Seeking the teaching design of junior high school mathematics

Teaching objectives

1. Cognitive goal: let students understand and master the basic properties of scores by analogy; Master the reduction method and the simplification method of the simplest score.

2. Ability goal: to enable students to learn the analogy thinking method and cultivate the thinking ability of analogy transformation; Make students master the basic nature of the score and cultivate their ability to calculate the correct deformation score.

3. Emotional goal: By analogy with the score, the basic nature of the score is deduced, and the infiltration of things is the dialectical relationship between connection and change and development. That is analogy-connection-induction-development.

Teaching emphases and difficulties

The key point is to understand and master the basic nature of scores.

The difficulty lies in the flexible use of the basic properties of the score to carry out the invariant deformation of the score and the simplification method of the simplest score.

Prepare teaching tools

Teaching process design

Teaching process design

First, the scene is introduced.

1.

Fill in the basis of each step in brackets.

Calculation:

Solution:

( )

( )

[By filling in the blanks and observing, let students know clearly that the essence of calculating and simplifying scores is points and points, and the basis of points and points is the basic nature of scores]

think

Question (1): Do you remember the basic nature of fractions?

Question (2): Does the score also have this property?

By asking questions, let students recall and review the basic nature of the score, then guide students to compare with the basic nature of the score, deduce the basic nature of the score, and let students understand the basic nature of the score, which is the basis for studying and studying the deformation of the score in the future. ]

discuss

(1) Rewrite the basic properties of the component formula according to the basic properties of the fraction:

The numerator and denominator of a fraction are multiplied (or divided) by a non-zero algebraic expression at the same time, and the value of the fraction remains unchanged, that is:

,

Where m and n are algebraic expressions, and

(2) What are the differences and connections between them?

Let the students understand through discussion that from score to score is to extend "number" to "shape". Fractions are a special case of fractions. ]

Second, learn new lessons.

Discrimination of the concept of 1.

The four letters A, B, M and N in the fraction all represent algebraic expressions, in which B must contain letters, except that A can be equal to zero, and B, M and N cannot be equal to zero, because if B=0, the fraction is meaningless; If M=0 or N=0, multiplying or dividing by the denominator of the fraction will make the fraction meaningless.

2. Example analysis

Example 1:

[Through the practice of this example (the example in the book is slightly changed), make students familiar with the basic nature of the score and pay attention to the key words in the basic nature of the score. Then the concepts of reduction and simplest fraction are introduced. ]

Example 2

Through the practice of simple examples (example in the book 1), let students correctly find out the same factor of numerator and denominator, and then simplify the score. The method of simplifying the fraction to the simplest fraction is summarized. ]

[Through the practice of Example 3, emphasize to the students that the final result of simplifying the score should be the simplest score. This exercise involves the sign-changing law of scores, which is a difficult teaching point. Students can experience it with appropriate examples, but it is not necessary to emphasize and give the name of the law of fractional sign change. ]

Consolidation exercise

Exercise after class 10.2

[The first question can be practiced after deducing the basic nature of the score, and the second, third and fourth questions can be practiced after explaining the corresponding examples 1, 2 and 3. Can also focus on practice, teachers can choose according to the actual situation. ]

Third, the problem expands.

(1) Discrimination of students' easy mistakes in applying the basic properties of scores;

(2) For the practice of converting the numerator and denominator of the fraction into integer coefficients by using the basic properties of the fraction, if the value of the fraction is not changed, the polynomial coefficients of the numerator and denominator in the fraction are converted into integers, and the coefficient of the highest term is positive.

(3) Practice and evaluate the topics that can simplify scores.

[The above questions can deepen the understanding and mastery of the basic nature of scores on the premise that students have spare time to study. ]

Fourth, class summary.

1, the basic properties of the fraction? The basic properties of fractions are the theoretical basis of fractional deformation and operation.

2. how to divide it? Simplification is a way to simplify fractions. Simplifying fractions is the goal, and simplest fraction provides convenient conditions for further operation between fractions.

Verb (abbreviation for verb) assignment

Workbook 10.2

Instruction design description

1, the content of this chapter is somewhat similar to the previous scores, so part of this chapter is based on the knowledge of analogy scores, and analogy is an effective way of thinking to find new problems. This section is no exception. The heuristic teaching principle is to explain the basic properties of scores by analogy. In teaching design, we emphasize the basic nature of students' comparison scores and the differences and connections between them, with the aim of further clarifying the characteristics of the basic nature of scores and cultivating students' ability to acquire knowledge independently.

2. The arrangement of examples and exercises is designed according to the cognitive rules and psychological characteristics from easy to difficult and from simple to complex. In this way, students can recall that the basis of general score and approximate score is the basic nature of score through a simple fractional addition calculation, and then draw the basic nature of score by analogy. After being familiar with the basic nature of the score, we should train students to use the basic nature of the score correctly through examples and exercises, and then we can choose some topics to expand the problem, so that students can use the basic nature of the score flexibly according to the characteristics of the problem, and at the same time cultivate their ability to analyze and solve problems.

3. Strengthen the training of students. After the teacher finishes the example, let the students do the problem by themselves, experience the basic nature of the score and the law of the sign change of the score in the process of doing the problem, and deepen their understanding, so as to apply the deformation and operation of the score freely.