The sum of prime numbers is 1, and a number has only 1 and its two divisors. This number is called prime number. 2. A number has other divisors besides 1 and itself. This number is called a composite number. 3. 1 is neither a prime number nor a composite number. 4. Natural numbers can be divided into 1, prime numbers and composite numbers according to the number of divisors. Natural numbers can be divided into odd and even numbers according to whether they are divisible by 2.
Decomposition of quality factors
1, every composite number can be written as the product of several prime numbers, which is called the prime factor of this composite number. For example, 18=3×3×2, and 3 and 2 are called prime factors of 18.
2. Multiplying several prime factors to represent a composite number is called prime factor decomposition. Short division is usually used to decompose prime factors.
2. Basic properties of decimals, fractions, ratios and proportions
Basic properties of decimals: add 0 or remove 0 at the end of decimals, and the size of decimals remains unchanged.
The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged.
The basic nature of the ratio: the first and last items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
The basic property of proportion: in proportion, the product of two external terms is equal to the product of two internal terms.
3. The meaning of percentage and proportion
Percentage: Divide a number into 100 parts, and take some of them.
The meaning of proportion
(1) ratio: two related quantities, one changes and the other changes. If the ratio (that is, quotient) of the two numbers corresponding to these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. ① Represented by letters: If two related quantities are represented by letters X and Y, and their ratio is represented by K,
(2) Inverse proportion: two related quantities, one changes and the other changes, and the product of the corresponding two numbers in these two quantities is certain. These two quantities are called inverse proportional quantities. Their relationship is called inverse relationship.
In the national "Mathematics Curriculum Standard (Experimental Draft)", it is required: "Everyone should learn valuable mathematics; Everyone can get the necessary mathematics; Different people have different developments in mathematics. " At the same time, it is pointed out that "mathematics learning should be realistic, meaningful and challenging, which is conducive to students' active observation, experiment, guess, verification, reasoning and communication." Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. " The duty of teachers is less and less to pass on knowledge, but more and more to stimulate thinking. Teachers must devote more time and energy to those effective and creative activities.
"the State Council's Decision on the Reform and Development of Basic Education" points out: "Building a high-quality teacher team is the key to solidly promote quality education." To build a high-quality teaching team, teachers must change the traditional educational concept and establish a new educational concept that meets the requirements of the times. With the implementation of the new curriculum standards, teachers can't wait to update their educational concepts, and the comprehensive implementation of quality education should be guided by updating their educational concepts.
1, advocating "diversification" algorithm.
Because students' life background and thinking angle are different, the methods used must be diverse. Teachers should respect students' ideas, encourage students to think independently and advocate the diversification of calculation methods. Algorithm diversification means that in the process of learning, teachers encourage students to think independently, encourage students to solve problems in their own way, and then cooperate and communicate. This will leave space for students to think and explore, and help to spread students' innovative thinking.
For all kinds of calculations, teachers should not be eager to evaluate various algorithms, but should guide students to choose the method that suits them by comparing the characteristics of various algorithms. Even if the students' methods are naive and immature, the evaluation should have an angle. From the perspective of students' thinking, students have experienced a process of inquiry in their thinking, and the methods are more in line with children's understanding level.
Teachers should encourage all kinds of methods and provide opportunities for students to communicate, so that students can constantly improve their own methods in mutual communication, which will not only help teachers understand the learning characteristics of different students, but also help to promote the development of students' personality. At the same time, teachers should always ask students to think about such questions: What do you think? What did you do just now? What if? What's the matter? Which method do you think is better? For the best method, students are encouraged to reflect, evaluate and further explore, so that students can choose among choices, cooperate in cooperation, guide students to think and exchange solutions to problems.
2. Pay attention to the "digital" generation
The focus of modern mathematics teaching has changed, that is, paying attention to the generation of "numbers". Teachers can't spend all their energy on imparting professional knowledge, but should work hard on researching and teaching students to learn. The emergence of "digitalization" is to digitize practical problems and express practical problems in life with numbers, figures and symbols.
Also, students have a vague understanding of the concepts of "making the left and right sides of the equation equal is called the solution of the equation" and "the process of finding the solution of the equation is called solving the equation", so I design it like this:
X-8= 16
Solution: X= 16+8 ↓
X=24
.
Can you understand the meaning of the two symbols "↓" and "."? Students' understanding of mathematical symbols is concrete and easy, and there is naturally a difference between "solving equations" and "solving equations".
3. Pay attention to the development of "great wisdom"
"Great wisdom" refers to students' innovative thinking, which has become the characteristic of curriculum reform in all countries of the world. Teachers should pay more attention to the development of students' innovative thinking and valuable thinking.
A teacher asked students to say the number 8 from different angles. The students said noisily: there are 8 groups in the classroom, 8 is less than 9 times 1 more than 7 times 1, 8 plus 2 is 10, 10 eggs are left, 4 plus 4 equals 8,1minus 3 equals 8. But one student kept thinking hard, and then he held his hand high. Seeing that he didn't stop until he reached his goal, the teacher talked to him. He said seriously, "8 is the son of 16!" "At the same time, the students burst into laughter. The teacher told the students not to laugh and asked them to tell his reasons. He said confidently, "Because 8 is half of 16, it is the son of 16. The teacher asked again, "Does that 8 have a son?" "He said," The son of 8 is 4, the son of 4 is 2, the son of 2 is 1, and the son of 1 is 0! "The teacher said," Great, you found a secret of 16. But according to your idea, the son of 1 is not 0. Think again about what it is, and the teacher will tell you later. "
Although the student's idea is not perfect, his way of thinking is unique. Teachers focus on developing students' "great wisdom".
4. Advocate "developmental" evaluation
The existing educational evaluation system in China can no longer meet the needs of social development and people's own development, so the reform of educational evaluation is imperative. The new curriculum advocates "developmental" evaluation, which must be people-oriented and promote the harmonious development of individuals, that is, pay attention to individual situations and needs, promote the realization of individual values and stimulate people's subjective spirit. Developmental evaluation is mainly reflected in the interaction of evaluation subjects, the dynamics of evaluation methods and the diversification of evaluation contents.
For example, make a growth record bag.
Establish a growth record bag to reflect students' progress in learning mathematics and enhance their confidence in learning mathematics well. Teachers can guide students to add important materials reflecting their learning progress to the growth record bag. For example, satisfactory homework, favorite small productions, impressive problems and solutions, unforgettable discussions, experiences of reading math books, and messages from parents.
What is more noteworthy is that teachers should follow the basic idea of standards and take the knowledge and skills objectives of this period as the standard to examine students' understanding and mastery of basic knowledge and skills. The semester goal is the goal that students should achieve at the end of this semester, and promises that some students will gradually achieve it with the accumulation of mathematics knowledge and skills after a period of hard work. Therefore, teachers should be good at "delaying judgment" and let students' learning difficulties and problems be stored in the "question bank". After a period of study, they are allowed to "quit" and answer again. For students with learning difficulties, this "problem path" and "delayed judgment" can make them see progress, feel the joy of success, develop students' self-awareness, and thus stimulate new learning motivation.
5. Strengthen "practice" activities.
Comprehensive practical activities mainly include information technology education, research-based learning, community service and social practice, and labor technology education, which is a new curriculum in the new round of basic education curriculum reform. The establishment of comprehensive practical activities effectively improves the curriculum structure of primary and secondary schools, enriches the curriculum types, and effectively promotes the transformation of students' learning methods and the renewal of teachers' teaching views and curriculum views.
1. Comprehensive practical activities return to the life world. Select some comprehensive, practical and realistic problems, events and phenomena from students' real life world as the course content, so that students can return to the real life world to the maximum extent.
2. Comprehensive practical activities are based on practice. Let students participate in practice, actively and comprehensively apply what they have learned to solve various practical problems in practice, and improve their ability to solve practical problems. Teachers should pay attention to creating practical situations for students, so that students can find, ask and solve problems themselves.
3. Comprehensive practical activities mainly focus on research-based learning. Research-based learning is a learning method in which students actively acquire knowledge and comprehensively use knowledge to solve problems in a way similar to scientific research under the guidance of teachers.
I designed it in the teaching with full application interest. Students use their hands and brains to collect data and information about "lucky money" and actively guide discussion and thinking. Lucky money brings us not only joy, but also thinking, which requires our objective evaluation and rational analysis.
If you had a lot of money, what would you do with it?
I will invest this money in my aunt's supermarket in the name of my parents, so that my parents will also have Dong Quan's share in the supermarket.
Deposit in the bank, buy government bonds, stock market, donate to disaster areas, buy computer knowledge, buy books, travel, invest in small self-employed, and invite others to dinner.
A person takes a train to do a small survey, meet strangers and see the outside world.
B, I find it strange that the annual interest rate was 5.67% in 1997, 2.7% before New Year's Day, and now it is 1%. Why is the interest rate getting less and less every year when the country is prosperous?
C. why should interest rates fall? ① Less loans and more deposits;
② 9. 1 1 event affects the American economy;
(3) In order to ensure large state-owned enterprises.
D, elders know a lot about lucky money. For example, when my dad was a child, the lucky money was only one or two yuan, and it would be nice to have more than two yuan. But now we have hundreds of lucky money, so our next generation can be tens of thousands, even hundreds or millions. ...
There are many questions about lucky money, so I won't mention them here. I'll talk about them again when I have a chance. ...
Also: is the third grade of primary school discussing how to participate in community activities? A student said: There is one mailbox missing in our community, so it is suggested to add another one.
The teacher's eyes lit up, which is a good topic. Q: Why is there a missing mailbox? What is the reason for adding mailboxes? What are the conditions for adding a mailbox? )
Discussion: Do parents think this is necessary?
What does the postman think?
What does the postmaster think?
How far is the distance between mailboxes?
What are the policy provisions for adding posting boxes?
If so, is there any difficulty in funding?
Where is the most suitable location?
Students investigate and interview in groups, and write the results into suggestions or reports.
The next day, the teacher and classmates sorted out their opinions and formed a proposal to add a mailbox somewhere.
On the third day, when the children went to school, they were very excited to see that the mailbox of green new clothes had been erected there.
In the discussion and research of e-mail, students not only learned research methods, but also learned cooperation, which enhanced their sense of community belonging.
Whether the curriculum reform can be successfully completed depends on the teachers. We teachers should constantly learn and experience mathematics curriculum standards and master and apply new educational concepts. Only in this way is the most effective guarantee for curriculum reform.