First of all, the teaching of Olympic mathematics can stimulate primary school students' interest in learning mathematics. The topic of Olympic Mathematics from structure to solution is often full of artistic charm, which makes it easy for primary school students to actively explore the solution. In the process of exploring solutions, primary school students experience the profundity of mathematical thinking and the creativity of mathematical methods, so they will have a sense of yearning and infatuation for learning mathematics.

Secondly, the teaching of Olympic mathematics can stimulate primary school students' mathematical aesthetic feeling. The beauty of mathematics is embodied in many Olympic mathematical problems. First, let's observe a series of problem-solving skills of Olympic math problems: construction, correspondence, backward deduction, differentiation, coloring, symmetry, pairing, specialization, generalization, optimization, hypothesis, auxiliary charts … dazzling. These problem-solving skills are an art with a high level of intelligence, which can bring another kind of aesthetic feeling independent of poetry, music and painting to primary school students.

Third, the teaching of Olympic mathematics can stimulate the creativity of primary school students. The solution of the Olympic Mathematics problem depends on the overall insight, keen intuition and original conception, which are the main elements of creativity, and these main elements of creativity are also the strengths of primary school students who have systematically received Olympic Mathematics teaching.

First-year Olympic competition:

The first-grade children have just entered primary school. Both study habits and study methods need comprehensive cultivation and correct guidance, which requires parents to have a comprehensive plan for the whole six-year primary school study.

Analysis of key points and difficulties in learning;

1. Basic knowledge of clever calculation and fast calculation: For first-year students, calculation is the first problem that students encounter when they study. If we can find some rules in the seemingly chaotic formula and simplify it, then students will definitely enhance their confidence and interest in learning mathematics. In addition, calculation and quick calculation are the basis of learning various follow-up questions. To learn mathematics well, you must first pass the calculation.

2. Know and learn to count various basic figures: square, cuboid, circle and cube are the most common figures in primary school learning. Through systematic guidance, first-year students can calculate the number of various basic graphics; Enable students to establish orderly thinking and lay the foundation for establishing thinking mode.

3. Learn simple enumeration method: enumeration method is really difficult for first-year students. In China's mathematics textbook, this difficult problem is introduced in a more intuitive way of counting, and the complicated and abstract problems are visualized for children to understand. The training of enumeration method focuses on orderly thinking mode, and visualizing abstract problems at the beginning of learning can better guide students to think positively and establish their own thinking mode.

4. Basic knowledge of number theory, such as parity, inequality, phase, etc. The problem of number theory is a key point in the follow-up study, and what we are going to learn this semester, such as parity, inequality, phase, etc., is undoubtedly the basis for future study. Here, we divide the problems of number theory into various types and explain them one by one, which makes the study of China numbers more systematic.

Second grade Olympic competition:

The second grade is the best time to develop children's intelligence and form good thinking habits. Learning Olympic Mathematics can not only greatly exercise children's thinking ability, but also lay a solid foundation for their future study. For parents of Grade Two students, it is most important to stimulate their children's interest in China numbers.

Analysis of key points and difficulties in learning;

1, calculation must pass: For students in Grade Two, the first question is calculation, which is the key and difficult point. Judging from the learning situation of school mathematics, children have never learned the column vertical form of multiplication and division, especially the column vertical form of multiplication, which requires more in China's number learning in the second grade. For example, multiplication is often used in the third lecture of China Numbers, and it will also be used in other application problems. Therefore, for students who study the next volume of Chinese mathematics, the first calculation must be passed.

2. It is difficult to enumerate: For the students in Grade Two, it is difficult to think in an orderly way and abstract way. For questions, second-year students are more willing to try to answer questions by making up numbers. The problem of enumeration method needs children's orderly thinking, such as the method of collecting money with several coins in the first volume of Chinese mathematics textbook, and the integer splitting in the second volume are all problems of enumeration method. This kind of question not only requires children to be organized, but also is not intuitive and difficult for children to understand. Parents are advised to visualize abstract problems, such as hamburgers and soda mentioned above.

3. Contact with application problems: The last few lectures in the second volume of the second grade Chinese mathematics textbook have already touched on application problems, and some concepts such as multiples have also been learned. It is suggested that children with spare capacity can properly contact some problems in the third grade, but the difficulty should not be as great as that in the third grade Chinese mathematics textbook.

Third grade Olympic competition:

The third grade Olympic Mathematics learning is the most important basic stage of primary school Olympic Mathematics. Only by firmly mastering the most basic knowledge and skills of junior high school olympiad can we effectively promote future mathematics learning and finally gain something in competitions and junior high schools.

Analysis of key points and difficulties in learning;

The third grade belongs to the basic stage of learning Olympic Mathematics. After children enter the third grade, with the growth of age, their computing ability, cognitive ability and logical analysis ability have been greatly improved compared with those in the first and second grades. This period is the key period for the formation of Olympic Mathematics thinking, and it is also the golden time for learning Olympic Mathematics, so whether they can grasp the golden time of grade three is related to the success or failure of junior high school. Here is a brief introduction to the key knowledge points of the third semester.

1. Use algorithms and properties to make quick and clever calculations.

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. You can consider applying the multiplication allocation rate in groups first. In observation, the original formula is = (17× 5+17× 7)+(13× 5+13× 7) =17× (5+7)+655.

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

The problem of chickens and rabbits living in the same cage originated from China's great mathematical work "Sun Zi Shu Jing" about 1 500 years ago, which recorded the title of 3 1, "Today, chickens and rabbits live in the same cage, with 35 heads above and 94 feet below. What are the geometric figures of 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 general cage problem of chickens and rabbits, we have the number of chickens = (rabbit's feet-total feet) (rabbit's feet-chicken's feet)

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, at the end of last semester, the math scores of five students in the second group of Class One, Grade Three, Affiliated High School of National People's Congress were 93, 95, 98, 97 and 90 respectively. What is the average math score of 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 numbers, the formula can generally be applied: the sum of numbers and multiples corresponding to ÷ = "1" times; 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 Olympic competition:

The fourth grade is a link between the past and the future. The difficulty and breadth of learning content have increased, and the importance of various competition tasks and entrance examinations has greatly increased. No matter whether your child has just started to learn Olympic Mathematics or has already started to prepare for competitions and further studies, how to better complete the study plan for the fourth grade, how to make a good transition from the fourth grade to the fifth grade, and how to plan the first two years of junior high school.

Analysis of key points and difficulties in learning;

1, calculation: calculation is the key point throughout the primary school stage, and every grade's olympiad 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-digits is mainly based on scaling to make all multi-digits consist of 9 digits, and then the calculation is made by using the distribution rate of multiplication. 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 addition, subtraction, multiplication and division. 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 learning calculation in grade four is to focus on basic calculation, master various simple operation skills, and improve accuracy and speed.

2, the average problem: when learning the average problem, we must first have a good understanding of the concept of the average. In the teaching process, we often find that most students often make a mistake when solving general problems, especially in a problem in travel itinerary, where the error rate is the highest. Xiao Ming's speed from school to home is 12, and the speed from home to school is 24. What is the average speed of going back and forth? The answer of many students is 18, which is wrong to think that the average degree is the average speed. When learning the average problem, we will also use the benchmark number to deal with the sum of a large number of data and the problem of finding the average. Many complex average problems can be solved by the method of concentration triangle, especially some complex average problems behind the guidance of thinking. Students should try to solve the average problem with the method of concentration triangle. The study of average problem is very beneficial to the study of concentration problem in the future, because most of the problems of average problem and concentration problem are essentially the same.

3. Travel problems: The following problems should be mastered in the fourth grade travel problems: encounter problems, catch-up problems, train encounter problems, ship running problems, multiple encounter problems, etc. First of all, we must have a very deep understanding of the basic problems of meeting and chasing. In the process of learning, students often make mistakes in the sixth grade, and it is also easy to make mistakes about whether two people walk at the same time. Secondly, we should be familiar with and master the two basic topics of travel problems, namely, the train encounter problem and the running water boat problem, which is of great help to our later study of complex travel problems. Finally, we should master the common skills of solving complex problems in travel questions, the habit of underlining paragraphs, and develop good and concise problem-solving habits. The method of drawing line segment diagram is a common method to solve many complicated travel problems. Many students are not concise enough when drawing line segments, and there are often too many redundant line segments and conditions in line segments, which makes the drawn line segments more complicated than the topic itself and cannot be analyzed and solved. In the usual study, try to imitate the teacher and develop good problem-solving habits.

4. Permutation and combination: Permutation and combination are the sublimation of addition principle and multiplication principles learned last semester. In the principle of addition principle sum multiplication, everyone has a certain degree of understanding and mastery of step-by-step and classification. On this basis, permutation and combination provide a more professional and effective method to solve the counting problem. In permutation and combination, we should first understand the concept of permutation and combination, the calculation of permutation and combination number, the difference of permutation and combination, especially the difference of permutation and combination. We need to master some classic examples to understand the difference between permutation and combination. At the same time, many problems need to be solved by combining the principle of permutation and combination with the method of classification and step by step, rather than simply solving the application of combination formula. For some students with poor foundation, before learning the knowledge of permutation and combination, we must master the principles of addition principle and multiplication. You should be comfortable with the arrangement and combination of some common problems and common methods.

5. Geometric counting and periodicity: Geometric counting and periodicity are two smaller topics relative to itinerary and arrangement, but they are also common questions in major competitions and entrance examinations. In particular, many comprehensive questions contain knowledge points related to number theory and periodicity at the same time, which is the top priority of competition and preparation. To master geometric series, we should start with line segments, angles, triangles and rectangles, and learn the steps to solve complex counting problems with simple methods. Periodic problems are often combined with arithmetic progression and number theory, and students tend to make mistakes when doing problems, so it is necessary to increase the amount of questions in this area.

Fifth grade Olympic competition:

The next semester of grade five is the last semester before junior high school, which plays a vital role in mathematics learning in the whole primary school stage. Only after this pass can we easily prepare for junior high school. Therefore, this semester's Olympic mathematics study should be more targeted, and choose the appropriate course type according to your actual situation and goals.

Analysis of key points and difficulties in learning;

The fifth grade belongs to the upper grade of primary school. After entering the fifth grade, children's computing ability, cognitive ability and logical analysis ability have been greatly improved with their age. This period is the key period for the formation of Olympic mathematics thinking and the golden time for learning Olympic mathematics. Therefore, whether we can grasp the prime time of the fifth grade is related to the success or failure of junior high school. So what are the key knowledge of the whole fifth grade? In order to let children better grasp the learning focus of grade five, the following are the key knowledge points of grade five.

1. An analytical method that enters the treasure house of mathematics-recursive method: the development of anything always goes from simple to complex, and so does the Olympic number. For complex problems, we might as well start with the simplest situation, and get rules or tricks from them by dealing with simple problems, so as to solve complex problems. This is a recursive method. For example, how many intersections do 2008 straight lines on a plane have at most? When students see this problem for the first time, they will definitely want to draw 2008 straight lines and then count the number of intersections. How much trouble it would be! In fact, we can solve the simple situation first and find out how many intersections these lines have respectively: 1, 2, 3, 4.

1 line has at most 0 intersections 0.

Two straight lines have at most 1 intersections 1.

Three straight lines have at most three intersections 1+2=3.

Four straight lines have at most six intersections 1+2+3=6.

Five straight lines have at most 10 intersections 1+2+3+4= 10.

Six straight lines have at most 15 intersections 1+2+3+4+5= 15.

……

So the 2008 straight line has1+2+3+4+5+…+2007 = 2015028 intersections.

So clever, can you figure out how many parts a circle can be divided into by 2008 straight lines?

2. Endless and uncertain travel problems: When it comes to travel problems, students may feel headache, which is really good, because the speed, time and distance of every object in travel problems are changing, and every object is moving, so it is very troublesome to analyze. In order to solve this problem better, we subdivide the travel problem: basic travel (single object), average speed and average speed. As long as you master each of these small types and form an analysis idea, no matter how complicated the travel problem is, it will be much easier to solve it.

3. The abstract and messy problem of number theory: number theory is the core knowledge of grade five. No matter which textbook, there are many chapters to explain number theory. To solve the complex problems of number theory, we must first master the basic knowledge of number theory: parity, divisor (now called factor), multiple, common divisor and greatest common divisor, common multiple and least common multiple, prime number and composite number. There are some representative examples in these basic knowledge points. As long as we can master these knowledge points well and then do a certain amount of comprehensive practice of number theory, we can easily solve the difficult problems in number theory.

4. Interesting archiving principle: There are many interesting things in life. For example, if you put four apples in three drawers, there will always be at least two apples in one drawer no matter how you put them. This is the pigeon coop principle.

For the pigeon hole principle, as long as the number of apples a and the number of drawers b are found, the following conclusions can be obtained:

If a ÷ b = r...q

When q=0, we say that there are always at least R apples in a drawer;

When q0, we say that there are always at least (r+ 1) apples in a drawer.

For example, put 32 apples in 8 drawers, because 32 ÷ 8 = 4, no matter how you put them, there are always 4 apples in one drawer. If you put 35 apples in 8 drawers, because 35 ÷ 8 = 4...3, no matter how you put them, there will always be 4+ 1 = 5 apples in a drawer.

But most Olympic math problems don't tell us the number of drawers, so we have to construct our own drawers and find out the number of drawers.

5. Calculation of graphic area: The calculation of graphic area is also a difficult point. For this kind of problem, we should first master the formulas for calculating the area of various basic figures, and then remember some important conclusions, such as the equal product deformation of triangles, the side facing 30 degrees in a right triangle is half of the hypotenuse, the pythagorean theorem, the principle of butterfly wings in a trapezoid, and the relationship between the middle side of similar triangles and the area. The methods to calculate the area are: direct calculation method, excavation and filling method, equation method, etc. In the calculation of graphic area, it is often difficult to add auxiliary lines, which is the difficulty, because adding auxiliary lines is very flexible, which requires us to do more problems in this area, accumulate more skills in adding auxiliary lines, and be aware of it.

Sixth grade Olympic competition:

Now is a particularly critical period for junior high school students. We should be fully prepared in information and self-study. I think through the recent activities organized by Giant, we can at least see a group of very dedicated teachers, hoping to provide as many opportunities as possible, and there will be activities in the future. Parents certainly don't have to worry about information and opportunities. Below I mainly talk about how we should seize the opportunity when it is in front of us. First of all, it must be clear that junior high school is not our ultimate goal, but to lay a good foundation for children's future study. So we must pay attention to the cultivation of children's study habits. Let's give a simple example: many students are not careful when doing problems, and often make mistakes in the problems they can do. Even the best students can't get the questions right if they are wrong. This is particularly important, whether it is the junior high school entrance examination or the future college entrance examination, because the current measure is actually not smarter than anyone, but more serious and more solid. From the recent exams in some schools, we can see a trend, that is, the number of questions is large, the time period is high, and the efficiency of doing questions in unit time is required. This efficiency is reflected in two aspects, namely, speed and accuracy.

Analysis of key points and difficulties in learning;

1, fractional percentage problem, ratio and proportion:

This is the key content of grade six, which accounts for a very high proportion in various school exams over the years. Focus on the following contents:

Correctly understand the unit 1 and know the difference between how much A is more than B and how much B is less than A;

The correct solution of the unit of 1, divided by the specific quantity, is the key to find the corresponding relationship;

Conversion between fractional ratio and integer ratio, understanding the relationship between positive ratio and inverse ratio;

Through the understanding of "number of copies" and proportion, the problems of sum times (proportional distribution) and difference times are solved;

2. Travel problems:

The most important content in the application problem, due to the comprehensive investigation of students' proportion, the application of equations and the ability to analyze complex problems, often appears as the finale problem, and the focus should be on the following contents:

The proportional relationship between distance, speed and time, that is, when the distance is constant, speed is inversely proportional to time; When the speed is constant, the distance is proportional to the time; When time is fixed, speed is proportional to distance. In particular, we must first find this "certain" quantity in many topics;

When the three quantities are not equal, learn to find the ratio of the third quantity through the proportional relationship between two of them;

Learn to analyze and solve general travel problems by proportional method;

With the above foundation, we will further strengthen our understanding of the problems of repeated encounters and chases, special trips such as trains crossing bridges and running water. The key point is to learn how to analyze a complex topic, instead of just doing it.

3. Geometric problems:

Geometry is the focus of investigation in various schools, which is divided into two parts: plane geometry and solid geometry. Specific plane geometry is divided into linear problems and circles and sectors. Solid geometry is divided into two parts: surface area and volume. Students should focus on the following:

Application of equal product transformation and area proportion;

Geometric problems related to the perimeter area of circles and sectors, and related methods to deal with irregular graphics problems;

Three-dimensional graphics area: dyeing problem, section problem, projection method, cutting problem;

The volume of three-dimensional graphics: simple volume solution, volume transformation, soaking problem;

4, number theory problems:

The content of the regular exam can also be applied to strategic questions, crossword puzzles, calculation questions and other topics, which are quite important, and we should focus on the following contents:

Master the properties that can be divisible by special integers, such as numbers and integers that can be divisible by 9 must be multiples of 9;

It is best to understand the reason, because this method can be used in many topics, including some number puzzles;

Mastering the nature of divisor multiple, I can find the greatest common factor and the least common multiple of two numbers by decomposing prime factor method, short division and division.

Learn the method of finding divisor. In order to improve the ability of flexible application, we need to understand the principle of this method.

Understand the concept of congruence and learn to turn the remainder problem into an divisible problem. The following property is very useful: two numbers are divided by the third number, and if the remainder is the same, the difference between the two numbers can be divisible by this number;

It can solve the problem of finding the remainder of multiple digits divided by smaller natural numbers, such as finding the remainder of101314 ... 9899 divided by 1 1, and finding 20082008.

5, calculation problems:

Calculation problems are usually more likely in the first few topics, mainly in two aspects. One is the basic ability of four operations, while some skills such as quick calculation and split term substitution are often the focus of investigation. We should focus on the following points:

Training in basic computing skills;

The multiplication distribution rate is used for fast calculation and ingenious calculation;

Conversion and operation between fractions and decimals, complex fraction operation;

Estimation and comparison;

Application of calculation formula. Such as arithmetic progression summation and square difference formula.

Formula of crack term, substitution term and general term.