First of all, bring forth the old and bring forth the new, and infiltrate the idea of "transformation"
Before learning new knowledge, guide students to recall the derivation methods of rectangle, parallelogram, triangle and trapezoid area formulas, and guide students to find that "reduction" is a good way to explore new mathematical knowledge and solve mathematical problems, laying the foundation for the later method of calculating the area of a circle.
Second, start to cut and fight, and experience "turning joy into straightness"
After highlighting the significance of the area of a circle, let the students guess how to deduce the area of a circle by comparing and reviewing the area deduction methods of plane graphics. After the students guess, take out two prepared disks of the same size, divide one of them into several parts, and then put it into a parallelogram or rectangle. After students cut them together, they choose 2~3 groups to observe and compare. It is found that if a circle is divided into more parts, the figure will be closer to a parallelogram or rectangle. Then compare the relationship between the circle and this mosaic figure. By comparing the cut mosaic with the original image, the parts related to the mosaic are marked with colored pens, which forms a sharp contrast and fully paves the way for the area calculation formula to be deduced later.
Third, demonstrate the operation and feel the formation of knowledge.
Through observation, comparison and analysis, find out the relationship between the area, perimeter and radius of a circle and the area, length and width of an approximate rectangle, so that students can deduce the formula for calculating the area of a circle. In this way, students are guided from support to release, from phenomenon to essence, and always participate in the exploration of how to transform circles into rectangles and parallelograms, and feel the formation of knowledge.
Fourth, practice at different levels and experience the application value.
Combined with the examples in the textbook, three levels of basic exercises, improving exercises and comprehensive exercises are designed to test students' learning situation from three different levels. First, basic exercises consolidate the application of calculation formulas and emphasize the standardized writing format; Second, improve the practice, collect the actual content around you, and make the content learned in this lesson relate to life and use it flexibly; Thirdly, the comprehensive exercise not only links the knowledge learned before (first know the circumference of the circle, then find the radius, and then find the area of the circle), but also exercises the students' comprehensive application ability. In the setting of each exercise, there are different purposes, focusing on the guiding points of each exercise.
However, the new lesson time in this class is too long, which leads to insufficient practice and needs to be paid attention to in future teaching.
Teaching objectives
1. Knowledge objective: Understand the meaning of the area of a circle, go through the derivation process of the formula for calculating the area of a circle, and master the formula for calculating the area of a circle.
2. Ability goal: Be able to correctly calculate the area of the circle by using the area formula of the circle, and solve some simple and practical problems by using the knowledge of the area of the circle.
3. Emotional goal: in the activities of estimating and exploring the formula of circular area, I realized the idea of "turning curves into straight lines" and felt the limit thought initially.
Important and difficult
Key points: The area of a circle can be correctly calculated by using the area formula of the circle, and some simple practical problems can be solved by using the knowledge of the area of the circle.
Difficulties: the derivation process of the formula for calculating the area of a circle.
Training/teaching AIDS
A set of multimedia courseware
Teaching process:
First, create situations and introduce topics.
Introduce a new lesson with a short story: please listen to a short story in this lesson and see if you can solve the problems in the story. The white rabbit and the little goat each cultivated a field on the hillside. The white rabbit cultivated a round land, while the little goat cultivated a square land. They all think that they are very capable, and they all say that they have reclaimed a large area of land, but they can't say anything. So, which piece is bigger? what do you think?
Health: Can't finding out the area of two plots solve the problem?
Teacher: But we can calculate the area of a square. Can you calculate the area of a circle?
Health: No.
Teacher: Then, don't lose heart. As long as we study this lesson carefully, we will easily solve this problem. Today, let's discuss the area of a circle.
Words on the blackboard: the area of a circle
Second, establish concepts and explore methods.
1, Teacher: The circle is the most beautiful plane figure we have learned recently. Please contact the meaning of plane graphic area we have learned before and think about what is the area of a circle. The students answer, and then the courseware shows that the size of the plane occupied by a circle is called the area of the circle.
2. Question: How to calculate the area of a circle? Instruct the teacher (let the students recall the previous methods of deducing the calculation formulas of parallelogram, triangle and trapezoid) and discuss them.
3. Summary method: digging and filling conversion method.
Third, explore the law and summarize the formula.
1, using courseware to show the situation of 4 bisecting circle, 8 bisecting circle and 16 bisecting circle. Therefore, the conclusion is that the finer the division, the closer it is to a parallelogram or rectangle.
Step 2 ask questions:
(1) What is the relationship between the length of a rectangle and the circumference of a circle?
(2) What is the relationship between the width of a rectangle and the radius of a circle?
3, courseware display, students observe and discuss, get the law:
(1) The length of a rectangle is equal to half the circumference.
(2) The width of a rectangle is equal to the radius of a circle.
4. Question: What is the relationship between the area of a circle and the area of a rectangle?
Area of circle = area of rectangle
5, export formula:
Area of circle = area of rectangle = length × width = half circumference × radius.
S =πr2
Fourth, apply formulas to solve problems.
1, the radius of a circle is 4 cm. How many square centimeters is its area?
2. The perimeter of the circular flower bed in the street garden is18.84m. What is the area of the flower bed?
Verb (abbreviation of verb) course summary
Can correctly use the formula of circle area to calculate the area of circle, and can use the knowledge of circle area to solve some simple and practical problems.
Sixth, blackboard design
Area of a circle
Area of circle = area of rectangle = length × width
Area product of circle =πr × r
S =πr2