Slope analysis in teaching materials is one of the simplest machines. In production and life, people often use inclined planes to achieve the purpose of saving labor. The distance that a cylindrical object rolls down an inclined plane is not only related to the length of the inclined plane, but also related to the included angle between the inclined plane and the ground. This practical activity arranged by the textbook is to let students get data through experiments, compare and analyze, and find out what angle the inclined plane makes with the ground, so that the cylindrical object can roll further.
Teaching objectives
1. Knowledge and skills: By rolling at different angles on the inclined plane, compare which angle is the farthest, and let students know the distance that a cylindrical object rolls down from the inclined plane, which is not only related to the length of the inclined plane, but also related to the angle between the inclined plane and the ground, and at which angle the cylindrical object rolls farthest.
2. Process and method: Through practical operation and group communication, let students know at what angle the cylindrical object rolls farthest.
3. Emotion, attitude and values: Through hands-on practice and independent inquiry, students can cultivate their problem-solving ability and innovative consciousness and stimulate their interest in learning mathematics.
[Teaching Emphasis] Let students know that the distance that a cylindrical object rolls down an inclined plane is not only related to the length of the inclined plane, but also related to the included angle between the inclined plane and the ground, and at which angle the cylindrical object rolls farthest.
Teaching difficulties: how to make the experiment more accurate and summarize the experimental results in time.
[Teaching AIDS] Wooden boards, cylindrical objects, tape measures, triangles, etc.
[Teaching process]
First, create situations and introduce new lessons.
The teacher asked: how can a person transport an elephant to a truck?
Recognize the students' creative answers and realize that slope construction is both economical and labor-saving!
Teacher's introduction: In production and life, people often use inclined planes to achieve labor-saving purposes.
Show the situation map: how to get the oil drum off the truck? How to transport the cut wood down from the mountain? After discussion, it is concluded that using slopes is labor-saving and economical, which is what workers' uncles usually do! )
Guided observation: What are the shapes of these rolling objects?
Further thinking: what factors may be related to the rolling distance of an object rolling down a slope?
Students can guess freely: the weight of the object, the rolling height, the angle between the slope and the ground, the smoothness of the ground and the length of the slope. ...
The teacher concluded by introducing a new lesson: there are many factors that affect the rolling distance. Today, we will choose one of them to study: under the same other conditions, what angle does the inclined plane make with the ground and the object rolls farthest? (Showing courseware) (Writing on the blackboard: how i roll Yuan)
[Design Description: Bevel is widely used in life. Inferred from students' real life experience, the rolling distance of cylindrical objects is related to many factors. Therefore, only under the same conditions can the data obtained be of comparative significance. This lesson only studies one aspect, when the slope is at a certain angle with the ground, the object rolls farthest]
Second, cooperate in experiments and explore conclusions.
1, guess
Teacher's question: Do you think the angle of the slope is bigger or smaller? Let the students speak freely first.
The courseware shows that there are three different slopes of 30 degrees, 45 degrees and 60 degrees, all made of the same board. Now roll the same object down these three slopes. Which slope do you think can make the object roll farthest? The teacher asked the students to guess first, and then told the reason for this guess.
Further guidance: Is the student's guess right? How to verify? It is revealed that doing experiments is a good way to verify the conjecture.
Let's look at the steps and requirements of the experiment first!
Step 2 experiment
(1) experimental steps (see pictures in the textbook)
The teacher asked: Can you tell me the steps needed to do such an experiment? What is the first step to cultivate students' language expression ability? What's next?
Teacher's summary: these steps can be summarized as: sit, roll and measure.
How many people do you need to do this experiment? How to assign tasks? (Look at the group experiment photos)
Two people board the board, 1 roll, two people measure, 1 record.
(2) Operation demonstration
In order to better guide everyone in the experiment, the teacher demonstrated the experimental process of 30-degree slope. Because there is not enough space, the students behind can't see clearly. Please watch the live video of the teacher's experiment. (Play the courseware)
The experimental operation needs to be scientific and rigorous, otherwise the experimental result is a drop in the bucket. What details do you think should be paid attention to? (Students speak freely)
(Take: the inclined plane is smooth and the angle is aligned)
(Scroll: put the top lightly and slide freely)
(Quantity: measured at the bottom and drawn as a straight line)
Experiments at 45 degrees and 60 degrees also follow the same methods and steps.
Before class, the teacher asked the students to prepare many cylindrical objects. Today, in order to make the experimental data more comparable, our classmates in the same group did experiments with the same object. Many unexpected things will happen in the experiment. Under the leadership of the team leader, each group has a reasonable division of labor, unity and cooperation, and the courage to solve problems to ensure that the experimental results are true and credible.
In the end, which degree of slope rolls far, this mystery is solved by everyone!
(3) Students in each group do inclined plane experiments of 30 degrees, 45 degrees and 60 degrees respectively.
With the experimental guidance just now, students can experiment independently, and teachers can observe and guide them to help individual team members in trouble in time.
3. Conclusion
(1) Team Report:
The same slope, is the data measured the same every time?
What do you find by comparing the average values obtained each time?
Did you encounter any difficulties in the process of doing the experiment?
On the basis of the experimental data obtained by the group, organize students to communicate, draw conclusions through comparative analysis, feel the rationality of studying problems by experimental methods, and gain successful experience.
When the angle of the slope is 45 degrees, the cylindrical object is farthest from it.
(2) Teacher's summary: (Show courseware)
(3) Expansion and extension
Today, we studied a three-degree slope and found that the object rolled farthest when the slope angle was 45 degrees!
Life has many slopes. Is there a slope that rolls further than a 45-degree slope? We need further research. Limited to the test site and the number of experiments, it can only be concluded that when the slope is about 45 degrees, the object rolls further.
We want to know how many degrees can make an object roll farthest? What other angles can be studied? (30—45,45—60)
After class, please experiment with the slope from other angles and see what else you can find.
[Design Description: Provide three kinds of slopes, which slope can make the object roll further, let the students guess first, and then guide them to find ways to verify their guesses. The classroom leaves time and space for students, and through hands-on operation, cooperation and communication, comparative analysis, full exploration and correct conclusion are drawn. ]