The sixth grade mathematics "proportion" courseware [3]

The sixth grade elementary school mathematics "proportion" courseware I

Teaching objectives:

1. Solve some simple life problems with positive proportion and feel the wide application of positive proportion in life.

2. Whether two related quantities are proportional can be judged according to the meaning of direct ratio.

3. Combine rich examples to understand the direct ratio.

Teaching focus:

1, combined with rich examples, understand the direct ratio.

2. According to the meaning of positive proportion, we can judge whether two related quantities are in direct proportion.

Teaching difficulties:

We can judge whether two related quantities are in direct proportion according to the meaning of direct proportion.

Teaching tools: courseware

Teaching process:

First, preview before class

Preview 19-2 1 page content

1. Fill in all the forms in the book.

2. Understand the meaning of the words in the pink box and understand the relationship between the two quantities.

3. If you don't understand it, mark it with a pen and ask questions in class.

Second, display and communication.

Activity 1: the change law between two related quantities in the feeling situation.

(1) Scenario 1:

1. Observe the chart and fill in the changes of the perimeter and side length, area and side length of the square respectively. Please fill in the data in the form according to your observation.

2. Think after filling in the form: Does the circumference of a square have anything to do with the side length, and does the area have anything to do with the side length? What are their changing rules? Are the rules the same?

Tell me what you found in the data.

3. Summary: The perimeter and area of a square increase with the increase of side length. In the process of change, the ratio of the perimeter to the side length of the square must be 4. The ratio of the area of a square to the length of one side is an uncertain value.

Tell me about the pattern you found.

(2) Scenario 2:

1, the speed of a car is 90 km/h, and the driving time and distance of the car are as follows:

2. Please fill in the form below completely.

3. What rules did you find from the table?

Tell me about the law you found: the ratio of distance to time (speed) is the same.

(3) Scenario 3:

1. Some people buy apples. The quality of the apples they bought and the amount they should pay are as follows.

2. Fill in the form completely.

3. What rules have been found from the table?

The ratio of the amount payable to the quality (that is, the unit price) is the same.

4. What do the above two examples have in common?

Summary: the distance changes with time, and the ratio of distance to time is the same in the process of change; The amount of money payable varies with the quality of the apples purchased, and the ratio of the amount of money payable to the quality is the same in the process of change.

5. Proportional relationship:

(1) The time increases, so does the distance traveled, and the ratio of distance to time (speed) remains unchanged. Then we say that distance is proportional to time.

(2) What is the relationship between the amount of money payable for buying apples and the quality?

6. What are the characteristics of the quantity that is directly proportional to observation and thinking?

One quantity changes with another quantity, and the ratio of these two quantities is the same in the process of change.

(4) think about it:

1. Is the circumference of a square proportional to the length of its sides? What about area and side length? Why?

Teacher's summary:

(1) The circumference of a square changes with the change of side length, and the ratio of circumference to side length is 4, so the circumference of a square is proportional to the length of the side.

Please also try to say.

(2) Although the area of a square varies with the side length, the ratio of the area to the side length is a variable value, so the area of a square is not proportional to the side length.

Please speak in your own language.

2. The age changes of Xiao Ming and his father are as follows:

Xiaoming's age/year 6789 10 1 1

Dad's age/year 3233

(1) Fill in the form completely.

(2) Is the age of father and son proportional? Why?

(3) Dad's age = Xiaoming's age +26. Although Xiao Ming's age increases, so does his father's age, but the ratio of Xiao Ming's age to his father's age changes with time, not a certain value, so the age of father and son is not proportional.

Communicate with your deskmate and report collectively.

Feel and summarize the characteristics of the positive proportion relationship in the teacher's summary.

Mathematics "Proportion" Courseware II for the Sixth Grade of Primary School

Teaching objectives:

1. Find out the examples of direct ratio in life by constructing the process of direct ratio, and correctly judge direct ratio through specific problems.

2. Through observation, comparison, analysis, induction and other mathematical activities, the characteristics of positive proportional quantity are found, and the meaning of positive proportional quantity is tried to be abstractly summarized. Improve the ability of analysis, comparison, induction, judgment and reasoning, and at the same time infiltrate the preliminary function thought.

3. In the process of actively participating in mathematical activities, I feel the order of mathematical thinking process and the certainty of mathematical conclusions, and I am willing to communicate with others.

Teaching process:

First, dialogue import

1. Show pictures of apples, pears and oranges. Q: What is the general name?

2. Presentation: Fill in the blanks according to the first question.

(1) Time: 3 hours and 20 minutes, 2 hours and 45 minutes.

(2) Total price: 5 yuan () ()

(3) (): 6 kg 800 g, 3 tons 350 g.

After filling it out, ask: What's on the left? What's on the right? Can you name another quantity and its corresponding number?

Second, learn new lessons.

(a) Relevant quantities

In the experiment, the teacher put a tick on the spring scale and asked:

(1) What are the two variables? (2) Why does the spring length change?

It is pointed out that the length of the spring varies with the number of hook yards, and two quantities like this are called correlation quantities.

Follow-up: Do you know what the correlation is now? Can you give me an example?

(B) Learning is directly proportional to quantity.

1. Displays the table on page 19.

Observe the image, fill in the form and answer the following questions:

(1) What are the two associated quantities in the table?

(2) How does the circumference of a square change with the change of side length?

(3) How does the square area change with the change of side length?

(4) Do they change in the same way?

Group discussion exchange report

2, Page 20, Question 2

3. The meaning of direct ratio

(1) What are the similarities between Example 1 and Example 2? (two related quantities, the proportion is certain)

The teacher pointed out: these two quantities are proportional quantities, and their relationship is called proportional relationship.

Q: Do you know what proportional quantity is now? Free speech means that students answer reading textbooks.

Teacher's blackboard writing relationship: y/x=k (certain)

(2) So, what should we look at to judge whether two quantities are proportional?

Third, consolidate and improve: 19 pages.

Fourth, the class summarizes.

The third part of "proportional" courseware for sixth grade primary school mathematics

Teaching objectives:

1, so that students can understand the image characteristics of the quantity expressed in direct proportion and solve related simple problems according to the image.

2, through practice, consolidate the understanding of the significance of positive proportion.

3. Emotion, attitude and values: the concept of initial infiltration.

Key points and difficulties:

Whether two quantities are proportional can be judged according to the quantitative relationship or image.

Teaching preparation:

Projector.

Teaching process:

First, the new teaching

Teaching page 46.

The teacher shows the form (see the book) and draws points according to the data in the form. (See this book)

Teacher: What do you find in the picture?

Health: These points are all on a straight line.

Look at the picture and answer the questions.

If the number of pencils is seven, what is the total price of the pencils? ② What is the number of pencils with a total price of 4.0? The number of pencils is three, so what is the total price of pencils? Draw this corresponding point. Are they on the same straight line?

What other questions can you ask? What experience do you have?

Organize students to report in groups, and what students may say during the report.

① The image of the proportional relationship is a straight line passing through the origin.

(2) Using the positive proportion image, the corresponding value of one quantity can be directly obtained from the value of another quantity without calculation.

Second, practice teaching.

1, basic exercise.

(1) Projection shows the question on page 49 of the textbook 1.

Teachers guide students to review the meaning of positive proportion and the method of judging whether it is positive proportion. Students finish the exercises independently.

The teacher asked the students to explain why it is proportional from two aspects. A. the electricity consumption increases with the increase of electricity consumption; B. the ratio of electricity bill to electricity consumption is always equal.

Teachers and students make the same changes.

(2) Projection demonstration: a train travels 90km 1 hour,180km for 2 hours, 270km for 3 hours, 360km for 4 hours, 450km for 5 hours, 540km for 6 hours, 630km for 7 hours, 720km for 8 hours. ...

① Show the following table and fill in the form.

Time and distance of the train.

Fill in the form and think about what you found.

(3) Teacher's teaching: With the change of time, distance is also changing, so we say that time and distance are two related quantities. (blackboard writing: two related quantities)

Teacher: What did you find according to the calculation? It is pointed out that the ratio of two corresponding numbers is fixed, which is mathematically called certainty.

⑤ Express their relationship with a formula: distance ÷ time = speed (certain).

Teacher: Last class, we learned proportional quantity. Let's continue to study and practice.

2. Guide the exercises.

(1) Complete the second question on page 49 of the textbook.

(2) Complete the third question on page 49 of the textbook. Students should finish it independently first, and then the teacher will make a spot check. Ask different students to answer (1) questions. When doing the second question, let the students communicate more. (3) When reporting a small problem, ask how you estimate it, and go on stage to show the thinking process of estimation on the projector.

(3) Answer the fourth question on page 49 of the textbook: ① Show the tables in the book by projection to guide students to observe the data in the tables.

② Organize students to explore in groups. A. Draw a picture and report the image characteristics by name. B. organize students to talk and communicate with each other.

Tip: To judge whether two quantities are directly proportional, we should first judge whether they are related quantities, and then judge whether their ratio is determined.

Third, class assignments.

1. Fill in the blanks in the table according to the direct ratio between X and Y.

2. Look at the picture and answer the questions.

(1) In this process, which quantity has not changed?

(2) What is the relationship between distance and time?

(3) Not counting, how many kilometers did you drive in 4 hours?

(4) How many kilometers do you drive in 7 hours?

Course summary:

Teacher: What are the three factors to judge the direct ratio of two related quantities?

What did you get from this lesson?

Homework after class:

Complete the exercises in this lesson in the workbook.