The first part: the teaching objectives of the design and selection of mathematics teaching plans for senior one;
(1) Understand the meaning of set and the relationship between elements and set.
(2) You can choose natural language, graphic language and set language (enumeration or description) to describe different concreteness.
Ask questions and feel the meaning and function of assembly language;
Teaching focus:
Basic concepts and representations of sets.
Teaching difficulties:
Using two common representations of sets-enumeration and description, some simple sets are correctly represented; Teaching process:
First, introduce the topic.
Before the military training, the school informed: at X, X and X, senior three students will gather in the gymnasium for military training mobilization; Is this notice addressed to all senior one students or to individual students?
Here, set is a common word, and we are interested in the whole of some specific objects in the problem (not individual objects). To this end, we will learn a new concept-set (announcement theme), which is the sum of some research objects.
Second, the new curriculum teaching
(A) the related concepts of set
1. Cantor, the founder of set theory, called a set the sum of some different things. People can recognize these things and judge whether a given thing belongs to this whole.
2. Generally speaking, the research objects are collectively referred to as elements, and the whole composed of some elements is called set, also referred to as set.
3. About the characteristics of set elements.
(1) Determinism: Let A be a given set and X be a specific object, then either it is an element of A or it is not an element of A, and one and only one of the two cases must be true.
(2) Reciprocity: The elements in a given set refer to different individuals (objects) belonging to this set, so the same element should not appear repeatedly in the same set.
(3) Set equality: the elements that make up the two sets are exactly the same.
4. The relationship between elements and sets.
(1) If A is an element of set A, it is said that A belongs to (belongto)A, and it is marked as a∈A(2) If A is not an element of set A, it is said that A does not belong to (notbelongto)A, and it is marked as aA (or aA).
5. Commonly used number sets and their symbols.
A set of nonnegative integers (or natural number set), denoted as n.
A set of positive integers, denoted as N__ or n+;
A set of integers, denoted by z.
Set of rational numbers, written as Q.
A set of real numbers, denoted as r.
(2) Representation of sets
We can use natural language to describe a set, but this will bring us a lot of inconvenience. In addition, enumeration and description are often used to represent a collection.
(1) enumeration: list the elements in the collection one by one and write them in braces.
Such as: {1, 2, 3, 4, 5}, {x2, 3x+2, 5y3-x, x2+y2}.
Idea 2: Introduce descriptive method.
Note: the elements in the collection are out of order, so when the collection is represented by enumeration, the order of the elements does not need to be considered.
(2) Description: describes the common attributes of the elements in the collection and is written in braces.
Specific methods: write down the general symbols and value (or variation) ranges of the elements in this set with braces, then draw a vertical line, and write down the * * * same characteristics of the elements in this set after the vertical line.
Such as: {x | x-3 >；; 2}, {(x, y)|y=x2+ 1}, {right triangle}.
Key point: the descriptive representation of a set should pay attention to the representative elements of the set.
{(x, y)|y=x2+3x+2} is different from {y|y=x2+3x+2}. As long as it does not cause misunderstanding, the representative elements of the set can also be omitted, such as {integer}, which represents the integer set Z.
Discrimination: The {} here already contains the meaning of "all", so there is no need to write {all integers}. It is also wrong to write {real number set} and {R} below.
Note: Enumeration and description have their own advantages, and it is necessary to decide which representation to adopt according to specific problems. It should be noted that enumeration is not suitable when there are many elements or infinite elements in a general collection.
Third, summary.
This lesson starts with examples, naturally and aptly leads to the concepts of set and set, illustrates the concept of set with examples, and then introduces the common representation methods of set, including enumeration and description. Subject: 1.2 Basic relationship between sets.
Teaching material analysis: Analogy of the size relation of real numbers introduces the inclusion and equality relation of sets.
Chapter two: The periodicity of trigonometric function in the design of mathematics teaching plan for senior one.
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 everything in the domain has 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)
(1) function (all of which are constants, and the period T=xx)
(2) Functions (all of which are constants with period T=xx)
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
Summary: Functions (all of which are constants, 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
The third part: Selected design of mathematics teaching plan for senior one 1. Guiding ideology and theoretical basis
Mathematics is an important subject to cultivate and develop people's thinking. Therefore, in teaching, students should not only "know what it is", but also "know why it is". Therefore, we should fully reveal the thinking process of acquiring knowledge and methods under the principle of taking students as the main body and teachers as the leading factor. Therefore, in this class, I focused on the constructivist teaching method of "creating problem situations-putting forward mathematical problems-trying to solve problems-verifying solutions", which mainly adopts the teaching method of combining observation, inspiration, analogy, guidance and inquiry. In teaching methods, multimedia-assisted teaching is adopted to visualize abstract problems and make teaching objectives more perfect.
Second, teaching material analysis
The inductive formula of trigonometric function is the content of the third section of Chapter 1 of Compulsory Mathematics 4 in the standard experimental textbook for senior high schools (People's Education Edition), and its main content is formulas (2) to (6) in the inductive formula of trigonometric function. This is the first lesson, and the teaching content is Formulas (2), (3) and (4). On the basis of the definition and inductive formula of trigonometric function of arbitrary angle (1) that students have mastered, the textbook requires students to discover the symmetrical relationship between arbitrary angle and terminal edge, the relationship between the coordinates of its intersection point and the unit circle, and then the relationship between its trigonometric function values, that is, to discover, master and apply trigonometric function inductive formulas (2), (3) and (4). At the same time, the textbooks are permeated with mathematical thinking methods such as conversion and conversion, which puts forward requirements for cultivating students to develop good study habits. Therefore, the content of this section occupies a very important position in trigonometric functions.
Thirdly, the analysis of learning situation.
The teaching object of this class is all the students of Grade One (X) in our school. The level of students in this class is below the average, but the students in this class have good study habits of being good at hands-on, so the teaching content of this class should be easily completed by using the discovery teaching method.
Fourth, teaching objectives.
(1) Basic knowledge Objective: Understand the discovery process of inductive formulas and master the inductive formulas of sine, cosine and tangent;
(2) Ability training goal: correctly use inductive formula to find sine, cosine and tangent at any angle, and evaluate and simplify simple trigonometric functions;
(3) Innovative quality goal: through the derivation and application of formulas, improve the ability of triangle constant deformation, infiltrate the mathematical thought of number reduction and combination, and improve students' ability to analyze and solve problems;
(4) Personality quality goal: through the study and application of inductive formulas, we can feel the general relationship between things, reveal the essential attributes of things by using mathematical thinking methods such as transformation, and cultivate students' historical materialism.
Key points and difficulties in teaching verbs (abbreviation of verb)
1, teaching focus: understand and master inductive formulas.
2. Teaching difficulties: correctly using inductive formula, finding trigonometric function value and simplifying formulas of trigonometric functions.
Six, teaching methods and expected effect analysis
Teaching design and teaching reflection of excellent teaching plans for senior high school mathematics
As teachers, we should not only teach students mathematical knowledge, but also teach students mathematical thinking methods. How to achieve this goal requires every teacher to study hard and explore seriously. Below I make the following analysis from three aspects: teaching method, learning method and expected effect.
1, teaching methods
Mathematics teaching is the teaching of mathematical thinking activities, not just the result of mathematical activities. The purpose of mathematics learning is not only to acquire mathematical knowledge, but also to train people's thinking ability and improve their thinking quality.
In the teaching process of this class, I take students as the theme, take discovery as the main line, try my best to infiltrate mathematical thinking methods such as analogy, transformation and combination of numbers and shapes, and adopt teaching modes such as questioning, inspiration and guidance, joint exploration and comprehensive application to give students "time" and "space", from easy to difficult, from special to general, and try my best to create a relaxed learning environment so that students can realize the happiness and success of learning.
Step 2 study law
"Modern illiterates are not illiterate people, but people who have not mastered learning methods." Many classroom teaching often adopts the practice of high starting point, large capacity and fast progress to teach students more knowledge points, but ignores that it takes time for students to absorb knowledge, thus undermining students' interest and enthusiasm in learning. How to make students digest knowledge to a certain extent and improve their learning enthusiasm is a problem that teachers must think about.
In the teaching process of this class, I guide students to think about problems, discuss problems together, solve problems simply, reproduce the exploration process and practice consolidation. Let students participate in the whole process of exploration, let students cooperate and communicate with each other after acquiring new knowledge and solving problems, and make them change from passive learning to active independent learning.
3, the expected effect
This lesson is expected to enable students to correctly understand the discovery and proof process of inductive formulas, master inductive formulas, and skillfully apply inductive formulas to understand some simple simplification problems.
The fourth part: The preliminary study of solid geometry in the design of high school mathematics teaching plan.
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) truncated 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.
Chapter five: The teaching objectives of the topic selection of senior one mathematics teaching plan design.
1. Make students master concepts, images and properties.
(1) What kind of function can be judged according to the definition? Understand the rationality of cardinality restriction and define the domain clearly.
(2) Under the guidance of basic properties, the image drawn by the list tracking method can be identified from both numbers and shapes.
(3) We can compare the sizes of some powers by using the properties of, and we can draw a shape image by using the new image.
2. By studying the essence of concept image, cultivate students' ability of observation, analysis and induction, and further understand the thinking method of combining numbers and shapes.
3. Through research, let students realize the application value of mathematics, stimulate students' interest in learning mathematics, and make students good at finding and solving problems from mathematics in real life.
Textbook analysis
(1) is based on students' systematic study of the concept of function and their basic mastery of the nature of function. It is one of the important basic elementary functions. As a common function, it is not only the first application of the concept and properties of functions, but also the basis for learning logarithmic functions in the future. At the same time, it is widely used in life and production practice, and should be studied emphatically.
(2) The teaching focus of this section is to grasp the image and essence on the basis of understanding the definition. The difficulty lies in distinguishing the change of function value when the radix is sum.
(3) It is a function that students are completely unfamiliar with. How to make a systematic theoretical study of such a function is an important problem for students. Therefore, it is important to get the corresponding conclusions from the research process, but it is more important to understand the methods of systematically studying a class of functions. Therefore, students should be specially allowed to experience research methods in teaching so that they can transfer to other functions.
Teaching suggestion
(1) According to the textbook, the definition of "about" is a formal definition, that is, the characteristics of analytic expressions must be what they are, and there can be no difference, for example, and so on.
(2) Understanding and understanding the restrictive conditions of cardinality is also an important part of understanding. If it is possible for students to study the restrictive requirements and indices of cardinality by themselves, the teacher will supplement or illustrate them with concrete examples, because understanding this condition is not only related to the understanding and classification of nature, but also related to the understanding of cardinality in logarithmic functions, so we must really understand its origin.
Regarding the drawing of images, although the method of drawing points by list is adopted, we should avoid blind list calculation before drawing points in specific teaching, and we should also avoid blindly connecting points into lines. The list should be listed in key places, and the main points should be connected in appropriate places. Therefore, before drawing points with list, we should briefly discuss the properties of functions. After we have a general understanding of the existing scope, general characteristics and changing trend of the image to be drawn, we can draw points with list calculation as a guide to get an image.