Due to the need of practical application, different types of ratios should be used. In fact, there are many ratios in physics, chemistry and other knowledge, such as the ratio of distance to time, the ratio of mass to volume and so on. Primary school mathematics textbooks not only talk about the ratio of the same kind of quantity, but also talk about the ratio of different kinds of quantity. This is convenient for primary school students to understand the proportion of different categories that often appear in physics and other disciplines after entering middle school. Of course, compared with different kinds of quantities, it is only relevant. In this way, the ratio produces a new quantity, for example, the ratio of distance to time forms the speed, and the ratio of mass to volume forms the specific gravity.
When discussing the significance of teaching ratio in teaching materials, we can find out how many times the length of the red flag is wide and how many times the width is long, and then we can get the same number of ratios. Then, the relationship between distance and time can be expressed by speed, and the explanation can also be expressed by their ratio, thus obtaining the ratio of different kinds of quantities. On this basis, the meaning of ratio is summarized. Then explain the representation of the ratio of two numbers, and introduce the reading of the comparison symbols ":"and "ratio". Then it introduces the names of two terms in each ratio and the concept of ratio, and illustrates the solution of ratio and the relationship between ratio and division with examples. The textbook focuses on two points: the expression of (1) ratio, usually expressed in fractions, decimals or integers. (2) The latter term of the ratio cannot be zero. Inspire students to think, contact the relationship between fraction and division and answer correctly why. Then through the practice of "doing one thing", we can further understand the meaning of ratio and the solution of ratio. As will be further explained later, the ratio can also be expressed in the form of a fraction. Then through the relationship between fraction and division, the relationship between ratio and fraction is explained. In "doing one thing", focus on the practice of changing proportion into fractional form.
Then, the basic nature of teaching ratio. The textbook links the learned quotient invariance with the basic nature of the score, enlightens students to find out what the corresponding nature of the ratio is through "thinking", and then summarizes the basic nature of the ratio, that is, the meaning of "dividing by 0". Then it shows that the ratio can be changed into the simplest integer ratio by applying this property. Through three small questions of the example 1, the method of transforming the ratio of various situations into the simplest integer ratio is taught. (1) is an integer ratio. Generally speaking, the first and second terms of the ratio should be divided by their greatest common divisor. The calculation method is illustrated in the dotted box. (2) When both the front and rear terms of the ratio are fractions, it is generally to multiply the front and rear terms of the ratio by the least common multiple of the denominator of the two fractions, and then convert them into the ratio of two integers, and then simplify them. The textbook focuses on the method of the first step of transformation, and in the "thinking" on the right, it puts forward why we should take the exam together 18. The second step is left to the students to solve. (3) If the ratio in the previous paragraph is decimal, the first step is to convert the decimal ratio into an integer ratio. The textbook puts forward what to do in the "think" on the right, and guides students to think of a way to shift the decimal point to the right into an integer ratio, and then simplifies it for students to fill in. The calculation method representation in the dotted box can be omitted. Practice turning these ratios into the simplest integer ratios by "doing".
Practice 12, first practice the proportion of writing, focusing on the proportion of different categories and finding the proportion. Through the third question, the tooth ratio and revolution ratio of large and small gears, let students know that the tooth ratio and revolution ratio of two gears are just opposite, and add some perceptual knowledge for later study of inverse ratio. Through the practice of question 4, just like in the past, if one number is several times or a fraction of another number, it is meaningful to compare two similar quantities into the same unit number. Then, practice solving the ratio. Question 5, practice the simplification of integer ratio, fractional ratio and fractional ratio respectively, question 10, and then practice several situations together. In questions 6, 7 and 8, you should practice writing ratio first, and then simplify the ratio, which not only deepens the understanding of comparative value's meaning, but also preliminarily understands its wide application in daily practice. Through the question 1 1, we can deepen our understanding of the relationship among division, fraction and ratio. Question 13, through the proportion of writing, let students get familiar with some basic knowledge needed for computing engineering problems. In the exercise, we also arranged application questions whose conditions are known to represent quantitative relations in the form of ratios, such as 14 and 15. These questions not only deepen the understanding of the relationship between comparison, fraction and division, but also review the application problems of fractional multiplication and division, and also cultivate students' ability to use knowledge flexibly to solve practical problems.