Teaching Design and Thinking of Axisymmetric Graphics in Elementary Mathematics

Teaching design and thinking of axisymmetrical graphics in primary school mathematics: the teaching goal of 1;

1. Let students experience the process of exploring how many axes of symmetry exist in axisymmetric figures such as rectangles and squares, and draw the axes of symmetry of simple geometric figures to deepen their understanding of the characteristics of axisymmetric figures.

2. Let students further enhance their practical ability, develop the concept of space, cultivate aesthetic taste and improve their interest in learning mathematics.

Teaching emphases and difficulties:

Ask students to determine the axis of symmetry of an axisymmetric figure by origami, and they will draw the axis of symmetry of a simple axisymmetric figure.

Teaching preparation:

Teacher: Multimedia courseware, white paper, rectangular paper, square paper, trapezoid and triangle.

Student: A blank piece of paper, a rectangular piece of paper and a square piece of paper.

Analysis of teaching objects:

In this part, the symmetry axis of axisymmetric graphics is determined by origami and other methods to further understand the characteristics of axisymmetric. In the previous study, students have learned that a figure that is folded in half and completely overlapped on both sides of the crease is an axisymmetric figure, and they already know the axis of symmetry. Therefore, in view of this specific content, students play axisymmetric graphics by tearing paper at the beginning of class, and are very interested in this content.

Teaching process:

First, "play" symmetry, wonderful dialogue

Dialogue: If you are given a piece of paper, how are you going to play with it? ..... Do you want to know how the teacher fiddled with this paper? Look, fold it in half first, then there will be a crease (blackboard writing: crease), and then tear it from the crease. How's it going? Want to try it? (Stick the teacher's homework on the blackboard)

Second, independently explore the axis of symmetry of axisymmetric graphics.

1. Watch your work carefully. What number is it? (My figure is an axisymmetric figure) (There is a line and a crease, both sides are exactly the same and completely coincident) Blackboard: an axisymmetric figure.

Q: Why do you think your graph is axisymmetric? (A figure whose two sides can completely overlap after being folded in half is called an axisymmetric figure. )

2. Talk: There is a crease in the middle of the axisymmetric figure, and the straight line where the crease is located is the symmetry axis of this figure.

Problem: The straight line where the crease is located is called the symmetry axis. What does that mean? What are the characteristics of a straight line? (Infinitely extended) So how to draw the symmetry axis?

Dialogue: When we draw the symmetry axis, we usually use the dotted line. (blackboard writing: dotted line) that is, draw a little first, and then draw a horizontal line. Because the axis of symmetry is a straight line and extends infinitely, we should extend this dotted line upward and downward respectively.

3. Can you draw a symmetry axis on your work like a teacher? Have you finished painting? Look at each other between the same seats after painting.

4, I didn't expect it, just a blank sheet of paper, a simple folding, a tear, actually created a mathematical axisymmetric figure. In fact, axisymmetric graphics are not far away from us.

5, teaching to find the symmetry axis of rectangle

1) This is a rectangular piece of paper. What would you do if you were asked to find all the symmetry axes of this rectangular paper? Do you agree? Then we began to fold it and draw its symmetry axis.

2) Show your folding and painting methods by roll call in front of the podium.

3) Folding in half, we find that a rectangle has only a few symmetry axes. (2)

4) Just now, we found two symmetry axes of rectangular paper by origami (showing a rectangle drawn on the blackboard). There is also a rectangle here. Can the rectangle drawn on the blackboard be folded in half? If you draw its axis of symmetry, is there any way for you to return? Group discussion. Say its name.

(Measure the midpoint of the opposite side of the rectangle before connecting) Question: How did you find the midpoint of the opposite side? Dialogue: I tell you, the length of this rectangle is 30 cm. How do you find the midpoint of this side? 15cm. The midpoint of this side is the same as the one above. Then connect the two midpoints with a dotted line.

Question: Did you find the axis of symmetry? Please continue to use this method to find other symmetry axes of the rectangle.

5) Let the students draw a picture on the book. Remind the students after painting: draw the symmetry axis that the teacher just drew.

Question: How many symmetry axes have you drawn?

In this way, whether it is a rectangular paper or a rectangular diagram, there are only two axes of symmetry.

6. Symmetry axis of teaching square

1) studied the rectangle. What graphics do you think we should study next? (The teacher takes out the square paper) Take out the square paper. Please find out all the symmetry axes of the square and draw all the symmetry axes with the method of studying the rectangle just now.

2) How many symmetry axes can you draw through the research just now? (4) Which four? How did you find the diagonal? Are you looking for the same thing as him? It turns out that the teacher and you are looking for the same demonstration courseware. Are these four projects?

3) Now we know how many symmetry axes a square has? How does a square compare with a rectangle? How much more (than a rectangle) Which two? (two diagonal lines)

Third, consolidate and deepen, expand and extend.

I want to do it after I finish 1.

1. Through the activity just now, we found the symmetry axes of a rectangle and a square, and we know that a rectangle has two symmetry axes and a square has four symmetry axes. Show page 62 of the book and consider doing all the numbers in the first question. There are many numbers that we have learned. See which students can find the axisymmetric figure at a glance. You thought it was an axisymmetric figure. Put a tick on it with a pencil. Students judge independently.

2. Have you made a judgment? How do you think to test whether your judgment is right or wrong? Take out these pictures prepared in advance and fold them. If they are symmetrical, please draw their symmetrical axes in the book.

3, the students began to operate, the teacher patrol, collective feedback exchange.

Dialogue: The teacher found that many students have their own opinions. There are only six chances now. Each student can choose one that you are most sure of and say whether it is an axisymmetric figure. If so, how many?

4. Dialogue: Through the activities just now, everyone can accurately judge whether these six figures are axisymmetric, but Mr. Ji feels that he has something in his heart, and I wonder if the students have anything in their hearts. What I want to say in particular is that we take trapezoid as an example. What kind of trapezoid is the graph 1? (isosceles trapezoid) Although this isosceles trapezoid is an axisymmetric figure, ... not every trapezoid is an axisymmetric figure, such as the trapezoid No.6 and this trapezoid in my hand, they are not axisymmetric figures. It seems that the general trapezoid is not an axisymmetric figure, but only the isosceles trapezoid is an axisymmetric figure? Well, that's all I have to say. You can tell me the rest of the graphics.

Complete thinking and action 2

1, I brought you some beautiful graphics. Are all the following figures axisymmetric? This is an axisymmetric figure. Draw "√" below. Do it independently, answer by name, and tell me which figures are axisymmetric.

2. Show the first picture. How many axes of symmetry does this figure have? Discuss in groups of four. Answer by name, and then can you draw it? Is it the same as the teacher's painting? Can you find the symmetry axis of the other two figures?

3. Students independently complete the second and third figures. Collective communication.

4. How many symmetry axes did you find in the second picture? What about the third one?

After thinking, do the fourth question.

1, show the first three numbers, first carefully observe what are the three numbers in the question? If students say that the first figure is a triangle, ask what kind of triangle it is (equilateral triangle is also called equilateral triangle). If the students say that the third figure is a Pentagon, talk about it: this figure is not an ordinary Pentagon, its five sides are equal, and it is a regular Pentagon. 2. How many symmetry axes do these three figures have? Can you draw a picture on the book? The students drew a picture on the book.

3. Feedback: How many symmetry axes does a regular triangle have? Do you have any different opinions? Is that so? What about the regular quadrilateral? Right? What about regular pentagons?

The teacher pointed to the blackboard. An equilateral triangle has three axes of symmetry, an equilateral quadrilateral has four axes of symmetry and an equilateral pentagon has five axes of symmetry. What did you find? (A regular polygon has several axes of symmetry)

According to this conclusion, can you know how many symmetry axes the regular hexagon of the fourth figure has? Let's see if there are six. What about the regular octagon?

Fourth, class summary.

Today, in this class, we mainly studied axisymmetric graphics. In fact, nature's creation of axial symmetry is far more than that. Looking up at the blue sky and overlooking the earth, where there is life, there is no axisymmetric footprint. Look at butterflies and dragonflies flying among flowers, geese and pigeons soaring in the sky. Let's be a small designer in elegant music and design an axisymmetric figure. After reading page 63 of the book, consider doing question 5.

Teaching reflection:

Students learned axisymmetric graphics a year ago, and some students may have forgotten it. Therefore, the teaching review is designed at the beginning of the class, which can guide students to recall the existing knowledge and mobilize the existing knowledge reserve. In particular, the teacher's method of drawing symmetry axis demonstrates the method of drawing symmetry axis by students. This lesson focuses on the drawing of symmetry axis, so that students can clearly understand their learning objectives and concentrate.

In the new teaching content, first, let students find that a rectangle has two symmetry axes through origami, and then learn how to draw the symmetry axis of a rectangle in the form of group cooperation. This program can guide students to think from easy to difficult, from intuitive to abstract. The teacher predicted the possible situation in order to achieve a breakthrough in different situations. The teacher's demonstration diagram and necessary explanations give students a deeper understanding of the axis of symmetry.

In teaching, let students try origami and painting first. It is necessary and possible to do so. Pay attention to the cognitive status of underachievers in the evaluation, and inspire them to improve their cognitive level through operation.

In this part of the exercise, the operation flow of the exercise is clear and the topic is explained in place.

Of course, in the process of teaching, teachers have not prepared enough learning tools. For example, the rectangular paper and square paper prepared for students are so small that the students sitting below can't see the works displayed by the students above during the teaching feedback. In fact, teachers can use the projection of things to show students' works. Let the students talk about their own ideas.

In the whole teaching process, the classroom atmosphere is very dull, which is not as good as the usual classroom atmosphere. According to the analysis of teaching researchers, teachers are positive to students, and there are too few positive comments, which leads to students' low enthusiasm for answering questions. After class, I tried to positively evaluate the students' answers and had different reactions. It seems that young teachers should learn more from experienced teachers in their usual teaching activities and take more teaching and research classes in order to improve their classroom teaching ability.

Teaching Design and Thinking of Axisymmetric Graphics in Primary Mathematics (2) Teaching Design

I. Teaching Content: Geometry Volume II

Chapter III Triangle

Unit 6 Axis symmetry in the fourth quarter

Capital Normal University Press.

Second, the unit design:

The content of this unit is divided into four parts: inverse proposition and inverse theorem, the nature and judgment of angular bisector, the nature and judgment of the middle perpendicular of line segment, and the axial symmetry between figure and two figures.

Axisymmetry is put at the end. Through observation, comparison, induction and analogy, it helps students to strengthen their understanding of the problem.

Third, the teaching objectives:

1, to understand various symmetry phenomena.

2. Identify the axisymmetric phenomenon.

3. Understand the properties of axisymmetric graphics and use them to solve problems.

Fourth, the teaching process:

Activity 1: Show various symmetrical figures. Let students experience the beauty of symmetry in life and know mathematics, which can improve students' interest in learning mathematics.

Activity 2: Prepare angles, isosceles triangles, rectangles, circles, etc. Fold them in half completely and let the students draw a conclusion. Describe the process.

This activity can cultivate students' practical ability and language expression ability, but the observation conclusion is different, so it is difficult to narrow the scope and describe the language, so we should pay attention to it.

Activity 3 Question introduction: There are two symmetrical points. How to draw the symmetry axis?

Draw straight lines, angles and isosceles triangles, and try to draw the symmetry axis. Observe and analyze.

Discussion: How to explain the relationship between (1)△ABD and △ACD?

⑵ What is the relationship between symmetry point and symmetry axis?

Induce the conclusion. Property: Two parts of symmetry are congruent.

The axis of symmetry is the perpendicular bisector connecting the symmetrical points.

Activity 4: Show examples for students to analyze and answer.

Activity 5: Solve the problem.

Teaching Design and Thinking of Axisymmetric Graphics in Primary Mathematics Part III: Analysis of Textbooks;

Axisymmetric graphics is a learning content after six years of "understanding the characteristics of a circle" and "calculating the circumference and area of a circle" in mathematics. It plays a connecting role in the arrangement order of textbooks in this chapter. On the one hand, it can better explain the characteristics of axisymmetric graphics, on the other hand, it can have a comprehensive understanding of the symmetry in various plane graphics. So as to better develop students' concept of space.

Teaching emphasis: master the concept of axisymmetric graphics.

Teaching difficulty: finding the symmetry axis of axisymmetric graphics.

Student analysis: Students have learned simple plane graphics, have a certain understanding of plane graphics, and have a preliminary understanding of the methods and means of learning plane graphics. Senior students have the characteristics of being competitive, and the class has initially formed a good style of study such as cooperation and exchange, courage to explore and practice, and the atmosphere of mutual discussion among students is relatively strong.

Design concept: according to the specific objectives of the basic education curriculum reform, it is a feature of the mathematics curriculum standard to encourage students to discover knowledge in concrete and intuitive operations. Change the tendency of paying too much attention to knowledge transmission, emphasize the formation of active learning attitude, pay attention to students' learning interest and experience, implement open teaching, let students actively participate in learning activities, and guide students to feel the generation, development and change of knowledge in classroom activities.

Teaching objectives:

1. Infiltrate the particularity of things into students through teaching and experience the beauty of symmetry.

2. Cultivate students' observation ability and generalization ability through operation activities.

3. Make students intuitively understand the axisymmetric figure, understand and master the concept of axisymmetric in operation, and find out the symmetry axis of axisymmetric figure.

Teaching process:

-create problem situations and introduce topics.

1, (relevant pictures are displayed on the screen) Look at the following pictures. What are their characteristics?

2. It is pointed out that the first three figures are called axisymmetric figures.

3. Introduce the topic: Axisymmetric graphics.

Second, students strengthen their cognition and feelings of graphics through practical activities such as intuitive perception and operation confirmation.

1, revealing the concept of axisymmetric graphics.

Thinking: Now, what method can you use to check that these figures are axisymmetric?

A, students try to say the concept of axisymmetric figure.

B. Teacher's blackboard writing: the concept of axisymmetric graphics (emphasizing complete coincidence)

C, let the students talk about how you understand axisymmetric figures. (Take the group as a unit, and use the graphics in your hand to illustrate)

D. the teacher explained the concept of symmetry axis with pictures.

2. Finish it. Let the students report and demonstrate by computer. )

We have learned a lot about plane graphics. Now, let's see which figures are symmetrical. Please draw it. (Reports vary from disorder to order)

4. Do it 1 (oral answer, screen demonstration)

5. Just do it 2 (oral answer, screen demonstration)

Teacher's summary: In this lesson, we learned axisymmetric graphics. We know that if a graph is folded in half along a straight line, the graphs on both sides can completely overlap, and this graph is an axisymmetric graph. And we know that the straight line where the crease lies is called the symmetry axis. We also know which plane figures we have studied are axisymmetric and how many axes of symmetry there are.

6. problems.

Consolidation exercise: 1, math book P 102 1 (oral answer) (screen)

2. Math book P 1024 (oral answer) (screen)

3. Draw the symmetry axis of each group of figures.

4. Many things in nature and daily life are axisymmetric. Can you give me an example?

5. Appreciate axisymmetric things.

6. Judges:

Not all parallelograms are axisymmetric figures ()

All parallelograms are symmetrical figures ()

Third, summary: What have you gained from this lesson?