2020 Senior One Mathematics Teaching Plan 1
Subset, complete set, complement set
Teaching objectives:
(1) Understand the concepts of subset, proper subset, complement set and equality of two sets;
(2) Understand the meaning of complete works and empty sets,
(3) Master the symbols and representation methods of subsets, complete sets and complementary sets, and use them to correctly represent some simple sets, so as to cultivate students' symbolic representation ability;
(4) We will find the subset and proper subset of the known set, and we will find the complement of the subset in the complete set;
(5) Being able to judge the inclusion relationship and equality relationship between the two groups, and accurately express them with symbols and figures (Venn diagram), so as to cultivate students' mathematical thinking combined with mathematics;
(6) Cultivate students' ability to analyze and solve problems from the perspective of set.
Teaching emphasis: the concepts of subset and complement.
Teaching difficulties: make clear the difference between elements and subsets, and the difference between attribution and inclusion.
Teaching equipment: slide projector
Teaching process design
(A) the introduction of new courses
Last lesson, we learned about sets, elements, three attributes of elements in sets and the relationship between elements and sets.
Questioning (projection typing)
Known,,, q:
1. What collections are listed?
2. Which set representations are descriptive?
3. Set M and set P are graphically represented.
4. Name the elements in each set separately.
5. Symbolize the relationship between elements in each set and the set, and symbolize the relationship between element 3 in set N and set M. 。
6. What is the relationship between the elements in set M and set N? What is the relationship between the elements in set M and set P?
Ask the students to answer.
1. Set m and set n; (oral answer)
2. set p; (oral answer)
3. (Written practice combined with blackboard writing performance)
4. The elements in the set M are-1,1; The elements in set n are-1, 1, 3; The elements in the set p are-1, 1. (answer)
5.,,,, (pen practice combined with chessboard performance)
6. Any element in set M is an element in set N.. Any element in set m is an element in set p.
Introduce the set m and set n seen above; Set M and set P have established a certain relationship through elements, and two sets with this relationship will often appear in later learning. This section will study the relationship between these two sets.
(2) Newly granted knowledge
1. subset
(1) subset definition: Generally speaking, for two sets A and B, if any element of set A is an element of set B, we say that set A is contained in set B, or set B contains set A. ..
Note: read: a is contained in b or b contains a.
When set a is not included in set b, or set b does not include set a, it is marked as: A B or B A.
Properties: ① (Any set is a subset of itself)
② (An empty set is a subset of any set)
Doubt whether a subset can be said to be a collection of some elements in the original set?
We cannot interpret A as a subset of B, but as a collection of some elements in B. 。
Because the subset of B also contains itself, and this subset is composed of all the elements of B. An empty set is also a subset of B, and this set does not contain the elements in B. It can also be seen that it is inaccurate to interpret A as a subset of B that is composed of some elements of B. 。
(2) Set equality: Generally speaking, for two sets A and B, if any element of set A is an element of set B, and any element of set B is an element of set A, we say that set A is equal to set B, and write it as A = B. ..
Example: Visible set means that all elements of A and B are exactly the same.
(3) proper subset: For two sets A and B, if, and, we say that set A is the proper subset of set B, and write it down as: (or), which means that A is really contained in B or B really contains A.
Think about whether proper subset can be defined as follows: "If A is a subset of B and at least one element in B does not belong to A, then set A is called the proper subset of set B."
The relationship between set B and its proper subset A can be represented by Venn diagram, in which the interior of two circles represent sets A and B respectively.
Ask a question
(1) Write the inclusion relation of number set n, z, q and r, and express it by venn diagram.
(2) to determine whether the following writing is correct
① A ② A ③ ④A A
Nature:
(1) An empty set is a proper subset of any non-empty set. If a, and A≦, then a;
(2) If,, then.
Example 1 Write all subsets of a set and point out which of them are its proper subset.
Answer: All subsets of a set are,,, where proper subset is.
Note the direction of the (1) subset and the proper subset symbol.
(2) confusing symbols
① ""and "":there is a relationship between elements and sets; There is a containment relationship between sets. For example, r, {1} {1, 2,3}
②{0} and {0} are sets with one element 0 but no elements.
Example: {0}. Cannot be written as ={0}, ∈{0}
See textbook P8 (explanation) for example 2.
Example 3 Judge whether the following statement is correct. If not, please correct it.
(1) indicates an empty set;
(2) An empty set is the proper subset of any set;
(3) no;
All subsets of (4) are;
(5) If and, then B must be the proper subset of A;
(6) and cannot be established at the same time.
Solution: (1) does not refer to an empty set, but a set with empty sets as elements, so (1) is incorrect;
(2) incorrect. An empty set is the proper subset of any non-empty set;
(3) Incorrect. It is the same set as the representation;
(4) All incorrect subsets. Yes;
(5) Correct
(6) incorrect. If it is true, it can be established at the same time.
Example 4 Fill in the blanks with appropriate symbols (,):
( 1) ; ; ;
(2) ; ;
(3) ;
(4) if,,, then A B C.
Solution: (1) 00;
(2) = , ;
(3) , ∴ ;
(4)A, B and C all represent the set of all odd numbers, ∴ A = B = C. 。
Practice textbook P9
Fill in the blanks with the appropriate symbols (,):
( 1) ; (5) ;
(2) ; (6) ;
(3) ; (7) ;
(4) ; (8) .
Solution: (1); (2) ; (3) ; (4) ; (5)=; (6) ; (7) ; (8) .
Question: Please look at the example in the textbook P9.
(2) Complete works and supplements
1. Complement set: Generally speaking, let S be a set and A be a subset of S (that is, a set composed of all elements in S that do not belong to A), which is called the complement set (or complement set) of subset A in S, and it is recorded as, that is, the complement set of A in S can be represented by the shaded part on the right.
Attribute: S( SA)=A
For example: (1) If S={ 1, 2,3,4,5,6}, A={ 1, 3,5}, then SA = {2,4,6};
(2) If A={0}, then Na = n-;
(3) RQ is an irrational number set.
2. Complete works:
If the set S contains all the elements of each set we want to study, then this set can be regarded as a complete set.
Note: For a given complete set, the supplementary set will be different when the complete set is different.
For example, if and when; Then when?
Example 5 Set the Complete Works, Judgment Questions and.
Solution:
: see the textbook P 10 exercise.
1. Fill in the blanks:
,,, so,.
Solution:
2. Fill in the blanks:
(1) If it is a complete set, then it is the complement of n;
② If it is complete, then () = the complement of.
Solution: (1); (2) .
(3) Summary: This lesson has learned the following points:
1. Five concepts (subset, set equality, proper subset, complement set and complete set, with emphasis on subset and complement set).
2. Five attributes
(1) An empty set is a subset of any set. φA
(2) An empty set is a proper subset of any non-empty set. φA(A≠φ)
(3) Any set is a subset of itself.
(4) If,, then.
(5) S( SA)=A
3. Two groups of confusing symbols: (1) "He": (2){0} and.
(4) Homework after class: See the textbook P 10 Exercise 1.2.
2020 Senior One Mathematics Teaching Plan II
Monotonicity and (small) value of function
I. teaching material analysis
1, the position and function of teaching materials
(1) This lesson is mainly about the monotonicity of functions;
(2) Learning on the basis of learning the concept of function and laying a foundation for the learning of basic elementary functions, therefore, it plays an important role in connecting the past with the future in teaching materials; (You can look at the chapters before and after this topic to write)
(3) It is a hot and difficult issue in the college entrance examination over the years.
(just change it according to specific topics, and delete non-hot and difficult issues)
2. Textbooks are heavy and difficult.
Key point: the definition of monotonicity of function.
Difficulties: Proof of Monotonicity of Functions
Breakthrough of important and difficult points: On the basis of students' existing knowledge, through careful observation and thinking, through group cooperation and exploration, the breakthrough of important and difficult points can be realized. (This must be available)
Second, the teaching objectives
Knowledge Goal: Definition of Monotonicity of (1) Function
(2) Proof of monotonicity of function
Ability goal: to cultivate students' comprehensive analysis and abstract generalization ability, and to understand the reduction thought from simple to complex and from special to general.
Emotional goal: to cultivate students' spirit of exploration and sense of cooperation.
(This teaching goal design pays more attention to the teaching process and emotional experience, based on the diversification of teaching goals. )
Third, the analysis of teaching rules
1, analysis of teaching methods
"There must be laws in teaching, but not in teaching", and proper methods will be effective. Teachers are the organizers, guides and collaborators of teaching in the new curriculum standards, and students' enthusiasm and initiative should be fully mobilized in the teaching process. Based on this principle, I mainly adopt the following teaching methods in the teaching process: open inquiry, heuristic guidance, group discussion and feedback evaluation.
2. Analysis of learning methods
"It is better to teach people to fish than to teach them to fish", and the most valuable knowledge is about methods. As the theme of teaching activities, the state and degree of students' participation in the learning process is the most important factor affecting the teaching effect. In the choice of learning methods, I mainly use: independent inquiry, observation and discovery, cooperation and exchange, induction and summary.
(The first three parts should be controlled within three minutes and can be deleted appropriately. )
Fourth, the teaching process
1, introduce the new with the old.
Let the students draw the images of the first function f(x)=x and the second function f (x) = x 2 through the small research before class, observe the characteristics of the function images and make a summary. Through group discussion and induction in class, students are led to find that the teacher's conclusion is that the image of a linear function f(x)=x rises linearly in the defined domain, while the image of a quadratic function f (x) = x 2 is a curve, which falls at (-∞, 0) and rises at (0, +∞). (Add gestures appropriately to make it look more natural)
2. Create problems and explore new knowledge.
Then the question is raised. Can the expression of quadratic function f (x) = x 2 be used to describe the image of the function at (-∞, 0)? The teacher summed up and combined with books to reveal the definition of monotonicity of function, and emphasized that monotonicity of function can be judged by difference method.
Let the students imitate the expression just now to describe the image of quadratic function f (x) = x 2 at (0, +∞), and find some students to answer, thus standardizing the students' mathematical terms.
Let students learn the definition of monotone interval of function independently, and lay a good foundation for the next example study.
3. Give examples and apply what you have learned.
Example 1 mainly consolidates and applies the monotone interval of the function, and finds out the monotone interval of the function by observing the image with the function defined at (-5,5). This example is mainly based on students' individual answers. After the students answer, correct their answers through mutual evaluation and check their mastery of the monotonous interval of the function. It is emphasized that monotonous intervals are generally written in the form of half opening and half closing.
After explaining the examples, students can complete Exercise 4 after class by themselves, and test their learning effect by answering questions collectively.
Example 2 applies monotonicity of function to other fields, and proves Boyle theorem of physics through monotonicity of function. This is a hot and difficult issue in the college entrance examination over the years. This example should be proved by the teacher's performance, so as to standardize the steps of summary and proof. When comparing two differences with three and simplifying four, it is important to simplify f(x 1)-f(x2) into the form of sum-difference product quotient, and then compare it with 0.
After the students are familiar with the proof steps, do exercise 3 after class and find several students to perform on stage in groups. Other students will complete the proof steps by themselves below and evaluate each other through self-evaluation.
4. Summary
In this lesson, we mainly studied the definition and proof process of function monotonicity, and paid attention to cultivating students' exploration spirit and cooperation consciousness in the teaching process.
5, homework layout
In order to let students learn different kinds of mathematics, I will assign homework by layers: one set of exercises 1.3A group 1, 2, 3, two sets of exercises 1.3A group 2, 3 and group b 1, 2.
6. Blackboard design
I try to summarize the main points of this lesson concisely, so that students can see it at a glance.
(The most important part of this part takes six to seven minutes. The definitions and examples must explain the students' activities. )
Teaching evaluation of verbs (abbreviation of verb)
This lesson is based on students' existing knowledge. In the teaching process, students' enthusiasm and initiative are fully mobilized through independent inquiry and cooperative communication, and feedback information is absorbed in time. Through students' self-evaluation and mutual evaluation, internal motivation and external stimulation can coordinate and promote students' mathematical literacy.
2020 Senior One Mathematics Teaching Plan 3
Teaching objectives: ① To master the properties of logarithmic function.
② The following problems can be solved by using the properties of logarithmic function: compare the logarithm, and find the domain, range and monotonicity of the compound function.
③ Pay attention to the infiltration of functional ideas, equivalent transformation, classified discussion and other ideas to improve the ability to solve problems.
Emphasis and difficulty in teaching: the application of logarithmic function properties.
Teaching process design:
Review: the concept and properties of logarithmic function.
4. Start taking ordinary classes.
1 size of comparison number
Example 1 Compare the sizes of the following groups.
⑴loga5. 1，loga 5.9(a & gt； 0，a≠ 1)
⑵log0.50.6，logЛ 0.5，lnл
Teacher: Please observe the characteristics of these two logarithms in (1).
Health: The bases of these two logarithms are equal.
Teacher: So how do you compare the sizes of two logarithms with equal cardinality?
Student: You can construct a logarithmic function with a base and use the monotonicity ratio of the logarithmic function.
Teacher: Yes, please describe the process of solving this problem.
The monotonicity of logarithmic function depends on the size of radix: when 0
Tone drops, so log5.1>; Loga5.9 When a> is 1, the function y=logax is monotonically recursive.
Increase, so log 5. 1
Blackboard writing:
Solution: Ⅰ) When 0
∫5. 1 & lt； 5.9 ∴loga5. 1>； Logarithm 5.9
Ii) when a> is at 1, the function y=logax is the increasing function at (0, +∞).
∫5. 1 & lt； 5.9 ∴loga5. 1
Teacher: Please observe the characteristics of these three logarithms in [2].
Health: The bases of these three logarithms are not equal to the true numbers.
Teacher: Then how do you compare these three logarithms?
Health: looking for "medium quantity", log 0.50.6 >; 0，lnл& gt； 0，logл0.5 & lt； 0; lnл& gt； 1,
log 0 . 50 . 6 & lt； 1, so logл 0.5.
Words on the blackboard: abbreviations.
Teacher: The common methods of comparing logarithm size: ① Construct logarithmic function and use it directly.
The monotonic proportion of numbers, ② the indirect proportion of "intermediate quantity", ③ the logarithm.
Compare the position relationship of the functional image with the size.
The domain, range and monotonicity of 2 functions.
Example 2 (1) Find the domain of function y=.
(2) Solve the inequality log0.2(x2+2x-3) > log0.2 (3x+3).
Teacher: How to find the domain of the function in (1)? (Hint: Finding the domain of a function is to make the function meaningful. If the function contains a denominator, the denominator is not zero; There are even numbers, and the mold opening is greater than or equal to zero; If there is a logarithmic form in the function, the truth value is greater than zero. If the above situations appear in the function at the same time, we should take them all into account and find out the result of their interaction. ): denominator is 2x- 1≠0, even modulus is log0.8x- 1≥0, and real number is x>0.
Blackboard writing:
Solution: ∫2x- 1≠0x≠0.5
log0.8x- 1≥0，x≤0.8
x & gt0x & gt； 0
∴x(0,0.5)∪(0.5,0.8〕
Teacher: Next, let's solve this inequality together.
Analysis: To solve this inequality, we must first make it meaningful, that is, the real number is greater than zero.
Then according to the monotonicity of logarithmic function.
Teacher: Please write down the process of solving this problem.
Health:
Solution: x2+2x-3 >; 0x & lt； -3 or x> 1
(3x+3)>0，x & gt- 1
x2+2x-3 & lt； (3x+3) -2
The solution of inequality is: 1
Example 3 Find the range and monotone interval of the following functions.
⑴y=log0.5(x- x2)
⑵y = loga(x2+2x-3)(a & gt； 0，a≠ 1)
Teacher: We need to find the range and monotone interval of the function in Example 3 and the thinking method of the compound function.
Let the students solve it (1).
Health: This function can be regarded as a compound of y y= log0.5u and u= x- x2.
Blackboard writing:
Solution: (1) ∵ u (1) ∵ u = x-x2 > 0, ∴0
u= x- x2=-(x-0.5)2+0.25，∴0
∴y= log0.5u≥log0.50.25=2
∴y≥2
x x(0，0.5)x[0.5， 1]
u= x- x2
y= log0.5u
y=log0.5(x- x2)
The monotone decreasing interval (0,0.5) and monotone increasing interval (0.5, 1) of the function y=log0.5(x- x2).
Note: when studying the properties of any function, we must first ensure that the function is meaningful, otherwise,
If there is no function, there is no way to talk about it.
Teacher: On the basis of (1), let's solve (2) together. Please observe (1) and (2)
What is the difference?
Health: (1) radix remains unchanged, (2) radix is letters.
Teacher: So (2) how to solve it?
Health: As long as A is classified and discussed, the practice is similar to (1).
Words on the blackboard: abbreviations.
3. Summary
This course mainly explains how to solve some problems by using the properties of logarithmic function, hoping to
Through this lesson, students can apply the idea of equivalent transformation and classified discussion to improve their problem-solving ability.
4. Homework
(1) Solving inequality
①LG(x2-3x-4)≥LG(2x+ 10)； ②loga(x2-x)≥loga(x+ 1), (a is a constant).
⑵ known function y=loga(x2-2x), (a >；; 0，a≠ 1)
① Find its monotonous interval; ② When 0
⑶ known function y = loga(a >；; 0, b>0, and a ≠ 1)
① Find its domain; ② Discuss its parity; ③ Discuss its monotonicity.
(4) The known function y = loga (ax-1) (a >; 0，a≠ 1)，
① Find its domain; ② When x is what value, the function value is greater than1; 3 discuss it.
monotonicity
5. Description of classroom teaching design
This course is arranged as an exercise class, which mainly uses the properties of logarithmic functions to solve some problems. The whole class is divided into two parts: 1. Comparing the numbers, I want to pass this part of the exercise.
Cultivate students' ideas of constructing function, classified discussion and combination of numbers and shapes. Second, the domain, range and monotonicity of the function. I want to make students pay attention to finding the domain of function through this part of exercise. Because students often don't consider the definition domain of the function when finding the range and monotonous interval of the function, and this error is stubborn and difficult to correct. Therefore, try to let students have correct ideas and clear steps. In order to arouse students' enthusiasm and highlight that students are the main body of the classroom, examples are divided into levels, from easy to difficult, and each problem can be completed by students independently. But in the process of solving each problem, the teacher should write on the blackboard, which not only makes students happy to acquire new knowledge, but also does not have to worry about unfamiliar problem-solving format. After each problem is finished, the teacher briefly summarizes it, so that good students can master it better and poor students can keep up.
2020 Senior One Mathematics Teaching Plan 4
A preliminary study on solid geometry
Structural characteristics of 1, column, cone, platform and ball
(1) prism:
Definition: Geometry surrounded by two parallel faces, the other faces are quadrangles, and the common edges of every two adjacent quadrangles are parallel to each other.
Classification: According to the number of sides of the bottom polygon, it can be divided into three prisms, four prisms and five prisms.
Representation: Use the letter of each vertex, such as a five-pointed star, or use the letter at the opposite end, such as a five-pointed star.
Geometric features: the two bottom surfaces are congruent polygons with parallel corresponding sides; The lateral surface and diagonal surface are parallelograms; The sides are parallel and equal; The section parallel to the bottom surface is a polygon that is congruent with the bottom surface.
② Pyramid
Definition: One face is a polygon, and the other faces are triangles with a common vertex. These faces enclose a geometric figure.
Classification: According to the number of sides of the bottom polygon, it can be divided into three pyramids, four pyramids and five pyramids.
Representation: Use the letters of each vertex, such as a pentagonal pyramid.
Geometric features: the side and diagonal faces are triangles; The section parallel to the bottom surface is similar to the bottom surface, and its similarity ratio is equal to the square of the ratio of the distance from the vertex to the section to the height.
(3) Prism:
Definition: Cut off the part between the pyramid, the section and the bottom with a plane parallel to the bottom of the pyramid.
Classification: According to the number of sides of the bottom polygon, it can be divided into triangular, quadrangular and pentagonal shapes.
Representation: Use the letters of each vertex, such as a pentagonal pyramid.
Geometric features: ① The upper and lower bottom surfaces are similar parallel polygons; ② The side is trapezoidal; ③ The sides intersect with the vertices of the original pyramid.
(4) Cylinder:
Definition: Geometry surrounded by a surface with one side of a rectangle and the other three sides rotating around a straight line.
Geometric features: ① The bottom is an congruent circle; ② The bus is parallel to the shaft; ③ The axis is perpendicular to the radius of the bottom circle; ④ The side development diagram is a rectangle.
(5) Cone:
Definition: Rotate the geometry surrounded by the surface of Zhou Suocheng with the right-angled side of the right-angled triangle as the rotation axis.
Geometric features: ① the bottom is round; (2) The generatrix intersects with the apex of the cone; ③ The side spread diagram is a fan.
(6) frustum of a cone:
Definition: Cut the part between the cone, the section and the bottom with a plane parallel to the bottom of the cone.
Geometric features: ① The upper and lower bottom surfaces are two circles; (2) The side generatrix intersects with the vertex of the original cone; (3) The side development diagram is an arch.
(7) Sphere:
Definition: Geometry formed by taking the straight line where the diameter of the semicircle is located as the rotation axis and the semicircle surface rotates once.
Geometric features: ① the cross section of the ball is round; ② The distance from any point on the sphere to the center of the sphere is equal to the radius.
2020 Senior One Mathematics Teaching Plan 5
Periodicity of trigonometric functions
First, learning objectives and self-assessment
1 an image that grasps the geometric method using the unit circle as a function.
2. Understand the periodicity and minimum positive period of trigonometric function by combining the definition of image and function periodicity.
3 will use algebraic method to find the period of the equal function.
4 understand the geometric meaning of periodicity
Second, the focus and difficulty of learning
"The concept of periodic function", the solution of period.
Third, study the guidance of law.
1 is a periodic function, which means that all domains have it.
That is, it should be an identity.
2. A periodic function must have a period, but it does not necessarily have a minimum positive period.
Fourthly, learning activities and meaning construction.
A probe into the key and difficult points of verb (abbreviation of verb)
Example 1. If the height of the pendulum is a function of time as shown in the figure.
(1) Find the period of this function;
(2) Find the height of the pendulum.
Example 2. Find the period of the following function.
( 1) (2)
Abstract: (1) function (all of which are constant sums)
Period T=.
(2) Functions (All these are constants, and
Period T=.
Example 3, Verification: The period is.
Example 4, (1) Study the image of sum function and analyze its periodicity. (2) Verification: the period of is (where all are constants,
and
Abstract: Functions (all of which are constant sums)
Period T=.
Example 5, the period of (1).
(2) Known satisfaction, verification: it is a periodic function.
Thinking after class: Can you use the unit circle as a function image?
Six, homework:
Seven, independent experience and application
1, the period of the function is ()
A, B, C, D,
2, the minimum positive period of the function is ()
A, B, C, D,
3, the minimum positive period of the function is ()
A, B, C, D,
4, the period of the function is ()
A, B, C, D,
5. Let it be a function with domain r and minimum positive period.
If is, the value of is equal to ()
a、 1 B、C、0 D、
6. The minimum positive period of a function is, then
7. If the minimum positive period of a known function is not greater than 2, then it is a positive integer.
The minimum value of is
8. Find the minimum positive period of a function as t, sum, and then a positive integer.
The value of is.
9. It is known that the function is odd function with a period of 6, and then
10, if this function, then
1 1, analyze the period with the definition of the period.
12, known function, if it contains a period, find.
Value of positive integer
13, a mechanical vibration, the displacement and time of a proton from the equilibrium position.
The function relationship is as shown in the figure:
(1) Find the period of this function;
(2) Find the displacement of the particle from the equilibrium position.
14, known as a function defined on r, and for any
Established,
(1) proves that it is a periodic function;
(2) The value of if.
In 2020, there are five related math teaching plans for senior one;
★2020 Senior High School Mathematics 3 Teaching Plan
★ Five Work Plans for Mathematics Teaching in Senior One in 2020
★ There are 5 model essays on mathematics teaching plans in senior one.
★ Summary of Senior High School Mathematics Teachers' Work in 2020
★ 2020 high school mathematics teaching plan model essay
★ Five Highlights of Senior High School Mathematics Teaching Experience in 2020
★ 5 latest summaries of mathematics teaching in the next semester in 2020.
★ Five work plans for the new semester of senior high school mathematics teaching in 2020
★ There are 5 teaching work plans of senior high school mathematics teaching and research group in 2020.
★ Five Work Plans for Senior High School Mathematics Teachers in 2020