Unit 4: Possibility
Textbook analysis
Possibility is a part of "statistics and probability" in the four fields of learning mathematics. The preliminary knowledge of statistics in Statistics and Probability has been involved in students' previous study, but probability knowledge is still a brand-new concept for students and is the basis for students to learn related knowledge in the future. The main teaching content of this unit is the uncertainty and possibility of events, and we can know that the possibility of events is large or small. The key to teaching is how to make students sublimate their rich perceptual knowledge of "random phenomena" into rational knowledge.
Analysis of learning situation
Grade five students have had some life experience and statistical knowledge, a preliminary understanding of certainty and uncertainty in real life, and some simple analytical judgment skills. However, students have only a preliminary perception of this uncertain event, and have not deeply understood and applied specific concepts. According to students' age characteristics and life experience, teachers give appropriate guidance, and students will make correct analysis and judgment. Therefore, the textbook introduces learning content from the realistic situations that students are familiar with, and designs a variety of interesting activities and games at different levels, which stimulates students' interest in learning, makes them feel that mathematics is around them, realizes the connection between mathematics learning and reality, and creates opportunities for students to explore independently and study cooperatively.
In teaching, teachers should make use of these situations to let students actively participate in learning activities, let students think independently in specific operational activities, let students experience the formation of knowledge in the process of observation, speculation, experiment and communication, and gradually enrich the experience of uncertain phenomena and possibilities.
Teaching objectives
Knowledge and skills: Let students experience that some events are certain and some events are uncertain. Be able to list all possible results of a simple test and know the possibility of an event.
Mathematical thinking: cultivate students' ability of simple logical reasoning, reverse thinking and communication with others.
Problem solving: We can compare the number of events by the probability of some simple events.
Emotional attitude: Through the study of this unit, students can feel that there is mathematics everywhere in life, and can use the knowledge of possibility to solve problems in life, and gradually become interested in statistics and possibility knowledge, thus cultivating students' interest in learning mathematics.
Teaching emphasis: the possibility of an event will be described by "possibility", "impossibility" and "certainty". Be able to list all possible results in a simple experiment, and know how big and small the possibilities are.
Teaching difficulty: We can judge the number of objects according to the possibility.
Course arrangement: 3 class hours
1. Possibility 2 class hours in .......................................
2. Throw a throw ........................... 1 class.
Classroom teaching plan
Subject: Unit 4: Possibility (1) The first lesson plan in the total sequence of the first class.
Course Type: Newly Granted Writing Time: Year Month Day Execution Time: Year Month Day.
Teaching content: textbook P44 case 1 and textbook exercise 1 1 topic 1, 2, 3, 4.
Teaching objectives:
Knowledge and skills: Students initially experience that some events are certain, while others are uncertain.
Process and Method: Students explore new knowledge through personal experience in the process of observation, communication, hands-on, thinking and verification.
Emotion, attitude and values: cultivate students' expressive ability and logical reasoning ability.
Teaching emphasis: equal possibility of experiencing events.
Teaching difficulty: The possibility of an event can be correctly described by "possible" and "impossible".
Teaching method: Game teaching method is adopted to move the teaching situation into real life, so that students can accumulate and learn knowledge in the game and really participate in it.
Teaching preparation: teacher: multimedia, drawing cards, boxes, colored balls, pencils. Health: chess pieces.
teaching process
First, situational import
1. Introduction: Today, the teacher brought you a small gift. Guess what this is?
Let the students guess. Students guess it may be stationery, toys or books.
2. The teacher reveals the topic: What the students say is possible and uncertain events in mathematics. In this lesson, we will learn the possibility of events. (blackboard title: possibility)
3. Show me the riddle: The little black boy is thin and long, wearing a wooden flower dress. Draw and write, but can't sing. Students may say: pencil.
The teacher asked: Are you sure? Ask the students to say yes, it must be a pencil or a pencil.
4. Show me the prize pencil, indicating that it is for students who show their grades. I hope everyone can work hard.
Second, the new interactive award.
1. Introduction: Next week's class meeting, the teacher will organize everyone to perform, and everyone will have a chance to perform. However, the program form cannot be repeated, and each type can only have one program. Let's discuss it. How should we decide what program each student will perform?
Organize group discussions, and most students will think of drawing lots to decide.
2. Activity: Show three cards with singing, dancing and recitation on them, and ask your classmates to draw one to guide the students to think first. What can they draw?
Students will think: it may be singing, dancing or reciting. All three situations are possible.
Teacher's summary: Every student's performance type is an uncertain event, and there are three possible outcomes.
3. Drawing lots means drawing one. (Take dancing as an example)
Teacher's guidance: If you find another classmate to draw lots, what might you draw?
Students may answer: it may be singing or reciting.
Ask the students: Is it possible to draw a dance?
Zhisheng replied: impossible, because there is no dance in the remaining two tickets.
Take photos of the students to verify whether their guesses are correct.
(Take students' drawing as an example. )
4. Guidance: There is only one left in the end. Can you guess what this is?
Students may answer: it must be reciting, because only reciting this card is left.
5. Teacher's summary: Just now, when guessing what scheme will be drawn, the students used "possible" for the first time, "impossible" for the second time and "certain" for the third time. General things happen in three situations: possible, impossible and certain. Of course, they sometimes change under different circumstances. (blackboard writing: maybe not)
Third, consolidate and expand.
1. Complete "Doing" on page 45 of the textbook.
Display: two boxes. The first box contains all red pieces, and the second box contains red pieces and green pieces.
Let the students say first, which box can definitely touch the red chess pieces? In which box can I find green chess pieces? Which box can't touch the green chess pieces? Wait for questions.
Ask the students to organize a survey activity in the group, verify and report collectively.
2. Complete the exercise 1 1 on page 47 of the textbook.
Let the students say it and explain the reasons.
3. Complete the second question of exercise 1 1 on page 47 of the textbook.
Let the students connect independently first, and the teacher will send colored balls to the students for verification and touch, and then say why they are so connected.
4. Talk: Teachers guide students to talk about the possibility of some events in life with words such as "certain", "possible" and "impossible".
Fourth, class summary.
Teacher: What did you learn in this class? What did you get?
Guided induction:
1. Several situations to judge the possibility of an event: possible, impossible and certain.
2. Be able to judge some events according to the actual situation. Among them, "impossible" and "certain" are judgments that can be made under completely certain conditions, while "possible" is judgments made under uncertain conditions, which usually include both frequent and accidental situations.
Homework: Exercise 3 and 4 on page 47 of the textbook.
Blackboard design:
Possibility (1)
Possibility (uncertainty)
Impossible possibility
(completely sure)
of course
Topic: Unit 4: Possibility (2) The first lesson plan is the general sequence of the first lesson.
Course Type: Newly Granted Writing Time: Year Month Day Execution Time: Year Month Day.
Teaching content: textbook P45 ~ 46, cases 2 and 3, exercise 1 1, questions 5 and 8.
Teaching objectives:
Knowledge and skills: Let students know whether an event is likely or not.
Process and method: Further study the possibility of comparing multiple outcome events: first get the total number of outcomes, and then see which outcome accounts for more than the total.
Emotion, attitude and values: cultivate students' hands-on operation, inductive judgment ability.
Teaching emphasis: the possibility of two outcome events will be compared.
Teaching difficulty: We can compare the number of events according to the possibility.
Teaching method: game teaching method; Independent exploration, cooperation and exchange.
Teaching preparation: multimedia, boxes and colored chess pieces.
teaching process
First, review the introduction.
1.Show: (1) Describe the possibility of the following events in appropriate language.
The sun sets in the east. There will be an exam tomorrow.
It will snow in winter. 4 Flip the coin () face up.
(2) There are three red pieces and 1 yellow piece in the box. Can you touch what color any piece is? Why? Guide the students to say that it may be red or yellow. Because there are both red and yellow boxes.
Question: What color do you think is the easiest to touch the chess pieces? Why?
Guide students to think and discuss in groups. Students may say that they are most likely to touch red chess pieces, because there are more red chess pieces in the box than yellow ones.
2. Derived topic: It seems that the possibility of an event is large or small. Today, in this class, we will study the possibility of an event. (blackboard title: the size of the possibility)
Second, the new interactive award.
1. The possibility of experience varies greatly.
Show the situational diagram of Example 2 on page 45 of the textbook.
(1) instruction: There are two kinds of chess pieces in the box: red and blue. Pick out any chess piece. What color could it be? (It may be red or blue. )
(2) (Continue to show the situation diagram of the experimental part) One group did an experiment. They took out a chess piece, recorded its color, then put it back and shook it again, repeating it 20 times. Students observe the results after touching for 20 times. I find there is more red and less blue. )
(3) Question: What does this mean?
(It is more likely to touch the red piece, but less likely to touch the blue piece. )
(4) Question: If you touch it again, what color chess pieces might you find? (Red), are you sure you can touch red?
(Not necessarily, because the possibility of blue touch is very small, but it may be touched. )
2. Hands-on operation.
(1) Each group has a box with red and blue pieces. Please imitate the experiment in the textbook, touch it yourself, and the group leader will record the results.
After grouping, report and record the results. According to the results, tell which color of chess pieces are in your box. And ask: are the statistical results of each group the same?
Name the groups to report and compare groups with different results.
(2) Guide students to think: What possibility did you find through the operation just now?
Guide the students to sum up: it is related to the number in the total. The more numbers in the total, the greater the possibility of touching, and the fewer numbers, the less the possibility of touching. (blackboard writing)
(3) Ask students to give examples from life, such as lottery, lottery, etc. So as to carry out correct ideological education for students.
3. Show example 3 on page 46 of the textbook.
(1) Let the students observe the recorded results first, and then call the roll to answer the questions in the example.
(As can be seen from the test records, one group touched the ball 20 times, the yellow ball 5 times, the red ball 15 times, and the yellow ball was less than the red ball. The other group touched the yellow ball 20 times, the red ball 4 times, 16 times, and the number of times of touching the yellow ball was less than that of touching the red ball.
Eight groups * * * touched the red ball 123 times, touched the yellow ball 37 times, and touched the red ball more than the yellow ball. In other words, the possibility of a red ball in the box is high, and the possibility of a yellow ball is small. So we can judge that there are more red balls and fewer yellow balls in the box.
(2) Guiding summary method: When the possibility is related to quantity, the more the quantity in the total, the greater the possibility, and the less the quantity, the less the possibility.
Third, consolidate and expand.
1. Complete "Doing" on page 45 of the textbook.
Let the students think independently, communicate in groups and then report. And tell me why you think so.
Guide the students to sum up: it is more likely to occupy more colors in the total, but less likely to occupy less colors. You can further deepen the concept and painting method of "fairness".
2. Complete the "Do" question on page 46 of the textbook 1.
Ask the students to observe the information they can get from the pictures first, and then say it again.
There are many red pieces in the box, but few yellow ones.
Guide students to use the reverse thinking of the size of possibility: can numbers be inferred from the size of possibility? Ask the students to operate in groups and record the results. )
Four. Extended summary
Teacher: What did you learn in this class? What did you get?
Guiding induction: 1. The possibility of an event is large or small. 2. The more numbers in the total, the greater the possibility of touching, and the fewer numbers, the less the possibility of touching. 3. Descriptions with high contact possibility account for a large proportion in the total quantity, while descriptions with low contact possibility account for a small proportion in the total quantity.
Homework: textbook exercises on pages 47-48 1 1 questions 5 and 8.
Blackboard design:
Possibility (2)
Large/→ large quantity
possibility
Small-small amount