I. Objectives and requirements
1. Understand and master the concepts of monomial, polynomial and algebraic expressions, and find out the differences and connections between them.
2. Understand the concept of similar items, master the method of merging similar items, master the changing law of symbols when removing brackets, and be able to merge and remove brackets correctly. On the basis of accurate judgment and correct combination of similar items, add and subtract algebraic expressions.
3. Understand that the letters in the algebraic expression represent numbers, and the addition and subtraction operations of the algebraic expression are based on numbers; Understanding the basis of merging similar items and removing brackets is the distribution law; Understanding the operation rules and properties of numbers is still effective in the addition and subtraction of algebraic expressions.
4. Be able to analyze the quantitative relationship in practical problems and express it with a formula with letters.
Second, the main points
Single item and its related concepts;
Polynomials and related concepts;
Remove the parenthesis rule and apply it accurately to simplify algebraic expressions.
Third, difficulties.
Distinguish the coefficient and frequency of individual items;
Distinguish the degree of polynomial from the degree of single item;
When the "-"is added before the brackets, the brackets are removed, and the symbols in the brackets are easy to make mistakes.
Fourth, the knowledge framework.
Verb (abbreviation of verb) summary of knowledge points and concepts
1. monomial: in algebraic expressions, if only multiplication (including power) operations are involved. Or algebraic expressions that contain division but do not contain letters in division are called monomials; The product of numbers or letters is called a monomial (a single number or letter is also a monomial).
2. Coefficient: The numerical factor in a single item is called the coefficient of this single item. The sum of the exponents of all letters is called the degree of this monomial. The zeroth power of any nonzero number is equal to 1.
3. Polynomial: The sum of several monomials is called polynomial.
4. Number and degree of polynomials: the number of monomials contained in a polynomial is the number of polynomial terms, and each monomial is called a polynomial term; In polynomial, the degree of the term with the highest degree is called the degree of polynomial.
5. Constant term: the term without letters is called constant term.
6. The arrangement of polynomials
(1) Arranging polynomials in descending alphabetical order is called arranging polynomials in descending alphabetical order.
(2) Arranging a polynomial according to the exponent of a letter from small to large is called arranging polynomials according to the ascending power of this letter.
7. Please note when arranging polynomials:
(1) Since a single item contains its preceding attribute symbol, the attribute symbol of each item should still be regarded as a part of the item and moved together.
(2) The arrangement of polynomials with two or more letters should pay attention to:
A. first of all, it must be arranged according to the index of which letter.
B. determine whether to arrange letters inward or outward.
(3) Algebraic expression:
Monomial and polynomial are collectively called algebraic expressions.
8. Polynomial addition:
Polynomial addition refers to the coefficient addition of polynomial similar terms (that is, merging similar terms).
9. Similar items: items with the same letters and times are called similar items.
10. Merge similar items: similar items in polynomials can be merged, which is called merging similar items. The rule of merging similar items is: the coefficients of similar items are added, and the obtained results are used as coefficients, and the index of letters remains unchanged.
1 1. When grasping the concept of similar items, pay attention to:
(1) To judge whether several monomials or terms are similar, two conditions must be mastered:
(1) contains the same letters.
The same letter has the same number of times.
(2) Similar items have nothing to do with coefficient or alphabetical order.
(3) All constant terms are similar.
12. Merge similar projects:
(1) Find out the similar items accurately;
(2) Reverse the distribution law, and add the coefficients of similar items together (in brackets) to keep the letters and their indices unchanged;
(3) Write the merged results.
13. When mastering the merger of similar projects, we should pay attention to the following points:
(1) If the coefficients of two similar items are opposite, the result after merging similar items is 0;
(2) Don't leave out items that can't be merged;
(3) As long as there are no more similar terms, it is the result (either a monomial or a polynomial).
14. Development of algebraic expressions
Algebraic multiplication and division: the emphasis is on algebraic multiplication and division, especially the multiplication formula. It is difficult for students to master the structural characteristics of multiplication formula and the broad meaning of letters in the formula. Therefore, it is difficult to use the multiplication formula flexibly, and the handling of symbols in brackets is another difficulty when adding brackets (or removing brackets). Parentheses (or brackets) are the deformation of polynomials, which should be carried out according to the law of parenthesis (or brackets). In the multiplication and division of algebraic expressions, the single multiplication and division is the key, because the multiplication and division of general polynomials should be "transformed" into the single multiplication and division.
The main problems of the four operations of algebraic expressions are:
Four operations of (1) monomial
This kind of questions mostly appear in the form of multiple-choice questions and application questions, which are characterized by examining four operations of a single item.
(2) Operation of monomial and polynomial
This kind of problems mostly appear in the form of solving problems, which are highly skilled and characterized by examining the four operations of monomials and polynomials.
practise
1, as shown in figure 1. If D is the midpoint of AB, and AB=4, then DB = _ _ _ _ _ _ _ _ _ _ _ _
2. If ∠ α = 29 35', the complementary angle of ∠αis _ _ _ _ _ _ _ _;
3. As shown in Figure 2, to go to school from A's home, take a shortcut to B's school, and the shortest route is (fill in the serial number).
The reason is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _;
4. The geometric figure obtained by rotating the right triangle around the right side is ().
The website of the Ministry of Education recently published the third-party assessment of compulsory education. The evaluation of the evaluation team of Southwest University shows that there are some problems and difficulties that can not be ignored in the reform and development of compulsory education. For example, in some places, educational resources in cities and towns are tight and rural educational resources are idle. The problem of large class size in counties and townships in the central and western regions is prominent.
Entrusted by the Office of the Leading Group for the Reform of the National Education System, the evaluation team adheres to the principle of "independence, objectivity, fairness and seeking truth from facts", based on the third-party perspective and requirements, and revolves around the objectives, tasks and policy measures of compulsory education proposed in the Outline of the National Medium and Long-term Education Reform and Development Plan (20 10-2020).
The evaluation shows that "consolidating and improving the level of nine-year compulsory education" has risen steadily, "achieving a higher level of universal education" has achieved remarkable results, and "children of migrant workers receive compulsory education equally" has a good situation. The primary school enrollment rate and enrollment rate have remained at a high level, while the junior high school enrollment rate and enrollment rate have gradually increased. In 20 13 and 20 14 years, the proportion of students attending public schools with their children in China has always remained above 80%. Breakthrough progress has been made in "formulating measures for children of migrant workers to take entrance examinations in the local area after receiving compulsory education". In 20 13, 26 provinces across the country solved the problem of children taking entrance examinations locally. In 20 14, 28 provinces in China began to implement the reform of college entrance examination for children of floating population in different places.
The evaluation shows that "improving the quality of compulsory education and reducing the academic burden of primary and secondary school students" has achieved initial results. The goal of "taking the lead in reducing the burden on primary school students" has gradually emerged. The height, weight and vital capacity of students are increasing year by year, and the effect of "strengthening students' physique" is obvious. From 20 10 to 20 14, the average height of pupils increased from 135.69 cm to 137.82 cm, the average weight increased from 32.2 1 kg to 33.45 kg, and the average vital capacity increased from/kloc-0. The average height of junior middle school students increased from 155.85 cm to159.1cm, the average weight increased from 47.35 kg to 48.97 kg, and the average vital capacity increased from 25 19.9 1 ml to 266.
The evaluation also pointed out that in the five years since the implementation of the outline, there have also been some problems and difficulties that cannot be ignored in the reform and development of compulsory education. For example, the overall investment in funds is still insufficient, and there is a "central collapse". With the acceleration of urbanization in China, educational resources in some places are tense in cities and towns and idle in rural areas. The problem of large class size in counties and townships in the central and western regions is prominent. The academic burden of junior high school students has not been reduced. The phenomenon of "reducing the burden inside the school and increasing the burden outside the school" is prominent in urban schools.
At the end of 20 15, Tianjin Heping Wanquan Primary School will celebrate the 5th anniversary of1/kloc-0. In order to commemorate the upcoming school anniversary, and to let children enter the society, know the society and understand the society, more than 2,600 students in Tianjin Heping Bay School, divided into six grades, walked out of the classroom and entered the society. In more than a month, they have carried out 54 social independent practice classes in ten aspects, such as public service, environmental protection and gratitude education, in order to enrich themselves and feel responsible.
The school said that different from the social practice organized by the school in the past, in order to fully mobilize the active participation of students, Wanquan Primary School adopted the form of allowing students to participate and choose social practice projects independently, so that children can choose and determine their own practice themes independently. Teacher Zhang, the head teacher of Class Two, Grade Two, said: "At first, I had concerns about such practical activities. Because students are too young, all aspects of student safety need to be effectively guaranteed, and it is difficult to implement. But when I shared my thoughts with my parents, they all supported me and eliminated my previous worries. Of course, I am deeply encouraged by the enthusiasm of the children. "
It is understood that many classes have planned a visit experience of "knowing your hometown, loving your hometown and being a beautiful little master in Tianjin". Children of different grades walked into Tianjin Yangliuqing Woodblock New Year Pictures Memorial Hall, Clay Fighter Zhang Art Museum, 18th Street Twist Culture Museum, Yuan, Ming and Qing Dynasties Palace Site Museum and so on. I deeply felt the charm of Tianjin history and China's intangible cultural heritage. At the same time, under the guidance of teachers, many students have independently planned and completed public welfare activities with different themes, such as "We are all environmental protection treasures", "Innocent warmth to strangers", "Caring for urban beauticians" and "Caring for children with stars". They either walked into families with difficulties in the city, or expressed their condolences to the first-line builders in the city, or walked into SOS Children's Village and Autistic Children's Center to offer their love. In addition, there are many classes of children who have realized the miracle of life and learned to care more about life by entering the "Life Bank".
Through diversified practical activities, students broaden their horizons and learn knowledge that they can't learn in class. "Mom, I know for the first time that garbage can be turned into good things through science and technology," Guo Yutong, a senior two student, told his mother excitedly after visiting the Urban Garbage Treatment Experience Museum. Students from Class 3, Grade 3 walked into Yu Xiang Autism Hospital in Tanggu and had a happy day with the children there. "The children there communicate with us in different ways and show their happiness in different ways. When we give them the plush toys in our hands, one of the big sisters will only cry to express her happy mood ... "After this activity, the children in Class 3 (3) felt a lot. "Seeing that they are different from ourselves, we should not laugh at them, but try our best to help them."
"Without inculcation, children naturally learn how to love in practice, knowing that there are so many people in society who are different from themselves but everyone is equal." A third-year parent said with deep feelings. Another parent said that after her daughter participated in the social activities of "caring for nature, we are in action" in the class, she suddenly became a small supervisor at home. Under the supervision of her daughter, the garbage at home should be classified according to recyclable and non-recyclable standards. Even the uncles and aunts in the building should publicize their "environmental protection classics". A parent of Class 0/6 of Grade 2/KLOC said that he didn't expect a school to carry out independent practice courses in all classes. A century-old prestigious school can build such a growth platform for children, which is very meaningful for children to become responsible people. I hope the school can do more such activities.
"Everything is a course, and education is everywhere." Zhao Yan, principal of Wanquan Primary School, introduced this activity. "Our courses should be not only in the classroom, but also in society, family and community. This kind of classroom moves from school-based to class-based and student-based, and the educational content moves from singleness to pluralism, and the educational form moves from singleness to autonomy. It is necessary to pay attention to personal growth, so that they can all have a platform for exercise, let them walk into life, feel responsibility, and learn to take responsibility. I hope to give them as a gift for growth on the occasion of the school 1 15 anniversary, so that children can benefit for life. "
Summary of knowledge points of addition and subtraction of 2 1 algebraic expression in senior one mathematics. Monomial: a formula that represents the product of numbers or letters. A single number or letter is also called a monomial.
2. Coefficient and frequency of single item: the numerical factor in single item is called the coefficient of single item;
The sum of all letter indices in a monomial is called the number of monomials.
3. Polynomial: The sum of several monomials is called polynomial.
4. Number and degree of polynomials: the number of monomials contained in a polynomial is the number of polynomial terms, and each monomial is called a polynomial term; In polynomials, the degree of the term with the highest degree is called the degree of polynomials;
6. Similar items: monomials with the same letters and the same index are similar items.
7. Rules for merging similar items: When the coefficients are added, the letter index remains unchanged.
8. Rules for deleting (adding) brackets:
When deleting (adding) brackets, if there is a "+"sign before the brackets, all items in the brackets remain unchanged; If there is a "-"before the brackets, all items in the brackets should be changed.
9. Addition and subtraction of algebraic expressions: search: (underline); Two "+"(be sure to use+) to start merging) Three in one: (merging)
10. Ascending and descending order of polynomials: arranging the terms of a polynomial according to the exponent of a letter from small to large (or from large to small) is called ascending order (or descending order) of the letter.