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1)应用問题与方程:在我們講課中应明確:要解决我們生活实际中的应用問题,必須在數学中產生方程这个內容。反之任何一个具有实根的方程都有它的实际意义,方程式「現代学校代數課的內容的四个主要發展系統之一。」「在現在的代數課中無疑的是很重要的。」(伯拉斯基著,吳品三譯中学數学教学法第三册§2) 2)解应用問题之意义:解应用問題就是要把關於數量的事实問題,化成代數問題,換一句話說就是要做一次翻譯工作,把普通語言譯成代數語言,这首先是用字母代未知數,其次是用+、-、×、÷等符号联合字母与已知數成代數式,以表各种事实關係,再用等号联合兩代數式以表合乎条件的相等關係,於是事实間題,化成方程的關係,解方程即求出合於事实条件的未知數。事实問題中的限制很多,方程往往不能完全顧到,同時解方程的过程可能有違背事实的情形,故解方程求得根之後是否合事实仍須審查。 3)定未知數:一个題中未知數往往不止一个,题中指定要求的为直接未知數,題中不必求出的为
1) Application Questions and Equations: In our lectures it should be made clear: To solve practical problems in our lives, we must produce equations in mathematics. On the contrary, any real rooted equation has its practical meaning. The equation is one of the four major development systems for the contents of modern school algebra lessons. “Undoubtedly, it is very important in the current algebra class.” Laski, Wu Pinsan Translation Middle School Mathematics Teaching Method Book 3 § 2) 2) Solve the significance of the application problem: Solve the application problem is to turn the issue of the number of facts into an algebra problem, in other words, to do a translation Work, translating ordinary languages into algebraic languages, which first uses letters to generate unknowns, followed by the use of +, -, ×, ÷, and other symbols to unite letters with known numbers into algebraic expressions to express various factual relations, and then use equal signs. Combining the two generations of equations in order to meet the conditions of the equal relationship between the conditions, then the problem of the facts, the relationship between the equations, the solution of the equation is to find the actual conditions of the unknown. There are many limitations in the facts. The equations are often not fully taken into account. At the same time, the process of solving the equations may be contrary to the facts. Therefore, whether or not the equations are obtained after the roots of the equations must still be reviewed. 3) Fixed unknown: There is often more than one unknown in a question. The specified question in the question is a direct unknown number.