Free teaching plan for junior high school mathematics 1
mark
learning target
1. Knowing the concept of fraction, you can determine whether an algebraic expression is a fraction.
2. Fractions can be used to express the relationship between quantities in simple problems, and can explain the actual background or geometric significance of simple fractions.
3. Be able to analyze the situation that simple scores are meaningful and meaningless.
4. The value of the score will be obtained according to the known conditions.
Learning focus
The concept of score, grasp the conditions of meaningful score.
learning disorder
Conditions for the Existence and Meaninglessness of Fractions
teaching process
Preview navigation
First, create a situation:
Beijing-shanghai railway, with a total length of1462km, is the traffic artery running through the north and south in the eastern coastal area of China, and it is one of the busiest railway trunk lines in China. If the freight train speed is akm/h and the express train speed is twice the freight train speed, then:
1 How long does it take for the freight train to go from Beijing to Shanghai?
How long does the express train from Beijing to Shanghai take?
As we all know, the express train from Beijing to Shanghai takes less time than the freight train.
Look at the formula you just listed. What are their characteristics?
What are the similarities and differences between these formulas and fractions?
Cooperative investigation
First, the concept of exploration:
1, listing the following formulas:
1 The area of rectangular glass plate is 2m2. If the width is am, the length is
Xiaoli bought m bags of melon seeds with N yuan, so the price of each bag of melon seeds is RMB.
Every inner angle of a regular N-polygon is one degree.
Two cotton fields with an area of A hectare and B hectare produce M "and N" cotton respectively. These two cotton fields produce cotton on average per hectare.
2. When two numbers are divided, their quotient can be expressed in the form of component numbers. If letters are used to represent the numerator and denominator of fractions, what form can they be expressed?
3, thinking:
What are the characteristics of the above categories?
Through the discussion of the above practical problems, I learned to express the relationship between quantity in practical problems in the form of expressions, and felt the superiority and necessity of popularizing fractions to fractions.
The concept of score:
4. Summarize the problems that should be paid attention to in the concept of score.
The (1) fraction is the quotient of the division of two algebraic expressions, where the numerator is the divisor, the denominator is the divisor, and the fractional line acts as the divisor;
② The denominator of a fraction must contain letters, and the numerator may or may not contain letters, which is an important basis for distinguishing algebraic expressions;
(3) Like fractions, in any case, the denominator of a fraction cannot be 0, otherwise the fraction is meaningless. The denominator of the score is not zero, which is an implicit condition of this score and does not need to be specified.
Second, the case analysis:
Example 1: Try to explain the practical significance of the score.
Example 2: Find the score1a = 32A =-
Example 3: What value does the score 1 mean? 2 meaningful? The value of 3 is zero.
Third, the exhibition exchange:
1, which has _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _;
2, written as a fraction of _ _ _ _ _ _ _ _, and when m≦ is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
3. When x _ _ _ _ _, the score is meaningless; When x _ _ _ _ _, the value of the score is 1.
4. If the score is positive, then the value of X should be
A., b.c.d are arbitrary real numbers.
Fourth, refine the summary:
1, what is a score?
2. When does the score make sense? How to find the value of the score
Free teaching plan for junior high school mathematics II
Variables and functions
1. Think about the problem on page 72 in the book and summarize the relationship between variables.
2. Complete the thinking on page 73 of the book and understand the relationship between variables reflected in the graph.
3. Summarize the definition of function, and make clear the conditions that function definition must meet.
Induction: Generally speaking, if there are _ _ _ _ _ variables X and Y in a change process, And _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Supplementary summary:
Definition of 1 function:
This must be a process of change;
3 two variables; Every time a variable takes a value, another variable has a unique value corresponding to it.
Third, consolidate and expand:
Example 1: A car has 50L gasoline in its fuel tank. If you don't refuel, the fuel quantity of the fuel tank Y unit: L decreases with the increase of mileage X unit: km, and the average fuel consumption is 0. 1L/ km.
1 Write the functional relationship between y and x 。
2 refers to the range of the independent variable x.
How much gasoline is left in the fuel tank after driving for 200 kilometers?
Sublimation of classroom detection knowledge
1. Determine whether the following variables are functional:
When the width of 1 rectangle is constant, its length and area;
2. The length and area of the base of the isosceles triangle;
3 a person's age and height;
2. Write the analytical expressions of the following functions.
1 A rectangular box with a height of 3cm and a square bottom. The cuboid has a volume of ycm3 and a side length of the bottom surface of xcm. Write a formula to express the functional relationship between y and X.
When the car refuels, the flow rate of the refueling gun is 10L/min.
(1) If there is 5 L oil in the fuel tank before refueling, write the functional relationship between the amount of oil in the fuel tank yL and the refueling time xmin when refueling;
(2) If the fuel tank is empty when refueling, write the functional relationship between the amount of fuel in the fuel tank yL and the refueling time xmin.
The monthly interest rate of current deposit is 0. 16%, and the deposit principal is 10000 yuan. According to the national regulations, when withdrawing money, the interest part should pay 20% interest tax. Find the relationship between the principal and interest of this demand deposit after deducting interest tax and the number of months X.
As shown in the figure, each figure is a pattern composed of several pots of flowers, each side includes two vertices, each side has N pots of flowers, and the total number of flowerpots in each pattern is S. Find the relationship between S and N. 。
After-school homework knowledge feedback
1, P74-75: 1, 2 questions
Junior high school mathematics free teaching plan 3
Key points in teaching difficult points of function images;
1. Know different representations of functions and know their advantages and disadvantages.
2. The appropriate method can be selected according to the specific situation.
Teaching difficulties:
Application of function representation.
Self-review knowledge preparation
Last class, I saw or used list grids, formulas and pictures to express some functions. These three methods of expressing functions are called list method, analytical method and image method respectively.
Then, please think about it. From the previous examples, what do you think are the advantages and disadvantages of the three expressions of functions? How to choose the appropriate representation when encountering specific problems?
Self-inquiry knowledge application
The water level in the reservoir has been rising for the past five hours. The table below records the water level in these five hours.
T/ hour 0 1 2 3 4 5 …
y/m 10 10.0 5 10. 10 10. 15 10.20 10.25…
1. Draw the points corresponding to the data in the table in the plane rectangular coordinate system. Are these points on the same straight line? From this, can you find any law of water level change?
2. Is the water level height y a function of t? If so, try to write an analytical formula that matches the data in the table and draw an image of this function. Can this function express the law of water level change?
It is estimated that this rising trend will continue for 2 hours. How many meters is the water level expected to reach in 2 hours?
Conclusion: These three methods of expressing functions have their own advantages and disadvantages.
1. express the functional relationship by analytical method.
Advantages: simple and clear. All the dependencies between two variables can be clearly seen from the analytical formula, which is suitable for theoretical analysis and deduction calculation.
Disadvantages: When finding the corresponding value, sometimes complicated calculations are needed.
2. Use a list to represent the functional relationship.
Advantages: For each value of the independent variable in the table, you can directly find the function value without calculation, which is very convenient to query.
Disadvantages: It is impossible to list all the independent variables of the function and their corresponding values in the table, and the corresponding laws between variables cannot be seen from the table.
3. Image representation of functional relationship.
Advantages: the image is intuitive, which can vividly reflect the changing trend and some properties of the function relationship, and visualize the abstract function concept.
Disadvantages: It is often difficult to find the exact value of the corresponding function from the value of the independent variable.
The three basic representations of functions have their own advantages and disadvantages, and different methods should be adopted flexibly according to different problems and needs. In mathematics or other scientific research and application, these three methods are sometimes combined, that is, from the known resolution function, list the tables of independent variables and corresponding function values, and then draw their images.
Sublimation of classroom detection knowledge
The speed of car A is 20m/s, and the speed of car B is 25m/s. Now car A is 500m ahead of car B, and the distance between the two cars is y m after x seconds. Find the analytical expression of the function in which y varies with x0≤x≤ 100, and draw the function image.
After-school homework knowledge feedback
Textbook P83, Question 12.
My harvest
I want to talk to the teacher.
1. Junior high school math teachers must read.
2. What are the instructional designs of junior high school math teachers?
3. Three teaching stories of junior high school mathematics education
4. What are the teaching cases of junior high school mathematics?
5. What are the cases of junior high school mathematics teaching design?