In fact, there are mathematics everywhere in our lives, such as the wonderful circle.
The circle is the most common figure in life, and people use it almost everywhere. In the car, on the road, at home, and even in the air, you can always see the traces of circles.
One of the great advantages of a circle is that it has no edges and corners. Why can a car run very fast, but the people sitting in it don't feel bumpy? This is because the wheels of a car are round. Why is bowling a sphere instead of a cube or cuboid when bowling? Because the friction between the sphere and the ground is the smallest, the speed slows down for the longest time, and the speed is not easy to change. Because there are no edges and corners, people call circles and spheres the most beautiful plane figures and the most beautiful three-dimensional figures.
The circle is considered to be the most economical figure. As we all know, the area of a circle is larger than any other shape at the same time. According to this reason, people designed a round manhole cover, because when the round manhole cover is placed on the manhole perpendicular to the ground, it will not fall into the manhole like a square or rectangular manhole cover, but will be firmly stuck on it. How can such lovely graphics not be favored by people?
In addition to the circle, there are some three-dimensional figures related to the circle, such as cylinders and spheres, which also play an important role! Under the condition of the same material area, the cylinder has the largest volume and the largest supporting force. Trunks, bamboos, buckets and other things all use cylinders. There are decimal points and mathematics, which are everywhere in our lives. Gauss quadrature, planting trees ... these wonderful mathematical laws surprise us. Let's find a wonderful digital journey together!
Decimals are everywhere in weight and price. Anywhere, moving to the right represents expansion, and moving to the left represents contraction. This magical decimal point has opened our digital journey today.
In our measurement and calculation, sometimes we can't get integers, so there is a decimal point here. The decimal point has a huge "right". It has a decimal part on the right and an integer part on the left. It has a high prestige in the digital world, because its movement has changed the size of numbers. There are two ways to change the size of a number: 1, change the position of the number, and 2, move the decimal point.
In life, the decimal point becomes a number and a compound number. Decimal point not only changes the size of a number by moving the decimal point, but also changes the size of a number by multiplication and division. Multiplication means moving to the right, and moving one digit will expand 10 times. In addition to the left shift, moving one bit is reduced by 10 times.
The decimal point is really magical, and there are many magical laws in life. Let's explore together!
Mr. Qian Xuesen, the pioneer of thinking science in China, believes that human thinking can be divided into three types: abstract (logical) thinking, visual thinking and spiritual (epiphany) thinking. It is suggested that thinking in images should be regarded as the breakthrough of thinking science research. What is thinking in images? The so-called thinking in images is to use the images accumulated in the mind to think. Representation is the image of those object phenomena that we have perceived before and reproduced in our minds. Thinking in images has the characteristics of indirectness and generality. Like abstract thinking, thinking in images is an advanced form of cognition-rational cognition. Why should we cultivate students' thinking ability in images? According to the latest achievements of modern scientific research, the left and right hemispheres of the human brain have different functions. The left hemisphere is the language center, in charge of language and abstract thinking, while the right hemisphere is in charge of the comprehensive activities of image thinking materials such as music and painting. Only by matching, complementing and promoting each other can individuals develop harmoniously. From the characteristics of children's thinking, primary school students' thinking has gradually changed from concrete thinking in images to abstract logical thinking, but at this time, logical thinking is preliminary and still has concrete images to a great extent. Therefore, cultivating students' thinking ability in images is not only their own needs, but also their need to learn abstract mathematics knowledge. So how to cultivate students' thinking ability in images in primary school mathematics teaching? First, fully perceive, enrich appearances, and accumulate materials for cultivating thinking in images. Children can keenly perceive vivid images with rich colors, tones and sounds, and are good at using image colors and sounds to trigger thinking. Image is the cell of image thinking, and image thinking depends on image thinking. To develop students' thinking in images, we must lay a good foundation and enrich the accumulation of image materials. 1. Hands-on operation enriches the appearance of hands-on operation, allowing students to participate in learning with various senses and observe things from various angles. For example, to teach the concept of remainder, let the students divide the sticks first: (1) How many sticks are left in every two of the nine sticks? (2) 13, distributed to 5 people on average. How many sticks can each student get? How much is left? After the operation, guide the students to express the operation process in words and talk about how to divide the sticks, thus forming an image. Then let the students close their eyes and think about how to divide the following questions. (1) There are 7 biscuits. Each biscuit is divided into 3 pieces, which can be distributed to several people. How many pieces are left? ② Pencils 12, distributed to five people on average. How many pencils can each person divide, and how many pencils are left? In this way, students can think in operation and operate in thinking, and understand that dividend is the total number, divisor and quotient are the number of shares to be divided and each share, and the remainder is not enough, and the remainder is less than divisor. Correct and clear representations are formed in the mind, and correct thinking has a solid foundation. 2. Intuitive demonstration to enrich the appearance. Pupils' unintentional attention plays an important role, and the emergence of any new things will arouse students' interest in actively participating in the learning process. In the process of teaching, organize teaching with pictures, teaching AIDS or audio-visual means, visualize abstract knowledge and let students fully perceive the materials they have learned. Only with quantitative perceptual materials can they leave a clear image in their minds. For example, in the teaching of "cuboid cognition", teachers can first show cuboid objects familiar to students in their daily lives, such as matchboxes, chalk boxes, bricks and so on. These objects are cuboids. Then ask the students to list their own rectangular objects (bookcases, wooden cases, thick books, pencil boxes, etc.). ), through the feeling of the object, have a preliminary perceptual understanding of what kind of object a cuboid is. On this basis, teachers guide students to read books while observing the model, and understand the characteristics of the cuboid from different positions and directions, such as the equal area of six faces and opposite faces, the length of twelve sides and parallel sides. We can know the length, width and height of a cuboid by observing the length of a vertex and three sides intersecting with the vertex. Through the flat, lateral and vertical forms of the model, it is shown that the length, width and height are relatively fixed, and the knowledge is "alive", which enables students to establish a clear and profound representation in the process of learning with their mouths and brains, and provides conditions for the rationalization of thinking. The introduction of audio-visual teaching means into the classroom can turn the static into the dynamic and turn the near into the far. With its colorful and flexible teaching form, it provides students with demonstrations reflecting their thinking and thinking process, which can fully mobilize their psychological factors and achieve good results. For example, when teaching "Subtraction Application Problem of Finding Another Addendum", students can vividly understand the relationship between the total and the part through the slide presentation, that is, the total-part = another part. In teaching, we should use a variety of teaching methods to make students fully perceive, establish clear mathematical representations in their minds, and accumulate materials for improving students' mathematical imagination. Second, guide imagination and develop thinking in images. Modern cognitive psychology believes that images can not only be stored, but also the stored image traces (information) can be processed and reorganized to form new images, that is, imaginary images, which is also an important way of image thinking. Therefore, teachers should be good at creating problem scenarios in classroom teaching, such as graphic scenarios and language scenarios, to stimulate students' desire to participate in inquiry and give full play to their rich imagination. For example, after teaching trapezoidal knowledge, students can be guided to imagine: "What shape will the trapezoid become when one base of the trapezoid is gradually shortened to 0?"? When the short bottom of the ladder extends to be equal to the other bottom, what shape does it become? " With the help of representation, seemingly unrelated triangles, parallelograms and trapezoid can be organically combined. You can also memorize the area formulas of triangles and parallelograms according to the trapezoid area formula: 1 S[, trapezoid] =-(a+b) H2 1. When a = 0, it becomes a triangle, and the area formula is: S =-AH2; when A = b, it becomes a parallelogram, and the area formula is: S = AH. Different types of mathematical graphics provide the representation materials of brain thinking in images, arouse the enthusiasm and initiative of brain thinking, improve his thinking ability in images, promote the coordinated development of individual's left and right brains, and make people smarter. For example, illustrations designed with specific plots of applied problems in textbooks broaden the world of students' thinking in images and enhance their will to study hard. For example, examples and review questions in textbooks use colorful colors and various small animals, plants, rivers, mountains and rivers, modern airplanes, cars, ships, satellites, buildings, ancient cultural relics and books to express the quantitative relationship ... These are not only conducive to understanding the quantitative relationship, but also play an important role in the development of students' thinking ability in images and the improvement of their aesthetic ability. Besides, the application problem teaching, because the application problem is a combination of science, art and mathematics, the prototype of the application problem is more complex and abstract, and it is difficult for students to form a clear representation after they get into their heads. If we use the method of combining numbers and shapes to draw line segments, we can help students to establish a correct representation and make clear the hidden and complicated quantitative relationship. For example, "Xiao Liang has 18 yuan in its savings box, and Xiaohua's savings is 5/6 of that of Xiao Liang, and Xiao Xin's savings is 2/3 of that of Xiaohua. How much did Xiao Xin save? " It is often difficult for students to determine the unit "1". In teaching, students can be guided to draw the following line chart to analyze the quantitative relationship: According to the line chart, students can quickly list the formula: 18× 5/6× 2/3- 10 (yuan). Therefore, the line diagram is semi-abstract and semi-concrete, which can not only abandon the specific plot of the application problem, but also vividly reveal the relationship between conditions and articles and problems. The application of line graph and the combination of numbers and shapes here better stimulate students' creative imagination, which not only develops students' thinking in images, but also realizes the complementarity of thinking in images and abstract thinking.