course content

Example 4 and the corresponding "Try it" on pages 43~44 of the textbook. Complete the following "exercises" and exercises 10, and the questions 1~4.

Teaching objectives:

1. Make students understand the internal and external terms of proportion, and explore and master the basic nature of proportion.

2. In the process of exploring the basic nature of proportion, students can further understand the internal relationship of mathematical knowledge and form a good habit of thinking with their brains.

Teaching process:

1. Review old knowledge.

What is proportion? Which two proportions make up a proportion?

2. New teaching.

1. Example 4: Reduce the left triangle to get the right triangle.

4㎝

2㎝

6㎝ 3㎝

Can you write as many proportions as possible according to the data in the picture?

Discuss in groups and then report. The teacher writes several groups with different proportions according to the students' answers.

2. Introduce the names of the parts in the proportion.

The teacher introduced the meanings of "item", "former item" and "latter item" of proportion.

3 : 6 = 2 : 4

extreme term

Nakatomi

Question: Can you tell me what are the other internal items and external items in each ratio?

3. Explore the basic nature of proportion.

Guide the students to carefully observe the different proportions written, and let them find and think through observation. Recognize that among the four numbers that make up the ratio, 6 and 2 (or 3 and 4) can be both internal and external terms; Recognize that the product of two internal terms is equal to the product of two external terms.

Q: What laws have you found in these proportions through observation?

Do all the proportions have such a law? Ask the students to write some more ratios to verify whether the discovered rules also exist in these ratios.

Guide students to express this discovery rule in letters.

If the four terms of the ratio are expressed in letters, that is, a:b=c:d, then this law can be expressed as

.

Show the basic nature of proportion and let the students say.

In proportion, the product of two external terms is equal to the product of two internal terms, which is called the basic property of proportion.

If the proportion is written as a fraction (blackboard writing: =), please talk about the external term and the internal term.

Question: What is the relationship between the products of cross multiplication in this ratio?

Why are the products of cross products equal? (in proportion to basic nature)

4. Teaching "give it a try".

Let the students assume that these two specific energies make up a proportion, and tell what the external and internal terms of the proportion are, then calculate the products of the external and internal terms respectively, and judge whether the proportion is correct according to its basic properties.

3. Consolidate the exercises.

Do "exercises"

Let the students try to answer first, and then discuss the method of clearly judging whether four numbers are proportional. You can write two ratios with these four numbers and make corresponding judgments according to whether the ratios are equal. You can also divide four numbers into two groups and judge whether the products of two numbers in each group are equal. It is relatively simple to guide students to discover through communication and judge by using the basic nature of proportion.

Four. Standard inspection:

(1) Use the basic properties of proportion to judge whether the following two proportions can constitute a proportion, and write a proportion formula that can constitute a proportion.

6:9=9: 12 0.6:0.2= :

: =6:4 0.6:0.2= :

(2) Can the four numbers in the following groups form a proportion? Write down the proportion of the composition.

2、3、4、5 、 、 、

Verb (abbreviation for verb) class summary.

What did you learn in this class? What are your gains and experiences?

6. assign homework.

Exercise 10 questions 2, 3 and 4.

Second lesson

Teaching content:

Example 5 and the corresponding "Try it" on page 45 of the textbook, and complete the following "exercises" and exercises 5-8, totaling ten questions. And thinking about problems.

Teaching objectives:

1. Make students learn to apply the basic properties of proportion and solution ratio.

2. In the process of solution ratio, students can understand the connection and difference between proportion and equation, and realize the internal connection between mathematical knowledge.

teaching process

1. Review old knowledge

1. Question: What are the basic properties of proportion?

2. According to the basic properties of proportion, rewrite the following proportion into equal product formula. (oral answer)

4 3 = 2 1.5 = X 4 = 1 2

Question: According to the formula of product equation, can you find X in the last question?

3. Introduce new courses.

Today we will continue to learn the basic nature of proportion.

2. Teach new courses.

1. Example 5. Li Ming enlarged the following photos in proportion on the computer. The length of the enlarged photo is13.5cm. What is the width?

Question: What do you mean by "expanding the scale" in the question?

Let the students understand that the so-called "enlargement" of a photo is to enlarge all the line segments in the original figure in the same proportion. That is to say, the number of centimeters of related line segments before and after amplification can form different proportions.

Please try it. What proportion can you make up?

I don't know the width of the enlargement. What can we use to express it?

Please list the proportions with unknowns.

Can we use the basic nature of proportion to find the unknown term in proportion?

Ask the students to try to answer. Write a hypothetical sentence first, and then remind them of the proportion.

Solution: Let the width of the enlarged photo be x cm.

13.5:6=X:4

6X= 13.5×4 What is the calculation basis of the first step?

6X=54

X=

A: The width of the enlarged photo is centimeters.

After the answer, the teacher explained: finding the unknown item in the proportion as above is called the solution ratio.

2 Teaching "give it a try".

Students are required to complete it independently. After the completion, ask the students the thinking process when solving the problem.

3. Consolidate the exercises.

1. Do "exercises"

Students are required to complete it independently. After the completion, ask the students about their thinking process appropriately, and highlight the role of the basic nature of proportion in the process of solving the comparison.

Do "thinking"

Let the students read the questions and understand the meaning of the questions first, and then guide the students to understand the meaning of "two external terms are exactly reciprocal", that is, "the product of two external terms is 1". According to the basic properties of proportion, it can be inferred that "the product of two internal terms is also 1". So the other internal term should be reciprocal.

Four. Standard inspection:

(1) Fill in the blanks

1) () is called the solution ratio.

2) Any three terms in the ratio are known, and another unknown term can be found according to () of the ratio.

3) The two internal terms of a proportion are 1.8 and 0.6 respectively, and the product of the two external terms of this proportion is ().

4) Add, 0.5, 20% and a number form a proportion, and this number is ().

(2) solution ratio

Verb (abbreviation of verb) class summary

What is the content of this lesson? What are the basic properties of applying proportion and solving proportion?

6. assign homework.

Textbook exercise 10, questions 6, 7 and 8.