Calculation is the basic knowledge of mathematics learning, and it is also the basis of learning olympiad well. Whether the answer can be worked out quickly and accurately is a basic point in mathematical competitions over the years. The third grade mainly studies the laws of addition and multiplication, in which the application of multiplication distribution rate is a major focus in the competition. In addition, the signed "move" and parenthesis/parenthesis are often investigated in the competition, and the operation can be simplified by changing the operation order. For example:17× 5+17× 7+13× 5+13× 7.

Problem analysis: Because the four additions have no common multiplier, the multiplication allocation rate cannot be directly applied. We can consider applying the multiplicative distribution rate in groups first. The original formula is = (17× 5+17× 7)+(13× 5+13× 7) in observation.

= 17×(5+7)+ 13×(5+7)= 17× 12+ 13× 12=( 17+ 13)× 12=30× 12=360

2. Learn the hypothesis to solve the problem of chickens and rabbits in the same cage.

The problem of chickens and rabbits in the same cage originated from China's great mathematical work "Sun Tzu Shu Jing" about 1 500 years ago, which recorded the problem of 3 1, "Today there are chickens and rabbits in the same cage, with 35 heads above and 94 feet below. What are chickens and rabbits? " Translated into modern Chinese, there are a number of chickens and rabbits in a cage, counting from top to bottom, with 35 heads; It's 94 feet from the bottom. How many chickens and rabbits are there in each cage?

Problem analysis: We know that each chicken has two feet and each rabbit has four feet. We might as well assume that there is only one chicken in the cage, so there should be 94 feet, because we assume that some rabbits are chickens.

We know that each rabbit has two more feet than a chicken, so there should be one rabbit, leaving 35–12 = 23 chickens.

For the common problem that chickens and rabbits are in the same cage, we have

Number of chickens = (number of feet of rabbits-number of feet) (number of feet of rabbits-number of feet of chickens)

Number of rabbits = (total number of feet-number of chicken feet) (number of rabbit feet-number of chicken feet)

3. General application problems

The mathematical concept of "average" is often used in students' daily study and life. For example, after the final exam of last semester in Grade Three, we can calculate the "average score" of the whole class, the "average age" of classmates and their parents, and so on. These are the problems we often encounter in seeking the average. According to our example, we can sum up the general formula for finding the average: total number and number of people (or number) = average. For example, the five students in the second group of RDF Grade Three (Class One) had math scores of 93, 95, 98, 97 and 90 at the end of last semester, so what was the average math score of the five students in the second group?

Problem analysis: According to the formula we summarized, we can first find out that the total score of five students in the second group is 93+95+98+97+92=475, so their average score is 475÷5=95 (points).

4. Sum and difference times application problems

The sum-difference multiple problem consists of sum-difference problem, sum-difference problem and difference multiple problem. The sum and multiple problem is the relationship between the sum of two numbers of known size and their multiples. To solve the application problem of two large and small numbers, the general formula can be applied: the sum of this number and the corresponding multiples of ÷ = "1"; The problem of difference multiple is to know the difference between two numbers and their multiples, and to solve the application problem of two numbers, the general formula can be applied: number difference ÷ corresponding multiple difference = "1" multiple; The sum and difference problem is the sum of two numbers of known size and the difference of two numbers. The formula can generally be applied to the application problem of finding two large numbers: large number = (quantity sum+quantity difference) ÷2 and decimal number = (quantity sum-quantity difference) ÷2. In order to help us understand the meaning of the problem and find out the relationship between the two quantities in the problem, the method of drawing a line segment is often used to express the relationship between the two quantities with the relative length of the line segment, so as to find the way to solve the problem.

5. Age problem

The basic age problem can be said to be a typical application of the problem of differential times in life. At the same time, the age problem also has its distinctive characteristics: the age difference between any two people is constant. The key to solving the age problem is to grasp the above two points. For example, two years later, my brother is twice as big as my brother, and this year my brother is five years older than my brother. So how old is my brother this year?

Problem analysis: Because the age gap between them remains unchanged, after two years, my brother is still five years older than my brother. At this time, my brother's age is twice that of my younger brother, which becomes a differential problem. That is to say, my younger brother's age is 5÷(2- 1)=5 (years old) two years later, so my younger brother is 5-2=3 (years old) this year.

Fourth grade of primary school

1, calculating

Calculation is the key point throughout the primary school stage, and every grade's Olympic mathematics learning is based on calculation. Good computing ability is the guarantee to learn other chapters well and achieve excellent results. The calculation of each level has the characteristics of each level. The calculation of the fourth grade is mainly based on decimal calculation. For students who have a solid foundation in Olympic Mathematics and want to make achievements in the fifth grade, they should also add some points. The key problems to master in the calculation of grade four are the calculation of multi-digits, the basic operation of decimals and the simple operation of decimals. Among them, the calculation of multi-digit is mainly based on scaling, which is made up of all 9 digits, and then calculated by multiplying the distribution rate. The simple operation of decimals mainly combines arithmetic progression's summation, the distribution rate and combination rate of multiplication, method of substitution, etc., which requires students to master all kinds of questions, especially the calculation of multi-digits. Finally, the focus of decimal calculation is the most basic mixed operation of decimal. When beginners learn decimals, they often make mistakes because of decimal points. If the calculation is not accurate, no matter how good the methods and skills are. Therefore, the focus of four years of study and calculation is to focus on basic calculation, master various simple operation skills, and improve accuracy and speed.