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在布列方程解应用问题的教学中,不少学生对于解一类涉及多量,条件隐含及关系交错的应用问题感到困难,他们先后采取单从设直接未知数或间接未知数的方法多次进行尝试,都无济于事,均不易找到相等关系。此时,教师若能因势利导引导学生会采用巧设辅助未知数的方法来解决此类问题,则可以转难为易,化隐为显,起到铺路搭桥的过渡作用。以下略举几例说明之。一、辅助未知数在方程中呈过渡公因数。例1 甲乙二人绕城而行,甲绕城一圈需3小时,现两人同时同地相背出发,乙自遇甲后再过4小时达到原出发点求乙绕城一周所用的时间。解:(间接未知数)被乙经过x小时与甲相遇。(辅助未知数)设绕城一周周长为s公里。依题意得:
In the teaching of solutions to the application of Boulle equations, many students find it difficult to solve a class of application problems involving large quantities, conditional implied and intertwined relationships. They have tried several times to set up direct or unknown unknowns. It is useless to find equal relations. At this time, if teachers can use the tactics to guide students to use cleverly designed auxiliary unknown methods to solve such problems, they can make it easier for them to turn into problems, and they can play a transitional role. Here are a few examples to illustrate. First, the auxiliary unknown has a transitional common factor in the equation. Example 1 A and B were to walk around the city. It took three hours for A to circle around the city. The two are starting from the same place at the same time. After B has met A for 4 hours, it reaches the original starting point and asks for the time it takes for the B to circle around the city. Solution: (indirectly unknown) was met by B with XA for x hours. (Auxiliary unknowns) Set the perimeter of the city to be s kilometers. According to the title: