Teaching process:

First, practice and innovate.

In the fourth grade, we had a preliminary understanding of scores. Can you give some examples?

The students know a lot of scores. Look! Teacher, here are some materials (a circle, a meter line, five apples and six flowers). Can you divide them equally and use numbers to represent one or more of them?

(screen display material. )

Each student chooses the same thing, do it first, and communicate the scores with the students in the group. Why do you say that?

Students' activities, teachers' participation and understanding of the situation.

Second, cooperate and exchange, and build a "whole".

Did the students get the scores?

1. Who divides the circle equally? How many points did you get?

Health: divide a circle into two parts on average, each part is half of it;

Divide a circle into four parts on average, each part is a quarter of it;

Divide a circle into eight parts on average, each part is one eighth of it;

……

And so on, you can get many points.

2. Is there a score after averaging the useful line segments?

Take "divide one meter into eight parts" as an example, each part is one eighth;

How about making two copies like this? (two eighths)

Can you get any other scores?

Teacher: It means how many copies are like this?

3. What other average scores can be used to represent such one or several copies?

Take five fruits as a whole and divide them into five parts on average, each fruit is one-fifth of the whole;

Two fruits are two-fifths of the whole;

Why can it be expressed by two fifths?

The teacher concluded that when there are several objects, they can be regarded as a whole and divided equally. Such one, two or more copies can also be expressed by scores.

4. Can six flowers be divided equally? What points can you get?

Six flowers are regarded as a whole and divided into two parts on average, each part has three flowers, which is half of the whole;

Six flowers are regarded as a whole and divided into three parts on average, each part has two flowers, which is one third of the whole; Four flowers are in duplicate, which is two-thirds of the whole.

Take these six flowers as a whole and divide them into six parts on average, each part has 1 flower, which is one sixth of the whole; How about five?

Third, abstract generalization and construct the meaning of the score.

1, understand the meaning of the unit "1"

The students got a lot of marks through operation and communication. What are the similarities in the process of getting these scores?

Health: Are all the objects equally divided?

Q: Is the average score the same?

Divide a circle (called an object) and a one-meter line segment (called a unit of measurement) into several parts on average, and use fractions to represent one or several parts; It is also possible to average the whole composed of many objects, and such one or several parts can also be expressed by scores.

Whether it is an object, a unit of measurement or a whole composed of many objects, it can be expressed by the natural number 1, and we usually call the unit "1".

Q: What can the unit "1" mean?

2. Form the concept of score.

Can you use your own words to say what a score is with the example just now?

The teacher pointed out: divide the unit "1" into several parts on average, and the number of such 1 parts or several parts is called a score.

This is the "meaning of fractions" we are learning today.

What words should we pay special attention to in this sentence?

4. The meaning of numerator and denominator.

Take three fifths as an example, how many parts does a score consist of?

What do numerator and denominator mean?

Fourth, the whole class summarizes.

What did you learn today?

Verb (abbreviation of verb) consolidates development and deepens understanding of meaning.

Can you solve practical problems with the skills you learned today?

1, use the following fraction to represent the colored part of the picture?

2. Tell the meaning of the score in the following questions. What unit is "1"?

3, the game:

16 cubes, 1 students take them out. How many cubes did they take?

Student 2 took out the rest. How many pieces did he take?

Student number three took out the rest. How many pieces did he take?

Student No.4 took out the rest again. How many pieces did he take?

Everyone took it. Are these cubes the same number? Why?

mark

Knowledge network

(l) When comparing scores, the denominator is usually used for comparison. When the denominator is complex and difficult to divide, it can also be compared by numerator or reciprocal method; You can also compare each score with 1 by indirect comparison method.

(2) When calculating the addition and subtraction of scores, we first split some of them properly to make some of them cancel each other, thus simplifying the calculation. This is the so-called split term method.

Important and difficult

When the numerator and denominator of (1) fraction are both added or subtracted by a number, the result should be calculated first, then the numerator or denominator should be enlarged or reduced several times, and then the denominator or numerator should be enlarged or reduced several times.

(2) For the calculation problem that does not need to calculate the exact value, estimation is very important, which avoids complicated calculation. Generally speaking, in estimation, we often use zoom and zoom methods to estimate what a number is. When using this method, we must pay attention to proper scaling and reasonableness.

Learning method guidance

(1) splits the band fraction into the sum of integer and true fraction, which is convenient for observation and operation.

(2) When doing the mixed operation of fractions, sometimes the product of numerator and denominator is not calculated, which is more conducive to further calculation.

(3) In the calculation process, it is not necessary to convert false scores into component numbers, just convert the final results into component numbers (if possible).

(4) It is often used as a formula in various operation problems.

(5) It is sure to get twice the result with half the effort to draw a conclusion from the general form and then use the conclusion to solve individual problems.

Classic example

[Example 1] If so, what is the quotient of finding A÷B?

Thinking analysis

Find out what a and b are first. Because 1997 is a prime number, the approximate numbers are only 1 and 1997.

A= 1997× 1998 and B= 1998 can be obtained.

explain

because

So a =1997×1998b =1998.

a÷B = 1997× 1998÷ 1998 = 1997

A: The quotient of A÷B is 1997.

Between 2 and 6, how many simplest fractions with a denominator of 3 are there?

Thinking analysis

The denominator is 3, and the fraction between 2 and 6 is greater than but less than, that is,,,, * *17-7+1=1(pieces). Because it is the simplest fraction, the numerator is a multiple of 3. For example, to exclude it, there are 1 1-3=8 simplest fractions that meet the requirements.

explain

According to the above analysis, the score of * * is17-7+1=1(pieces), 1 1-3 = 8 (pieces).

Between 2 and 6, there are 8 simplest fractions with a denominator of 3.

[Example 3] When the numerator is added to 8, how much should the denominator be added to keep the size of the score unchanged?

Thinking analysis

Adding 8 to the molecule is 4+8= 12, so the molecule is magnified three times. According to the basic nature of the fraction, the denominator must also be enlarged three times, so the size of the fraction remains unchanged, that is, 15×3=45, and the original denominator is 15, so it is necessary to add 45- 15=30.

explain

☆ Scheme 1: (8+4)÷4× 15- 15.

=45- 15

=30

A: The denominator should be increased by 30.

☆ Scheme 2: From another point of view, molecule 4 plus 8 will increase by 2 times. In order to keep the size of the fraction unchanged, the denominator should also be increased by 2 times, 152=30.

Answer: add 30 to the denominator.