"Direct Proportion" Direct Proportion and Inverse Proportion PPT (Lesson 2)

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"Direct Proportion" Direct Proportion and Inverse Proportion PPT (Lesson 2)

Part One: Learning Objectives

1. Further understand direct proportion and be able to judge whether two related quantities are directly proportional. (emphasis)

2. Be able to use proportion to solve some simple life problems. (difficulty)

The ratio between the total price of the exercise books and the number of copies is certain. When the unit price is constant, the total price of the exercise books is proportional to the number of copies ( ) (fill in "Yes" or "No").

Proportional PPT, part 2: exploring new knowledge

Knowledge point: Determine whether two quantities are directly proportional

Is the area of ​​a circle proportional to its radius? what are you thinking? Communicate with peers.

According to the formula for the area of ​​a circle S=πr2, it can be seen that the area of ​​a circle changes with the change of the radius. So the area and radius of a circle are two related quantities.

The age changes of Lele and her father are as shown in the table on the right. Please fill in the table completely.

Are their ages proportional? Why?

Dad's age increases as Lele's age increases, so Dad's age and Lele's age are two related quantities.

Although the ages of Lele and her father are two related quantities, the ratio of these two quantities is not fixed, so the ages of Lele and her father are not proportional.

Give one proportional and one disproportionate example respectively and communicate with your peers.

(1) A quantity that is directly proportional to the relationship.

Example: The circumference of a circle is directly proportional to its diameter.

Rationale: The circumference of a circle changes as its diameter changes, and they are two related quantities. The distance on the picture/actual distance = pi (certain), so they are directly proportional.

(2) Quantities that are not directly proportional.

Example: A book has a certain total number of pages, but the number of pages that have been read and the number of pages that have not been read are not proportional.

Reason: The number of pages read + the number of unread pages = the total number of pages (certain). Although the number of pages read and the number of unread pages are two related quantities, one of them increases with the other. Changes with changes, but the sum of these two quantities is constant, not the ratio, so the number of pages read and the number of pages not read are not directly proportional.

Knowledge refining

To determine whether two quantities are directly proportional, first determine whether the two quantities are related. If the two quantities are related, then see whether their ratio (i.e. quotient) is certain. If it is certain, then the two quantities are directly proportional. Their relationship It is a direct proportional relationship.

Proportional PPT, Part 3: Consolidation Practice

1. Determine whether the two quantities in the following questions are directly proportional and explain the reasons.

(1) The mass of each bag of rice is certain, the total mass of rice and the number of bags.

(2) A person’s height and age.

(3) The width remains unchanged, the perimeter and length of the rectangle.

2. Complete the form. What did you find out? Is the amount payable proportional to the number of stamps purchased?

Answer: Directly proportional.

3. True or false questions.

(1) The oil yield rate of peanuts is certain, and the quality of peanut kernels is directly proportional to the quality of oil squeezed out. ( )

(2) The unit price of bananas is fixed, and the quantity purchased is proportional to the total price. ( )

(3) The height of a parallelogram is constant, and its corresponding base is proportional to its area. ( )

Proportional PPT, Part 4: Class Summary

What knowledge have you learned in this class?

To determine whether two quantities are directly proportional, first determine whether the two quantities are related. If the two quantities are related, then see whether their ratio (i.e. quotient) is certain. If it is certain, then the two quantities are directly proportional. Their relationship It is a direct proportional relationship.

Proportional PPT, Part 5: Homework

Assignment 1: Complete the exercises related to the textbook.

Assignment 2: Complete the corresponding exercises.

Keywords: Free download of Beijing Normal University edition sixth-grade mathematics PPT courseware for the second volume, direct proportion PPT download, direct proportion and inverse proportion PPT download, .PPT format;

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Update Time: 2024-11-16

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