Knowledge and skills:

Make clear the meaning of combined graphics, and master the method of solving the area of combined graphics by decomposition or addition.

Process and method:

According to the situation of various combination diagrams, the calculation method is effectively selected and the correct answer is given.

Emotional attitudes and values:

Infiltrating the teaching idea of transformation can improve students' ability to solve practical problems with new knowledge and cultivate their innovative spirit in independent exploration activities.

Emphasis and difficulty in teaching

Teaching focus:

In the exploration activities, in order to understand various methods for calculating the area of combined graphics, we will use the plane graphic areas of squares, rectangles, parallelograms, triangles and trapezoids to find the area of combined graphics.

Teaching difficulties:

According to the characteristics of graphics, what method is used to decompose the combined graphics, so that the calculation of the decomposed graphics is clear and accurate.

teaching tool

Multimedia equipment

teaching process

Teaching process design

1 Create a situation to guide exploration.

Teacher: There are many pictures in life. The teacher prepared four charts today. Let's observe. What simple figures are these diagrams made of? If we find their area, how?

Figure 1

Figure ii

Figure 3

Figure 4

The courseware shows Figure 1, Figure 2 and Figure 3 one by one. Figure 4 allows students to express their views.

Health 1: The surface of a small house consists of a triangle and a square.

Health 2: The face of a kite is made up of four small triangles.

Health 3: The front of the team flag is made up of trapezoid and triangle.

Health 4: Tangram consists of triangles, rectangles, squares and parallelograms.

Teacher: These are all combined figures. What kind of graphics do you think are combined graphics through everyone's introduction?

Health 1: A composite graph consists of two or more graphs.

Health 2: A figure composed of several plane figures is a combined figure.

Teacher's summary: Combination graphics are composed of several simple graphics.

Figure 1: It consists of a triangle, a rectangle and a square in the middle of the rectangle.

Area = triangular area+rectangular area-square area

Figure 2: Make an auxiliary line and divide it into a big trapezoid and a triangle.

Method 1: Segmentation: Divide the whole into several basic figures and find the sum of their areas.

It consists of two trapezoids.

Teacher: Why is it divided into two trapezoids? How to divide it into two trapezoids?

Guide the students to say how to turn it into a simple figure and make an auxiliary line in the figure.

Teacher: Yes, you can use it as an auxiliary line and convert it into a simple graph you have learned before for calculation.

(blackboard writing: transformation)

Think about it, are there different ways to use auxiliary lines?

Method 2: supplementary method: subtract a small figure from a large figure to find the area of the combined figure.

Make an auxiliary line to make a rectangle, so it becomes a big rectangle minus a triangle.

Figure 3: It consists of four triangles.

Area = triangle area+triangle area+triangle area+triangle area

2 New knowledge exploration

(1) The picture on the right shows the shape of the side wall of a house. How many square meters is its area?

(Triangle+Square)

The picture on the right shows the shape of the side wall of a house. How many square meters is it?

(Two identical trapezoids)

(2) To calculate the area of combined graphics, it is generally divided into basic graphics, such as rectangle, square, triangle, trapezoid, etc. , and then calculate their area.

3 Consolidation and promotion

(1) This is the plan of the school building. How many ways can we find its area?

(2) Cut a piece of cardboard into four small squares with a side length of 4 cm, and you can make a box without a lid. How much area is left in this cardboard?

(3) What learned graphics can the following graphics be divided into?

(4) The school should paint the front of 60 classroom doors. What is the area to be drawn?

(5) Find the area of the shadow part below.

(6) Find the area of the shadow part below.

(7) As shown in the figure, two squares with a side length of 200px are placed on the desktop to find the area of the covered desktop.

Summary after class

(A) student summary

What did you learn in this class? What did you get? What else don't you understand? (Group Theory-Intra-group Summary-Inter-group Communication)

(2) Teacher's summary

Today, we know the combined graphics. We can divide the combined graphics into the learned graphics and calculate its area.

Write on the blackboard.

Combined graphic area

A combination graph is a combination of several simple graphs.

Teaching plan of combined graphic area (2) Teaching objectives

1. In the activities of independent exploration, I understand various methods for calculating the area of combined graphics and the mathematical thought of infiltration transformation. 2. According to the conditions of various combined graphs, the calculation method is effectively selected and the correct solution is given. 3. Be able to use what you have learned to solve practical problems with graphics in your life. 4. Stimulate students' interest and initiative in learning in effective situations, and cultivate students' thoughts and emotions of loving mathematics.

Emphasis and difficulty in teaching

Teaching emphasis: explore the calculation method of combined graphic area. Teaching difficulties: according to the conditions of combined graphics, effectively choose the calculation method.

teaching process

First, review: courseware demonstration:

Teacher: What are the figures in the following objects?

Tell me where there are combination graphics in your life. Students speak freely.

Teacher: The area of a triangle is calculated by multiplying the base by the height and dividing it by 2. What does it mean to divide by 2 here?

Teacher's summary: We convert the area of triangle into parallelogram to deduce the calculation method of triangle area.

Second, introduce new courses.

1, transition: We can directly calculate the graph just now through the formula. Can such a diagram be calculated directly?

Teacher: Can you use what you have learned to find a solution to this problem?

Xiaohua's family has bought a new house and plans to lay the floor in the living room (the shape of the living room is as shown in the picture). Please estimate the minimum building area to be bought by his family, and then actually calculate it.

Arrange independent exploration tasks;

Clarify the requirements for exploration; Draw this idea on the map and try to find out the area of the floor.

Communication requirements: Students who come up with good ideas tell your deskmate your ideas and compare the differences between them.

Tip: Students who do have difficulties can cooperate with their deskmates.

2, students try independently, teachers patrol, looking for typical.

3. Feedback:

Teacher: Who will show your solution?

(Physical projection display, to help students clear: ideas and solutions. And the source of intermediate data. )

Supplementary knowledge includes: drawing auxiliary lines with dotted lines; Will the students? Cut? Is that clear? Integral? (Draw auxiliary lines).

The possible answers are:

Draw your idea on the graph and try to find out the area of the graph.

The complement method appeared. At the same time, students demonstrate the process of complement with physical model and explain the algorithm.

Some knowledge is cut and supplemented for students to show and help students understand, but in the end it is no longer displayed in a unified way.

4. Summary: Teacher: Students, just now we came up with so many methods to calculate the building area of 33 square meters. Let's group these methods together. How would you distribute them? One point, one point.

Teacher: We can divide this figure into two parts, or it can be said that this figure is composed of a small rectangle and a large rectangle as shown in figure 1, or two trapezoids as shown in figure 3, or a rectangle and a square as shown in figure 4. Graphics like this are generally called composite graphics. (blackboard writing: combined graphics)

Today, we are going to learn the area of composite numbers. (blackboard: the area of).

Teacher: In order to solve the floor problem of this living room, the students have come up with various methods. Of all these methods, which one do you prefer?

Students may say: it is easier to divide into fewer figures than more figures, and it is easier to divide into rectangles and squares than trapezoid in calculation. )

Teacher: Students, just now we solved the problem of finding the combined graphic area by looking for the floor of the living room. Among so many methods, some are relatively simple. For example, dividing into two graphs is relatively simple than dividing into three graphs; Also divided into two figures, divided into rectangle and square is relatively simpler in calculation than divided into trapezoid and triangle.

Third, practice.

Transition: Therefore, when solving this kind of problems, we can consider doing our best,,, (simpler). Ok, let's look at this problem in this way. Courseware demonstration:

The picture on the right shows the shape of the side wall of a house. How many square meters is its area?

After the students understand the meaning of the question, arrange exercise papers. Students try independently, teachers patrol and collect typical examples. Feedback: Show students' typical works through projection. The possible situations are as follows

Other possible problems are: please evaluate these two methods.

(divided into graphics that have not been learned)

(Too thin, too much)

Divide the numbers below into the numbers we have learned.

Transition: It is amazing that students have come up with so many simple methods for a problem. Please look below.

Xinfeng primary school has a vegetable field, the shape of which is as shown on the right. How many square meters is the area of this vegetable field?

How much cloth does it take to make the team flag?

There is a rectangular swimming pool in the middle of the trapezoidal land, and the rest are grasslands. How many square meters is the area of this grassland?

There is a square hollow floor tile. What is its actual floor space?

There is a rectangular piece of land on campus. I want to grow red flowers, yellow flowers and green grass. The design scheme is as follows. Can you calculate the planting areas of safflower, yellow flower and green grass respectively?

Please also design a plan and find out the planting area of each plant with the figures we have learned.

Teacher: It seems that not all methods can be used to find the area of combined graphics. Sometimes, we must choose the right method according to the situation.

Four: summary.

1. What did you learn after learning this lesson?

Finally, let's relax.

!