Knowledge points of quadrilateral mathematics in grade one and grade three
Concept of square: A quadrilateral with four equal sides and four right angles is a square.
Features: There are four right angles and four sides are equal. A square is both a rectangle and a diamond.
Perimeter: the circumference of a square = side length ×4.
rectangle
Concept: A parallelogram with a right angle is called a rectangle.
Features: A rectangle has two lengths, two widths, four right angles and equal opposite sides.
Perimeter: the circumference of a rectangle = (length+width) ×2.
parallelogram
Concept: Two groups of quadrangles with parallel opposite sides, with parallel opposite sides and equal diagonals. (Square and rectangle belong to special parallelogram)
Features: ① Equilateral diagonal. ② Parallelogram is easy to deform.
Perimeter: perimeter of parallelogram = side length of two sides plus ×2.
trapeziform
Concept: A quadrilateral with one set of parallel opposite sides and another set of non-parallel opposite sides.
Features: Only one set of opposite sides is parallel.
Circumference: upper sole+lower sole+waist circumference
isosceles trapezoid
Concept: Two isosceles trapezoids with equal bottom angles are axisymmetric figures with symmetry axes.
Features: there are a group of parallel opposite sides, with equal waist length.
Circumference: upper sole+lower sole+waist circumference
diamond
Concept: A set of parallel four-sided rows with equal adjacent sides is a diamond.
Features: ① All four sides are equal; ② Diagonal lines are perpendicular to each other and equally divided; ③ A diagonal line divides a set of diagonal lines respectively.
Perimeter: two different side lengths plus ×2.
What is the connection between each quadrilateral?
1, a square is both a rectangle and a diamond.
2. Square and rectangle belong to special parallelogram.
3. Square or special rectangle.
The quadrilateral teaching plan of mathematics in the third grade of the second primary school
First, teaching content: compulsory education curriculum standard experimental textbook (People's Education Edition), the first volume of grade three, page 35.
Second, the teaching objectives:
1, can distinguish quadrangles from various figures and know their characteristics.
2. Through the classification of quadrangles, we can understand the characteristics of different quadrangles, especially the characteristics of rectangles and squares.
3. Cultivate students' spatial concept through practical activities.
Third, teaching preparation:
Courseware. Everyone prepares a watercolor pen. Four people: a bag of quadrilateral pictures.
Fourth, the teaching process:
(1) Introduction of thematic map.
Students, do you like taking part in sports activities? What sports do you like?
2. On the campus of bright primary school, students are also carrying out various activities. Let's go and have a look. (Courseware shows the theme map)
(1) Look carefully. What figure did you find in this beautiful campus? (Find it yourself first, and then communicate at the same table)
(2) When exchanging reports, students may find the following graphics: (Answer by name, courseware sheet flashes)
3. Import the theme.
There are many figures in the beautiful campus, such as rectangle, square, parallelogram, diamond and trapezoid (these figures flash at the same time). These are all plane figures, all called quadrilaterals. Today, in this class, we will study quadrangles together.
Understanding of quadrilateral.
4. Preliminary impression: What kind of figure do you think quadrilateral is?
(2) Explore communication and summarize characteristics.
1, hands-on operation.
(1) Draw (let students feel the surface)
Students, there are also many numbers in math book 35. Can you find the quadrilateral? Then paint it with your favorite color. Compare and see who can draw quickly and beautifully.
(2) After painting, talk at the same table and explain the reasons.
(3) Collective feedback, why are these quadrangles and those are not?
2. Discuss and summarize the characteristics of quadrilateral.
(1) Take a closer look. What are the characteristics of these quadrangles? (Group first, then feedback)
(2) Write on the blackboard according to students' feedback.
3. Judge quadrilateral.
Teacher, here are some figures. Please judge whether it is a quadrangle. (collectively use gestures to judge and explain the reasons) If it doesn't work, can you turn it into a quadrilateral? (Courseware demonstration)
We know the characteristics of quadrangles. Can you tell us about the things in life? A surface is also a quadrilateral?
(3) Hands-on operation to acquire new knowledge.
1, one point: each group has an envelope, and there are six kinds of figures on the envelope: square, rectangle, parallelogram, diamond, irregular quadrilateral and trapezoid.
(1) Activity suggestion: Work in groups and classify these quadrangles. The team leader will record the results on the study card and tell me why you divide them like this. (teacher's patrol guidance. When students exchange points, the points that classify rectangles and squares finally appear)
(2) Students can be divided into:
① By angle: rectangle, square (all four corners are right angles), diamond, parallelogram, irregular quadrilateral and trapezoid (no right angles).
② By sides: rectangle, square, parallelogram, rhombus (two groups of opposite sides are equal), trapezoid, irregular quadrilateral (two groups of opposite sides are unequal), rectangle, parallelogram (opposite sides are equal), square, rhombus (four sides are equal), irregular quadrilateral and trapezoid (four sides are unequal).
③ Diagonal division: rectangle, square, parallelogram, rhombus (diagonal is equal), irregular quadrilateral and trapezoid (diagonal is unequal).
(3) In the process of grading students, gradually solve some basic quadrilateral features. (Edge-to-edge guidance: one group goes up and down the edge, and the other group goes left and right)
2. Further master the characteristics of rectangles and squares.
Let's look at the classification of rectangles and squares:
(1) How are rectangles and squares different from other quadrangles? Let's talk in the group. You can use a triangle and a ruler.
(2) Report to the group and draw a conclusion. (Put squares and rectangles on the blackboard)
(3) Let's ask a doctor of computer to give a demonstration.
(4) Compared with other quadrangles, rectangles and squares have certain particularity, so they are special quadrangles.
(4) (Mobile) Expand application.
1, someone help me.
(1) is a () shape and a () side shape.
(2) It is a polygon with () angles, including () right angles.
(3) There are () quadrangles in the graph.
2. Take out a quadrilateral and cut off a corner. What shape will it become? Please try it yourself.
(5) class summary.
Today, the teacher and classmates got to know the quadrangle together. Did you learn anything from this course?
Reflections on quadrilateral mathematics teaching in the third grade of Wensan Primary School
"Quadrilateral" is a conceptual course, and it is also a highly operational course. Students can further understand and consolidate concepts through operation. The teaching content of this textbook is arranged as follows: 1. Through students' existing knowledge and comparison process, students can distinguish quadrangles from many figures and realize that quadrangles have four straight sides and four corners.
Second, let students classify quadrangles by observing, measuring, drawing and comparing, so as to understand the characteristics of different quadrangles.
In this lesson, I did better:
1. Pay attention to life experience and provide perceptual materials.
The world and things that students live in are mostly related to "space and graphics" in mathematics, and life experience is a valuable resource for developing students' concept of space. Students have come into contact with many graphics in their lives and are no strangers to quadrangles. Therefore, this lesson takes campus scenes that students are familiar with as teaching materials, aiming at connecting students' life experience, enriching students' perceptual knowledge of graphics, especially quadrangles, and perceiving quadrangles in life as a whole. Not only let students feel that mathematics comes from life, but also let them have a strong interest and affinity for mathematics.
2. Give full play to the collective wisdom of students in the process of group cooperation.
One advantage of group cooperation is that students can inspire each other and solve problems from different angles. After learning about quadrangles, I arranged a group discussion class to let them classify graphics. Here, students' thinking has been fully developed, and there are many situations: there are angles, edges, symmetrical figures, and whether the edges are equal. In particular, students can associate new knowledge with existing knowledge according to whether it is a symmetrical figure or not. Although this is the idea of a classmate, it has inspired more students. In the process of discussion, students also cultivate the ability of speaking and listening, killing two birds with one stone.
In view of the actual reaction of students in the classroom, I think there are the following shortcomings, which need continuous efforts:
1. In this kind of teaching, teachers guide students to acquire knowledge in the first few links. However, in the process of classification, students are not given enough time to think and space to express their opinions, which limits their thinking too much and makes several good classification methods unable to be displayed in class.
2. Facing a generation of students, the classroom's coping ability is not strong. During the whole class, students communicate and speak actively, but in the process of classification, there is a one-to-one situation between students and teachers. When the student's classification method is exactly the same as I expected, it seems that the student is just communicating with me. Do students understand each other? This is a question worth thinking about.
After the whole class, I feel that this class is taught on the basis of students' existing knowledge of quadrangles. Students have a better understanding of quadrangles in the process of hands-on operation. Students are very interested in dividing, drawing and spelling quadrangles, and they are very interested in learning. However, the teaching process of quadrilateral classification is not ideal. Students can classify intuitively, but the classification standard is difficult to express in language. In several teaching sessions, the students all said that this was not ideal.