First, the trend analysis of mathematical propositions

Looking at all kinds of exams at all levels, mathematical propositions have the following three trends:

(1) comprehensiveness mainly examines students' "double basics" and their comprehensive application ability of knowledge.

For example, the scores of primary school mathematics and the elementary arithmetic of decimals. Pay attention to the alignment of decimal points when adding, subtracting and dividing decimals. Multiplier and multiplicand * * * in multiplication operation have several decimals, and the product obtained has several decimals. If it is not enough, you should add zero. The addition and subtraction of fractions should pay attention to the general division (first find out the least common multiple of the denominator, and then expand the numerator and denominator by the same multiple at the same time. ) Add and subtract fractions. Add and subtract the integer part and the decimal part respectively, and then combine the results. If the decimal part is not reduced enough, we should consider "borrowing" from the integer part. The idea of "reduction" in fractional operation is the theoretical basis of simplifying the complex, which should be trained by combining "reorganization" and "division" of relations.

(2) Continuity The so-called "continuity" refers to whether you will "meet" relevant mathematical knowledge again in future study. Judging from the mathematical system, the idea of "function" and the establishment of "three-dimensional sense" are very important. In primary school mathematics, these contents are often expressed in the form of applied problems, such as graphic recognition, operation and transformation of circles, cylinders, cones, cuboids and cubes.

(3) Flexibility The so-called "flexibility" refers to the ability of students to flexibly calculate relevant mathematical knowledge. Common ones are "the ability to discover new laws and define new operations", "the ability to optimize design (maximum and minimum)", "the ability to analyze and reason (depending on factors)" and "the ability to deform and iterate formulas (including unit conversion, counting, watch problems, etc.). )".

Second, the classification of mathematical application problems

The application problem of primary school mathematics is often the application of concepts and formulas.

Some concepts and formulas commonly used in primary school mathematics should be memorized. For example, the money deposited in the bank is called principal; The extra money paid by the bank when withdrawing money is called interest; Buying construction bonds is essentially the same as saving, and it is another way to support national construction, except that the interest rate of bonds is generally higher than that of time savings; "Ten percent" is one tenth, and if it is rewritten as a percentage, it is10%; Two expressions with equal ratios are called proportions; The ratio is the division of two numbers, and there are two items; Proportion is an equation, which means that two proportions are equal and there are four terms; In proportion, the product of two external terms is equal to the product of two internal terms (the basic property of proportion); Proportion * * *, there are four items. If we know any three terms, we can find another unknown term in this ratio. The unknown term in the proportion is called the solution ratio, which should be solved according to the basic properties of the proportion. The ratio of the distance on the map to the actual distance is called the scale; When one quantity changes, the other quantity changes. These two quantities are two related quantities. The circumference formula of a circle: c = 2 π r or c = π d; Lateral area of cylinder = perimeter of bottom × height; Cuboid volume = length × width × height = bottom area × height; Area of rectangle = length × width; Area of a square = side length × side length; Area of parallelogram = base × height; Area of triangle = 1/2× base× height; Trapezoidal area: = 1/2 (upper bottom+lower bottom) × height; Area of circle = ∈× r× r; The volume formula of cuboid, cube and cylinder can be written as "bottom area × height" and so on.

(1) The concept of "fraction (percentage, interest rate, discount)" is the key to solving the problem, and choosing the standard quantity "1" is the breakthrough.

(2) Engineering problems In engineering problems, the relationship among workload, work efficiency and working time should be clarified: workload = work efficiency × working time; Work efficiency = workload/working time; Working hours = workload/work efficiency; Total workload = sum of each workload

On the surface, the trip question is to examine students' understanding of the relationship between distance, time and speed. At a deeper level, it is actually to examine students' flexibility, because it is not just "distance = time × speed" that needs to be considered; Time = distance/speed; Speed = distance/time "often involves many factors such as time, place and direction." Therefore, the key to solve this kind of problem is to find out what is the "changing condition" and how to accurately use the "unchanging formula" in solving problems.

(4) concentration problem (no key requirements) This kind of problem requires understanding the following relationship: solution = solute+solvent; Concentration = solute/solution; Solution = solute/concentration; Solute = solution × concentration

Third, simple geometric problems.

Area and volume problems mainly consider the following contents:

How to get the calculation formula of parallelogram area? How to calculate the area of triangle and trapezoid? What about the formula for calculating the area of a circle? Think about how the square area is calculated. Why?

Tip: After we get the formula for calculating the rectangular area, we can cut and spell the graphics to get the formula for calculating the area of the corresponding graphics.

What is the surface area of three-dimensional graphics? How to calculate the surface area of a cuboid? Is there any simple way to solve this kind of problem? How to calculate the surface area of a cylinder?

Tip: The surface area of a three-dimensional figure is the sum of the areas of all faces, so we should first find out the areas of each part and then add them up. The surface area of a cuboid and a cylinder can be the side area plus two bottom areas.

What are the similarities between a cuboid and a cylinder?

Tip: A cuboid is actually a cylinder. The volume of cuboids and cylinders is actually multiplied by the height of the bottom area.

A cylinder (cone) is surrounded by two identical circles and a surface, and a cone is surrounded by a circle and a surface. Know the bottom, side and height of a cylinder; Know the bottom and height of the cone. If you want to know the unfolded figure of the cylinder side and the calculation method of the lateral area and surface area of the cylinder, you can calculate the lateral area and surface area of the cylinder, you can use the calculation method flexibly according to the actual situation, and you can know the method of obtaining approximate numbers. Knowing the formulas for calculating the volume of cylinder and cone can explain the derivation process of the volume formula, and can use the formula to calculate the volume and solve simple practical problems.

Fourth, simple statistics.

Simple statistical tables, charts, and learning to calculate averages and percentages are all preliminary knowledge of statistics.

In statistical work, in addition to sorting data, it can also be represented by statistical tables, and sometimes it can also be represented by statistical charts. There are three kinds of common statistical charts: bar statistical charts; Broken line statistical chart; Department statistical chart.

To understand the statistical chart and clarify its characteristics and functions, we must go through the process of "collecting and sorting out data, representing data with statistical charts and sorting out results". According to the statistical chart drawn, we can analyze some simple facts reflected by the data, make some simple reasoning and judgment, and further understand that statistics is a strategy and method to solve practical problems. While learning statistical knowledge, I feel the connection between mathematics and life and its application in life.

The key to finding the average is to find out what the average is and what the total is; And what is the required average, how much share should be divided equally, and so on.

Master some concepts related to percentage, such as germination rate, attendance rate, survival rate, interest, etc. Understand the preliminary knowledge about interest, know the meanings of "principal", "interest" and "interest rate", and make some simple calculations about interest by using the calculation formula of interest. Understand the meaning of number, know its simple application in actual production and life, and make some simple calculations. The calculation of tax is also the concrete application of percentage. Understand what personal income tax is and how to calculate it. What is the survival rate? What is its calculation formula?

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