For example:
1* 1= 1
2*2= 1* 1+( 1+2)=4
3*3=2*2+(2+3)=9
……
10* 10= 100
1 1* 1 1= 10* 10+( 10+ 1 1)= 12 1
12* 12= 1 1* 1 1+( 1 1+ 12)= 144
……
20*20=400
2 1*2 1=20*20+(20+2 1)=44 1
22*22=2 1*2 1+(2 1+22)=484
……
That is to say, the square of a number (natural number) is equal to the square of the number smaller than it 1 plus the sum of these two numbers. n * n =(n- 1)*(n- 1)+(n- 1+n)。
Specific language organizations can enrich themselves and give more examples.
Note: where * indicates the multiplication symbol.
The second article
Mathematical paper
About "0"
0, can be said to be the earliest human contact number. Our ancestors only knew nothing and existence at first, and none of them was 0, so 0 isn't it? I remember the primary school teacher once said, "Any number minus itself is equal to 0, and 0 means there is no number." This statement is obviously incorrect. As we all know, 0 degrees Celsius on the thermometer indicates the freezing point of water (that is, the temperature of ice-water mixture at standard atmospheric pressure), where 0 is the distinguishing point between solid and liquid water. Moreover, in Chinese characters, 0 means more as zero, such as: 1) fragmentary; A small part. 2) The quantity is not enough for a certain unit ... At this point, we know that "no quantity is 0, but 0 not only means no quantity, but also means the difference between solid and liquid water, and so on."
"Any number divided by 0 is meaningless." This is a "conclusion" about 0 that teachers from primary school to middle school are still talking about. At that time, division (primary school) was to divide a copy into several parts and figure out how many there were in each part. A whole cannot be divided into 0 parts, which is "meaningless". Later, I learned that 0 in a/0 can represent a variable with zero as the limit (the absolute value of a variable is always smaller than an arbitrarily small positive number in the process of change) and should be equal to infinity (the absolute value of a variable is always larger than an arbitrarily large positive number in the process of change). From this, another theorem about 0 is obtained: "A variable whose limit is zero is called infinitesimal".
"Room 203 105 in 2003", although all of them are zeros, they are roughly similar in appearance; They have different meanings. 0 indicator vacancy of 105 and 2003 cannot be deleted. 0 in Room 203 separates "Building (2)" from "House Number". (3) "(that is, Room 8 on the second floor) can be deleted. 0 also means that ...
Einstein once said: "I always think it is absurd to explore the meaning and purpose of a person or all living things." I want to study all the numbers of "existence", so I'd better know the number of "non-existence" first, so as not to become what Einstein called "absurd". As a middle school student, my ability is limited after all, and my understanding of 0 is not thorough enough. In the future, I hope (including action) to find "my new continent" in the "ocean of knowledge".
Junior one math thesis.
The role of multimedia technology in teaching
When writing a lesson plan, an experienced teacher should make clear the teaching purpose, key points, difficulties, class schedule and teaching process, even consider his own language, expressions and blackboard writing, and make preparations for teaching AIDS, objects, models and experiments in advance. Its purpose is to make students clear and accept the knowledge to be explained. With multimedia technology, all this has become easier to achieve. Due to the use of multimedia-assisted teaching, vivid pictures and pleasing sounds are used to create teaching style scenes, which makes abstract teaching content concrete and clear, makes students active in thinking and participate in teaching activities with interest, and helps students to play their initiative in learning, thus optimizing the teaching process. Specifically, in the current classroom teaching of various disciplines, multimedia technology has the following functions:
First, adjust students' emotions and stimulate their interest in learning.
Interest is an emotional state caused by the stimulation of external things, and it is the main motivation for students to learn. But many teaching contents are usually boring, which requires every teacher to be good at using different teaching methods to stimulate students' interest. According to the laws of psychology and the learning characteristics of primary school students, the duration of intentional attention is very short, and classroom thinking activities are tense. After a long time, students are prone to fatigue, inattention and reduced learning efficiency. At this time, choose appropriate multimedia methods to stimulate students, attract students, create new excitement, stimulate students' thinking motivation, and keep students in the best learning state.
For example, when teaching "rectangular area", students always use formulas to calculate the area and feel very tired. In order to attract students' attention, enliven the classroom atmosphere and broaden students' thinking, a thinking question of Grandpa Wisdom is displayed by multimedia: If a square is cut into two identical rectangles, what will happen to the sum of the perimeters of the two rectangles and the sum of the perimeters of the square? When two identical rectangles make a square, how do their perimeters change? Let the students imagine according to the meaning of the question first, and then demonstrate it by computer. During the demonstration, the picture keeps flashing, so that students can clearly feel the change of perimeter. As soon as the students saw it, their interest came. Finally, let students discuss with each other, let students solve problems in an open and free way and cultivate their imagination.
Second, the image into the new lesson, creating a learning situation
Introducing new courses is an important part of classroom teaching. A good beginning is half the battle. At the beginning of a class, it is very important to quickly concentrate students' attention, bring students' thoughts into specific learning situations, and stimulate students' strong interest in learning and thirst for knowledge. Using audio-visual media to introduce new courses can effectively open the floodgates of students' thinking, stimulate association and inquiry, make students' learning state change from passive to active, and make students learn knowledge in a relaxed and happy atmosphere.
For example, the orientation ability of junior students is still at a low level, and the state of attention still depends on the intuition and visualization of teaching, which is easy to be stimulated by new and different stimulating activities. In view of these situations, multimedia is used to stimulate students' interest in learning. To teach the lesson "Hoe", we can use a set of "animations" when the new lesson is introduced: "The sun is baking the earth, and the hardworking farmers are working hard with hoes, and big sweat drops from their foreheads and into the rice fields." Students have a deep perceptual knowledge of this situation. Later, I put ancient poems on the pictures, and the contrast between poems and pictures aroused the ripples of students' thinking. For the psychological state of "knowing in my heart but not knowing in my mouth" just now, it is explosive to immediately explain it with the words hoe, sweat and food.
Third, highlight the key points of learning and break through the difficulties of learning.
Traditional teaching often spends a lot of time and energy on highlighting teaching key points and breaking through teaching difficulties. Even so, students are still not deeply touched, and they are easily tired or even bored. The effective way to highlight key points and break through difficulties is to change teaching methods. Due to the concrete image of multimedia, the combination of dynamic and static, sound and emotion, if properly used, it can turn abstract into concrete, mobilize the cooperation of students' multiple senses, and solve the content that teachers can't explain clearly and students can't understand, so as to effectively realize intensive reading, highlight key points, break through difficulties and achieve teaching effects that traditional teaching methods can't match.
For example, in the teaching of "the volume of a cylinder", in order to let students better understand and master the key points of deducing the calculation formula of the volume of a cylinder, the computer demonstration divides the bottom of the cylinder into several equal parts (divided into 16 equal parts, 32 equal parts, etc.). ), and then the cylinder is cut and spliced into an approximate cuboid through animation (the more average parts, the closer to the cuboid). Repeated demonstrations, let students feel and finally realize that the approximate cuboid is completely equal to the original cylinder. Ask the students what else they have found. Through animation demonstration, we can understand the relationship between the base area and height of this approximate cuboid and the base area and height of the cylinder, and then deduce the calculation formula of the cylinder volume, which makes the important and difficult points of this course easily break through, greatly improves the teaching efficiency and cultivates the students' spatial imagination ability.
Fourth, strengthen the training density and improve the teaching effect.
In practice consolidation, due to the use of multimedia teaching, the time of writing on the blackboard and wiping is saved, and a large number of exercises can be provided to students in a short time, and the practice capacity is greatly increased. At this time, you can draw up the questions in advance and use the computer to set up a variety of questions in an all-round, multi-angle and step-by-step manner. When a student makes a mistake (computer recording), patiently persuade him not to lose heart, think again, which is in line with the aggressive character of primary school students and consolidate new knowledge through lively and interesting review.
In a word, to choose the best combination of multimedia application and classroom teaching properly, we should consider the acceptance and feedback of students at all levels, use multimedia in a timely and appropriate way, and enhance the intelligence of courseware appropriately. It can better stimulate students' interest and make them complete their learning tasks independently and creatively. Only in this way can teaching be said to be the essence of multimedia teaching.