In many counting problems, it is often necessary to divide all counted objects into several types that are not repeated or omitted, so that each type is convenient for counting. However, practical problems are often complicated, easily confused and difficult to distinguish. In order to accurately calculate the number of things, we must use the principle of inclusion and exclusion. This kind of problem is usually called overlapping problem, also called inclusion and exclusion problem. Teacher Xu Changqing's understanding of ability is that he can successfully solve unfamiliar problems with what he has learned. In the course, I explored and further expanded the overlap with children. It also constructs the relationship between mathematics and Chinese related words "Du … and ……", and further uses gestures to repeatedly establish and communicate the existing cognitive and unknown connections, thus transforming the existing fuzzy perception in the mind into graphic expression in mathematics. I did it. I can read, speak and express.

First, a brief introduction to the story

1) story import

A guest came to the barber shop. The guest said, "Uncle, my father and I want to shave our heads." Another guest said, "Master, shave my father and me." At this time, the barber shop looked up and wondered.

Teacher: "Can you guess why the barber is confused?"

Health: "Because two sentences should have been for four people, but he only saw three people."

2) Preliminary perception of repetition

Teacher: "Who are those three people?"

Health: "A son and his father, and a grandfather."

(gesture introduction, click, click)

Conveniently asked: "How did four fingers become three fingers?"

Student: "put two fingers together." "Why?"

Health: "Dad is the son's father, and Dad is grandpa's son. So there are only three people. "

Lead to the related word "both" ... and ... "

(Repeat the gesture "Chen Wenjing" to combine Chinese related words with body language)

Second, the game

1) chair grab game

Find two chairs and call two children up.

Teacher: "Everyone is here, why do people raise their hands?"

Health: "there are as many people as chairs, which are one-to-one correspondence and cannot be eliminated." We need to increase manpower. "

Please welcome four more people.

Health: "There are too many people, only three people".

Teacher: "What should we do now?"

Health: "Reduce people."

2) Invited four students who came up later to play rock, paper and scissors (fair game), 1 passed the exam, and three students were eliminated.

Third, deep experience.

1) explains the rules of the game.

Run clockwise, grab the bench and sit down when you hear the stop, don't sit on your legs, or you will be eliminated. After two rounds of competition, one girl remained to advance to the championship.

2) Interview the champion

Through moral education, leading girls to thank all their companions who participated in the game can lead to the birth of the champion.

3) Please ask the children who participated in the game to receive the honor.

Teacher: "There are six people standing up. Why are there fewer people? Don't shirk in front of honor. "

Health: "The guess and the chair snatcher are here, and the referee has played two roles, so it seems less, but everyone is here."

Teacher: "Then let's calculate, how many people guess boxing? How many people robbed the chair? "

Health: "4+3"

Teacher: "it is equal to 7! There is one person left, please stand up. "

Health: "Six people!"

Teacher: "Seven people!"

(Through confrontation between teachers and students, cognitive conflicts are triggered and new knowledge is experienced)

4) Hula hoop makes people stand up

Use a hula hoop to represent three people grabbing chairs, and a hula hoop to represent four people guessing fists. Please ask the children to enter the hoop.

Teacher: "Is there another person?"

At this time, a child was at a loss and didn't know which side to stand on. )

Teacher: "To tell the truth, if you can make three people in a circle and four people in a circle, you will win."

(The teacher leaves, getting farther and farther. Let children reduce their dependence on teachers and find ways to solve them themselves. The students are at a loss. After some confrontation, the children thought of combining the two hula hoops into one. Then ask the students to count the number of people in the two circles now, and three and four people have been satisfied. But there are only six people in total. )

Teacher: "Today I finally admit that 4+3=6".

Health: "No! * * * all participate in guessing boxing and grabbing chairs. He has both circles. Actually, there are two, but we only need one, so we have to subtract 1. 4+3- 1=6"。

Teacher: "Who is negative 1?"

Health: "* * *"

Teacher: "Then * * * go a little further first, and then we'll count. Something happened! Subtract 1 and it becomes 5. It seems that negative 1 is not him. Who is negative 1? "

Student: "Let's count both first, then subtract the extra first one and leave him a role."

Teacher: "If he plays three games, how much will he be reduced?" ? Eight games? 100 game? "

Health: "two, seven, nine nine".

Teacher: "that is to say, leave him a role, so there is a one-to-one correspondence." These are two rings in mathematics. "

(Repeat gestures, click, click)

5) Drawings

Teacher: "How should I draw?"

Health: "There must be some overlap."

(At this point, through the combination of gestures, students can already perceive non-repetition, complete repetition and incomplete repetition. )

Teacher: "Then these two are ... and ...".

6) Attach a name tag.

After the three people who robbed the chair posted it, the teacher adjusted the name bar and the students shouted "No".

(Build a diagram model of "both" ... and ... "In the child's mind)

Please ask four boxing guessers to come up and post their name tags. "Being a classmate of ... and ..."

Teacher: "Why did this classmate take his name tag away again?"

Student: "Because he posted it for the first time, and that position belongs to him, there is no need to post it again."

Teacher: "Now, please * * * challenge and paste your name labels."

The students suggested that he stick the names together, some with words and some with physical demonstrations, which made them particularly anxious.

(Now children have a deeper feeling about the amount of repetition. )

Teacher: "So when you play games, you need to split into two, and when you count the number of people, you need to merge into one." Because there is only one * * * in our class, we should subtract his redundant role and go back to one-to-one correspondence. "

(Repeat gestures, click, click)

Fourth, solve problems and apply new knowledge.

For example, girls in Class One, Grade Three 19, boys 17. How many people are there in the class?

Health: "19+ 17=36 (person)"

Teacher: "what I learned today is repetition, and I have to do subtraction." Why not reduce it? "

Student: "Because girls and boys are different, they are not the same kind of people, and there is no repetition, so boys and girls are both human beings."

Teacher: "So what you have learned can't be used to solve all problems. You should pay attention to the environment, conditions and laws applied in mathematics. "

Teach children to use knowledge flexibly, instead of rigidly applying mindset to solve problems. )

Five, return to the scene, expand new knowledge

Small survey: Dad's smoking and drinking (repeated gestures)

Children who smoke and drink stand up. Children who only smoke and don't drink stand up. Children who only drink and do not smoke stand up.

Teacher: "13+ 17=30, are you all our classmates?" Who else didn't stand up? "

Health: "Because my father neither smokes nor drinks."

Teacher: "Then where shall I put such a father?"

Student: "Add a rectangle outside, and put my good father outside the Wayne diagram, inside the rectangle."

Teacher: "We hope that the fathers in the circle will jump out early and be good fathers."

(Expand children's initial understanding of set and pave the way for later higher learning)

The harvest of this lesson:

1) In this lesson, we extended some knowledge about sets when learning the basic overlapping problem. In fact, there is also a lot of knowledge related to repetition in junior high school, such as the overlapping of line segments and angles, the proof of congruence of triangles, the area of repeated parts, mosaics and other issues, all of which should follow the principle of not weighing or leaking. Therefore, the content of this lesson plays a decisive role in the study of many contents later.

2) In order to make children realize the amount of repetition and learn how to deal with it, every step of xu teacher's design is gradual. In gamification learning, children can experience it by themselves, refute it constantly in teachers' questions, establish their own cognition, seek answers by themselves, successfully master methods and solve problems by themselves. Guided by one game after another and one conflict after another, the children enjoyed it and left a deep impression unconsciously. This kind of humor, which runs through the moral education classroom, is the essence that we can also learn and penetrate into our own teaching.