Teaching task analysis
The position and function of teaching materials
This lesson is the first lesson of grade eight in Beijing Normal University. Fraction is the basic knowledge of algebra after relay of algebraic expressions in junior high school mathematics. It is the extension and expansion of the scores learned in primary school. It is based on the factorization in Chapter 4 of this book. At the same time, it is also the basis and premise for continuing to learn the properties and operations of fractions and solving fractional equations in the future. Learning this lesson well can not only enhance students' computing ability and speed, but also provide important conditions and lay a solid foundation for solving more complex algebraic problems, such as "functions" and "equations" in the future.
Design teaching objectives according to students' situation.
Because students have studied algebra in the seventh grade, scores are algebraic like algebra, so the method of research and learning is similar to algebra. On the other hand, "fraction" is the algebra of "fraction", and students can learn fractions by analogy.
Students are not proficient in understanding and mastering fractions and algebraic expressions, which brings difficulties to the study of fractions in this section, because their properties and operations are completely similar. In this case, we should recall the basic knowledge and explore new knowledge simultaneously, and improve it on this basis, so that students at different levels can gain something. Therefore, according to the mathematics curriculum standards, starting from the characteristics of teaching materials and students' cognitive level, I have determined the following four aspects as the teaching objectives of this class:
1. Knowledge and skills objectives
(1) enables students to understand the background and concepts of fractions, as well as the differences and connections between fractions and algebraic expressions. Defining that the denominator should not be zero is an integral part of the concept of fractions.
⑵ Master the conditions of meaningful scores and understand the connections and constraints between things.
2. Process and method objectives
⑴ Fraction can be used to express the quantitative relationship in real situations, understand the model idea of fraction, and further develop the sense of symbol.
⑵ Through the teaching of analogy fraction research, students are guided to study and solve problems by analogy transformation.
Cultivate students' thinking of observation, induction and analogy, and let students learn to explore independently and cooperate and communicate.
3. Emotional and value goals
(1) By experiencing the learning process of hands-on, cooperation and communication, inquiry and solution, we can gain successful experience, experience mathematical activities full of exploration and creation, experience the idea of fractional model, and stimulate students' enthusiasm and initiative in solving problems.
(2) On the issue of land desertification, we recognize the importance of protecting human living environment. Cultivate students' rigorous thinking ability.
4. Modern teaching methods
Multimedia slide show
The use of courseware in classroom teaching is intuitive, with comprehensive teaching knowledge and rich teaching content.
(2) Using slides and projections to quickly show students' exercises in class is helpful for teachers to deal with the problems in this section. Achieve classroom effect.
Learning focus
The concept and meaning of fraction (that is, to understand the form of fraction (A and B are algebraic expressions, to understand one feature of the concept of fraction: the denominator contains letters; One requirement: the value of letters is limited to making the denominator not zero.
Design Intention: The concept of score is the starting point and foundation of studying the score in this chapter, so the concept of score is the focus of teaching.
Learning difficulties: understand and master whether the score is meaningful and the condition that the score is zero.
Design intent: Because the denominator of a fraction contains letters, that is, the denominator of a fraction is not a constant like the denominator of a fraction. When solving specific problems, students can easily confuse the situation that the score is meaningless and the situation that the score value is zero. Therefore, understanding and mastering the conditions when the fractional value is zero has become the teaching difficulty of this class.
Teaching preparation
(1) familiar with teaching materials, clear teaching objectives; (2) Let the students get ready and know their lack of basic knowledge of fractions and algebraic expressions. (3) Use the current teaching design and courseware for reference to improve the courseware content of this section. Courseware embodies the teaching idea of taking students as the theme, and most students can only master it by doing more. Classroom teaching should be intensive, practice more, and leave more time for students to practice and communicate. Finally, it should be ideal to choose a typical topic to test the effect of this section.
Teaching methods: group discussion, encouragement, analogy, guidance and analysis.
Teaching process design
This lesson consists of six teaching links, namely: ① independent inquiry: timely topic selection; ② Conceptual analysis; Implement the "two basics"; ③ Hands-on operation; Explore new knowledge; ④ Happy classroom; Improvement of thinking; ⑤ Self-examination; ⑤ Inductive summary of teachers and students; 5 homework.
Its specific content and analysis are as follows:
Teaching process (self-inquiry:
Write down your doubts after you finish the exercises in the textbook P 109.
1. Scene introduction: Facing the increasingly serious problem of land desertification, a county decided to fix sand and afforestation by stages. The first phase of the project plans to fix sand and afforest 2400 hectares within a certain period, and the actual monthly sand-fixing afforestation area is 30 hectares more than originally planned. As a result, the original planned task was completed ahead of schedule.
What if the original plan was to fix sand and afforest X hectares per month? therefore
(1 How many months will it take to complete the afforestation task?
(2) How many months did it take to actually complete the afforestation task?
2. Explain and explore
Observe the algebraic expressions in the above questions carefully. What are their common characteristics?
Objective: (1) With quality education and efficient classroom as the guiding ideology, students can learn first, and teachers should give teaching guidance according to the actual situation of students.
⑵ It has a subtle influence on the idea that mathematics comes from life and modeling.
Teaching premise: it is not difficult for students with good mathematical foundation.
(2) Analysis and implementation of the concept of "two basics"
The concept of 1. fraction
(1 Students discuss the definition of score in groups and draw the conclusion of the concept of score:
(2) Students give some examples of scores.
Generally, a and b are used to represent two algebraic expressions, and A÷B can be expressed as. If b contains letters, it is called a fraction, where a is called the numerator of the fraction and b is the denominator of the fraction.
(3) Students should pay attention to the problems in summarizing the concept of scores.
The denominator contains letters.
Like fractions, the denominator of fractions cannot be zero.
Quiz: Which of the following is an algebraic expression? What is a score?
The sea is wide and the fish jumps;
Can you use the following algebraic expressions to construct fractions?
-3，-a，ab-b，
Objective: To consolidate the concept of score and lay a foundation for future study.
Teaching presupposition: This topic is flexible and changeable, which gives students enough thinking space and plays a good role in detecting the mastery of concepts.
2. Is the score meaningful? The value is zero.
Thinking: What are the conditions for the denominator of (1) score?
When B=0, the score is meaningless.
When B≠0, the score is meaningful.
2 = 0, what conditions do numerator and denominator meet?
When A=0 and B≠0, the value of the score is zero.
Objective: The score has meaningless conditions, and the value is zero, which is easy to be confused. Teachers can guide students to draw correct conclusions and lay the foundation for breakthroughs in key and difficult points.
Teaching premise: it is not difficult, it should be written on the blackboard and organized.
(3) Hands-on operation to explore new knowledge,
Example 1 (1) When a= 1, 2,-1, find the value of the fraction;
⑵ When a takes what value, does the score make sense?
Solution: (1 when a= 1, when
When a=2
(2) When the denominator is equal to zero, the score is meaningless, and besides, the score is meaningful.
A= is obtained from the denominator 2a- 1=0, so when a takes any real number except, the score is meaningful.
Objective: To experience score evaluation and perceive the meaning of symbols, so as to lay a foundation for future study. Learn meaningful fractional mathematics situations.
Teaching premise: (the score is evaluated at 1, and students can learn by themselves; (2) the topic can be mastered as long as the teacher hints a little.
Problem solving: What is the significance of the following score when taking X?
Solution: (1 multiply denominator 4x+ 1=0, x=-.
Therefore, when a takes any real number other than-,the score is meaningful.
(2 from the denominator x2+ 1=0, x2=- 1.
Therefore, when a takes any real number, the fraction is meaningful.
Objective: To consolidate and improve scores.
Teaching premise: (1 Students can imitate examples by themselves1; (2 students do x2=- 1, and any real number may not be answered. The teacher will explain this.
Thinking: If the title requirement is changed to: "When what value does X take, the following score is meaningless?" What should I do?
Example 2: When x takes what value, the value of the following fraction is zero?
Solution: (1 x= 1 from the molecule x- 1=0.
And when x= 1, the denominator x2+2x-3≠0.
When x= 1, the original score value is zero.
Objective: The zero-score value of (1) is easily confused with the question of whether it is meaningful or not, which is ideal for guiding the idea of zero-score value. (2) Consolidate and master the fractional value of zero.
Teaching premise: (1 The students are vague about the steps of this problem, and the teacher explains and then summarizes the conditions of zero score and the steps of doing the problem are ideal. (2) Students do it themselves and communicate with each other.
Summary: If the score is zero, two conditions must be met: ① the molecular value is equal to zero; ② The denominator value is not equal to zero.
(4) Happy classroom and thinking improvement:
What is the value of the fraction x?
(1) significant (2) 0 (3) negative number (4) positive number.
Objective: ① To consolidate the difficulties in this lesson.
② Positive numbers and negative numbers have a more comprehensive understanding of fractional values.
Teaching premise: (1) It is not difficult to make a small question; (3) Most students should give hints when making small questions; (4) Students do it themselves, no problem.
(Five major performances: self-test)
1. When-,does the score make sense?
2. Judge that there is-the following algebraic score.
3. When x _ _ _ _, the score =0.
4. The following is correct.
A. the numerator of the fraction must contain letters.
B. When the denominator is zero, the score is meaningless.
C. when the denominator is zero, the fractional value is zero.
Target: 1. Efficient classroom, most classroom knowledge points need to be mastered.
2. Test the effect of this class, and check for missing parts in time.
Teaching premise: These topics are generally difficult, and the knowledge coverage is comprehensive, which can achieve the detection effect and the effect should be ideal.
(6) summary of teachers and students:
What knowledge and methods have you learned in this course?
1. The difference between a score and a score.
2. When does the score make sense?
3. When will the score be zero?
Design intention: Teachers and students communicate, so that students can speak freely, talk about their own gains and feelings boldly, give full play to students' dominant position, summarize from three aspects: learning knowledge, methods and extension, and cultivate the habit of summing up knowledge in time and the ability to refine and summarize.