The comprehensive application of "determining the starting line" is designed on the basis that students have mastered the concept and circumference of a circle. Through this activity, on the one hand, students can understand the structure of elliptical track and learn how to determine the starting line of the track; On the other hand, let students really realize the wide application of mathematics in sports and other fields.

The activity of "Determining the Starting Line" consists of the following four parts.

1. Put forward research questions.

Based on the background of track and field 400 m runway, the textbook puts forward the question "Why do athletes stand at different starting lines", which arouses students' concern and thinking about the starting line position. After discussing with the students in the group, we reached the conclusion that the finish line is the same, but the length of each runway is different. If the students in the outer ring run a long distance on the same runway, the starting line position of the outer ring runway should be moved forward. " On the basis of this cognition, the textbook leads to the question of "how many meters should the starting line of each runway be different", that is, how to determine the starting line of each runway.

2. Collect data.

The second picture on page 75 of the textbook shows a set of data related to students' measurement to help students understand the structure of the 400 m runway and the scene of each part of the data: the length of the straight runway is 85.96 m, the diameter of the first semi-circular runway is 72.6 m, and the width of each runway is1.25m. ..

3. Analyze the data.

Students collate the obtained data and make clear the following information through discussion: (1) Two semi-circular runways together are a circle. (2) The straight line length of each runway is the same. (3) The length of each runway is equal to the circumference of the circle formed by two semi-circular runways plus the length of two straight lanes. The above analysis process is mainly reflected in the third picture on page 76.

4. Draw a conclusion.

After the students have made clear the ideas and methods of solving problems, the textbook gives a table in the fourth picture. By asking students to calculate the diameter of semi-circular runway, the perimeter of two semi-circular runways and the total length of runways, the difference between the lengths of adjacent runways can be calculated and the starting line of each runway can be determined. Finally, in order to consolidate the understanding of this kind of problem, please further determine the position of the starting line of the runway in the 200-meter race.

Teaching suggestion

1. This part can be taught in 1 class hour.

2. The sixth-grade students are no strangers to the starting line, and they also know that when running 200m, 400m and 800m races on the 400m runway, the starting positions of athletes on different runways are different. But why? Students may rarely think seriously from the perspective of mathematics. Therefore, at the beginning of the activity, the teacher can present the 400 m track in the track and field field in the form of pictures, slides or multimedia courseware, and directly ask the question "Why do athletes stand at different starting lines?" In order to arouse students' thinking and discussion, students should be able to quickly sort out their thoughts and answer questions by virtue of their daily sports activities and experience in watching sports competitions. According to the students' answers, the teacher can ask questions in time for further research: "How many meters should the starting line of each runway be different?" Obviously, this is difficult to get through experience and observation. Students need to collect relevant data and specifically analyze what the starting line is related to.

3. In the part of data collection, the textbook gives the situation of team cooperation field measurement, but because the specifications of different track and field fields may be different, it takes more time to carry out field measurement, and the measurement may also produce errors, so it is not necessary to lead students to actually measure the data of various parts of track and field in actual teaching. As long as the students can make it clear that the relevant data are obtained through measurement, the specific data can be given in combination with the previous pictures, slides and other corresponding forms. The teacher can also explain to the students how the diameter of the semi-circular runway is specified here and how the width of the runway line is ignored here.

4. When analyzing the data in detail, the teacher can guide the students to fully discuss and realize that because each runway is 1.25 m wide, the diameter of the outer circle of two adjacent runways is equal to the diameter of the inner circle plus 2.5m When discussing specific solutions, the teacher should also guide the students to think flexibly, instead of just calculating the total length of each runway. When the students make it clear that the straight line length of each runway is the same, the teacher can inspire the students in time: "Since the straight line length is the same, what can we do to find out the difference between the adjacent runways?"

5. After the students have a clear idea to solve the problem, the teacher can show the table in the fourth picture and ask the students to talk about the meanings of each item in the table and calculate the corresponding results. Teachers should help students make it clear that the distance between the starting lines of each runway can be obtained not only by calculating the difference of "total length", but also by calculating the difference of "perimeter". It is particularly important to note that in the result, the difference between two adjacent runways is actually (72.6+2.5N) π-[72.6+2.5 (n-1)] π = 2.5π, because the value of π (π ≈ 3.141)

6. At the end of the textbook, the problem of determining the starting line of the 200 m runway, such as insufficient class hours, can be solved by students after class.