Junior high school mathematics teaching case 1
Goal 1 Contact specific things in life. Through observation and hands-on operation, we can initially understand the symmetry phenomenon in life, understand the basic characteristics of axisymmetric graphics, and know and make some simple axisymmetric graphics.
2. In the process of understanding, making and appreciating axisymmetric graphics, feel the symmetrical beauty of object graphics and stimulate students' positive feelings about mathematics learning.
focus
It is difficult to understand the basic characteristics of axisymmetric graphics.
Training/teaching AIDS
Prepare scissors, paper (including parallelogram and letter N S), teaching wall chart and ruler.
teaching
way
Means of observation, comparison, discussion and hands-on operation.
teaching
Process 1. New lesson
1. The teacher took a hinge on the door frame to fix the door, and asked the students to observe whether it was symmetrical.
2. Show the teaching wall chart: Tiananmen Square, plane and trophy pictures.
Further abstract the physical picture into a plane figure and ask the students what they found after folding it in half.
Health: The two sides can completely overlap after being folded in half.
Division; A figure that can completely overlap after being folded in half is an axisymmetric figure. The straight line where the crease lies is called the symmetry axis.
First, the teacher demonstrates, let the students know the symmetry axis of Tiananmen Gate, and then let the students find out where the symmetry axis of the plane map and the trophy map is.
3. Exercise: (Show the small blackboard)
(1)P57 "Try it"
Determine which figures are axisymmetric. Try to draw the symmetry axis.
It is estimated that students will regard the parallelogram as an axisymmetric figure, and let two students fold it in half with parallelogram paper first, and then go to the podium to see if the two parts are completely coincident after folding. Draw a conclusion from this; Parallelogram is not an axisymmetric figure.
(2) Cut an axisymmetric figure with scissors and paper.
teaching
Process 2. practice
1. Show the flip chart: (p58 "Think and do" question 1)
Determine which figures are axisymmetric.
Student: Harp diagram, automobile diagram, five-pointed star diagram, iron anchor diagram, science and technology logo diagram, China Agricultural Bank logo diagram.
Teacher: Why not the key map and the bauhinia map?
Health: Because the two parts do not completely overlap after being folded in half.
2. Read p58 "Thinking and Action" Question 2
Determine which English letters are axisymmetric figures.
Students: A, C, T, M, X (some students may not choose C, while others may choose N, S, Z).
Teacher: students who didn't choose C, except vertical folding, look at horizontal folding and oblique folding. Have you tried? Considering that N, S and Z are axisymmetric figures, I asked two students to go to the podium and fold the paper representing the letters N and S in half to see if the two parts overlap completely after folding.
Students will find that the two parts are not completely coincident after the test.
When the teacher crosses the letter N, it becomes the letter Z. Similarly, the two parts will not completely coincide.
Junior high school mathematics teaching case 2
The teaching goal is 1. The "matching problem" will be solved by the column equation;
2. Master the general steps of solving practical problems by using equations;
3. Solve practical problems through column equations and experience the idea of modeling.
Teaching focuses on establishing models to solve practical problems.
A general method to establish a model to solve practical problems in teaching difficulties.
Learning situation analysis 1, I have learned the solution of linear equations before, and I can simply solve practical problems with linear equations.
2. Cultivate students' ability to analyze and solve problems and logical thinking.
Learning methods guide self-study and mutual assistance.
Teaching and learning process
Teaching content, teachers' activities, students' activities, effect prediction (possible problems), remedial measures, and revision opinions.
I. Review and review
Question 1: What steps were involved in the previous process of solving application problems through column equations?
1. Examination: Examining the questions and analyzing the quantitative relations in the questions;
2. Assumption: Set an appropriate unknown to represent the unknown;
3. Column: list the equations according to the quantitative relationship in the topic;
4. Solution: Solve this equation;
5. Answer: Test and answer.
Second, the application and exploration
Question 2: Apply retrospective steps to solve the following problems.
There are 22 workers in a workshop, and each person can produce 1 200 screws or 2,000 nuts every day. 1 The screw requires two nuts. How many workers should be arranged to produce screws and nuts every day to make the screws and nuts just match?
Third, classroom exercises.
1: A set of instruments consists of a part A and three parts B.. The 40 A part or the 240 B part can be made of 1 m3 steel. How many steel parts do you need to make this instrument now, how many steel parts do you need to make A and B, and how many sets do you need to make this instrument?
2. Before the Mid-Autumn Festival, the pastry factory should make a batch of boxed moon cakes, each containing 2 large moon cakes and 4 small moon cakes. It takes 0.05kg flour to make 1 big moon cake and 0.02kg flour to make 1 small moon cake. At present, there are 4500 kilograms of flour. How much flour does it take to make two kinds of moon cakes to make the most boxed moon cakes?
Fourth, summary and induction.
Question 4: How many steps are there in the basic process of solving practical problems with linear equations of one variable? What is the difference?
Verb (abbreviation for verb) homework after class
Exercise 3.4, questions 2, 3 and 7 on page 106 of the textbook; 1, the teacher helps students master the steps of solving application problems by using equations by examining questions.
2, the teacher demonstration, and patrol the students' independent completion, guide students to analyze and solve problems.
3. Teachers show exercises, guide students to analyze and solve problems, and patrol.
4. The teacher asks questions and asks the students to make a summary. 1. Students recall and answer independently.
2. Students should read the courseware first, think independently first, and then cooperate to solve problems.
3. Students should read the courseware first and solve the problems.
Students independently summarize what they have learned in this class.
Can't solve the problem
The teacher showed the solution process.
The third case of junior high school mathematics teaching
algebraic expression
Teaching objectives
1, so that students can know the meaning of numbers expressed by letters and can say the quantitative relationship expressed by an algebraic expression;
2. Initially cultivate students' ability of observation, analysis and abstract thinking;
3. Through the teaching of this course, educate students to study hard for building socialism with China characteristics?
Third, the focus and difficulty of teaching
Key point: use letters to express the meaning of numbers?
Difficulties: Correctly state the quantitative relationship expressed by algebraic expressions.
Fourth, teaching methods.
Modern classroom teaching means
Verb (abbreviation of verb) teaching method
heuristic teaching
Sixth, the teaching process.
(1) Introduction
Mathematics is a widely used subject, and it is an essential basic knowledge and tool for studying and studying modern science and technology? Learning mathematics well plays an important role in building China into a powerful socialist country with China characteristics?
Middle school math class starts with algebra? Besides algebra, students will also study plane geometry, solid geometry, analytic geometry and so on?
Learning algebra, like learning other subjects, requires a clear learning purpose and a correct learning attitude? Without persistent efforts and indomitable spirit to overcome difficulties, it is impossible to learn algebra well?
When learning algebra, we should pay attention to the connection and difference between algebra and elementary school mathematics, and consciously compare it with arithmetic: which are the same or similar to elementary school mathematics and which are different in a strict sense, and gradually clarify the characteristics of algebra?
An important feature of algebra is that numbers are represented by letters. Let's start our junior high school algebra study by using letters to represent numbers.
(A), from the original cognitive structure of students to ask questions
1. How many arithmetic laws did we learn in primary school? What are they? What if they can be represented by letters?
Through inspiration and induction, teachers and students finally came up with five arithmetic rules for expressing numbers by letters. )
(1) additive commutative law a+b = b+a;
(2) Multiplicative commutative law A? b=b？ a；
(3) Additive associative law (A+B)+C = A+(B+C);
(4) multiplicative associative law (ab) c = a (BC);
(5) Multiplication and distribution law a(b+c)=ab+ac?
Point out: (1) "? "can also be written as"? " No or omitted, but multiplied by the number, generally still use "?" ;
(2) In the above arithmetic laws, the letters A, B and C are all letters representing numbers, representing all the numbers we have learned in the past?
2. (Projection) The distance from A to B is 15km, which takes 3 hours to walk, 0 hours to ride a bike 1 hour and 0 hours to drive. 25 hours, what are the speeds of walking, cycling and riding?
3. if s represents distance and t represents time, Represents speed, can it be represented by s and t? Really?
4. (Projection) If the side length of a square is one centimeter, what is the circumference of the square? What is the area?
(If the circumference is expressed by I cm, I = 4 cm; If the area is expressed in S square centimeters, then S=a2 square centimeters)?
At this point, the teacher should point out: (1) using letters to represent numbers can simply express the relationship between numbers or numbers; (2) In formulas and, using letters to represent numbers will also bring convenience to the operation; (3) A, as shown in Figure 5 above, 15? 3, 4a, a+b, a2 and so on are all called algebraic expressions?
So what exactly is algebra? What is the meaning of algebra? This is what we are going to learn in this class. Third, teach new lessons.
1, algebraic expression
A single number or a single letter and a formula formed by connecting numbers or letters representing numbers with operation symbols are called algebraic expressions?
To learn algebra, we must first learn to use algebraic expressions to express quantitative relations and clarify algebraic meanings?
Step 2 give an example
Example 1 Fill in the blanks:
(1) each Bao Shu has 12 volumes, and n Bao Shu has _ _ _ _ _ _ _ _ _;
(2) When the temperature drops from t℃ to 2℃, it is _ _ _ _ _ _ _ _℃
(3) The volume of a cube with a side length of one centimeter is _ _ _ cubic centimeter;
(4) The output increased from m kg 10% to _ _ _ _ _ kg?
(This example is given by the projection. Let's answer it. )
Solution: (1)12n; (2)(t-2)； (3)a3； (4)( 1+ 10%)m？
Example 2, tell the meaning of the following algebraic expressions:
( 1)2a+3(2)2(a+3)； (3) (4)a- (5)a2+b2 (6)(a+b) 2
Solution: (1)2a+3 means the sum of 2a and 3; (2)2(a+3) refers to the product of 2 and (a+3);
(3) means the quotient of c divided by ab; (4) The meaning of A-is the difference of A minus;
(5) The meaning of A2+B2 is the sum of squares of A and B; (6) Is the meaning of (A+B) 2 the square of the sum of A and B?
Note: (1) This question needs to be demonstrated by the teacher;
(2) For the meaning of algebraic expression, there is no uniform provision for the specific expression, and the starting point is that simplicity does not cause misunderstanding? For example, the term (1) can also be said to be "2 times a plus 3" or "the sum of 2 times a plus 3" and so on?
Example 3, expressed by algebraic expression:
(1) the sum of m and n divided by the quotient of 10;
(2) the square of the difference between m and 5n;
(3) the sum of 2 times of x and y;
(4)? The product of the cube of t and three times of t?
Analysis: We need to pay attention to the algebraic expression of the quantitative relationship described by language: ① Make clear the usage of brackets in the algebraic expression; When multiplying letters and numbers, it is customary to write the numbers before the letters?
Solution: (1); (2)(m-5n)2(3)2x+y； (4)3t？ 3?
(4) Classroom exercises
1, fill in the blank: (projection)
(1)n boxes of apples weigh p kilograms, and each box weighs _ _ _ _ _ kilograms;
(2) A is high 1 cm, and B is 2 cm shorter than A, so B is _ _ _ _ cm higher;
(3) The area of a triangle with a base a and a height h is _ _ _ _ _ _;
(4) The number of students in the school is X, of which 48% are girls, so the number of girls is _ _ _ _ _ _ _ _ _.
2. Tell the meaning of the following algebraic expression: (projection)
( 1)2a-3c； (2) ; (3)a b+ 1； (4)a2-b2？
3. Expressed by algebraic expression: (projection)
(1) the sum of x and y; (2) the difference between the square of X and the cube of Y;
(3) The sum of 60% of A and 2 times of B; (4) The sum of the quotients of A divided by 2 and B divided by 3?
(5) Teacher-student summary
First, ask the following questions:
1. What did you learn in this lesson? 2? What does it mean to use letters to represent numbers?
3. What is algebraic expression?
On the basis of students' answers to the above questions, the teacher pointed out: ① Algebraic formulas are actually arithmetic formulas, and letters can also be operated like numbers; (2) If there are units in algebraic expressions and operation results, should parentheses be used correctly?
Seven, practice design
1, the length of three sides of a triangle, a, b, c, find the perimeter of this triangle?
Zhang Qiang is three years older than Wang Hua. When Zhang Qiang was one year old, how old was Wang Hua?
The speed of an airplane is 40 times that of a car, and the speed of a bicycle is the speed of a car. If the speed is? Km/h, then, what are the speeds of airplanes and bicycles?
The price of one kilogram of rice is 6 yuan. /kloc-how much is 0/kg rice?
The radius of a circle is r cm. What is its area?
6. Use algebraic expressions:
(1) The perimeter of a rectangle with a length of a and a width of b meters;
(2) The perimeter of a rectangle with a width of b meters and a length twice as wide;
(3) The length is one meter and the width is the circumference of a long rectangle;
(4) What is the circumference of a rectangle with a width of b meters and a length of more than 2 meters?
Eight, blackboard design
? 3. What does the letter1stand for?
(1) Knowledge review (3) Example analysis (5) Class summary
Example 1, example 2
(2) Observation and discovery (4) Design of classroom exercises.
Nine, teaching postscript
1. Most of the questions encountered in this course should be answered by students first, but on the question of "the meaning of algebra", it should be emphasized that students must strictly follow the requirements of the teacher's demonstration. For example, "a-" means "the difference between A and A", not "the difference between A and A"?
Because this is the first lesson of middle school mathematics, an introduction is designed to educate students' learning objectives, learning attitudes and learning methods? In practical teaching, students can master it flexibly according to their own actual situation, and the principle is to encourage more.
Guess you like:
1.3 Excellent cases of mathematics teaching in primary schools
2. Successful teaching cases
3. What are the physics teaching cases in Senior Two?
4. What are the math teaching plans for the seventh grade in junior high school?
5. What are the templates for junior high school math teaching plans?