1, the so-called teaching focus is "the content that plays an important role in the whole knowledge system". That is, students must master basic knowledge and skills, such as meaning, law, nature, calculation methods, including quantitative relations, problem-solving strategies and so on. 2. Teaching difficulties generally refer to key knowledge points that are difficult for most students to understand and master, or problems that are easy to be confused and make mistakes. The focus of teaching comes from knowledge itself, because of the inherent logical structure of mathematical knowledge, knowledge exists objectively; Teaching difficulties depend on students' own understanding and acceptance, both of which are determined by the teaching objectives of the same teaching content. Second, what is the significance of studying the teaching emphases and difficulties can be summarized in this sentence: implementing the teaching emphases is the premise for students to master knowledge, and breaking through the difficulties is the key to teaching success. Teachers' methods of breaking through difficulties in the teaching process are often the catalysts for students' active thinking and stimulating interest. Three, several main strategies to break through the key and difficult points 1. Mastering teaching materials is the premise of guiding students to learn to walk. First, they must know the way. In order to highlight the key points and break through the difficulties in teaching, we must first dig deep into the teaching materials and grasp the key points and difficulties of each lesson from the knowledge structure. Second, according to the students' actual cognitive level and considering the differences of different students' cognitive structures, prepare enough students to grasp the key and difficult points of teaching. Careful preparation and accurate positioning before class provide favorable conditions for highlighting key points and breaking through difficulties in teaching. The key content grasps the main characteristics: first, it is widely used; Second, it has the most direct and close relationship with future study. This is usually called the growth point of new knowledge or the connection point of old and new knowledge. When determining the difficulties, we should pay attention to two points: first, put ourselves in the students' shoes and carefully analyze the difficulties in the process of students' understanding and mastering knowledge; Secondly, we should fully consider all kinds of obstacles that may appear in students' cognitive and psychological processes. So I decided that the teaching focus of this class is to understand acute triangle, right triangle, obtuse triangle, isosceles triangle and equilateral triangle, and to understand the characteristics of each type of triangle; The difficulty in teaching is to understand and master the characteristics of various triangles. 2. Finding the growth point of knowledge is conditional. Primary school mathematics is a highly systematic subject. Mathematics teaching is to guide students from the old to the new, organize active migration, promote reasoning from the known to the unknown, understand the relationship between simple problems and complex problems, and constantly improve the cognitive structure. Therefore, the formation of new knowledge has its fixed growth point, and finding the growth point of knowledge can highlight the key points and break through the difficulties. We can identify the growing point of knowledge according to the following three points: (1) Some new knowledge is similar or similar to some old knowledge, so we should highlight "* * * similarities". For example, the divisor divided by two or three digits is based on the divisor divided by one digit, and the latter is the divisor changed from one digit to two or three digits, and the dividend should be divided from which digit. But no matter how many digits the divisor is, the trial commercial law is the same, that is, there are * * * similarities, which should be grasped in teaching; (2) Some new knowledge is composed of two or more old knowledge, so it is necessary to highlight the "connection point". For example, "addition and subtraction of fractions with different denominators" is composed of addition and subtraction with the same denominator and general division of two old knowledge. Its key problem is that the fractional units are different, so the general division becomes the connection point of two old knowledge. (3) Some new knowledge is developed from some old knowledge, so it is necessary to break through the "evolution point", such as "checking calculation of division with remainder", which is based on the division checking calculation that can be divisible in front. Both kinds of checking calculations must be multiplied by quotient and divisor, and the evolution behind it is "adding remainder". This lesson is a further study on the basis of students' preliminary understanding of triangles, so teachers always grasp the characteristics of angles and sides to deeply understand the "evolution points" of various triangles, carry out teaching activities, and then constantly break through. 3. Adopting appropriate teaching methods is the key. Curriculum standards point out that teachers' teaching should be based on students' cognitive development level and existing experience, face all students, and pay attention to heuristic and personalized teaching. Teachers should play a leading role, properly handle the relationship between teaching and autonomous learning, and guide students to think independently, actively explore and cooperate through effective measures, so that students can understand and master basic mathematical knowledge and skills, mathematical ideas and methods, get necessary mathematical thinking training and gain basic mathematical activity experience. Therefore, according to students' reality, adopting appropriate teaching methods is the key to highlight key points and break through difficulties. The commonly used teaching methods are: reviewing the past to learn the new method (transfer method), hands-on practice method, intuitive demonstration method, inspiration and guidance method, contact life method, trial method, comparison method, discovery method, transformation method, verification method, game method and so on. This lesson mainly adopts hands-on practice, intuitive demonstration, inspiration and guidance, comparison, discovery, verification and games. For example, when looking for classification criteria, "We just classified these people in the room according to different criteria. What criteria are you going to classify these triangles according to? " Heuristic guidance method is adopted; In triangle classification activities, through independent exploration and group cooperation, the methods of hands-on practice, comparison and discovery are used. When we know all kinds of triangles, we use intuitive demonstration method, discovery method, comparison method, verification method and game method, especially when we break through the difficulty of "knowing and mastering all kinds of triangle characteristics", we mainly use comparison method, verification method and game method. In the students' visual presentation, the teacher found that although students know the names and concepts of various triangles on the basis of preview, the classification is not accurate, which shows that students simply don't understand their characteristics. So the teacher decided to teach by learning, change the design idea in advance, conform to the students' thinking, first let the students say all kinds of triangle concepts, then guide the students to verify by comparison, verification and other methods, and finally sum up their memories. In this process, students actively participate in activities by watching, watching, dividing, discussing, comparing, testing and speaking. Due to full experience, teachers have broken through the key and difficult points of teaching from the perspective of classroom learning effect. However, due to the late organization of intuitive demonstration, students' thinking ability and expression ability are poor, and the teaching link of "activity experience and exploration of new knowledge" takes a long time. 4. Reasonable blackboard writing design is the way out. Blackboard writing is the epitome of classroom teaching, a schematic diagram to reveal the key points and difficulties of teaching, and a radiation source to grasp the key points and difficulties. The blackboard writing plays the role of outlining, which is designed according to the teaching requirements, characteristics and students' actual situation on the basis of thoroughly understanding the teaching materials. It integrates the outline, artistry and intuition, which not only plays the role of opening the outline, but also stimulates the interest and receives the effect. 5. Well-designed exercises are the guarantee. Carefully designed classroom exercises are an important guarantee to improve teaching quality. Students can further understand and consolidate what they have learned through practice, and turn knowledge into skills, thus improving their comprehensive application ability. The key to well-designed exercises is "precision", that is, to highlight key points-new knowledge points and strengthen difficult points-places that are easy to be confused and difficult to understand. Therefore, when preparing lessons, we should carefully study the exercises in the textbook, understand the arrangement intention, clarify the purpose and function of the exercises, and design the exercises with levels, slopes and pertinence. This class has corresponding real-time exercises and game activities in the process of inquiry, so I designed three levels of exercises in the whole class, namely, the basic exercises of filling in the blanks, the variant exercises of judgment and the extended exercises of solving problems. However, due to time, only the immediate exercise was completed, which failed to better reflect the teaching purpose of this link. In addition, it is not enough to deal with difficult content only by teaching methods, methods and means. Also pay attention to: First, teachers should not inform or hint at the difficulties determined in advance. This will easily cause psychological pressure to students. For example, don't say, "The content of this class is very difficult and difficult to learn, so students should pay attention." "This topic is very difficult, so don't be nervous." Second, the pace of teaching should be slow, and the speech speed, intonation and tone should be adjusted appropriately. Especially when explaining difficult content, we should pay close attention to students' expressions. If it is found that most students are frowning blankly, or when there are few people raising their hands, the teacher should slow down the speaking speed, give students enough time to think, set the steps in time and make good preparations. On the other hand, encourage them in time with the tone of encouragement and trust to help them overcome difficulties. After the difficult is easy, we should restore the rhythm and continue to explain the content of criticism.