1. Understand and master the basic properties of fractions, and know the relationship between the basic properties of fractions and quotient invariance in integer division.

2. We can use the basic properties of fractions to divide a fraction into fractions with different parents and equal size.

3. Cultivate students' logical thinking ability of observation, comparison and abstract generalization, and infiltrate? Things are interrelated? Dialectical materialism viewpoint.

Emphasis and difficulty in teaching

Understand the meaning of the basic properties of fractions and master the derivation process of the basic properties of fractions. Using the basic properties of fractions to solve practical problems.

teaching tool

courseware

teaching process

First, review old knowledge and communicate.

1. Answer the following questions.

12? 3 = ( 12? 10) ? (3? □)

18 ? 6 = ( 18? □) ? (6? 3)

What did you fill in according to? Remember how the constant quotient law is described?

4 ? 5= ( )? three

What did you fill in according to? What is the relationship between fraction and division?

2. Guess.

Students, in division, there is a law of constant quotient, and fractions are related to division. Then, please guess, will there be similar properties in the score?

Are there any similar attributes in the score? If so, what are they like? Today we will study this problem together.

Second, explore new knowledge and reveal the law.

1. Perception law

(1) Hands-on operation

① Group cooperation divides three circular pieces of paper with the same size into two, four and eight pieces on average.

(2) Color: Color one of the two halves, color two of the four halves, and color four of the eight halves.

(3) Colored parts are expressed by scores.

4 Comparison: What is the relationship between these three scores?

Through hands-on operation, students find that these three scores are equal.

After the students report, the teacher demonstrates with the computer.

Students observe the changing law of numerator and denominator, and find that the numerator and denominator of a fraction are multiplied by the same number at the same time, and the size of the fraction remains unchanged.

(2) Continue to discover

The teacher's courseware shows three rectangles with the same size and shape. Ask the students to use scores to represent the colored parts, and observe the colored parts to see what they find.

It is found that the colored parts are the same.

Observing the changing law of numerator and denominator, it is found that the numerator and denominator of a fraction are divided by the same number at the same time, and the size of the fraction remains unchanged.

Cannot divide by 0 at the same time.

2. Summarize abstractly and summarize the rules.

Guide students to observe, compare and recall the formation process of knowledge, and summarize the basic properties of scores. Imperfections complement each other. (Discuss why 0 is excluded)

Think about it: according to the relationship between fraction and division, and the invariable nature of quotient in integer division, can you explain the basic nature of fraction?

3. Use rules and learn examples by yourself.

(1) Group discussion.

Divide sum into fractions with the letter 12, but the size remains the same. How should molecules change? What is the basis of change?

(2) Report the discussion.

(3) Summary: We can apply the basic properties of fractions to divide a fraction into different fractions with the same size.

Third, multi-layer exercises to consolidate and deepen

1. Basic exercises.

According to the basic properties of fractions, complete the following equations.

After the students answer, ask them to say what they think.

2. Judges. (Gestures, and explain why. )

The numerator and denominator of the (1) fraction are all multiplied or divided by the same number, and the size of the fraction remains the same. ( )

(2) The numerator of15/20 is reduced by 5 times, the denominator is also reduced by 5 times, and the size of the fraction remains unchanged. ( )

The numerator of (3) is multiplied by 3, and the denominator is divided by 3, and the size of the fraction remains unchanged. ( )

3. Divide 2/3 and 4/24 into fractions with the letter 12, but the sizes are the same.

What did you gain today?

The Basic Nature of Fractional Teaching Plan (2) Teaching Objectives

1. 1 knowledge and skills:

Make students understand and master the basic properties of fractions, and use the basic properties of fractions to turn a fraction into a fraction with a specified denominator and constant size.

1.2 process and method:

Through the process of observation, comparison, discovery, induction and application, students experience the process of exploring the basic properties of scores and learn the methods of induction and generalization.

1.3 Emotional attitudes and values:

Stimulate students' positive emotional state and experience the fun of mutual cooperation.

Emphasis and difficulty in teaching

2. 1 teaching focus:

Let students know the basic nature of scores.

2.2 Teaching difficulties:

Let students explore, discover and summarize the basic properties of scores independently and apply them to solve related problems.

teaching tool

courseware

teaching process

First, the introduction of story situations

1, an old man gave a piece of land to his three sons. The boss got the land.

The second child was assigned to this land.

. The third child got this.

. The boss and the second thought they were suffering, so the three men quarreled. Avanti happened to pass by and asked the reason for the quarrel. He smiled and said a few words to them, and the three brothers stopped quarreling.

Do you know why two generations of love laugh? What did he say to the three brothers?

2、 120? What is the quotient of 30? Dividend and divisor have both tripled. What is the quotient? Dividend and divisor minus 10 times?

120? 30= 4 ( 120? 3)? (30? 3)= 4 ( 120? 10)? (30? 10)= 4

3. Say:

What is the nature of (1) quotient invariance?

(2) What is the relationship between fraction and division?

4. Let the students guess boldly:

There is the property of quotient invariance in division, will there be a similar property in fraction? What is the nature of this?

With the students' answers, the teacher wrote down on the blackboard: the basic nature of the score. )

Second, explore new knowledge.

1. Hands-on operation to verify properties.

(1) Let the students take out three identical rectangular pieces of paper, divide them into two, four and six pieces on average, and color 1, two and three pieces respectively, and use scores to indicate the colored parts.

What did you find?

(2) Through observation and comparison, guide students to draw the following conclusions:

According to what law do their numerator and denominator change?

(3) Looking from left to right:

What are the changes in the average number of copies and the number of copies expressed?

Guide the students to make a preliminary summary: the numerator and denominator of the score are multiplied by the same number at the same time, and the size of the score remains the same.

(4) Looking from right to left:

Guide students to observe clearly:

The numerator and denominator of are divided by 2 at the same time.

Blackboard writing:

Let the students sum up again: the numerator and denominator of a fraction are divided by the same number at the same time, and the size of the fraction remains the same.

(5) Guide students to summarize the basic nature of scores and respond to previous conjectures.

(6) Question: Here? Same number? Any number will do? (Supplementary blackboard writing: except zero)

(7) Summary:

The numerator and denominator of a fraction are divided by the same number at the same time (except 0), and the size of the fraction remains the same. This is called the basic nature of fractions.

2. Comparison of the basic properties and quotient invariance of fractions.

In division there is the property of constant quotient, and in fraction there is the basic property of fraction.

Think about it: according to the relationship between fraction and division and the invariance of quotient in integer division, can you explain the basic properties of fraction?

3. Learn to turn a fraction into a fraction with the same size specified by a denominator.

Teaching example 2

Play music

Fractions whose mother letter is 12 and whose size is constant.

(1) Example 2 helps students understand the meaning of the question.

(2) Inspiration: Put

The denominator of the group is 12, and how should the molecule change when the size is constant? What is the basis of change?

(3) Let the students fill in the blanks in the book and ask a student to answer. Teacher's blackboard writing:

8.3 Consolidation and promotion

1. Is the following formula correct? If there is a mistake, where is it? Why is it so wrong?

2. Judge and explain the reasons.

The numerator and denominator of the (1) fraction are all multiplied or divided by the same number, and the size of the fraction remains the same. ( ? )

(2) release

When the numerator is reduced by 5 times, the denominator is also reduced by 5 times, and the size of the fraction remains the same. ( ? ) (3)

Multiply the numerator by 3 and divide the denominator by 3, and the size of the fraction remains the same. ( ? )

Summary after class

What did we learn in this class? What do you have?

When using the basic properties of fractions, we should make the following points clear:

① The numerator and denominator perform the same operation and can only be multiplied or divided.

② The numerator and denominator are multiplied or divided by the same number. And must be operated simultaneously.

(3) numerator and denominator multiplied or divided at the same time can't be 0.

(4) The size of the score is constant.

Write on the blackboard.

Basic properties of fractions

The numerator and denominator of a fraction are divided by the same number at the same time, and the size of the fraction remains the same.

The numerator and denominator of a fraction are divided by the same number at the same time (except 0), and the size of the fraction remains the same. This is called the basic nature of fractions.