Teaching objectives:

1, through observation, we can find the symmetry of the graph, and we can describe our findings in the graph in our own language. Explore the relationship between folding method and graphics;

2. Cultivate students' language expression ability, spatial imagination ability and hands-on operation ability in the process of exploring graphic cutting;

3. Infiltrate a sense of mathematical thinking to see the world from a mathematical perspective, and open a window for students to discover mathematics in their lives.

Teaching content:

Characteristics and cutting methods of axisymmetric graphics, folding methods of two-connected and four-connected graphics

Teaching process:

First of all, enjoy the beauty of art in appreciation.

China's paper-cutting art is profound, and students appreciate China's precious art: "Chinese paper-cutting" feels the beauty of paper-cutting works in the slide show, and puts forward the topic of "Mathematics and paper-cutting"

Teacher: Listen to beautiful music. How do you feel after enjoying the wonderful paper-cut works?

Arouse students' patriotic enthusiasm, arouse students' appreciation of the beauty of China's traditional art, and give students a desire and passion to start work. )

Teacher: Today, my math class is related to paper cutting. Let the teacher take the students to cut paper and look for the wonderful mathematics.

Second, feel the law of discovering graphics,

Discovery of Axisymmetric Graphs

The first group:

This is a relatively simple group of paper-cut works. Please read these works carefully. What kind of feeling does it bring you? Have you found some features of the graph?

Give students time to think, then communicate in groups and use "whispering" (whispering is a strategy I use in group cooperation. In group cooperation, I only focus on helping some groups that need help. However, due to the lack of teacher's supervision after liberalization, individual children who lack consciousness are easily separated from the group. This is a common problem in our group cooperation, and it becomes a cooperation in which individual students discuss and discuss, and cannot fully participate. In order to make all the students better participate in the group discussion and make the discussion between the groups real, I adopted "whispering". Before speaking, I will find a child at random, quietly tell me the results and process of their group discussion, and then ask the students in their group to speak, and make a reasonable evaluation of the group's activities through the speaker's answers and whispers. This can promote the participation of group cooperation.

Focus of observation: I will use "whispering" because of the usual group cooperation, but not all activities, and I will not tell my classmates every time I use it. So this time, at the beginning of the class, when I can't say "whispering", I will discuss it in groups and see how the children react. What is their participation? Listen and observe.

Bear, butterfly, radish, peach heart

(They are all axisymmetric figures. I hope that through children's observation, the two sides of the figure are exactly the same, and the two sides can completely overlap after being folded in half. )

Third, imagine what kind of graphics will be cut out after folding, verify the desired results in operation, and compare the relationship between thinking results and imagination.

1, think about what kind of graphics will be cut out after folding, and verify the desired effect in operation.

Fold and draw a peach heart, make a peach heart by yourself in the process of imagination, and experience the origin of axisymmetric graphics.

The reason why I chose the simplest peach heart is because this is a math class. It is important to exercise students' spatial imagination through the medium of paper-cutting, and to verify the thinking process with the simplest paper-cutting. The purpose is to verify, not the real paper-cutting, which is also the reason for choosing peach hearts in the design process.

Think independently first, and then make full use of group cooperation to communicate, laying a good foundation for follow-up activities.

Stick the work cut by each student on the white paper 1 and write your student number on the heart of the peach.

2. Observe the teacher's process of folding and cutting, and imagine the cutting pattern.

The teacher folded it in half, then folded it in half and cut it himself. Let the children imagine how they cut the graphics and draw the graphics that you think the teacher cut.

3. Exploration after liberalization and verification in comparison.

In the process that the teacher just cut it without showing it to the students, the students are more willing to experience the process of cutting two hearts together. After cutting it out, compare it with the previous imagination, and verify your spatial imagination ability in comparison. The teacher opened the grade she had just cut.

Question: Do you still want to cut more connected hearts from the paper in your hand? First guess, how many hearts can you cut out to connect? Then tell everyone how you fold and cut it. Finally, use the materials in your hand to personally verify whether your guess is the same as the result you cut out?

Write the student number on the picture cut by each student and stick it on No.2 white paper.

4. Look at the graphic folding method (anti-verification)

The second group: this is a group of hand-held numbers, which are constantly changing.

Bear (company two), butterfly (company four) and radish (company eight) stop here and let the students guess what the teacher's next picture will look like. Why Peach Hearts (Sixteen Companies)?

(They are all "hand in hand" paper-cuts with axisymmetric figures in front, which are Erlian, Quadruple, Badian and Shilian respectively)

Every time you show a graphic, you should ask your classmates how to fold it before cutting it.

Fourth, give students a pair of mathematical eyes to observe the world.

Appreciate the pictures. Just now we found some math problems in paper-cut works. We first guess through our own minds, and then verify through our own hands. What we thought, we did. Look at the picture below There are many math problems in your life. Four identical rectangles and a square make up a new square (chord diagram), seven simple wooden boards (puzzles) and a simple note (Mobius circle). Ah, there are many math problems hidden in these figures. Do you want to continue exploring? Let's have a pair of math eyes to discover the math in your life and tell your parents what you found. I'm sure they will say that you are great children with mathematical wisdom!