Solving life problems with mathematical knowledge

1. Solving small problems in life with mathematical knowledge

Solving small problems in life with mathematical knowledge 1. Solving problems in life with mathematical knowledge (for example)

Original publisher: Shen Minqin

Solving problems in daily life with mathematical knowledge Mathematics originates from reality and is used in reality. Applying mathematical knowledge to solve practical problems in daily life and work is the destination of learning mathematics. Everyone should learn useful math. In teaching, we must make full use of students' existing life experience and attach importance to excavating factors related to teaching materials and real life. Teachers should always guide students to apply what they have learned to real life, so as to experience the significance and function of what they have learned. For example, after learning "classification", students can sort out their schoolbags and desks by themselves, and let the sorted students say what they are sorting according to; After learning the "living space", students can tell who is around their seats and where the school is around. After learning Statistics, let the students count the number of various cleaning appliances in the classroom, the number of classes in Grade One and the number of boys and girls. The students in the class were born in that season. After learning "addition and subtraction within 20", consciously lead students to engage in a social practice activity, so that each child can take 20 cents to buy food in the vegetable market. In this activity, many students can't figure out the accounts, some can't figure it out verbally, and some can't figure out the relationship between Yuan and Jiao ... Either way, students are deeply aware of how important mathematics is to our lives and how valuable it is to learn mathematics, thus stimulating their strong desire to learn mathematics well. Students not only understand and master mathematical knowledge from activities, but also observe and solve mathematical problems in life. There will be some small problems when solving, and then use your brains to solve them, so as to gain application skills. In short, in order to make mathematics and life "close contact", our mathematics teaching must move from book mathematics to life mathematics, and life and mathematics are closely related.

2. Experience in using mathematical knowledge to solve real life problems

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 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. 1, triangles are very stable, and many brackets are triangles. Many supports are supported by three feet, and a mathematical axiom is used to determine the plane at three points. 2. Someone nailed diagonal strips on wooden doors to overcome the instability of quadrangles.

So is the rolling gate. 3. The stargazing platform in Dengfeng, Henan Province and Sun Yat-sen Mausoleum in Nanjing are both central symmetrical figures. 4. The holes of mosquito nets are hexagonal ~ 5. Chopsticks are tapered.

The disc is round. 6. Wires are line segments, refrigerators are cuboids, doors are rectangular, tires are round and the earth is round. Mathematics is a very useful subject.

Since the day when human beings appeared on the earth, people have gradually gained a profound understanding of mathematics while understanding and transforming the world. As early as ancient times, there was a legend that primitive people "dabbled in counting" and "knotting a rope".

It can be seen that "in some early ancient civilized societies, the beginning and bud of mathematics have been produced" (quoted from the first volume of Ancient and Modern Mathematical Thoughts, p1-author's note). "Before the emergence of mathematics in Babylon and Egypt around 3000 BC, mankind did not make greater progress in mathematics", "After the emergence of ancient Greek scholars from 600 BC to 300 BC", mathematics began to "become an organized, independent and rational discipline" (quoted from the first volume of Ancient and Modern Mathematical Thoughts, P1-author's note) about the history of human development.

Nowadays, mathematical knowledge and ideas are widely used in industrial and agricultural production and people's daily life. For example, after shopping, people should keep an account for year-end statistical inquiry; Go to the bank to handle savings business; Check the water and electricity charges of each household. These facilitate the use of knowledge of arithmetic and statistics.

In addition, the "push-pull automatic telescopic door" at the entrance of the community and government compound; Smooth connection between straight runway and curved runway in sports field; Calculation of the height of the building whose bottom cannot be closed: determination of the starting point of two-way operation of the tunnel; The design of folding fan and golden section is the property of straight line in plane geometry, and it is about the application of solving Rt triangle knowledge. Because these contents don't involve a lot of high school mathematics knowledge, I won't go into details here.

It can be seen that throughout the ages, human society has been developing and progressing in the process of constantly understanding and exploring mathematics. Mathematics has played a decisive role in the development of human civilization.

For example, when teaching "Finding the least common multiple of two numbers", at the beginning of the class, I created such a scene: there is a bus from Tanghuang to Changzhou (East) every 6 minutes, and there is a bus from Tanghuang to Danyang (North) every 8 minutes. Now there are only two cars going to Changzhou and Danyang at the same time. How many trains will leave for Changzhou and Danyang in a few minutes? Mathematics is everywhere in our life, from the bargaining of buying vegetables to the design of rockets.

In fact, in the process of learning mathematics, we aim to cultivate our logical judgment ability and make our thinking more rigorous. We study mathematics in school not only to remember a formula, but to gradually cultivate our logical thinking ability in the process of learning this formula. It can be said that a person's ability to judge a thing will be greatly enhanced if he learns mathematics well, so learning mathematics well is not only to cope with exams, but to learn a basic skill to survive in society.

3. Ask for an article: Solving life problems with mathematical knowledge.

I found a paper, I wonder if I can use the title: on the application of mathematics in life.

Let students feel the connection between mathematics and real life in classroom teaching. Initially learn to use mathematical knowledge to solve problems in daily life and enhance the awareness of applied mathematics; Experience the close relationship between mathematics and real life, understand the practical value of mathematics, enhance the understanding of mathematics knowledge and confidence in learning mathematics well, thus stimulating students' interest in learning mathematics.

Keywords mathematics; Life; Interest in mathematics comes from life, and there is mathematics everywhere in life. The new curriculum standard puts forward that mathematics should be combined with real life, and teachers should use a variety of teaching methods to combine with reality, so that students can feel the connection between mathematics and real life and obtain the mathematical knowledge needed to adapt to future social life and further development; Initially learn to observe and analyze real life by using mathematical thinking mode, solve problems in daily life, and enhance the awareness of applied mathematics; Experience the close relationship between mathematics and real life, understand the practical value of mathematics, enhance the understanding of mathematics knowledge and confidence in learning mathematics well, thus stimulating students' interest in learning mathematics.

As math teachers, we must make math teaching come alive. Teaching methods should be vivid, and learning methods should be more vivid.

To do this, teachers need to build an open mathematics learning model for students, let "mathematics in life" enter the classroom, and let the mathematics classroom truly become a paradise for students to learn. 1. Solving practical problems with life examples In the teaching process, teachers should clearly put forward the significance and importance of explaining the content of the topic, and let students know how to use what they have learned to solve some practical problems through examples.

For example, when I was teaching the mixed operation of addition and subtraction in senior one, I used this life scene to describe and perform: "There used to be five students in the classroom, but now four students come in and go out 1 student. How many students are there now? Solve "5+4–1=? "By describing the situation, students can easily master the operation process. For another example, when I was teaching Yuan, Jiao and Fen, I first created such a teaching situation: after the Wenchuan earthquake, Xiaohong wanted to donate money to the children in the disaster area and take out all her pocket money. She counted 50 coins with 1 angle. It was inconvenient to take so many coins, so she asked her neighbor's aunt to help her find a way. Aunt received 50 coins 1 dime from Xiaohong.

Do you think Xiaohong will lose money by changing 50 1 dime into 5 1 yuan notes? Why? Organize students to discuss first, and then tell everyone that 10 1 angle is 1 yuan, and 5 10 angles are 5 yuan, so 50 angles are equal to 5 yuan. Then according to the students' analysis, organize students to observe the divided coins and find out the law: "What is the relationship between yuan and angle?" Students quickly come to the conclusion that "1 yuan and 10 angle are equal", "1kloc-0/ angle is 1 yuan" and "1yuan is10/kloc-0". 2. Create life situations to stimulate learning enthusiasm. Teachers usually only pay attention to teaching methods when teaching calculation problems, and then let students practice repeatedly in order to calculate correctly.

This will not only be boring, but also affect students' enthusiasm. At this time, teachers can create teaching situations, imitate real life, and let students be there.

For example, in the "addition and subtraction of decimals" class, I asked students to act as salespeople and customers to experience the fun of mathematics in life: a small customer bought a ham sausage 1.8 yuan and a loaf of bread 1.5 yuan, so the teacher asked questions. How much do you think he should pay? Students attracted by the scene can list the addition formula 1.8+ 1.5=? , but equal to a few? At this time, not only the small customers and sales staff were shocked, but also a suspense was set for all the students. So we communicated, discussed and argued together, and finally found the answer. This interesting simulated life situation has entered the mathematics classroom, and students have a strong interest in learning knowledge, so they can maintain a positive attitude in the future mathematics study.

3. Strengthen practical activities and experience the fun of mathematics life. 3. 1 classroom practice activities; Mathematics curriculum standards suggest that teachers "let students experience and understand mathematics in real life". Primary school students, especially junior three students, mainly stay at the level of "intuitive image".

For example, when I teach "Understanding Grams and Kilograms", I give students a kilogram of salt, a kilogram of rice, a kilogram of beans and a kilogram of sand to weigh, see, touch, count, measure and try, so that they can feel the weight of one kilogram. Then let the students practice practical things by themselves.

Then divide the students into groups and weigh oranges, bananas, pears, soybeans, rice, etc. This stimulates students' enthusiasm for learning, cultivates students' practical ability and achieves the teaching goal.

3.2 Extracurricular practical activities; Mathematics in life is always associated with social life practice. In the process of imparting mathematical knowledge and cultivating mathematical ability, teachers should make students understand the application value of mathematical knowledge, enable students to directly apply mathematical knowledge and skills, create practical application opportunities as much as possible, and make students feel the importance of learning mathematical knowledge. For example, after learning One Point, arrange students to tidy up their lockers, schoolbags and drawers at home and experience the practical application of mathematics knowledge in life.

Teachers can integrate mathematics into life and guide students to apply what they have learned to life practice in the process of learning mathematics. This design is not only close to students' life, but also meets their psychological needs, and also leaves some reverie and expectation for students, so that they can connect their mathematical knowledge with real life more closely. In short, teachers should actively create conditions for students to create vivid and interesting situations to inspire and induce, actively use mathematical knowledge to solve practical problems after class, stimulate students' strong thirst for knowledge, let students explore, find and solve problems independently, enjoy the fun of creation, reap the joy of success, and truly become the masters of learning.

References [1] edited by Guan Wenxin. The concept of new curriculum and the implementation of mathematics classroom teaching in primary schools. Version 1. Published by Capital Normal University Press, May 2003. [2] Yang Jiujun and other editors. The change of learning style. Version 1. Published by Jiangsu Education Press, 2006. 1.

4. Solving practical problems in life with mathematics

I found a problem when I was doing my homework today. This is the cycle in life.

What is a circle in life, that is, what is the circumference, area and symmetry axis of a circle in life, that is, the application of circle knowledge in life.

In our real life, there are many places where circles are needed. As long as we observe them carefully, we will certainly find them. As far as I know, the distance traveled by the wheel is the circumference of this circle; The route that the minute hand of the clock passes is the circumference of the clock face; The length of the cloth edge around the round dining table is also the circumference of the table top; The bracelets that people often wear on their hands also contain knowledge about the circumference … really too much.

The circular area is actually very simple. As long as you can observe, the size of the round table is also the area of the round table; The size of the surface swept by the hour hand is also the area of this clock; There is also a possibility that everyone is rare, that is, tie the cows up with ropes to eat grass, and seek the maximum range of grazing for the cows, that is, the area of the circle.

Also, a circle has countless axes of symmetry.

By studying the circle, I have a better understanding of the use of the circle in life and the calculation method of things, which has benefited me a lot!

5. Solve problems in life with mathematical knowledge (for example)

Original publisher: Shen Minqin uses mathematical knowledge to solve problems in daily life. Mathematics originates from reality and is used in reality. Applying mathematical knowledge to solve practical problems in daily life and work is the destination of learning mathematics.

Everyone should learn useful math. In teaching, we must make full use of students' existing life experience and attach importance to excavating factors related to teaching materials and real life. Teachers should always guide students to apply what they have learned to real life, so as to experience the significance and function of what they have learned.

For example, after learning "classification", students can sort out their schoolbags and desks by themselves, and let the sorted students say what they are sorting according to; After learning the "living space", students can tell who is around their seats and where the school is around. After learning Statistics, let the students count the number of various cleaning appliances in the classroom, the number of classes in Grade One and the number of boys and girls. The students in the class were born in that season. After learning "addition and subtraction within 20", consciously lead students to engage in a social practice activity, so that each child can take 20 cents to buy food in the vegetable market. In this activity, many students can't figure out the accounts, some can't figure it out verbally, and some can't figure out the relationship between Yuan and Jiao ... Either way, students are deeply aware of how important mathematics is to our lives and how valuable it is to learn mathematics, thus stimulating their strong desire to learn mathematics well.

Students not only understand and master mathematical knowledge from activities, but also observe and solve mathematical problems in life. There will be some small problems when solving, and then use your brains to solve them, so as to gain application skills.

In short, in order to make mathematics and life "close contact", our mathematics teaching must move from book mathematics to life mathematics, and life and mathematics are closely related.

6. Solve problems in life with mathematical knowledge. A 400-word diary

On Sunday, my mother and I went out for a walk. In an alley, I smelled a strong smell of baked sweet potatoes. When I smell this smell, my stomach growls, "Mom, let's buy a sweet potato to eat. I'm hungry. " I took my mother's hand and begged, "You can buy one, but …" "But what?" I quickly asked: "But I bought it and went home to calculate the volume of sweet potatoes before eating." "all right! Ok! " I readily promised. When I got home, I had forgotten about calculating the volume of sweet potatoes, and I wanted to eat them when I picked them up. "Hey, how did you start eating? Didn't we agree to calculate the volume of sweet potatoes? It doesn't count if you can't talk! " "Ah?" I'm surprised. "Really?" "Of course!" Mom said, "Sweet potatoes must be measured before they can be eaten!" ""Hum! What's the big deal? Is it not the size of a sweet potato? Can you beat me? "I opened the math book, and there were only calculation methods of cuboids, cubes and cylinders in the book. And this sweet potato is an irregular three-dimensional figure, which can't be kneaded. How to calculate? I think hard with my chin cupped. At this moment, I saw a short story of a famous mathematician on the table. I opened it and read my first short story with great interest. This story tells that Archimedes used equal product generation to transform the golden crown. I had a brainwave and thought, can't I also get the volume of sweet potato through equal product generation? So, I took a cylindrical glass and measured it. Its bottom diameter was 6 cm. I poured 10 cm of water into the cup, and then completely submerged the sweet potato in the water. At this time, the water in the glass rose. I measured it again, and now the water in the cup is 15 cm, which means the water in the cup has gone up: 15-6544. The volume of rising water is the volume of sweet potato, so it can be calculated that the volume of sweet potato is: (6 ÷ 2) 2 * 3.14 * 5 =141.3 (cubic centimeter) "Mom! I figured it out! I figured it out! It's 14 1.3 cubic centimeter! I figured it out! I can eat sweet potatoes! " I trotted to my mother, "Oh? Calculated? " Mom put down what she was doing and looked at me with a smile. "Well, it's 14 1.3 cubic centimeters." I proudly said, "How did you calculate it?" My mother asked again. I told my mother the process of my experiment. My mother gave me a thumbs-up and praised me as a "little doctor in mathematics". In fact, in life, many seemingly impossible things can be obtained through equivalent product substitution. As long as everyone is willing to use their brains and loves to use their brains, nothing can beat me.

7. How to make students use mathematical knowledge to solve practical problems in life?

Students should be able to use what they have learned to solve practical problems.

Both the Mathematics Curriculum Standards of the United States and the mathematics education in other countries generally attach importance to solving practical problems. China's new curriculum standard requires: "let every student learn valuable mathematics;" Everyone can get the necessary mathematics; Different people get different development in mathematics; Everyone can use what they have learned to solve simple application problems in life. "

Learning is to apply mathematical knowledge to solve practical problems. Therefore, teachers should collect the background related to new knowledge in real life and other disciplines and create mathematical problem situations. When students master the relevant knowledge and skills, they can guide students to explore and apply in the real world and build mathematical models to solve problems in real life. In this way, theory and practice are inseparable in the learning process, and teachers can connect with real life to cultivate students' awareness and ability to use what they have learned flexibly to solve practical problems.

In addition, as a teaching form, "problem solving" emphasizes students' hands-on, so teachers should not just demonstrate the correct way to solve problems like coaches, but should choose appropriate questions, encourage students to discuss with each other, and let students exchange their own solutions and understanding, so it is more important to create the conclusion of the studied problem than to get the correct answer. In addition, let the students do their own work, do their own calculations, draw their own pictures and answer their own questions, and let the students do some small investigations and experiments, ask their own questions and solve their own problems.

The following are my thoughts on this issue since I started teaching mathematics: 1. To cultivate students' awareness of applying mathematics in their lives, such as teaching the stability of triangles, students can explain: Why should the roof of the house where we live be framed into triangles? Why did the carpenter fix the desk for his classmates and nail a diagonal strip at the foot of the desk? Another example is teaching the characteristics of parallelogram. Ask the students to explain: Why should the gate be made into a parallelogram grid instead of a triangle? Through the explanation of some life phenomena, students can feel the close connection between mathematics and real life more deeply. In addition, students should use mathematical knowledge to solve practical problems. For example, in the initial understanding of teaching statistics, the teacher first shows a map of China and asks the students, "What map is this?" The student answered and asked, "Do you know the territory of our country?" After the student answered, he asked, "Do you know the population of our country?" On the basis of students' approximate figures, the teacher accurately stated that the population of China was1295.33 million, and introduced that this was the result of the fifth population census in China recently.

At this time, students are interested in the census, and teachers can take the opportunity to introduce a new lesson: "There are many census items, but no matter which one needs to be applied to statistics, we will learn this knowledge today. Do you want to learn? " Then, under the students' strong thirst for knowledge, the topic was revealed. At the same time, practical homework was assigned at the end of this class: a "small census" was conducted in groups to investigate the number of students in the whole fifth grade of our school.

This not only makes students realize the role of statistics, but also strengthens the impression of statistics in students' minds, makes students actually investigate and makes students understand that mathematical knowledge is actually used to solve problems in life. Second, arouse students' interest in learning with practical problems. Psychological research shows that the closer the learning content is to students' familiar life background, the higher the students' conscious acceptance of knowledge.

Therefore, in classroom teaching, we should combine the teaching content with students' life background as much as possible, and introduce new lessons from practical problems close to students' lives to stimulate students' interest in learning. For example, when learning the concept of "vertical line", we can put forward such a question in combination with reality: "What is the relationship between the positions of two roads at the intersection of roads? For example, what is the relationship between telephone poles and the position of wires above them? " These are concrete examples of mathematics in real life, which can stimulate students' desire for knowledge, make students have the consciousness of "there is mathematics everywhere in life", understand the meaning of vertical line intuitively and realize the importance of learning this content.

In teaching, teachers should make full use of modern educational technology to assist teaching, adopt modern teaching methods such as models, slides, videos, computers, etc., increase the interaction between teachers and students, visualize mathematics content, and visualize abstract knowledge at the same time. This can attract students' attention, stimulate students' interest in learning knowledge actively, deepen their understanding of knowledge and improve learning efficiency.

Third, it is not a simple and natural thing to combine teaching with practice, find problems from life and ask questions from mastering knowledge to applying knowledge. Without adequate and conscious training, students' awareness of application will not be formed. In teaching, we should pay attention to extracting mathematical problems from concrete things and guide students to solve some problems in daily life with mathematical knowledge, which is helpful to the formation of students' awareness of mathematical application.

For example, when talking about "travel application", we use such a problem that we often encounter in life: there are three roads connecting A and B. Under normal circumstances, we choose the shortest road from A to B (saving time and road); Under special circumstances, if the shortest road is too crowded, we will choose another road to get from A to B within a certain period of time. We would rather walk more and speed up the pace (speed) to ensure the time (time is fixed, distance is proportional to speed). Analyzing this problem for students from the perspective of mathematics is the practical application of the relationship between distance, time and speed.

Fourth, carefully compile questions to cultivate students' application ability. At present, most of the questions and test questions in mathematics textbooks in China are pure mathematics questions divorced from the actual background, or applied mathematics questions with no background. Such training, over time, makes students have a strong ability to solve ready-made mathematical problems, but their ability to abstract practical problems into mathematical problems is very weak.

Mathematics takes the spatial form and quantitative relationship of the real world as the research object, and many of its concepts, theorems and methods are derived from reality. But it has more conclusions to serve all walks of life in production and society.

Therefore, under the premise of following the teaching requirements, teachers can carefully compile some problems related to life and science, which can make students feel that mathematics is everywhere around them, let them sprout and learn mathematics well to solve them.

8. How to use mathematical knowledge to solve mathematical problems in life?

"New Curriculum Standard" emphasizes that students should learn to observe and analyze reality by using mathematical thinking mode, solve problems in daily life, enhance students' awareness of applying mathematics, make students truly understand the close relationship between mathematics and human society, understand the value of mathematics, and enhance their understanding of mathematics and confidence in learning mathematics well. It is very necessary to cultivate students' application consciousness. The ultimate goal is to apply what I have learned and let students learn mathematics. I actively encourage students to use what they have learned to solve simple practical problems and gain successful experience, thus stimulating students' interest in learning mathematics. Enable students to have initial innovative spirit and practical ability. First, combine calculation with problem solving 1. In primary school mathematics textbooks, calculation accounts for a large proportion. Students' computing ability is the basic knowledge that primary school students must master. However, some students feel that simple calculation is boring and their enthusiasm for learning is not high, so I pay special attention to the connection with students' daily life when teaching calculation. For example, when teaching addition and subtraction, I ask students to collect data about shopping in their own lives. Therefore, they pay special attention to the price of goods and the payment situation. Their enthusiasm is very high when they show the application problems compiled by the students themselves in class. While mastering the calculation, they found that mathematics was at hand.