The teaching goal of "Understanding the Circle" in the sixth grade mathematics teaching plan 1
1. Through origami, it is found that the circle is an axisymmetric figure, and the relationship between radius and diameter in the same circle is understood.
2. Further understand the characteristics of axisymmetric figures and the symmetry of circles.
3. Find the center of origami to verify that the circle is an axisymmetric figure, and develop the concept of space.
Textbook analysis
focus
Understand the radius of the same circle is equal, the relationship between radius and diameter in the same circle, and understand the symmetry of the circle.
difficulty
Experience the characteristics of circle in the process of origami
Training/teaching AIDS
Teaching compass
audio-visual aids
courseware
First, create a situation:
Liangliang drew a circle with the help of CD and cut out a round piece of paper. Where is the center of this circle? He soon found out. Do you have a way to know?
Second, exploration activities:
1, guide students to carry out origami activities and find the center of the circle.
(1) Find the center of the circle by yourself.
(2) Report the process of finding the center of the circle through communication, and express the idea of doing so.
2. What did you find by origami? Understand the symmetry of a circle.
(1) Enjoy beautiful axisymmetric graphics.
(2) Fold the paper in half again to understand the symmetry of the circle and draw the symmetry axis of the circle.
(3) A circle has numerous symmetry axes. The axis of symmetry is the straight line where the diameter lies.
3. What else did you find through origami? Understand the relationship between the inner diameter and radius of the same circle.
(1) What are the characteristics of the radius in the same circle when observing and thinking about origami?
(2) Observing and thinking while folding paper, what is the relationship between the diameter and radius in the same circle?
(3) Guide students to express the relationship between the diameter and radius of a circle with letters.
Third, classroom practice.
1, let students complete the test independently and exchange reports after the test.
2. Complete the exercise to further consolidate the relationship between the radius and diameter of the circle.
3. Complete the filling.
Let the students observe and think independently, and try to fill in the blanks. If you have any difficulties, ask the teacher or your deskmate.
Report the exchange and tell the basis of the answer.
4. Complete the third question at the end of the book.
Fourth, class summary.
Guide the students to summarize the contents of this section.
Students can easily find the center of the circle by using experience. If students are asked to explain why they can find the center of the circle by folding it in half and then folding it in half, it is difficult for them to say clearly. Find the answer by observing and thinking about origami in teaching. Communication report, from which we can further understand the symmetry of circles, and the radii of all circles are equal.
Appreciating beautiful symmetrical figures can guide students to sort out the axisymmetric figures they have learned, further understand the characteristics of axisymmetric figures, and find out the different characteristics of these axisymmetric figures through comparison, thus highlighting the good axial symmetry of circles.
Explore, discover and verify in the process of origami many times. Experience communication in operation, experience the characteristics of the circle and the concept of development space.
Individual students will have difficulty trying the topic, so pay attention to individual guidance.
blackboard-writing design
Understanding of Circle (2)
Our findings
All radii in the same circle are equal.
D=2r or r= 1/2d in the same circle.
A circle has countless symmetry axes, and the symmetry axis is the straight line where the diameter lies.
Students can easily find the center of the circle by using experience. If students are asked to explain why they can find the center of the circle by folding it in half and then folding it in half, it is difficult for them to say clearly. Find the answer by observing and thinking about origami in teaching. Communication report, from which we can further understand the symmetry of circles, and the radii of all circles are equal.
"The Understanding of Circle" —— The Teaching Goal of Math Teaching Plan II of Grade Six in Primary School
1. Guide students to feel and discover the relevant characteristics of a circle in activities such as observation, circle drawing and measurement, know what the center, radius and diameter are, and draw a circle with compasses.
2. Feel the difference between the circle and other figures in the activity, communicate their relations, gain rich mathematical beauty experience, and enhance students' recognition of mathematical culture.
Teaching clues
(A) the overall perception of activities
1. Thinking: How to find the circle from various plane figures?
2. Operation and experience: What's the difference between a circle and other figures? Perceive the characteristics of the circle as a whole in communication.
(B) rich operational experience
1. communication: the construction of compasses.
2. Operation: Students try to draw a circle and sum up the general method of drawing a circle with compasses in communication.
3. Experience (students draw circles for the second time): If the method is correct, why can't you draw straight lines or other curves with compasses?
4. Guidance (teacher demonstrates drawing a circle): Make students focus on the distance between two feet of compasses and realize that the distance between two feet of compasses is equal, which is the internal reason why a circle is a circle.
(3) In exchange and understanding.
1. Guide: Guide students to draw the above distance, thus revealing the center and radius of the circle, and then introduce their respective letter representations.
2. Thinking: What is the radius, how long is it, and how did you find it?
3. Summary: Introduce the relevant findings of ancient mathematicians and compare them with those of students.
4. Analogy: First introduce the diameter, then guide students to think analogously, find the characteristics of the diameter, and put forward the relationship between the diameter and the radius in the same circle.
5. Communication: What is the organic connection between the internal and external characteristics of a circle?
(D) deepen understanding in comparison
1. Comparison: How many similar equal-length "paths" are there in regular triangles, squares and regular pentagons? How many radii are there?
2. Communication: What is the internal relationship between these curves of regular polygons and circles?
(5) Forming structure in practice.
1. Discovery: What is the radius of a given circle without a center?
2. Imagine: What will happen to the size of circles with different radii? What is the size of a circle related to?
3. Guess: How to draw a circle without compasses? Further enrich students' understanding of the relationship between radius and diameter in communication.
4. Communication: How to draw a circle of a specified size with compasses?
(6) Deepen experience in the process of expansion.
1. Penetration: Compared with the straight line graph, the rotation invariance of the circle is revealed.
2. Introduction: Show the situation after the rotation of the straight line graph, guide students to feel the connection between the circle and the straight line graph again, understand the internal connection between the circle and the rotation, and enrich the understanding of the inherent aesthetic feeling of the curve graph of the circle.