Teaching plans for multiplication and division of fractions

Teaching Plan for Mathematics Assessment Course

Teaching time: November 8, 2004 Class: Grade 2 (3) Coach: Yang Liquan

Teaching content: 9.3 Multiplication and division of fractions (1 reduction)

1. Teaching objectives:

(1) Knowledge objectives:

1. Be able to say fraction reduction The meaning, basis and key of fraction;

2. Be able to tell the meaning of the simplest fraction.

(2) Ability goals:

1. To enable students to master the method of reduction,

2. To enable students to skillfully reduce a fraction .

(3) Emotional goals:

1. Create situations and cultivate interest in learning mathematics through analogies, conjectures and inductions.

2. By cultivating students’ awareness of cooperative learning, cultivating students’ spirit of mutual help and enhancing their sense of collective honor.

(4) Process and Thought:

By comparing with the reduction of fractions, you can realize the commonality of numbers and formulas and penetrate the thinking method of "analogy".

2. Teaching focus, difficulty and key points

Focus: Method of fraction reduction.

Difficulty: When reducing a fraction, the signs of the factors in the numerator or denominator of the fraction change.

Key: Correctly find the common factors in the numerator and denominator.

3. Teaching methods:

1. Teaching method: guided analysis, analogy exploration, discussion style

2. Learning method: autonomy, cooperation, inquiry style Study

4. Teaching preparation: Projector

5. Class schedule: 1 class hour

6. Teaching process:

(1 ) Create situations and stimulate interest (projection display) Mathematical jokes:

Big Po, a son of a rich family, whose parents have gone away, leaves it to the chef to take care of him.

Make steamed buns for three meals a day, "Two for each of the three meals a day?" Abao cried and said, "Not enough."

"I'll make six for you a day." Abao said "enough" as soon as he heard it.

Dear students, who knows why A Bao is such a fool?

(Answer with mathematical knowledge, see who can solve the mystery? Ask students to write a mathematical formula to explain, and students can discuss with each other.

Students express their opinions, and the teacher makes final comments)

Give equation 1:

Question: What is the reduction of a fraction? What is the basis for the approximation? What is the purpose of approximation?

(Answer: Reducing the common divisors in the numerator and denominator of a fraction is called reduction. The basis for fraction reduction is: the basic properties of fractions. The purpose of reduction: to reduce a fraction to its simplest form Fraction (or whole number)).

Given Equation 2:

Question: Is this "reduction" thorough? So do you know what the key is?

(Determine the greatest common divisor of the numerator and denominator)

(2) Introduce new lessons through analogies

We just learned fractions earlier. Study, students, think about it, fractions are similar to what concepts you have learned in many ways?

(Let students discuss the answers and point out which ones are similar?) (1. Basic properties, 2. Rule of sign change, 3. The denominator cannot be zero,...)

Since there are so many similarities between fractions and fractions, can fractions be reduced? If so, how can we divide it? Is it similar to the reduction of fractions?

Let’s discuss these issues together.

(3) Question introduction, inspiring exploration, observation and thinking:

(1) The common factor of 6ab2 and 8b3 is _________

(2) If If the common factors of the fraction are eliminated, then the most reasonable result is ( )

1. The topic raised above is:

Can fractions be reduced? Based on what? How to make an appointment? Until when?

(Students discuss in groups, and finally reach ***knowledge through reduction and comparison of fractions.)

2. Teacher’s summary: The reduction of fractions and the reduction of fractions are indeed very similar: Reduction of fractions (projection display)

(1) The concept of reduction: the common denominator of the numerator and the denominator of a fraction Reducing factors is called the reduction of fractions

(2) The basis for fraction reduction: the basic properties of fractions.

(3) Method of reducing fractions: Find the common factors of the numerator and denominator of the fraction, and then reduce the common factors of the numerator and denominator.

(4) The concept of the simplest fraction: When the numerator and denominator of a fraction have no common factors, it is called the simplest fraction.

(4) Exploring example questions to improve skills

Example 1: Reduction:

(1); (2).

(Ask students to observe and think: ①Is there a common factor? ②What is the common factor?)

Solution: (1).

(2)

Summary: ①The numerator and denominator of a fraction are both in the form of the product of several factors. It is necessary to remove the lowest power of the same factor in the numerator and denominator. ,

Teacher’s point: ① Note that the coefficients should also be reduced. ②When the coefficient of the numerator or denominator is a negative number, the negative sign is usually put in front of the fraction itself.

Example 2: Reduction:

(1) (2).

(Ask students to analyze how to reduce and propose solutions after discussion).

Solution:． (1)

(2)

Summary ① When the numerator and denominator of the fraction are polynomials, factorization must be performed first before reduction can be made based on the basic properties of the fraction ． ② Pay attention to the handling of the symbols of the numerator and denominator.

The teacher focuses on the steps of fraction reduction:

1. Find the common factor in the numerator and denominator;

2. Reducing the common factor Factor.

(5) Variation training to improve abilities

Are the following methods correct? If it's wrong, how to correct it?

(1) (2)

(3) (4)

(Students observe and discuss. Help students further understand fraction reduction and avoid occurrences of Similar error)

The teacher’s precise reduction result may be a simplest fraction or an integer.

(6) Learn and practice immediately to consolidate new knowledge: (students’ blackboard performances, group competitions)

(1); (2);

(3); (4).

After teachers focus on reduction, they should ask three questions:

1. Is the coefficient reduced? 2. Are symbols processed correctly? 3. Is the appointment thorough?

(7) Learn and apply immediately, cultivate abilities. See who can learn faster? (You don’t need a pen to calculate, students rush to answer)

When a = 2004, b = 2003, find the value of:

Teacher’s points: 1. To learn a magic weapon, observation is indispensable; 2. To learn a trick, it is inseparable to apply it.

Explain that learning is inseparable from observation. Only with observation can you make discoveries, and only with discoveries can you increase knowledge. Learning knowledge is for application. Only by knowing how to use knowledge can you improve your ability and knowledge can reflect its value.

(8) Discussion summary, deepen understanding

Ask students to think back and summarize for themselves:

1. What did we learn in this lesson? What is it similar to?

2. What are the steps of fraction reduction? What should you pay attention to when making an appointment?

Teacher’s Points

1. The basis for reduction is the basic properties of fractions.

2． If the numerator and denominator of a fraction are both in the form of the product of several factors, then the lowest power of the same factor in the numerator and denominator is reduced, and the numerator, denominator and coefficient are reduced by their greatest common divisor.

3. If there are polynomials in the numerator and denominator of the fraction, the factors must be factored first and then reduced.

4. Pay attention to the correct use of the sign rules of powers in fraction reduction, such as

(x-y)2n=(y-x)2n, (x-y)2n 1=-(y-x )2n 1. (n is an integer)

(9) Assign homework and check learning effectiveness

1. Textbook: Exercise 9.3 Group A, Questions 1, 2, and 3;

2. Textbook: Questions 1 and 2 of Exercise 9.3 Group B (must be done by A-level students).