1, the new curriculum standard points out that effective mathematics learning activities can not only rely on imitation and memory, but also hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. The new curriculum standard advocates "autonomy, cooperation and inquiry" learning methods, and does not require students to use these learning methods in every class. We must choose effective learning methods according to the age characteristics, learning content and knowledge level of students. For example, when understanding the changing law of surface area and volume of three-dimensional graphics in the process of separation and integration, the teacher did not choose to let students listen passively, but asked students to bring some objects from home, cut and think in class, and understand and feel in the process of operation. It is concluded that the volume of three-dimensional graphics will remain unchanged during the process of separation and combination, but the surface area will change. Vivid and intuitive operation not only makes students have a deeper understanding of knowledge, but also cultivates and improves students' hands-on operation ability and spatial imagination ability. The classroom effect is self-evident. 2. The teaching methods should be effective (1), and the classroom presupposition and generation should be skillfully grasped. Teachers can't carry out the preset teaching plan mechanically in classroom teaching. Teachers should give full play to their wisdom, adjust teaching ideas, teaching processes or teaching methods in time according to the interaction between teachers and students, so that students can gain rich emotional experience while gaining knowledge. (2) Reasonable arrangement of classroom structure. This phenomenon often appears in mathematics classroom: the designed teaching content is endless, and the amount of practice is not enough. This requires our teachers to preset the time of each teaching link (especially students' independent inquiry activities) when preparing lessons, and make adjustments in different classrooms according to different realities, so as to minimize the phenomenon of "borrowing money" and improve classroom efficiency. (3) Pay full attention to the differences. If a standard is used in classroom teaching or a standard is used most of the time to perform teaching tasks, it is not conducive to the hierarchical development of students, and the effectiveness of such classroom is greatly reduced. Therefore, paying attention to differences and implementing differentiated teaching can promote the development of all students and fully improve the effectiveness of the classroom. 3. Designing flexible and diverse homework exercises The so-called flexible homework exercises refer to exercises that can train students' mathematical thinking. The so-called diversified exercises refer to designing games, nursery rhymes, exploring, treasure hunting, solving problems and other activities, and carrying out oral practice, choosing, contacting and finding friends ... in various forms. So how can we design flexible and diverse homework exercises? (1) Design exercises according to teaching objectives. That kind of blind repetition of exercises is often useless. In our practical design, purpose and pertinence are combined, which should be both purposeful and targeted. All exercise designs should fully embody the principles of teaching students in accordance with their aptitude, teaching students in accordance with their aptitude and teaching students in accordance with their aptitude. (2) Design exercises that combine hierarchy and integrity. The quality of practical design is directly reflected in the level of practice. According to the students' learning process and the principle of step by step, carefully designing the practice level is not only the objective law of students' ability transformation, but also the reflection of students' cognitive law. (3) Design interesting and open exercises. As we all know, interest can guide, maintain and strengthen students' learning. Once students have a strong interest in what they have learned, they can actively, easily and persistently go deep into classroom practice, which will help students improve their knowledge and ability. Effective classroom should really make every student "move", which is fully reflected in the openness of teaching, classroom and students' thinking in modern classroom teaching activities.