The new syllabus stipulates four application problems, including engineering problems; The practical application of percentage includes the calculation of germination rate, qualified rate and interest. , no more than three steps, limited to relatively easy calculation. This makes specific restrictions on the content and difficulty, which is conducive to ensuring the implementation of basic knowledge and problem-solving ability, preventing arbitrary high demands, artificially fabricating many unrealistic problems, and increasing students' learning burden. ?
1. Can you answer the application questions of fractions and percentages?
Being able to solve the requirements of fractional and percentage application problems generally means being able to understand the meaning of application problems, master the most basic quantitative relationship, correctly judge the calculation method, be able to calculate continuously, and be good at checking the rationality and accuracy of the solution. ?
Because of the quantitative relationship between fractions and percentage application problems, compared with integer application problems, it has both * * * and particularity, which requires students to understand both its * * * and its particularity, so as to improve their cognitive level. In this regard, a few examples are given below. ?
1. Fraction addition and subtraction application problem?
There are two kinds of known fractions in the application of fractional addition and subtraction: one is to represent a specific quantity, and the other is to represent the ratio of two quantities. For example:?
(1) The canteen burns tons of coal on the first day, tons of coal on the second day, and how many tons of coal are burned in two days? The known scores in the questions all represent specific quantities, which are consistent with the quantitative relationship with the application questions on integers. Ask students to know that this is the sum of two quantities in the same unit. ?
(2) There was a batch of coal in the canteen, which was burned on the first day and the next day. How much was burned in two days? The known score in the problem is the ratio of two quantities, not a specific quantity. Although the quantitative relationship conforms to the application problem of integer summation, it is * * *; But students should understand that the sum in the question is for this batch of coal, not the specific quantity. ?
(3) The surface area of the earth is ocean, and the rest is land, which accounts for a fraction of the surface area of the earth? The quantitative relationship of this problem is consistent with the calculation of the remainder in an integer by subtraction, which is * * *, but only one known condition is given in the problem. Another condition is that students should imagine the whole earth surface area as "1" and then use 1-=, which is different from the integer application problem. ?
2. Fraction, percentage multiplication and division application questions?
The application problem of fractional multiplication and division not only contains the quantitative relationship of integer multiplication and division, but also has new quantitative relationship, which needs students to distinguish clearly. For example:?
(1) The average car travels kilometers per minute. How many kilometers does it travel in 30 minutes? The quantitative relationship of this kind of problem is consistent with seeking the sum of an addend in an integer, or 30 times. ?
② 10 egg weight kg. How many kilograms does each egg weigh on average? The quantitative relationship of this problem is consistent with the integer division problem. ?
In addition to the quantitative relationship of integer multiplication and division, the application problems of fractional multiplication and division have new quantitative relationships, which are usually divided into three situations, or three basic application problems of fractions:
(1) Find the division problem that one number is the fraction of another number.
(2) The multiplication problem of finding the fraction of a number.
(3) Know the fraction of a number and find the division of this number. (There is no such name in the new syllabus. For the convenience of analysis, the author uses these common names. If the above three situations are percentages, then these three situations are the three basic application problems of percentages.
I have to explain here that the new syllabus only asks for four application problems of the score, including the practical application of engineering problems and percentages, and does not specify which application problems to teach. Considering the different styles of textbooks, there may be some choices, so we should study the teaching requirements according to the contents of the current general textbooks for reference.