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约数和倍数的有关知识是学习被2、3、5整除的数的特征,质数和合数,最大公约数与最小公倍数的求法等的基础。所以,它是“数的整除”这一章的一个重点。教学这一节时,应该掌握一个原则,讲清两个方法,区别三对概念。一个原则是:在算术数的范围内讲整数,在自然数范围内讲整除。两个方法是:求一个数的约数的方法,求一个数的倍数的方法。三对概念是:自然数与整数,整除与除尽,约数与倍数。现就三对概念、两个方法的教学提几点建议。
The knowledge of divisors and multiples is the basis for learning the characteristics of numbers divisible by 2, 3, and 5, the prime numbers and composite numbers, the greatest common divisor and the least common multiple. So, it is a key point in the chapter “Dividing Numbers”. Teaching this section, we should grasp the principle of clarifying the two methods, the distinction between the three pairs of concepts. One principle is to say integers in the range of arithmetic numbers and divisions in the range of natural numbers. The two methods are: Find a number of divisors, find a multiple of the number of ways. Three pairs of concepts are: natural and integer, divisible and divisible, divisible and multiples. Now three pairs of concepts, two methods of teaching make a few suggestions.