Teaching Plan of Mathematics "The Meaning of Proportion" in the second volume of the sixth grade of People's Education Press.

teaching plan of the meaning of proportion (1)

teaching objectives

1. Understand the meaning of proportion, judge whether two ratios can form a proportion by using the meaning of proportion, and make a proportion.

2. Explore the mathematical knowledge contained in the national flag, infiltrate patriotic education and improve students' cognitive ability.

3. Experience the pleasure of success and build up self-confidence in learning mathematics well.

teaching focuses on difficulties

teaching emphasis: understanding the meaning of proportion.

Teaching difficulty: Use the meaning of proportion to judge whether two ratios can form a proportion.

Teaching tools

ppt courseware

Teaching process

Please recall what we learned about comparison last semester. Who can say:

1. What is comparison? What are the writing forms of Bi?

2. What is the ratio?

First, situational introduction

Students, what activities will be held in our school every Monday morning? Let's talk together.

(students say in unison: flag-raising ceremony)

courseware shows: the scene of flag-raising ceremony

You are already very familiar with this scene. Do you know the length and width of this national flag respectively?

I don't know, do I? The teacher told everyone:

The courseware showed and introduced: The length of our national flag is 2.4 meters and the width is 1.6 meters.

question: where else in your life have you added the national flag besides the flag-raising ceremony?

Answer by name (the national flag on the playground, the national flag on the meeting table and the national flag behind the classroom when the school raised the national flag on Monday)

We can see the solemn national flag on many occasions, such as our classrooms and large-scale celebrations.

so do you know the size of these national flags? Follow-up: Do you know?

then let's take a look at some information collected by the teacher.

courseware shows the national flags on different occasions

courseware shows the national flags on different occasions

Question: Who can describe where the four national flags appear in the shortest language? And read its length and width (1) The national flag of Tiananmen Square is 5 meters long and 1/3 meters wide.

(2) The national flag of the school is 2.4m long and 1.6m wide.

(3) The national flag in the classroom is 6 cm long and 4 cm wide.

(4) The national flag on the conference table is 15cm long and 1cm wide.

So are all the national flags we see now the same size?

teacher's summary: the size of the national flag is different on different occasions.

ask: are they the same shape? (same)

Although they are different in size, they are the same in shape. We look like every national flag is still so solemn and beautiful in our eyes, so harmonious and unified, right? So according to what standards can we make such national flags with different sizes and the same shape? In fact, does each national flag also contain our mathematical knowledge? Proportion! (blackboard writing topic: proportion) Let's study this problem together.

2: Explore new knowledge

Next, please take out your exercise books and listen to the requirements:

Write the ratio of the length and width of the flag in China, and then work out the ratio.

students calculate independently and teachers patrol.

Reminder: Students must be careful when calculating. Pay attention to the accuracy of the calculation results.

which student would like to share your achievements with you? Bravely share your achievements with everyone. Answer by name

Report and classify the blackboard books according to the students.

5: 1/3 = 3/2

2.4:: 16 = 3/2

6: 4 = 3/2

15: 1 = 3/2

Do you agree with his calculation?

teacher: please observe the calculation results on the blackboard and see what you find.

Answer by name

Teacher's summary: That's very good. This is a very important discovery. The length and width of these four national flags have changed, but the ratio is all 3/2. Actually, not only the ratio of the length and width of these two red flags is 3: 2, but also the ratio of the length and width of all national flags is 3/2, which is clearly stipulated in the National Flag Law. Teacher: Two ratios like this are equal, that is to say, they are equal, so what symbol can we use to put them?

Let's read this equation together (students read it together) 5:1/3=2.4:1.6

Question: So who can make use of these four 5: 1/3 = 3/2

2.4: 1.6 = 3/2

6: 4 = 3/?

answer by name and call it proportion mathematically according to the equations we wrote on the blackboard

. Who can say what proportion is according to their own understanding? Answer by name

The teacher made it clear that we call the expression that two ratios are equal proportion. (Emphasis on equal ratio)

Read it twice, and start.

students read it all

is this what we are going to learn today? The meaning of proportion

blackboard writing topic

Question: After reading the meaning of proportion, what words do you think are very important in this sentence?

Answer by name

The teacher makes it clear that the formula that two ratios are equal and a black dot is marked below the word of this sentence

indicates that the two ratios are equal is called proportion.

　。 . . . .

2. Understand the meaning of proportion deeply

Then let's have a look: Can 15∶3 and 6∶12 form a proportion? How do you judge? Yes, the ratio of 15: 3 is 5; The ratio of 6: 12 is also 1.5, so 15: 3 and 6: 12 can form a ratio.

So, students, what is the key to judge whether the two ratios can form a proportion? Yes, the key to judging whether two ratios can form a proportion depends on whether their ratios are equal.

Ask and show the courseware: So, students, what is the key to judge whether the two ratios can form a proportion?

(answer by name)

Do you agree?

Evaluate the students' answers

Ask: If they are not equal, can they form a proportion?

Another way to write the teaching ratio: Students know that there is another way to write the ratio (score), such as 2.4:1.6=15:1. This ratio can also be written as 2.4/1.6=15/1. These are two different ways to write it!

(3) cooperative inquiry: in the data of the length and width of the four national flags, which ratios can you find out?

Please discuss in groups! Let's see which group of students are looking for more. Let's start!

In-class communication: Who can tell us what proportion your group has found?

Students are really amazing. From these four national flags of different sizes, there are so many different proportions. More than the teacher, please see the screen

: 2.4: 1.6 = 6: 4 (length: width = length: width)

1.6: 2.4 = 4: 6 (width: length = width: length)

2.4: 6 = 1.6.

2. What is the difference between ratio and proportion?

(1) Students, you used to learn ratio, but now you learn proportion. Do you think ratio and proportion are the same? Now the teacher has a problem that the students need to help solve. Please look at the screen. What's the difference between ratio and proportion? Let's discuss it in groups and tell the teacher later, ok? Ok, let's get started!

(2) communication: who would like to talk about the results of your group discussion?

(Answer)

(3) Show: That's very good. The ratio consists of two numbers, which is a formula, indicating the division of two numbers. Proportion consists of four numbers and is an equation. It is an expression that two ratios are equal. Please look at the table on the screen

III. Teacher's Summary of Smart Castle

: Today, the students performed very well in this class. Do you have confidence in going to Smart Castle together?

Fourth, talk about the harvest

In this class, everyone is very active and serious. The teacher believes that the students must have gained a lot, so who wants to share your gains with you?

V. Summary of the whole class:

Teacher's Summary: The knowledge of proportion is widely used in our lives. The famous French building Eiffel Tower, the Greek statue Venus with a broken arm and the flashing five-pointed star can give us a sense of beauty because they all share the same structure? Golden ratio? Related. I hope you can find more from your life after class? Proportion? Discover more mathematical knowledge. By that time, I believe you can feel more deeply that mathematical knowledge is really ubiquitous and ubiquitous in our lives.

After-class summary

The knowledge of proportion is widely used in our life. The famous French building Eiffel Tower, the Greek statue Venus with a broken arm, and the flashing five-pointed star can give us a sense of beauty because their structures all share the same word? Golden ratio? Related. I hope you can find more from your life after class? Proportion? Discover more mathematical knowledge. By that time, I believe you can feel more deeply that mathematical knowledge is really ubiquitous and ubiquitous in our lives. The meaning of proportion teaching plan (2)

teaching goal

knowledge goal: understanding the meaning of proportion.

skill goal: to correctly judge whether two ratios can form a proportion, and to cultivate students' abstract generalization ability.

emotional goal: to make students initially feel that things are interrelated, changing and developing.

teaching focuses on difficulties

emphasis: understanding the meaning of proportion.

difficulty: judge whether two ratios can form a proportion.

teaching tools

multimedia courseware

teaching process

first, the introduction of new lessons

please recall the knowledge of comparison, the former, the latter and the ratio of comparison.

2. Teaching process

1. Significance of proportion

(1) Show P4 Example 1

What is the ratio of the length and width of the two national flags on the playground and in the classroom?

2.4: 1.6 = 3: 2

6: 4 = 3: 2

2.4: 1.6 = 6: 4

The formula that two ratios are equal like this is called proportion.

Proportion can also be written as =

Do it

1. Can two ratios in the following group form a proportion? Write down the proportion of the composition.

(1) 6: 1 and 9: 15 (2) 2: 5 and 1: 4

(3): and 6: 4 (4) .6: .2 and:

Answer: (1) 6: 1 = 3: 59: 15 = 3.

Answer: 2 ∶ 4 = 1.5 ∶ 34 ∶ 2 = 3 ∶ 1.53 ∶ 4 = 1.5 ∶ 24 ∶ 3 = 2 ∶ 1.5

Summary of the whole class

What have we learned from this lesson? What is proportion?

expand and extend

How many proportions can you make with four numbers, namely, 8, 12?

summary after class

what have we learned through this lesson? What is proportion?

exercises after class

1. Fill in the blanks

1. () is called proportion.

2. If the () of two ratios are equal, the two ratios are equal.

3. Put 6? 8=24? 2 rewritten into four proportions.

4. Rewrite 7m=8n into four proportions.

5. according to 8? 9=3? 24. Write the ratio ()

6. If 7a=6b, then a: b = (): ().

7. if 9a=5b, then b: a = (): ().

2. Choose

1. Among the following ratios, () can make up a ratio of 3: 8.

A.3.5∶6 B.1.5∶4 C.6∶1.5

2. The quotient of a number divided by b number is 1.8, so the ratio of a number to b number is ().

a.9: 5b.5: 9c.1: 8

3. Among the following numbers, the one that can be proportional to 6, 9 and 1 is ().

A.7 B.5.4 C.1.5

blackboard writing

the expression that two ratios are equal is called proportion.