Basic properties of proportion

Bacun school Huang

Teaching content: "The Basic Nature of Proportion" People's Education Press sixth grade primary school mathematics volume II page 34.

Teaching objectives:

1. Make students further understand the meaning of proportion and know the names of each part of proportion.

2. Make students understand and master the basic nature of proportion.

3. The basic nature of proportion can be used to judge whether two proportions can form a proportion.

Teaching emphasis and difficulty: judging whether two ratios can form a ratio by using the basic properties of ratio, and correctly forming a ratio.

Teaching aid preparation: multimedia courseware

Teaching process:

First, exciting calibration.

1. What is proportion? Last class, we learned the meaning of proportion. Today, we will learn the basic nature of proportion.

2. Exhibition topic: the basic nature of proportion

3. Learning objectives:

(1) Know the names of the parts of the proportion;

(2) Understand and master the basic nature of proportion;

(3) Using the basic nature of proportion, we can correctly judge whether two proportions can form a proportion.

Second, self-study interaction

1. Understand the names of the parts of the scale.

(1) What are proportional terms, external terms and internal terms? Point out the external and internal terms in the ratio of 6: 100 = 9: 150.

(2) Can the ratio of 1.4: 2 = 7: 10 be rewritten as a component number? After rewriting the component number, can you still find the outer and inner terms of the proportion? Please have a try.

2. Explore the basic nature of proportion.

There is a relationship between the inner term and the outer term of (1). Can you find it?

(2) Is there such a relationship among all the proportions? Please calculate the outer product and inner product of the following proportions.

① and ② 0.8: 1.2 and 4: 6③ sum.

(3) Communicate your findings with your deskmate.

(4) Report the results

(5) induction

Blackboard writing: In proportion, the product of two external terms is equal to the product of two internal terms. This is called the basic nature of proportion.

3. Apply what you have learned:

(1) Use the basic properties of proportion to determine which of the following two groups can constitute a proportion.

①10: 20 and 0.5: 0.9 ③ and

Third, timely inspiration.

(1) When the proportion is written in fractional form, the numerator and denominator at both ends of the equal sign intersect respectively to form the outer and inner terms of the proportion.

(2) Write the proportion as a fraction. The basic property of proportion is that the cross product of numerator and denominator at both ends of equal sign is equal.

(3) In proportion, the product of two external terms = the product of two internal terms.

Fourth, detection training.

1. Use the basic properties of proportions to judge whether the following proportions can constitute proportions.

① 16: 20 and 12: 15 ②: 7 and: 20.

2. Can the following four numbers form a proportion? The proportion of writing (as much as you can write).

2, 3, 4 and 6

Verb (abbreviation of verb) course summary

What have you gained from studying in this class? Is there a problem?