Teaching topic: graphic area on carpet
Teaching goal: We can directly count the area of related figures on the grid diagram. You can use the method of segmentation to turn a more complex figure into a simple figure, and use a simpler method to calculate the area. Experience the diversity of strategies and methods in the process of solving problems.
Teaching emphasis: We can use the segmentation method to transform complex graphics into simple graphics and calculate the area in a simpler way.
Difficulties in teaching: You can convert complex figures into simple figures by segmentation, and calculate the area by a simpler method.
Teaching preparation: ellipsis
Teaching process:
First, create situations and introduce new lessons.
I want to say that everyone in the class is an excellent designer! Because everyone is designing their own bright future, they all study hard. I hope you will continue to work hard to make your beautiful design a reality. Let's take a look at the patterns designed by our colleague, who is a carpet pattern designer.
The courseware shows the graphics on the carpet, so that students can observe the characteristics of the graphics carefully and say that they have found them.
The carpet is square with a side length of 14M, and the blue part is symmetrical.
Let the students ask math questions. Students may ask what the area of the carpet is, which can be calculated directly. Students can also ask other questions and show them according to their answers: "What is the area of the blue part of the carpet?"
Teacher's blackboard theme: graphic area on carpet
Second, explore and learn new knowledge independently.
1, students solve problems independently
Teacher: The area of each small square represents 1M2.
Ask students to think independently, solve problems, think as simply as possible, and record the methods to solve problems.
2. Group communication and discussion
3. Classroom feedback
Ask the students to report the area of the blue part, focusing on the method of finding the blue area. For each method, as long as the students make sense, they will give affirmation.
It is estimated that the students' answers are:
A, according to the grid diagram provided, count one by one and count the area of the blue part. After the students answer, simple induction: count according to the grid diagram and count on the blackboard.
B. "Split the graph" to narrow the counting range.
Students may divide graphics in different ways. First, let the students compare the methods of dividing graphs and say that they have found them. Let the students know that these different methods are to divide a complex figure into several small figures with the same area. This method is called "breaking the whole into parts". Then let the students compare several segmentation methods and find a simple one, so that the students can know how to do it.
C, a large area to reduce the area.
Students can also use the method of "reducing the area in a large area" to find the area of the graph.
When students introduce the method of segmentation, the area of several small figures may be reduced to a large area. At this time, they can also directly summarize and consolidate the book: reduce the area on a large scale.
4. Students summarize the method of finding the area of the blue part.
5. The teacher makes a summary.
When we find the area of complex graphics, (1), we can count them one by one according to the provided grid diagram to get the required area. (2) The area can be reduced by simply "dividing the graph into several parts". (3) You can also use the method of "reducing the area in a large area" to get the area of the graph.
When summarizing each method, use courseware to cooperate with demonstration methods.
Third, consolidate practice and expand application.
1, deal with the textbook page 19, exercise 1 topic.
(1) Students independently find the area of the graph 1.
(2) Students independently solve the after-class feedback, focusing on the method of finding the graphic area by feedback. All three methods will do. Guide students to understand "the number of semilattices less than one lattice"
(3) Students independently find the areas in Figure 2 and Figure 3.
After the students are independent, two people at the same table communicate with each other about the method and process of finding the area.
2. Exercise the second question on page 19.
(1) Students read the questions and make clear the meaning of the questions.
(2) Students think independently and solve problems.
(3) classroom feedback.
Students can count, break the whole into parts, or use a large area to reduce the area to find the graphic area.
3. Exercise the third question on page 19.
(1) Students fill in the blanks independently. Find the area of each group of graphs. After the students finish, exchange feedback answers in class.
(2) Students observe the results and say they have found them.
The areas of the four graphs in (1) are the squares of 1, 2, 3 and 4 respectively; Question (2) Compared with question (1), the areas of the three figures in question (2) are respectively half of the areas of the first three figures in the previous group of questions.
Fourth, feedback summary in class.
1. What activities did you do in this class? What did you get?
2. Evaluate the performance of classes and groups. (Source: Qu Teacher's Teaching Plan Network)