What part of the teaching content in the mathematics textbook do you have your own ideas? Please talk about your design ideas and the harvest of this part of teaching. ?

1. prime numbers and composite numbers

The teaching of prime numbers, composite numbers and factorization of prime factors is based on the characteristics of divisors, multiples and numbers divisible by 2, 5 and 3. The factorization of prime numbers and composite numbers and prime factors is the basis for finding the greatest common divisor, the least common multiple, divisor and general division. Therefore, the teaching of this part should not only make students master the concepts of prime numbers and composite numbers, but also quickly see whether common numbers are prime numbers or composite numbers and decompose a number into prime factors. There are many abstract concepts in this section, some of which are easily confused, such as prime number and prime factor, prime number and odd number. Therefore, this section is the difficulty of teaching.

When teaching the concepts of prime numbers and composite numbers, the textbook first guides students to find all the divisors of each number from 1 to 1 2 through the example, and then classifies them according to the number and characteristics of the divisors of each number. On this basis, the concepts of prime number and composite number are given. It also shows that 1 is neither a prime number nor a composite number. Judge which numbers are prime numbers and which numbers are composite numbers through example 2 and "do-do" exercises, and deepen students' understanding of prime numbers and composite numbers. Then look-up table is also a method to judge whether a number is a prime number. Because there are few prime numbers used in primary schools, only the prime numbers within 100 are listed in the textbook. Students don't have to memorize these prime numbers, but they should be familiar with prime numbers within 20.

2. Prime factorization

When teaching the factorization of prime factors in textbooks, first of all, through observation, the numbers given in (1) are all prime numbers, and the numbers given in (2) are all composite numbers. Ask students whether these two groups of numbers can be written in the form of multiplication of two numbers smaller than each number itself, and then draw the conclusion that a composite number can always be written in the form of multiplication of several prime numbers, thus leading to the concepts of prime factor and prime factor decomposition.

How to decompose prime factors in teaching? The textbook is divided into two columns, the tower decomposition on the left and the formula decomposition on the right. Because students are not familiar with this representation, the decomposition prime factor of 6 is specially explained in the textbook. Then, on the basis of decomposing 28 and 60 into prime factors, the textbook explains what is the prime factor of composite numbers and what is the prime factor of decomposition.

Then, the textbook introduces the method of decomposing prime factors by short division. Short division is essentially the same as the decomposition formula above, but in different forms. The decomposition results can be obtained conveniently and quickly by using short division. At the same time, learning to decompose prime factors by short division is also a preparation for finding the greatest common divisor and the least common multiple by short division. After giving examples, the textbook summarizes the steps of decomposing prime factors.

By the end of this textbook, concepts such as divisor, multiple, odd number, even number, prime number, composite number and prime factor have appeared. Some of these concepts are easily confused by students. So in exercise 13, pay attention to arrange some exercises to distinguish concepts. For example, in the third question, we should apply the concepts of odd number, even number, prime number and composite number we have learned to let students understand the connections and differences between these concepts in comparison. The fourth question is the question of judgment. Odd numbers and prime numbers, composite numbers and even numbers are confusing concepts. Through this question, students can distinguish the meaning of each concept, as well as the connections and differences between these concepts. Question 6 is to find out the relationship and difference between factor and prime factor. 14 is a comparative exercise to decompose the prime factor of a complex number and find the divisor of a number. On the one hand, it clarifies the difference between the two, on the other hand, it also enables students to learn to use the results of decomposing prime factors to find all the divisors of a composite number.