Primary school sixth grade mathematics first volume understanding courseware
Teaching objectives:
1. Know the names of all parts of the circle, master the basic characteristics of the circle, and draw the circle correctly.
2. Cultivate students' hands-on exploration ability, develop students' inductive reasoning ability and inspire students' creative thinking.
3. In the process of observation, guessing, verification and application, students develop the concept of space and accumulate experience in mathematical activities.
4. Feel the relationship between things, understand the history of mathematics development in China, and enhance national pride.
Teaching emphasis: master the characteristics of the circle and draw it correctly.
Teaching difficulties: summarize the characteristics of circle, cultivate students' reasoning ability and develop the concept of space.
Teaching resources: round paper, square compasses, rulers, triangular plates.
Teaching process:
First, the pre-class study survey
1. Investigation and Research on "Understanding Circle" Learning before Class
(1) What do you already know about circles? What else did you learn?
(2) How to draw a circle with compasses? What are the skills?
(3) What is the difference between a circle and other plane figures?
(4) What are the characteristics of a circle?
(5) Where is the circle in life used? Can you explain why?
(6) What other questions can you ask about the circle?
Please select the questions you already know and share them with everyone.
3. Determine the starting point of teaching from students' answers. Write on the blackboard.
Second, understand the characteristics of the circle.
1. Understanding Curve Graphics: The teacher closes his eyes and draws an unclosed curve with his bare hands.
Is this a circle? Where is the least round?
Courseware demonstration: a plane figure surrounded by closed curves.
A plane figure surrounded by a closed curve is called a circle. Right?
The courseware shows ellipse and irregular curve graphics.
Like a circle, it is a plane figure surrounded by curves, which is called curve figure in mathematics.
2. Explore the characteristics of the circle
(1) overall grasp curve
We often use the method of "contrast and comparison" to discuss the characteristics. Can you think of those plane figures?
Courseware demonstration: triangle rectangle square parallelogram trapezoid
Classify these numbers. How would you classify them? Why?
(2) Show a set of combined figures: regular triangle, regular quadrangle, regular pentagon, regular hexagon, regular octagon and regular dodecagon with the largest inscribed circle.
(3) Guess: What are the characteristics of the length of the line segment from the center of each regular polygon to the vertex of the corner?
(4) Hands-on verification conjecture: Are the distances from the center point of a regular polygon to the vertices of each corner the same? How many equal line segments are there?
(5) Students report one by one, and teachers guide thinking, "The variables of regular polygons are increasing. What did you find? "
The variables of a regular polygon are increasing, and the regular polygon is getting closer to a circle. However, the number of equilateral segments of a regular polygon is limited, while the number of equilateral segments from a circle to the center of the circle is infinite.
(6) Summarize the characteristics of the circle:
3. Know the names of the parts of the circle:
Blackboard writing: radius and diameter of the center of a circle
4. Understand "a circle, an equal length":
People have studied circles for a long time. Mozi in the Spring and Autumn Period recorded in Mojing that "the circle is as long as a Chinese". What does this mean? The same length? What is the diameter? This understanding predates other countries 1000 years.
5. Summary: What are the characteristics of a circle? What is a circle?
Third, draw a circle.
1. Can the compass draw a circle? Please try to draw a circle with compasses and mark the names of the parts.
How much is the distance between two feet equal to a circle?
2. The drawing method of special circle:
Four, the connection between straight line graphics and curve graphics
Just now I found the characteristics of the circle through comparison. Things are often related. From the point of view of connection, is there any connection between curve graphics and straight lines?
Five, solid circle
Reflection after class:
Through the understanding of the circle, develop students' spatial concept and geometric intuition.
Geometric intuition is one of the core concepts in mathematics curriculum standards, which mainly cultivates students' abstract thinking ability through geometric intuition. But I personally think that geometric intuition should cultivate students' thinking ability in fitness, which is not the main goal of graphic geometry. Graphics and geometry mainly cultivate students' spatial concept. According to students' psychological characteristics, this course gradually cultivates students' spatial concepts from one-dimensional space to two-dimensional space and then to three-dimensional space.
Circle is a special plane figure, which is the basis of learning the surface area, volume and cone volume of a cylinder.
There are two basic knowledge points in the textbook, one is to know the characteristics of a circle (the relationship between center, radius, diameter and radius), and the other is to draw a circle.
The first knowledge point is declarative knowledge, which students can memorize by reading, but teaching must not let students know "what" but "why". This requires teachers to create a process for students to generate, put forward, analyze and solve problems, so that students can experience the process of observation, conjecture, exploration, verification and application, thus implementing the "four basics" and "four abilities".
China people's spirit of exploration has existed since ancient times, and ancient China was at the forefront of the world in the exploration circle. Students must be made aware of this in class to enhance national pride.