Knowledge and skills:
1, understand the concept of quadratic equation in one variable.
2. Master the general form of quadratic equation with one variable and correctly understand quadratic coefficient, linear coefficient and constant term.
Process and method:
Guide students to analyze the quantitative relationship in practical problems, organize students to discuss, and let students abstract the concept of a quadratic equation by analogy.
Emotional attitudes and values:
1. Cultivate students' awareness of actively exploring knowledge, autonomous learning and cooperative communication.
2. Stimulate students' interest in learning mathematics, experience the happiness of learning mathematics, and cultivate the consciousness of using mathematics.
Analysis of learning situation
1, the students in the teaching class have a poor foundation, so we should give enough time to think in teaching and beware of cramming teaching.
2. The students in this class have formed a good spirit and atmosphere of cooperation in their usual training, which can give full play to the advantages of cooperation and pay attention to the effectiveness of classroom teaching.
This class is a self-study class. Usually, it knows students better. When solving specific problems, we can give consideration to students with different abilities and fully mobilize their enthusiasm. In the design of exercises, we should adopt the method of hierarchical design according to the differences of students.
Important and difficult
Emphasis: the concept and general form of quadratic equation with one variable.
Difficulties: 1, the transformation process from practical problems to mathematical problems.
2, correctly identify the "term" and "coefficient" in the general formula.
teaching process
Activity 1 teaching content 1. Create situations and ask questions.
Question: 1 Basketball League, every game must be divided. Each team wins 1 with 2 points, loses 1 with 1 points, and a team wins 16 points in 10 games. So what are the winning and losing competitions of this team? Can you solve this problem with linear equations?
Teacher-student activities: Students answer: Yes. Suppose X wins and (10-x) loses. According to the meaning of the question, 2x+( 10-x)= 16.
X=6, you win 6 games and lose 4 games.
The teacher asked: can you set two unknowns and list two equations reflecting the meaning of the problem according to the equal relationship between the two problems?
Teacher-student activities: Students answer: Yes. Suppose you win x games and lose y games. According to the meaning of the question, x+y = 10, 2x+y = 16.
Teacher's summary: Like this, every equation contains two unknowns (X and Y) and the equation with the unknown term degree of 1 is called binary linear equations.
Design intention: Introduce the content of this lesson with the introduced questions, first do a linear equation to solve this problem, change the thinking, and then do a linear equation with two variables to pave the way for the later teaching.
Question 2: Can you find the relationship between the two equations by comparing them?
Teacher-student activities: Through the analysis of practical problems, we know that the two X's and Y's in the equation are the winning and losing fields of this team.
Numbers, they must satisfy these two equations at the same time, so that they can be written together.
It forms a system of equations. In this system of equations, each equation contains two unknowns (x and y), and the number of terms containing the unknowns is 1. Systems like this are called binary linear equations.
Design intention: Starting from reality, the concept of equation is introduced to adapt to students' cognitive process.
Question 3: Asking
What are the values of x and y that satisfy equation ① and conform to the actual meaning of the problem? Fill them in the form.
x
y
Which values of x and y in the above table still satisfy equation ②?
Students work together in groups.
The teacher concluded: Generally speaking, the values of two unknowns that make the values on both sides of the binary linear equation equal are called the solutions of the binary linear equation. The common * * * solution of two equations of general binary linear equations is called the solution of binary linear equations.
Design intention: To learn the solution of two-dimensional linear equations and two-dimensional linear equations by analogy with the solution of one-dimensional linear equations.
2. Apply new knowledge and improve your ability
Example 1 Circle a 20-meter-long iron wire into a rectangle. If one side is xm, its adjacent side is ym.
(1) the relationship between x and y;
(2) When x= 15, the value of y; .
(3) When y= 12, the value of X.
Teacher-student activities: discuss in groups, and then send a representative from each group to the blackboard to finish.
Design intention: With the help of this topic, give full play to the spirit of students' cooperative inquiry, and further understand the significance of binary linear equation and the solution of binary linear equation through comparison.
3. Deepen understanding, consolidate and improve
Exercise: A boat goes downstream with a speed of 20km/h and goes upstream with a speed of16km/h. Find the speed of the ship in still water and the velocity of the water.
Teacher-student activities: group discussion. One group is solved by one-dimensional linear equations, and the other group tries to establish equations (no need to solve), which lays the foundation for solving binary linear equations. Then each group sends a representative to the blackboard to finish.
Design intention: Remind and guide students to analyze the two unknown relations of the problem first, and try to find out two equal relations and establish equations by combining the meaning of the problem. It is more intuitive to set two unknowns directly and set equations and equations.
Inductive summary
Teacher-student activities: * * Review the learning process of this lesson and answer the following questions.
1. Concepts of binary linear equations and binary linear equations
2. The concept of binary linear equation and its solution.
3. What thinking methods are used in the process of inquiry?
4. What else have you gained?
Design intention: through the design of this activity, improve students' transfer ability and application consciousness of what they have learned; Cultivate students' ability of self-induction.
Homework
Page 90 of the textbook, questions 3 and 4
Why aren't the numbers in the first section of chapter 2 in the first volume of eighth grade mathematics enough? Why is the number of editions of Beijing Normal University insufficient?
I. teaching material analysis
"How many numbers are not enough" is selected from the second section of the third chapter of the compulsory education curriculum standard experimental textbook "Mathematics" by Shandong Education Press. The expansion of rational number to real number is the last stage of the expansion of number system in the third period. Most problems in middle school are carried out in the range of real numbers, and real numbers are also the basis of subsequent content learning. Based on the knowledge of rational number and Pythagorean theorem, this chapter extends the logarithmic system for the second time, introduces irrational number, and extends the rational number to the real number range, so that students can have a deeper understanding of logarithm.
Second, student analysis
In the last semester of the sixth grade, students have experienced the first expansion of the number system-that is, introducing negative numbers on the basis of the knowledge of non-negative rational numbers in primary schools, expanding the understanding of logarithm to the scope of rational numbers and learning the operation of rational numbers. At the same time, with the growth of age, students' thinking level is also constantly improving. They are able to accept greater challenges from the inside of mathematics knowledge and conduct in-depth mathematical thinking and exploration, which have laid the foundation for the study of this section.
Third, the teaching objectives
1. Let students feel the actual background of irrational numbers and the necessity of introducing them through jigsaw puzzles.
2, can judge whether a given number is rational, and can tell the reason.
3. Encourage students to actively participate in teaching activities, guide students to fully communicate and explore, and cultivate students' practical ability and cooperative spirit.
Four, the focus and difficulty of teaching
Key points: 1. Let students experience the discovery process of irrational numbers and perceive that there are indeed numbers different from rational numbers in life.
2, will judge whether a number is reasonable.
Difficulties: 1, the hands-on operation process of combining two squares with side length of 1 into a big square.
2. Judge whether a number is rational.
Teaching process of verbs (abbreviation of verb)
(A) creating problem situations and introducing new courses
Teacher: Students, we learned non-negative numbers in primary school and negative numbers in junior one, which is to expand positive numbers and zeros into rational numbers. Can rational numbers meet the needs of real life?
Introduce the topic by reviewing the numbers you have learned.
(2) teaching new courses
1, activity 1:
Teacher: Students, please work in groups of four. Cut two squares with a side length of 1 and put them together with your own scissors to get a big square as much as possible.
Through this kind of hands-on activity, students' enthusiasm for participation can be mobilized, students can fully communicate and explore, and then students' cutting and spelling methods can be displayed.
Teacher: Let each group talk about their own cutting and spelling methods.
1 group speaker: Cut two small squares diagonally to get four congruent isosceles right-angled triangles, and then make a big square.
Students' starting point analysis Grade eight students have realized that numbers are not enough in the process of learning rational numbers. As soon as they learned Pythagorean Theorem, they felt it necessary to study new numbers. On this basis, students can actively participate in the discussion in the course of "Need-Inquiry-Discovery-Demonstration", boldly express their views and opinions, and find problems from very intuitive operation. Realize the development of numbers. Second, the task analysis of teaching materials "How many are not enough" is the first section of the second chapter "Real numbers" in the eighth grade of the experimental teaching materials of Beijing Normal University Edition. This section has been completed in two classes. In 1 class, students can feel the development of numbers and establish the concept of irrational numbers. In the second class, they can feel that irrational numbers are infinite acyclic decimals with the help of calculators. Will judge that a number is irrational. This is 1 class. Students will feel the actual background and the necessity of introducing irrational numbers through operations, estimation, analysis and other activities in a specific background, and can judge whether a number is irrational and give reasons.
The teaching goal of the teaching design of "How long is the classroom", the first volume of the second grade mathematics of Beijing Normal University;
1, experienced the process of measuring the length of the classroom with different tools.
2. Accumulate the experience of learning centimeters and meters in mathematics activities, and initially cultivate students' measurement consciousness.
3. Learn cooperative learning initially and experience the fun of success in measurement activities.
Difficulties and emphases in teaching:
1, experienced the process of measuring the length of the classroom with different tools.
2. Accumulate the experience of learning centimeters and meters in mathematics activities, and initially cultivate students' measurement consciousness.
Training points for education and training:
Cultivate students' estimation habits.
Teaching process;
First, create situations and introduce topics.
Teacher: during the festival, the teacher bought some flowers to decorate the classroom first, but I don't know how long the classroom is. Can you help the teacher test it? (Leading topic: How long is the classroom)
Second, practical activities.
Activity 1: Measure the length of the classroom.
1. How to measure the length of the classroom?
2. Students are divided into groups to make actual measurements.
Question before the activity: first, think about what measuring tools your group chooses, then actually measure, and finally fill in the selected measuring tools and measurement results in the table in the book.
3. Organize students to discuss: What problems are encountered in the measurement? How to solve it,
Teachers' Entry: A tool can measure how long a teacher takes, but the measurement results are different. What happened?
Activity 2: Swing with cans to see who swings high.
1. Did the teacher put forward the activity rules? Swing one by one, out of reach, 30 seconds, whoever swings the highest will win.
2. Find two teams to pose in front, and the other teams will be referees.
3. All the students in each group put a pendulum and say.
Activity 3: Tell me the length of that piece of wood.
1, Naughty and Xiaoxiao measure the length of two sticks with paper clips respectively. Tell me whose wood is long.
The first volume of the first grade of Beijing Normal University Edition, the first chapter of mathematics, the teaching plan of who scored high.
I. Teaching content
"Who scored high" (textbook pages 2 and 3)
Second, the teaching objectives
1, master the operation sequence of continuous addition and the writing method of vertical calculation;
2. Cultivate the good habit of neat handwriting and careful calculation;
3. Cultivate students' ability to find mathematical information and solve problems.
Iii. Key Points and Difficulties
Key point: master the simple writing method of vertical calculation.
Difficulties: Using vertical calculation to solve problems.
Fourth, teaching AIDS and learning tools.
courseware
Teaching design of verb (abbreviation of verb)
(A) the problem situation
Teacher: Students, do you like the competition? The teacher told you that naughty and smiling are good friends. One day, they had a ring race. Do you want to know their results? Let's take a look together.
Courseware presentation: situation map and score statistics on page 2 of the textbook.
Teacher: This is a record of naughty and smiling in the hoop competition. What mathematical information have you learned by observing this table?
Students may say:
Naughty 24 points for the first time, 30 points for the second time and 4 1 point for the third time.
Naughty scored 24 points the first time, smiling scored 23 points the first time, naughty scored higher than smiling for the first time.
Naughty scored 30 points the second time, smiling scored 44 points the second time, and smiling scored higher than naughty.
Naughty scored 4 1 for the third time, smiling scored 29 points for the third time, naughty scored higher than smiling for the third time.
Naughty scores are twice as high as laughing.
How long is the teaching design of the first volume of second-grade mathematics 1 meter published by Beijing Normal University? How long is the instructional design of 1 meter?
Link: pan.baidu./s/1kt3x3p1password: x9mb.
How long is the first volume 1 meter of Grade Two Mathematics published by Beijing Normal University? How long is 1 meter?
Teaching objectives:
1. Understand the meter and its practical significance in observation and measurement activities, initially establish the concept of the length of 1 meter, master 1 meter = 100 cm, and carry out simple unit conversion.
2. Initially learn to measure the length of an object in meters (limited to whole centimeters), estimate the length of the object, and choose a suitable unit to represent the length of the object.
3. Experience the significance of measuring length in daily life in measuring activities.
Key points: the practical significance of rice and the relationship between rice and centimeter.
Difficulty: Choose a suitable unit to represent the length of an object.
Teaching preparation: PPT courseware and three meters.
First, the scene introduction:
1. Last class, we learned the unit of length-centimeter. How long is 1 cm? Can you tell your deskmate with your finger?
2. Summary
How many pieces of sugar are there in the first volume of the second grade mathematics of Beijing Normal University?
Look, what did the teacher bring you today? (A bag of candy) I want to reward the students who listened carefully, observed carefully and thought positively today.
Activity 1 Count Activity (Count) Count Activity (Count)
1, can you guess how many pieces there are in this bag of sweets?
Students have all kinds of ideas. What should we do if we want to know how many sweets are in the bag? (Count) Then let's count how many sweets we have together today. (Blackboard: How many sweets are there)
In order to make it convenient for students to count, we use disks instead of candy. The number of discs in the students' hands is the same as that in the teacher's bag. Now please count quickly! (Number of students)
4. Who can introduce the number method to you?
It seems that students have all kinds of counting methods, all of which are counting the number of sweets. Let's look at these counting methods again. (Courseware demonstrates various mathematical methods)
6. Students, come and look at these figures. What did you find? (Name)
7. (Play the courseware while talking) We counted 1 block and 1 block 20 times. Let's count them together. Two dollars, two dollars. How many times do you need to count? What about five dollars and five dollars? How many times? 10. 10? How many times will it take? Please have a look. What did you find? (Student: The number of counts is different) The more blocks you count each time, the fewer times you count, and the fewer blocks you count each time, the more times you count.
Activity 2 Count activities (two numbers)
1. Teacher, there are other sweets here. Let's have a look. Look carefully. What do you think of the arrangement of these sweets? (health: neatness)
2. "Horizontal counting"
It's really neat Look (the teacher points sideways). How many people are there in this neat arrangement? How do you calculate it? (Student: Counting horizontally) He counts horizontally like this, and there are seven in a row. In mathematics, counting horizontally like this is called counting by rows. Please reach out your hand and do it with the teacher. (Teachers and students point horizontally with their hands) Because there are 7 blocks in each row, we call it 7 blocks in each row. How many lines are there? (second line) What about the * * * organic block? Can you say it again in this language? Courseware demonstration: each line has a block, a line and a block. )
3. "vertical counting"
(1) We just counted horizontally, and we know that it is by line. What else can it be? (Student: Count vertically) How to count vertically? The method of counting vertically like this is mathematically called counting by column.
(2) Can you count the pictures column by column again? (Show new drawings) 4 pieces in each column, 3 columns, one * * * 12 pieces. Who will say it again in this language? Courseware demonstration: each column has a block, a column and a block. )
Activity 3 Activity Count Activity (three numbers)
1. Please observe "look horizontally" or "look vertically". What can you find?
2. By counting horizontally and vertically, we can calculate the quantity accurately. Can these two numbers be expressed by formulas? Please open page 16 of the book, and write the method of horizontal counting here and the method of vertical counting here. (courseware description)
Tell me how you worked out this formula. (Blackboard Maps and Formulas)
Vertical number, how many 3s are there? (Health: 5 3) Can you order? (For every 1 3, the teacher posts 1 3. )
This formula is calculated horizontally, and several 5s add up to a point. (When the teacher posts it, the students order it)
4. The students listed two different formulas by their own numbering methods. What are the characteristics of the two formulas? (Name) If the formulas are different, how can we get the same number? (Student: One is the number five of five, and the other is the number thirteen of three) You have discovered all the secrets in the small formula. It's like the same picture, counting horizontally and vertically, the result is the same.
Activity 4 Activity expansion
1, the students counted so well that the little frog joined in. He wants to play checkers with us. (Show/kloc-question 4 on page 0/7) Did you see how the little frog jumped? (Born in a book)
This little frog is so naughty that it jumps on the teacher's ruler. He wants to jump three squares, so our formula will keep adding up. Is there a better way? If only we could have a simpler method, which we will learn next class.