C=3. 14×77.677.6=243.664

s = 3. 14×(77.6÷2)2 = 4 15.7

Anyway, there is a rule: d +2.5 C +7.85 S +7.85.

Teaching objectives

1. Let students understand that "the outer circle of the curved part of the runway is longer than the inner circle" by using the relevant knowledge of the circle to calculate the curve distance, so as to learn the method of determining the starting line.

2. Combining with specific practical problems, through observation, comparison, analysis, induction and other mathematical activities, improve students' ability of independent thinking, cooperative communication and solving practical problems.

The focus of teaching is to understand the structure of track and field track through the calculation formula of circumference, and correctly calculate the position of the starting line according to the principle of starting line setting.

Difficulties in teaching comprehensively use the knowledge of circle to answer practical problems encountered in life and explore what the starting line position is related to.

teaching process

First, introduce the situation and put forward the learning objectives.

1. scene import: event playback. Appreciate the pictures of athletes starting on the sports ground.

Teacher: What do the students think of this game? How do you think the game is fair?

Teacher: The students have the same idea as our sports competition. They will take part in the 400-meter race. If starting from the same starting line, the outer lane is longer than the inner lane, and there is a gap between adjacent runways, for the sake of fairness, the starting line will move forward in turn.

2. Question: In sports competitions, two adjacent starting lines advance a certain distance. Is this distance moving casually? How many meters is the difference between adjacent starting lines? Can you tell?

3. Learning goal: Understand "the length of the outer ring at the corner of the runway" and learn how to determine the starting line.

(blackboard writing topic: determining the starting line)

Second, show the learning results.

(1) Let the students know "the curve part of the runway, the outer ring is longer than the inner ring" and sort out the methods to determine the starting line.

(2) Observe and make clear the gap: (Show a complete runway map)

Teacher: Look at this picture. Is the length of each runway equal?

Health: inequality.

Teacher: What's the difference?

Health: The difference lies in the curved part of the runway. The curve of the outer ring is long and the curve of the inner ring is short. The finish line is the same. If you are at the same starting line, the athletes in the outer circle will run a long distance.

Teacher: So in the competition, in order to be fair, the starting line of the outer ring should be in front to ensure that every athlete runs the same distance.

(C) analysis, determine the train of thought:

1. Group sending: Observe the above picture. What is the specific part of each runway?

Report: Each runway consists of two straight runways and two semicircular runways.

Teacher: What part of the length is 85.96 meters?

Health: It means that each straight road is 85.96 meters.

Teacher: Since each straight is 85.96 meters, that is to say, the length of the runway has nothing to do with the straight. In order to facilitate our better observation, shall we take the straight for the time being?

Teacher: What is the combination of left and right semicircles?

Health: Together, it is a circle.

Teacher: What is the length of each lap of the runway now?

Health: Because two semi-circular runways are a circle together, the length of each runway can be regarded as the sum of the length of two straights and the circumference of the circle.

2. Panel discussion:

How to find the gap between two adjacent runways?

Summary of report:

(1) Calculate the length of each runway separately, that is, calculate the sum of the length of two straight lines and the circumference of a circle, and then subtract it to know the gap between two adjacent runways.

(2) Because the length of the runway has nothing to do with the straight road, as long as the perimeter of each circle is calculated, and then the difference between the perimeters of two adjacent circles is how many meters, it is the difference between adjacent runways.

Third, stimulate knowledge conflicts.

Teacher: What do you need to know to calculate the circumference of a circle?

Health: diameter

Teacher: The diameter of the first lane is 72.6 meters. What is the diameter of the second pass? What about the third way?

(Let the students choose their favorite method to calculate) Method 1: Complete the calculation in the table below.

(Instruct students to change 3. 14 159 into π for calculation)

Teacher: Just now, we all know that the length of two adjacent runways in the 400-meter race is about 7.85 meters, which means that the starting lines of adjacent runways should be 7.85 meters apart. Which method is faster and simpler?

Health: The second method is relatively simple.

The difference between the starting lines of adjacent runways is "runway width ×2×π"

(blackboard writing: difference between adjacent starting lines in 400-meter race: runway width ×2×π)

Teacher: It can be seen from here: What is the most closely related to the determination of the starting line?

Health: It is most closely related to the width of the runway.

Teacher (summary): The students finally found the secret of determining the starting line through hard work! By the way, as long as you know the width of the runway, you can determine the starting line.

Fourth, expand applications.

1, Teacher: Students are really interested! However, the referee adjusted the width of the runway in a certain game. Can you help the referee calculate the difference in starting lines between two adjacent runways?

400 meters race, runway width 1.5 meters. How many meters should the starting line advance in turn? What if the runway width is 1. 1 m?

2. There are 200m races on the sports field, the runway width is 1.25m, and how many meters should the starting line advance in turn?

Verb (abbreviation for verb) class summary:

Tell me about it. What did you learn from this course?