The first part of mathematics courseware for the sixth grade of primary school: "the understanding of circle"
Teaching objectives:
1. Knowledge objective: to master the names of all parts of the circle and the characteristics of the circle; Can draw circles with compasses.
2. Ability goal: with the help of hands-on activities, cultivate students' ability to solve practical problems by using what they have learned.
3. Emotional goal: Infiltrating knowledge comes from practice, and the purpose of learning is to apply ideas.
Teaching methods:
Guide training method, transfer method, example method
Teaching preparation:
Multimedia courseware, compass, ruler, etc.
Teaching process:
First, introduce new courses by combining practice and dialogue.
Introduction: I am very happy to study with my classmates today.
Study a mathematical problem. We knew this circle before. Can you find out which things in life are round?
Teacher: It seems that everyone doesn't pay attention to observation at ordinary times. Please draw two circles of different sizes and cut them out before class. Are you ready?
Teacher: Lift them up and let's have a look at each other. Looking back at the process of drawing and cutting a circle, can you tell me what a circle looks like? (The teacher has a circle in one hand)
Teacher: The students observe carefully. The edge of the circle is curved, followed by
The sides of a rectangle and a square are different. Today, we are going to study the curve figure on this plane. (blackboard writing topic)
for instance
The teacher emphasized-refers to the surface of the object.
The circle has no edges and corners, and the edges are curved; The edge of a circle is a curve.
Second, guide the exploration of new knowledge.
1. Guide: What secrets are hidden in the circle? Let's do a little experiment. Fold your circle in half, fold it again, fold it several times, draw creases, see what you find, and report your findings in the group. Finally, see who gets more. (1 min)
2. Teacher: Your group has observed very carefully! You have found a lot. Now let's sort out what we just found.
3. Display the query results. Fully understand the characteristics of the circle with the help of multimedia courseware (8 minutes)
Who will tell the teacher what you have found?
What is the reason?
How did you find out?
Combine students' communication and report the results of inquiry, and guide them in time. Mainly from the center, radius, diameter and other aspects. Here, we should pay special attention to helping students master new knowledge through blackboard writing and make purposeful arrangements.
4. Learn to draw a circle (5 minutes).
How do you draw a circle?
The courseware shows how to draw a circle. Then the students began to practice, emphasizing what should be paid attention to when drawing a circle. -Displays the size of the circle.
Determination of position
The school plans to build a flower bed with a diameter of 20 meters. Can you draw this circle for the school? Student demonstration operation
Third, application expansion.
1. Basic exercise (4 minutes).
<1> projection presentation
Find the radius and diameter of the following circle.
< 2 > calculation of radius and diameter.
< 3 > Judgment and identification of concepts.
2. Application exercises. (10 minutes)
← 1 \8592; Why are the wheels round and where should the axles be installed?
If the wheels are made into squares and triangles, how will we feel sitting on them? Combined with courseware demonstration
〈2〉 Can you explain some life phenomena with the knowledge of circle learned today?
When a bonfire party is held, people always form a circle unconsciously. Why?
What will happen if you throw a pebble on a calm lake? Why?
Moon cakes are usually made into circles. Why? )
It seems that many phenomena in life contain rich truths, which need us to explore, understand, explain and apply constantly.
< 3 > The students are very tired after learning, so let's relax. The teacher guessed a riddle for everyone. A man nailed a stake in a meadow and tied a sheep there with a rope. (with computer graphics)
Teacher: Does herding sheep have anything to do with what I learned today? Let's see how much the sheep eat grass, shall we?
Use computer to demonstrate the situation that the sheep tightens the rope and rotates once, so that students can intuitively see that the range of grass that the sheep can eat is a circle. Does the rope tied to the sheep have anything to do with this circle?
What is the circle of the stake nailed there? (It is the center of this circle) What should I do if I want this sheep to eat more grass? (Make the rope longer, that is, enlarge the radius) What should I do if I want the sheep to eat grass in another place? (you can move the stake one position, that is, the position of the center of the circle), which shows what the radius and center of the circle have to do with the circle?
The radius of the circle determines the size of the circle, and the center of the circle can determine the position of the circle.
Fourth, the class summary (3 minutes)
1. Ask
Is basketball round? Can the letters representing the center, radius and diameter be changed at will? )
2. What did you learn in this class?
Anyway, the teacher thinks that the students' academic performance is good. I suggest that everyone reach out and come to a satisfactory conclusion together. (Period is an integer)
expand
1. Draw with a circle.
2. Tell me about the circle in my eyes.
Blackboard design:
Understanding of Circle-Plane Curves
Center of the circle (O) The point at the center of the circle, which is used to determine the position of the circle.
Radius (r) line segment
Connect the center of the circle to any point on the circle to ensure that the circle is equal in size and length.
The line segment with diameter (d) passes through the center of the circle, with both ends on the circle and equal length. In the same circle
The relationship between radius and diameter is d=2r.
Teaching reflection:
Let the students understand that all radii are equal only in the same circle or in the same circle; All diameters are equal; The radius is half the diameter, and the diameter is twice the radius.
Mathematics Courseware for the Sixth Grade of Primary School Part II: Understanding of Circle
Teaching objectives:
Knowledge and skills
(1) Know the names of the circle and its parts.
(2) Make students master the characteristics of a circle, understand and master the relationship between radius and diameter in the same circle, seek for any radius and diameter in a circle, and independently solve the problem of finding a known radius or diameter.
(3) Let students learn to draw circles with compasses. A circle with a known radius or a circle with a known diameter can be drawn with a compass.
Process and method
(1) Cultivate students' drawing ability through hands-on activities.
(2) Cultivate students' innovative consciousness and abstract generalization ability through group learning, hands-on operation and active exploration, and further develop students' spatial concept.
(3) In the process of learning, cultivate students' ability to cooperate with others and exchange thinking process and results.
Emotions, attitudes and values
Through the understanding of the circle, I feel that beauty comes from life, that the circle is closely related to daily life, and I feel the charm of mathematical knowledge.
Teaching objectives:
1. Through activities such as drawing a picture, folding it, measuring it, etc. Observe and experience the characteristics of a circle, know the names of each part of the circle, and understand the relationship between the inner diameter and radius of the same or equal circle.
2. Understand and master various methods of drawing circles, and learn to draw circles with compasses initially.
3. 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 focus:
Explore the names, characteristics and relationships of each part of a circle.
Teaching difficulties:
Experience the characteristics of the circle through practical operation.
Teaching process:
First, the whole perception circle
1. Slide Show: Cycle in Life
Photography, what graphics do you find in these beautiful pictures? Where have you seen a circle in your life?
2. Demystifying the topic: The circle is everywhere, and we will know it in this class.
Blackboard Writing: Understanding of Circle
3. Do the students like playing basketball? Why don't you try it now?
I have a toy here. I ask you to stand three meters away from it and throw a circle. Where can you stand?
We use three centimeters to represent three meters. Can you mark your place in this book?
2. Real investment in students' grades (from drawing a few points to many points to circles)
Q: Is it okay to stand on all these points? Why? Can we only stand on these points?
After the circle appears, ask, is there a place to stand?
3. Courseware demonstration
Teacher: Where should I stand? (Any point on the circle)
How many such points are there on the circle?
Second, understand the circle in operation.
1. There is a circle on the screen. Can students make a circle with existing tools?
2. Students draw circles and teachers patrol.
3. Report different methods of drawing a circle (first find the report of drawing a circle with a circle tool).
Demonstration on the blackboard with line drawing
Talk: This classmate drew such a big circle on the blackboard with such a long rope. What if I want to draw a big circle on the playground?
Practical demonstration of compass project
4. Summarize the method of drawing circles with compasses.
5. Students practice compasses and draw some circles.
Why invent compasses when you can draw circles with the help of circular tools?
6. Observe the circle you draw. What else is there besides a closed curve? (a little)
Give it a name-the center of the circle (if students can say it) is represented by the letter O.
7. Take out the round paper in your hand. Is there any way to determine the center of this circle?
The students began to fold.
Q: Besides the center of the circle, what else did you find? (crease)
What is the crease you found?
Teacher: Who wants to go to the front and introduce their findings? Reveal the definition of diameter and radius.
Can you draw the diameter and radius on the circle?
Mark the center, radius and diameter of the circle you draw.
Third, exchange exploration circles.
What are the functions of the center and radius? Just draw a picture.
1. Draw several different circles on the book with compasses to see who draws them beautifully.
2. Projection display
Q: Some of your pictures are round, some are up, some are down, some are left and some are right. What is the decision?
Student report, why is Yuan so obedient?
Teacher's summary: The center of the circle determines the position of the circle. No wonder people call it the center.
These circles vary in size. How can we draw them?
Summary: The radius of the circle determines the size of the circle (the distance between two feet of the compass).
3. Teacher: The ability of radius is not small. Want to know what other characteristics of radius are? Should I tell you directly or study it myself?
Then combine the teacher's tips, use the tools in your hand, and study with the group.
4. Research tips
What is the relationship between the radius and diameter of the same circle?
How many radii does the same circle have?
Are the radii of the same circle equal in length?
report
The diameter of the same circle is twice the radius. d=2r。
Q: How do you know?
The same circle has countless radii. Why? There are countless points on the circle, which are found in the crease.
There are countless radii of the same circle, so what is the diameter?
It is written on the blackboard that the same circle has countless inner radii.
The radius of the same circle is equal. Why? (by measurement, by reasoning)
The radius of the same circle is equal, so is the diameter equal?
Blackboard: The inner diameter of the same circle is equal.
Therefore, the ancients said: a circle is the same length.
What does this finger mean? What do you mean the same length?
Read this sentence while watching the slide.
Equal length circle is widely used in life.
Can you explain why the shape of the wheel is round?
Why not make the wheels into these shapes? (Show regular polygon picture)
Fourth, deepen the understanding of the circle in comparison.
1. What happens when a regular triangle becomes a regular dodecagon?
2. Imagine what a regular 100 polygon would look like. (Close to a circle, but not a circle)
What about the regular 3072 polygon? (Closer to a circle, but not yet a circle)
How many faces are round?
3. There is a record in the Classic of Weekly Calculation that "the circle comes from the square and the square comes from the moment". The so-called circle comes from a square, which means that the original circle is not drawn with the current compasses, but is continuously cut from the square. Now, if I tell you that the side length of a square is 6 cm, what information can you get about the circle?
4, Yin and Yang Taiji diagram.
Teacher: Do you want to know how this painting is made? It consists of a big circle and two small circles of the same size. Now, if I tell you that the radius of the small circle is 3 cm, what can you know?
Next, we will face the challenge of three practical problems. Do students dare to accept the challenge?
Question 1. Can you measure the diameter of 1 round coin? (Reference tools: ruler, a pair of triangles)
Question 2: Can you draw a circle with a radius of 1 m on the ground? (Reference tools: rope, chalk)
Question 3. The wheels are all round. Where is the axle? Why? (Reference tool: bicycle)
After class, each student chooses a topic he is most interested in to study.
Verb (abbreviation of verb) abstract
Do the students have any ideas after learning this lesson? There are endless mysteries hidden in the circle, waiting for the students to study and discover! May our study life be as perfect as a circle!