The first volume of eighth grade mathematics function courseware 1 teaching purpose;
1. Understand the meaning of constants and variables, and be able to distinguish between constants and variables in examples;
2. Understand the meaning of independent variables and functions, list examples of functions, and write simple functional relationships;
3. Cultivate students' abilities of observation, analysis, abstraction and generalization;
4. Educate students with the dialectical materialism viewpoint of mutual connection, absolute and relative, and movement change, with the education of patriotism, love for the party and the people, and with the math lesson plan-function.
Teaching straightness:
The formation process of function concept.
Teaching difficulties:
Understand the concept of function.
Teaching AIDS:
Multimedia.
Teaching process:
First, create a situation
First of all, please look at a set of scenes: (microcomputer plays video of flood fighting this summer) to arouse students' memories of the flood this summer and infiltrate the education of patriotism, love for the party and love for the people.
Second, form a concept.
(A) the formation process of the concepts of variables and constants
1. Examples and induction
Quote 1: Water level map of Shashi in July and August this summer (microcomputer map)
Students observe the change of water level with time and draw "variables".
Example 2: The car runs at a constant speed on the highway (instructed by microcomputer)
Students observe the process of a car driving at a constant speed and deepen their understanding of variables.
Knowledge leads to "invariability".
Q: A quantity is changing, specifically what is it changing? What remains the same? The microcomputer shows that the car below is driving at a constant speed, and the S value above changes with the change of T value ...
Guide students to observe and find that it is the change of numerical value and the invariance of quantity.
The definitions of inductive variables and constants are merged.
2. Analyze concepts
Constants and variables must exist in a changing process. Judging whether a quantity is a constant or a variable requires two aspects: ① whether it is in the process of change, and ② whether it is implanted in the process of change.
3. Consolidate the concept
Exercise 1:
1. Throwing a stone into a calm lake will form a series of concentric circles (indicated by a microcomputer) centered on the landing point. (1) What are the variables during this change? ② If the area is S and the radius is R, what is the relationship between S and R? ; Is π a constant or a variable? ③ If the circumference is C and the radius is R, what is the relationship between C and R?
2. (See exercise on page 92 of the textbook 1)
After the students answered, they pointed out that constants and variables are not absolute, but a changing process.
(B) the formation process of the concepts of independent variables and functions
1. Examples and induction
(One screen of microcomputer displays two cited examples) Students observe the two changing processes of cited examples 1 and 2 again, and look for the similarities of * * * *: ① one changing process, ② two variables, ③ one quantity changes with the other.
If two quantities satisfy the above three conditions, they are said to have a functional relationship. (Draw out the topic and write it on the blackboard)
Question: The third item above describes the relationship between two variables in the image. What exactly does that mean?
Illustration of cited example 2: (instructed by microcomputer)
Question: In S = 30t, when T = 0.5, does S have a corresponding value? How many/much?
Repeatedly ask: When t = l, 1.5, 2, 3 ...?
Guide students to observe and find that for each value of variable T, variable S has a unique value corresponding to it. So the relationship between two variables can be described as: for each value of one variable, the other variable has a unique value corresponding to it. That is, a corresponding relationship. (presented by microcomputer)
When S = 30t, S and T have this correspondence, that is, T is an independent variable and S is a function of T ... which leads to "independent variable" and "function".
Summarize the definitions of independent variables and functions and write them on the blackboard.
2. Analyze concepts
To understand the concept of function, we should grasp three points: ① a changing process, ② two variables and ③ a corresponding relationship. Judging whether two quantities have a functional relationship is also based on these three points.
3. Consolidate the concept
Exercise 2:
L) The temperature in a certain place on a certain day is as shown in the figure (microcomputer diagram). Is there a functional relationship between temperature and time?
After the students answer, they point out that the functional relationship here is given by the image.
2) The number of tourists received by a tourism company in Yichang in recent years is shown in the table: (microcomputer shows the table) Is there a functional relationship between the number of tourists and time? After the students answer, they point out that the functional relationship here is given in tables.
3) in s =? Is there a functional relationship between s and r in d? C = z π r, what about C and R? After the students answered, they pointed out that the functional relationship here is composed of mathematical expressions.
4) * * * relationship between teachers and students and examples of enumeration functions.
Third, the example demonstration
The microcomputer gives an example of 1, demonstrating the process of enclosing the fence into a rectangle. )
Guidance: 1. The length of the fence is equal to the perimeter of the rectangle; 2. The relationship between S and 1, that is, the algebraic expression of 1 represents S; 3. To represent the area of a rectangle, we must first represent the length of a group of adjacent sides of the rectangle.
The process of solving problems is abbreviated.
Variant exercise:
Form a rectangle with a 60m fence, so that one side of the rectangle is against the wall and the other three sides are surrounded by fences (indicated by microcomputer).
1. Write the rectangular area s(m? ) and the length l (m) parallel to one side of the wall;
2. Write the rectangular area s(m? ) and the length l(m) perpendicular to the wall. The constants and variables, functions and independent variables in the two formulas are pointed out.
Fourth, feedback exercises (microcomputer)
Verb (abbreviation of verb) abstract
1. Four concepts: constant and variable, function and independent variable.
2. Two notes: ① Judging constants and variables depends on two aspects. ② Understand the concept of function and grasp three points.
Distribution of intransitive verbs
1. Required question: textbook page 95, exercise 1, 2.
2. Think about the problem:
① In y = 2x+L, is y a function of x? ? Is y a function of x?
② In the cited example 2, S = 30t, and T can take different values, but T can't take any value?
Description of teaching plan design
According to the characteristics of this section-abstract and difficult to understand.
I designed this course according to the following ideas: adhere to the purpose of taking observation as the starting point, taking problems as the main line and cultivating ability as the core; Follow the teaching principles of teacher-oriented, student-oriented and training-oriented; Follow the cognitive rules from special to general, from concrete to abstract, from shallow to deep, from easy to difficult. The teaching process highlights the following ideas:
First, the real scene reappears and is fascinating.
After class, a group of touching flood fighting scenes will be played first, which will gather students' scattered thoughts at once, adjust students' emotions and classroom atmosphere to the best state, and create a good teaching atmosphere for the development of new courses. Because it is true and close to students' life, it evokes their memories of the catastrophic flood this summer, and teachers have organically infiltrated the education of patriotism and love for the party and the people.
Second, highlight the process and stick to the main points.
The formation process of function concept is the focus of this section, so this section highlights the teaching of concept formation process and divides the process into three stages: induction, analysis and consolidation. In the first stage, make students familiar with vivid examples, guide them to observe, analyze and then summarize. In the second stage, help students master the essential characteristics of concepts and ask questions to attract attention. In the third stage, guide students to use concepts and give timely feedback. At the same time, in the process of concept formation, cultivate students' ability of observation, analysis, abstraction and generalization. When guiding students to look at problems from the viewpoint of movement change, we should infiltrate the education of dialectical materialism into students.
Third, the dynamic appearance, change difficult to easy.
Conventional teaching methods can not highlight the abstraction of function concepts. In order to remove the obstacles in students' thinking, this section gives full play to the characteristics of multimedia, such as sound, image and animation, visualizes abstract problems, makes static methods dynamic, reveals the essence of function concepts intuitively and profoundly, and breaks through the difficulties in this section. At the same time, the vivid, colorful and dynamic pictures in teaching activities not only open the door of students' thinking, but also open the window of their hearts, so that they can actively, easily and happily acquire new knowledge in the process of appreciation and enjoyment.
Fourthly, examples show that multi-party infiltration
In order to make the abstract concept of function concrete and easy to understand, this section lists a large number of examples from life and other disciplines, which cultivates students' divergent thinking, strengthens the infiltration between disciplines and the connection between knowledge and problems, and also enhances students' consciousness of learning mathematics.
Teaching objectives of eighth grade mathematical function courseware, volume 1, article 2
1. Knowledge and skills
If we can apply the learned function knowledge to real life to solve problems, we will establish a function "model".
2. Process and method
Explore the application of functions once and develop abstract thinking.
3. Emotions, attitudes and values
Cultivate variables and their corresponding relationships, form a good function view, and experience the application value of linear functions.
Key points, difficulties and key points
1. Emphasis: the application of linear function.
2. Difficulties: the application of linear functions.
3. Key: Starting with the combination of numbers and shapes, improve the applied thinking.
teaching method
By adopting the teaching method of "combining teaching with practice", students are gradually familiar with the application of linear functions.
teaching process
First, click on the example to apply what you have learned.
Example 5 After Xiao Fang started at the speed of m/min, he first accelerated for 5 minutes, increased the speed by 20 meters /min, and ran at a constant speed of 10 minute. Try to write the functional relationship between her running speed y (unit: m/min) and running time x (unit: min) during this period, and draw the functional image.
y=
There are 300 tons of chemical fertilizers in 6A city and 300 tons in B city. Now we have to transport all these fertilizers to C and D townships. The cost of transporting chemical fertilizer from City A to Township C and Township D is 20 yuan and 25 yuan respectively. The cost of transporting chemical fertilizer from B to C and D townships is per ton 15 yuan and 24 yuan respectively. Now township C needs 240 tons of chemical fertilizer, and township D needs 260 tons of chemical fertilizer. How to transport the lowest total freight?
Solution: If the total freight is Y yuan, the amount of fertilizer transported from City A to Township C is X tons, and the amount of fertilizer transported to Township D is (-x) tons. The amount of chemical fertilizer transported from City B to Township C and Township D is (240-x) tons and (60+x) tons respectively. The relationship between y and x is: Y = 20x+25 (-x)+
As can be seen from the figure, when x=0, y has a minimum value of 10040, so it takes 0 tons to transport from city A to township C and 0 tons to township D; 240 tons will be transported from B to C and 60 tons to D. At this time, the total freight is the least, and the lowest total freight is 10040 yuan.
Capacity expansion: If there are 300 tons of chemical fertilizer in City A and 300 tons of chemical fertilizer in City B, other conditions remain unchanged, how should it be shipped?
Second, in-class practice, consolidate and deepen
Textbook P 1 19 exercises.
Third, the classroom, develop potential
Students are required to behave in class.
Fourth, homework, special breakthroughs
Textbook P 120 exercise 14.2 question 9, 10,1.
blackboard-writing design
14.2.2 linear function (4)
1 and an application example of linear function;
Exercise: