w is 0, 1, 2, 3, 4.
At this time N=32w+8.
three
There have been X exams, and now the average score is A.
(xa+ 100)/(x+ 1)= 9 1
(xa+80)/(x+ 1)=86
The two expressions are subtracted, and 20/(x+ 1)=5.
Then x=3 a=88
That is, the results of the existing three exams.
3. Mathematical stories in life
Please ask me again if you want something original. If you were here, you would answer. Let me give you an answer first.
During the National Day holiday, my mother and I went shopping in the supermarket to find kilograms and grams. Walking into the supermarket, we first came to the biscuit cabinet. Among so many dazzling cookies, I chose my favorite casual cookie. I looked at it carefully and finally found the "net content100g" in the corner, indicating that the weight of this packet of biscuits excluding the bag is100g. If there is100g,
Then we went to the place where we bought rice. I found that a bag of rice costs 10 kg. If our family eats 2 kilograms a day, our family will eat 60 kilograms a month, which is six bags of rice.
Later, I saw 16 eggs, about 1 kg, a pineapple about 2 kg and a watermelon about 3 kg.
Today, I have gained a lot. I feel the knowledge of kilograms and grams in mathematics. Mathematics is really important in life.
This afternoon, my mother and I went shopping in the supermarket.
When we finished buying what we needed, we were about to leave. I saw sausages on the shelf, so I asked my mother to buy some sausages, and my mother agreed. But just after a few steps, I saw a package with the same brand and weight on the shelf, which contained 10 pieces at 4.30 yuan each. Do you want to buy a pack or a slice? I hesitated. Suddenly, my mind turned and I understood. Just compare and see which one is cost-effective. So I started to calculate: if I buy 10 pieces in retail, each piece costs 40 cents, which is equal to 4 yuan, and the whole package costs 4.30 yuan, which is 3 cents more, so I decided to buy it in bulk. I told my mother the process of my calculation, and my mother praised me for my love of brains.
I read a book today; I feel heavy.
It tells the story of a mathematician. His family was poor, but he was eager to learn, so he was sent to school. But he's not serious. Keep playing. One day, the teacher talked to him: "The food you ate and the money you spent at school were all the fruits of your father's hard work. Who do you deserve if you don't study hard now? " He was inspired a lot. He thought: When I grow up, I want to be an astronomer and a writer.
But later, influenced by a teacher who came back from studying in Japan, he turned his interest to mathematics. Do you know who he is?
He is Sue, a famous mathematician in China.
Smoking is harmful to health. Dad smokes a newspaper every day, 20 cigarettes per pack. I learned that each cigarette can shorten people's life span by 3 minutes, so it will be shortened every day.
20X3=60 minutes = 1 hour life, which shortens life by 365 days per year X 1 hour =365 hours. So I said to my father, "Smoking is harmful to health."
4. Mathematical knowledge in life
In life. For example, when you go shopping, you will naturally use addition and subtraction, and you always have to draw pictures when you build a house. There are countless problems like this, and this knowledge comes from life and is finally summed up as mathematical knowledge, which solves more practical problems.
I once saw a report that a professor asked a group of foreign students, "How many times will the minute hand and the hour hand overlap between 12 and 1?" Those students all took off their watches from their wrists and began to set hands; When the professor tells the same question to the students in China, the students will use mathematical formulas to make calculations. The commentary said that it can be seen that China students' mathematical knowledge is transferred from books to their brains, so they can't use it flexibly. They seldom think of learning and mastering mathematics knowledge in real life.
From then on, I began to consciously connect mathematics with daily life. Once, my mother baked a cake, and two cakes could be put in the pot. I thought, isn't this a math problem? It takes two minutes to bake a cake, one minute in front and one minute in the back. At most, two cakes are put in the pot at the same time. How many minutes does it take to bake three cakes at most? I thought about it and came to the conclusion that it takes 3 minutes: first, put the first cake and the second cake into the pot at the same time, 1 minute later, take out the second cake, put the third cake and turn the first cake over; Bake again 1 min, so that the first cake is ready. Take it out. Then put the reverse side of the second cake on it, and turn the third cake upside down at the same time, so it will be all done in 3 minutes.
I told my mother about this idea, and she said, actually, it won't be so coincidental. There must be an error, but the algorithm is correct. It seems that we must apply what we have learned in order to make mathematics serve our lives better.
Mathematics should be studied in life. Some people say that the knowledge in books has little to do with reality now. This shows that their knowledge transfer ability has not been fully exercised. It is precisely because learning cannot be well understood and applied in daily life that many people do not attach importance to mathematics. I hope that students can learn mathematics in their lives and use mathematics in their lives. Mathematics is inseparable from life. If they study thoroughly, they will naturally find that mathematics is actually very useful.
5. A little knowledge about numbers
The origin of numbers Numbers can be described as the cornerstone of the building of mathematics, and they are also the earliest mathematical objects studied by people.
Millions of years ago. Our ancestors only knew the concepts of "you", "nothing", "more" and "less", but they didn't know what numbers were.
With the progress of civilization, these vague concepts can no longer meet the needs of production and life. For example, in the ancient book Zhouyi, there is a record of "knotting the ancient".
That is, when an important event happens, tie a knot on the rope as a mark. Although this method is simple, it at least shows that people already have the concept of number.
After writing appeared, people tried to record mathematics in the form of symbols. So there are all kinds of recording methods.
The ancient Egyptians used "|" to indicate one and "∨" to indicate two; The ancient Romans used "I" for one and "II" for two. Although this method is effective, it is very inconvenient to record in a very large number of cases.
For example, if we want to express for one hundred hours, should we write one hundred "|"? Of course, the ancient Romans also saw the problem, so they invented Roman numerals I, II, III, IV, V, VI, VII, VIII, IX, X, L and C to stand for 1, 2, 3, 4, 5, 6, 7 and 8 respectively. It seems that the problem has been solved, but it is still difficult to express 10 thousand.
This is why Roman numerals are not widely used. The failure of Roman numerals shows that any counting method that wants each number to correspond to a symbol is futile.
Until the eighth century, Indians invented a notation that only contained 1, 2, 3, 4, 5, 6, 7, 8, 9 and 9 symbols, and agreed that the position of numbers determined the size of numbers. For example, in the number 89, 8 means eight tens and 9 means nine ones.
This means that any number is a piece of cake. As a result, the invention was quickly brought to Baghdad, the capital of * * * by businessmen.
And soon spread, and called it * * * Numbers. Because this notation is simple and clear, it has been used ever since.
Become the universal language of mathematics in the world. No wonder Engels called it "the most wonderful invention".
* * * * * * * * * * * * * * * * * * * * * * There are many sources of figures all over the world, and one of them is internationally used, namely * * * number: 0, 1, 2, 3, 4, 5. In fact, * * * numbers were not invented by * * people, but by ancient Indians.
Ancient Indians carved some horizontal lines on stone tablets to indicate numbers, one horizontal line indicated 1 and the other horizontal line indicated 2 ... Later, they used palm leaves or birch bark as writing materials and connected some strokes, for example, two horizontal lines of 2 were written as z, three horizontal lines of 3 were written as z, and so on. In the 8th century AD, an Indian mathematician named Kank came to Baghdad, the capital of * * * *, with his digital books and astronomical charts on his back.
At this time, China's papermaking has just been introduced into * * *. As a result, his book was quickly translated into * * * and spread on the * * * peninsula, and the characters of * * * also spread to * * * places.
With the commercial exchanges between the East and the West, this set of figures was introduced to Europe by * * * merchants in the12nd century. Europeans like this convenient and practical symbol. They thought it was a * * * number, which caused this historical misunderstanding.
Although people later knew the truth of the matter, they never corrected it because they were used to it. * * * Numbers spread to European countries, and their appearance gradually changed due to reproduction. After more than 65,438+0,000 years of continuous improvement, to 65,438+0,480, the writing of these numbers is almost the same as the current writing.
1522, when the number * * * appeared in the English book with Stowe, it was basically consistent with the current writing. Because * * * numbers and their decimal notation have many advantages, they are gradually popularized around the world and used by countries all over the world.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * By the 3rd century A.D./KLOC-0, the Italian mathematician Fibonacci wrote Abacus, in which he introduced the number of * * * in detail.
Later, these figures spread from * * * to Europe. Europeans only know that these numbers are imported from * * * regions, so they are called * * * numbers. Later, these figures spread from Europe to all countries in the world.
* * * Numbers were introduced into China from about 13 to 14 century. Because there was a number called "Chip" in ancient China, which was convenient for writing, the number * * * was not popularized and used in China at that time.
At the beginning of this century, with the absorption and introduction of foreign mathematical achievements in China, the number * * * began to be used slowly in China, and it has only been popularized and used in China for more than 100 years. * * * Numbers have now become the most commonly used numbers in people's study, life and communication.
* * * * * * * * * * * * * * * * * * * The origin of Roman numerals is a quantitative representation that is rarely used now. It came into being later than the numbers in China and Oracle Bone Inscriptions, and even later than the Egyptian single digit.
However, its appearance marks the progress of an ancient civilization. About 2500 years ago, the Romans were still in the early stage of cultural development, when they used their fingers as computing tools.
To represent 1, 2, 3 and 4 objects, extend 1, 2, 3 and 4 fingers respectively; It means that five objects stretch out a hand; It means that 10 object sticks out two hands. This habit has been used by human beings until today.
People often use such gestures to represent numbers in conversation. At that time, in order to record these numbers, the Romans drew I, II and III on sheepskin instead of the number of fingers. In order to represent a hand, it is written as a "V", which represents the open shape of thumb and forefinger; When expressing two hands, it is drawn as "ⅴ ⅴ", and later it is written as "ⅹ", with one hand up and the other hand down, which is the prototype of Roman numerals.
Later, in order to represent a larger number, the Romans used the symbol C to represent 100, which is the first letter of the Latin word "century", which means 100. The symbol m stands for 1000.
M is the first letter of the Latin word "mile", which means 1000. Take half of the letter c as the symbol l, which means 50.
500 is represented by the letter D. If you draw a horizontal line at the top of the number, it will expand.
6. A short story about numbers in life
One day, when the digital cards were having lunch together, the youngest one spoke. Brother 0 said, "Let's take some photos together. What do you think? " 0' s brothers and sisters said in unison, "Good."
Brother 8 said, "Brother 0' s idea is really good. I will be a good person once. Shall I provide camera and film for Brother 8? "
Old 4 said, "Brother 8, it's good, but it's a little too much trouble. Better use my digital camera. That's settled. "
So, they got busy. Finally, they took pictures for them and immediately sent the digital camera to the print shop. The computer sister tried to ask them for money, but who paid for it? They stared at each other one after another. This is what the computer sister said, "A ***5 yuan, a * * * eleven brothers and sisters, how much does one person pay on average?"
Among the eleven of them, Lao Liu is the cleverest, and this time he is the first to work out the result. Do you know how it is worked out?