Summary of courseware teaching plan exercises in grade one, grade two, grade three, grade four and grade five of primary school. 6. Understand their knowledge relationship, and cultivate students' mathematical thoughts from special to general, analogy, transformation, transformation and equivalent replacement. For example, in the teaching of parallelogram area, let students use the transformation method to derive the parallelogram area formula, transform the parallelogram into a rectangle, analyze the relationship between the rectangle area and the parallelogram, and then derive the parallelogram area calculation formula from the rectangle area calculation formula. In the teaching process, the situation should be skillfully set to pave the way for the introduction and stimulate students' curiosity to further explore the calculation method of parallelogram area. Cooperate in exploration, migration and creation, so that students can transform a parallelogram into a rectangle through hands-on operation, cutting, spelling and swinging, and express their own findings, thinking about the relationship between rectangle and parallelogram, the relationship between the length of rectangle and the bottom of parallelogram, and the relationship between the width of rectangle and the height of parallelogram. In this link, students can operate and cooperate. Actively explore and discover the calculation method of parallelogram area. In the process of communication, students explain the relationship between cutting methods and parts, and ask questions and answer each other. In the communication between students, students understand the internal relationship between parallelogram and spliced rectangle, which not only deepens their understanding of new knowledge, but also cultivates their language expression ability, thinking ability, and ability to ask and solve problems. Finally, the practice design gradually develops, expands and deepens, covering problems from different angles, which not only allows students to develop their thinking in practice, but also temper their innovative quality. Infiltrate mathematical thinking methods in problem-solving teaching to improve students' mathematical literacy and ability. The process of solving problems is essentially rational association under the guidance of reductionism. Call a certain mathematical thinking method to deal with the problem setting conditions, use mathematical thinking method to analyze and solve problems, open up students' thinking space and optimize problem-solving strategies. For example, chickens and rabbits live in the same cage. Students can go through the process of solving problems by combining numbers and shapes, which is more intuitive, easy to learn and easy to teach. They can also use the three-level list method of one-to-one list, jumping list and compromise list. This method of "trial and error" step by step on the basis of calculation is more in line with students' cognitive laws and problem-solving habits. The essence of this method of returning to the origin of thinking without teaching is to "approximate" three different ways of thinking, including three different mathematical ideas: list method embodies the idea of "classification", hypothesis method contains the idea of "approximation" and equation method contains the idea of "algebra". In teaching, we can start with the basic hypothetical method, and through the teaching of examples, let students master the skills of solving problems with hypothetical methods, realize the thinking method, and consolidate it in the practice of solving some practical problems. Then it can be extended to some special hypothetical thinking teaching, such as "half rabbit method" and "chicken wings as legs method" in "Chicken and Rabbit in the Same Cage", so that students can fully understand the cleverness and flexibility of hypothesis and use this thinking to solve some mathematical problems again. Another method is to show a variety of problem-solving strategies through example teaching, but it is necessary to return to the hypothesis method in time and integrate it from the perspective of hypothesis. In this approach, how to introduce other strategies into the hypothesis method is the key to the classroom. For the drawing method, it can be used as an intuitive auxiliary means to understand the calculation process of the hypothesis method, which plays a role in deepening understanding by combining numbers and shapes. For enumeration method, it can be used as a foreshadowing material to understand the hypothesis method, because mastering the changing law of chicken (or rabbit) feet in the list can promote students to break through the difficulties in the hypothesis method, that is, to understand the reasoning and adjustment process; For equation method, it can be understood as another form of hypothesis method. Assumption has four key steps: assumption-calculation-reasoning-adjustment (replacement). In these four steps, reasoning and adjustment are difficult to understand, and students can't pass these two levels unless they master assumptions, so this is the difficulty of teaching. On the one hand, some enlightening questions can be used to guide students to think and understand, such as: "Why are feet missing?" "Every time I treat a rabbit as a chicken, how many eight feet are different?" "What is the relationship between the total number of feet and the different number of feet each time?" "Does this figure represent a chicken or a rabbit?" These questions, like cocoon peeling, can clearly show the hypothetical steps. On the other hand, students can intuitively understand the process of reasoning and adjustment, including the meaning of each step in the formula, by making full use of intuition and other means, such as drawing and combining numbers and shapes. In the review process, we should infiltrate the mathematical thinking method, enrich the knowledge connotation, and give full play to the role of thinking method in knowledge connection and exchange when combing the basic knowledge, so as to help students build a reasonable knowledge network and optimize the thinking structure. For example, the review of Graphics and Geometry can't rely on didactic knowledge combing and intensive topic training, but should fully expand students' subject space, and guide students to combine concept combing, formula internalization, skill training with spatial imagination, feeling geometric model and implementing evidence-based reasoning through careful design and effective guidance of teachers. When reviewing "the volume of three-dimensional graphics", the teacher thought like this: Why can the volumes of cuboids, cubes and cylinders be calculated by V=sh? Stimulated students' mathematical thinking. Then, by observing the model, demonstrating the courseware, guessing and summarizing by the teacher, the students can finally understand the general formula for calculating the volume of a cylinder clearly. Through this review, students can see the forest through the trees, which is conducive to improving their strategic level of volume calculation of three-dimensional graphics. At the same time, students' spatial imagination, geometric intuitive consciousness and guessing and reasoning literacy have also been cultivated accordingly.