The teaching design of circle mathematics in the sixth grade of primary school —— 1 Analysis of teaching content;
The area of a circle is taught on the basis that students understand the characteristics of a circle, learn to calculate the circumference of a circle, and learn the formula for calculating the area of a plane figure surrounded by a straight line. Because the previous calculation of graphic area is the calculation of straight line graphic area, and the calculation of curved edge graphic area like circle is the first time for students, so it is difficult and challenging. The focus of teaching is to enable students to explore and deduce the formula of circle area through observation, guess, hands-on operation and calculation verification, and to flexibly apply the formula of circle area to solve practical problems. Therefore, the teaching of this course should closely focus on the idea of "transformation" and guide students to analyze, research and summarize new knowledge into existing knowledge, so as to complete the construction process of new knowledge, establish mathematical models and cultivate comprehensive ability to solve problems.
Analysis of students' situation:
The primary school's understanding of geometric figures belongs to the learning stage of intuitive geometry to a great extent, and geometry itself is abstract. In this section, it is another leap for students to develop from a straight line to a curve, but from the perspective of students' thinking, grade six students have certain abstract and logical thinking ability. Students in this period have had many opportunities to come into contact with rich mathematical contents such as number and calculation, spatial graphics and so on. , and had the preliminary experience of induction, analogy, reasoning and other mathematical activities, and had the transformation of mathematical ideas. Therefore, in teaching, we should pay attention to the connection with real life, organize students to carry out exploratory mathematics activities with the help of learning tools, and pay attention to the process of knowledge discovery and exploration, so that students can feel the mathematical ideas such as transformation and limit, gain the positive feeling of mathematics learning, and experience and feel the power of mathematics. At the same time, in learning activities, students should learn autonomous learning and group cooperation to cultivate their ability to solve mathematical problems.
Teaching objectives:
1. Cognitive goal
Let students understand the meaning of circular area; Master the formula of circle area, and can use the knowledge to solve simple problems in life.
2. Process and method objectives
Experience the derivation of the formula of circle area, experience the experimental operation and learn the method of logical reasoning.
3. Emotional goals
Guide students to further understand the mathematical thought of "transformation" and initially understand the limit thought; Experience the joy of discovering new knowledge, enhance students' awareness and ability of cooperation and exchange, and cultivate students' interest in learning mathematics.
Teaching emphasis: mastering the formula for calculating the area of a circle can correctly calculate the area of a circle.
Teaching difficulty: understanding the derivation of the formula for calculating the area of a circle.
Teaching preparation: correspondence; Demonstration teaching aid for the area of circle.
teaching process
First, situational introduction
Show the scene-horse's confusion
Teacher: Boys and girls, do you know the range of grazing for horses?
Health: It's a circle.
Teacher: So, if you want to know the size of the grazing area of horses, what do you want to find a circle for?
Health: the area of a circle.
Teacher: Today, let's learn the area of a circle. (blackboard title: the area of a circle)
[Design intention: Through the scene of "horse's confusion", let students discover the problems themselves, and at the same time let students realize that what they want to learn today is closely related to their lives around them, and at the same time understand the learning tasks and stimulate students' interest in learning. ]
Second, explore cooperation and deduce the formula of circular area.
1. Infiltrate the mathematical thought and method of "transformation".
Teacher: Do you want to know the area of a circle?
What is the area of a circle? How to calculate the area of a circle? What is the calculation formula? How to deduce the calculation formula? ……)
Let's first recall how the area of the parallelogram is derived.
Student: Cut it into two parts along the height of the parallelogram and put the two parts into a rectangle. Teacher: Oh, look, is that right? (Teacher demonstrates).
Yes, the base of the parallelogram is equal to the length of the rectangle, and the height of the parallelogram is higher than the width of the rectangle. Because the area of a rectangle is equal to the length times the width, the area of a parallelogram is equal to the bottom times the height.
Teacher: The students have mastered the original knowledge well. Just now, we cut a figure first, then spell it out and then transform it into other figures. What are the benefits of this?
Health: This will turn a problem that we don't understand into a problem that we can solve.
Teacher: Yes, it's a good way for us to learn math. Today, we use this method to convert the circle into the learned figure.
Teacher: What figure can that circle be transformed into? Do you want to know? (thinking)
2. Demonstrate to solve doubts.
Teacher: (Explain the demonstration) Divide this circle into 4, 8, 16 evenly, cut it along the diameter, and turn it into two semicircles, making it into an approximate parallelogram.
Teacher: If the teacher divided the circle into 32 equally, what figure would he spell? Let's have a look (teacher's demonstration).
Teacher: Imagine that if the teacher keeps dividing, the more copies are divided, the smaller each copy is, and the closer the total number is to what number. (Rectangular)
[Design Intention: Through this link, an important mathematical idea, namely, the idea of reduction, is infiltrated, and students are guided to abstract and summarize new problems, transform them into old knowledge, and use old knowledge to solve new problems. With the help of computer demonstration, the process of cutting and spelling from curve to straight is vividly displayed. ]
3. Students cooperate to explore and deduce formulas.
(1) Discuss and display the prompt.
Teacher: Let's look at three questions given by the teacher. Please work in groups of four, take out the learning tools prepared before class and spell them out. Observe and discuss to complete these three questions:
(1) Their (shapes) changed during the transformation, but their (areas) remained unchanged?
② The length of the transformed rectangle is equivalent to the length (half circumference) of the circle, and the width is equivalent to the width (radius) of the circle?
③ Can you deduce the formula for calculating the area of a circle from the area of a rectangle? Try to use a relative word like "because ...".
Teacher: Do you understand the requirements? Ok, let's get started.
The students reported their grades and the teacher scribbled on the blackboard.
After observation and discussion, the students found out the formula for calculating the area of the circle, which is really remarkable.
(2) Teacher: If the radius of a circle is represented by R, how can half of the circumference be represented by letters?
(3) Reveal the letter formula.
Teacher: If S is used to represent the area of a circle, the formula for calculating the area of the circle is: S=πr2.
(4) Read the formula in chorus, emphasizing r2=r×r (representing the multiplication of two r's).
According to the formula, what conditions must be known to calculate the area of a circle? What should be calculated first in the calculation process?
Design intention: Through group discussion, students can further clarify the corresponding relationship between the spliced rectangle and the circle, which effectively breaks through the difficulty of this lesson. ]
Third, use formulas to solve problems.
1. Students, from this formula, we can see that what must we know first to ask for the area of a circle?
(Show me the sketch of the cow eating again)
Teacher: What area of grass can this horse eat at most? Will you beg now?
Teachers should strengthen inspection, give timely guidance when problems are found, and remind students whether formulas and units are used correctly.
2. Teaching examples 1.
If we know that the diameter of a circular lawn is 20, how much does it cost to cover the lawn with 8 yuan turf per square meter?
How much does it cost to cover the lawn? What do you need first? (Ask how many square meters the circular lawn is first. )
How do we find its area? Please write and calculate the area of this circular lawn!
Teacher: In our daily life, we often encounter practical problems related to the calculation of circular area.
(Show the third question)
Xiao Gang measured the circumference of a trunk as 125, 6c. What is the cross-sectional area of this trunk?
After analyzing the meaning of the question, students finish it independently (organizing communication and evaluating feedback)
The students are great. After solving the above three problems, do you dare to challenge the following questions?
4. It is known that the triangle ABC in the semicircle has a height of 5cm and an area of 30cm. What is the diameter of a semicircle? Find the shadow area.
[Design Intention: Students have mastered the formula for calculating the area of a circle, so they can boldly try to solve it, thus promoting the combination of theory and practice and cultivating students' ability to flexibly use what they have learned to solve practical problems. ]
Fourth, the whole class summarizes, reviews and reflects.
Teacher: Have you solved the problem about the circular area now? What did you get from this lesson?
Do you know under what conditions you can find the area of a circle?
(Know radius, diameter or circumference)
Know the radius: S=πr2
Know the diameter: S=π(d÷2)2
Know the circumference: S=π(C÷π÷2)2
Teacher: Students, conjecture verification and arithmetic discovery are the methods we often use when exploring unknown fields in mathematics learning. I believe that if we make good use of them, students will make more discoveries!
Design intention: The class summary should not only pay attention to the review and reproduction of learning achievements, but also pay attention to the reflection and improvement of learning experience. In this process, students not only gain knowledge, but also learn the methods of scientific inquiry.
Fifth, after-school expansion
Besides rectangles, what other shapes can a circle become?
The area of the circle in the sixth grade of primary school is designed in mathematics teaching 2. Target preset;
1. Make students experience mathematical activities such as operation, observation, estimation, verification, discussion and induction, explore and master the formula of circle area, correctly calculate the area of circle, and apply the formula to solve related simple practical problems.
2. Make students further understand the value of reduction method, cultivate students' ability to use existing knowledge to solve practical problems and reason rationally, cultivate the concept of space and infiltrate the idea of limit.
Teaching process:
First, guide estimation and preliminary perception.
1, show me the round computer hard disk. Guide the students to think: What are the requirements for the area of this hard disk? What is the size of the circular area related to?
2. Estimate the relationship between circle area and radius.
The teacher draws a square first, and then draws a circle with the' side length' of the square as the radius. It is estimated that the area of a circle is several times that of a square. The side length of the square here is R. What is the area of the square in letters? What is the relationship between the area and radius of a circle?
Second, hands-on operation, * * * with exploration.
1. Start the transformation and form the scheme.
(1) How do we derive the area formulas of triangle, parallelogram and trapezoid?
(2) How are you going to deduce the area of the circle?
2, hands-on operation, * * * with exploration
(1) Divide a circle into eight parts. What is the shape of each part? Can you put these approximate triangles together into a learned figure?
(2) Hands-on operation. The deskmate is a group. Can you spell 16 copies prepared before class into an approximate parallelogram?
(3) Contrast: What's the difference between it and the graph that the teacher just pieced together?
(4) Imagine: If we divide this circle into 32 parts and 64 parts on average, what will happen to the graph?
If you keep dividing it like this, what will happen to the mosaic?
3. Guide the comparison and deduce the formula.
What is the connection between a circle and a rectangle?
Guide students to think from three angles: area, length and width of a rectangle.
Write on the blackboard according to the students' answers.
Area of rectangle = length × width
↓↓↓
Circular area =∏rr
=∏r2
Follow-up: was our estimate right when we first started class?
What conditions do you need to know to find the area of a circle?
Third, apply formulas to solve problems.
1, basic training, practice applying formulas, and find the area of a circle.
Step 2 solve the problem
(1) Example 9 Guide students to understand the meaning of the question.
What is the area required for sprinkler irrigation to rotate once? What does the spraying distance of 5 meters mean?
(2) student computing
(3) communication, highlighting the calculation of five parties
Fourth, consolidate practice.
1, Practice 19 1 Find the area of the CD presented at the beginning of the class.
2. On a rectangular meadow, a sheep was tied to a stake in the middle of the meadow by a 3-meter-long rope (regardless of joints). What area of grass can this sheep eat at most?
5. What did you learn from this course? What do you think is important?
What are the places?
Guide students to review the derivation process of circle area and know how to calculate the area of circle perimeter. Summarize the calculation method of circular area)
Classroom assignment of intransitive verbs
Supplementary Exercise 5 1 Pages 2, 3 and 4
The area of the square in the expansion diagram on the right is 8 square centimeters. How to find the area when the diameter of a circle is known, and how to find the area when the circumference of a circle is known.
How many square centimeters is the area of a circle?
Reflection:
1, change the textbook into a textbook. Through Example 7, the textbook allows students to initially perceive the calculation formula of circular area by counting squares. The specific process is as follows: first, let students calculate the area of 1/4 circle by counting squares, then deduce the area of the circle, and then fill in the table. By observing the data, we can find the relationship between the area of a circle and its radius. The whole process is time-consuming and laborious, and it is difficult to teach. After deducing the calculation formula, students should not rush to teach Example 9, so as to do exercises. After students master the calculation formula of circle area, they can learn Example 9 to solve practical problems, which conforms to students' cognitive law.
2. Pay attention to hands-on operation and participate in the process of knowledge formation. When the sparks of students' inquiry thinking are ignited, teachers skillfully guide demonstrations and demonstrate to tap students' creativity step by step. Friedenthal, a Dutch mathematics educator, believes that mathematics learning is an activity, just like swimming and cycling without personal experience. It is impossible to learn by reading books, listening to explanations and observing others' demonstrations. Therefore, in the key link of "turning a circle into a square", let students experience it by hand, and let students' thinking change from quantitative to qualitative. At the same time, they skillfully use students' imagination, infinitely refine the segmentation process and infiltrate extreme thoughts.
3. Mathematics comes from life and is applied to life. Sprinkler spraying water, CD-ROM and herding sheep are common life situations for students. By mathematizing the problems in life, students can not only experience the happiness of using mathematical knowledge to solve problems, but also feel the practical application value of mathematics. The problem of sheep eating grass has triggered students' "mathematical thinking" about the phenomenon of blindness. At the same time, the range of herding sheep is round and intangible, which requires the participation of students' imagination and deepens the level of practice. Solving practical problems prematurely is not conducive to the formation of students' basic skills.
Mathematics teaching design in the circular area of the sixth grade primary school 3 teaching objectives;
1. Knowledge and skills: Know the area of the circle, and guide students to explore and deduce the calculation formula of the area of the circle through operation, and can use the formula to answer some simple practical questions.
2. Process and method: In the process of exploring the calculation formula of circular area, students' interest in participating in the whole classroom teaching activities is stimulated through bold guessing and hands-on operation, and students' sense of cooperation and spirit of inquiry are cultivated; Through students' discussion and communication, we can cultivate students' ability of analysis, observation and generalization, further understand the transformed mathematical ideas and methods, cultivate students' migration ability and develop students' spatial concept.
3. Emotion, attitude and values: Through application, students can experience the application value of mathematics, experience the close relationship between mathematics and life, and infiltrate the transformed mathematical thoughts and extreme thoughts.
Teaching emphasis: Derive the formula of circle area and use it to solve practical problems.
Teaching difficulty: understanding the derivation process of the formula of circular area.
Teaching preparation: courseware, round white paper, scissors.
teaching process
First, create situations and introduce new lessons.
1, show the theme scene:
What mathematical information do you get from the picture?
② Question: "How many square meters does this circular lawn cover?" What does "floor space" mean?
2. Say: What is the area of the circle?
3. Reveal the topic: Today we will study the area of the circle. (blackboard title: the area of a circle)
Design intention: Show the situation diagram, organically combine the teaching content with life, make students abstract mathematical problems from specific problem situations, and improve students' learning enthusiasm.
Second, cooperate and exchange, and explore new knowledge.
1, review old knowledge:
Looking back, how is the formula of plane graphic area derived?
It is pointed out that the reduction method is a good and useful idea and method for us to learn new mathematical knowledge. The purpose of transformation is to transform the graphics that have not been learned into the graphics that have been learned.
Design intention: through knowledge review, stimulate students' thirst for knowledge and strengthen the life of mathematics learning.
2. Thinking: Can you also convert a circle into a learned figure to calculate its area?
3. Cooperative exploration:
(1) conjecture
(2) Hands-on operation to verify the conjecture.
(3) report and exchange, show the results (show the students' research results layer by layer).
Design intention: Through activities, mobilize students' hands-on, brains and other senses to participate in activities, mobilize students' enthusiasm and consciousness, cultivate students' observation, comparison and judgment thinking ability, cultivate students' awareness of cooperation and exchange, apply the transformation and connection between knowledge, further understand the transformed mathematical ideas and methods, cultivate students' migration ability and develop students' spatial concept.
4. With the help of the dynamic courseware made by the network sketchpad, the derivation process of the circle area is displayed.
Show the idea that different equal parts are put together into different parallelograms and feel the limit.
Design intention: Through the animation demonstration of tangent circle and spelling circle, we can observe different figures with different parts, discover the rules and let students feel the extreme thoughts.
5. Derive the formula of circular area.
① Compare the transformed graph with the circle. What did you find?
(2) class communication, according to the students' narrative blackboard writing:
Rectangular area = length × width
Area of circle = half of circumference × radius
=лr×r
=лr
6. Summary: Formula for calculating the area of a circle: s = л r.
Design intention: Through transformation and comparison, let students participate in the process of acquiring knowledge and actively participate in the learning exchange of observation and discussion in an open learning atmosphere, so as to hand over the process of discovering knowledge to students. The combination of static and dynamic presentation is beneficial for students to understand and break through the teaching difficulties, and plays a very important role in the formation of students' spatial concept and the development of students' spatial imagination.
7. Knowledge application and internalization improvement
(1), find the area of the circle below. (Only in the form of columns, not counting)
R = 3 cm
(2) Example 1: Example 1: The diameter of the round flower bed is 20m. What is its area?
(1) Read the question carefully and understand the meaning.
(2) How do you think to solve this problem?
(3) Students try to calculate independently.
(4) Report the solution process and results, and make collective evaluation.
Design intention: Let students use new knowledge to solve practical problems in life and experience the joy of success.
4. Contact life, expand and extend
1. The range of automatic rotary sprinkler irrigation device on the park lawn is 10 meter. What is the area it can irrigate?
2. Change a rectangle with a perimeter of184cm into a circle. What is the area of this circle?
3. Find the perimeter and area of the following circle.
R = 2 cm
4. Find the area of the semicircle.
R = 4 cm
Design intention: expand and extend, let students realize that there is mathematics everywhere in life, and truly realize the practicality of mathematics.
5, the whole class review and summary
What new knowledge have we learned today? What have you gained?
Design intention: guide students to review the learning process, cultivate the habit of reflection, and attach importance to the cultivation of students' mathematical thinking methods.