Ability goal:
Through the process of solving simple problems in real life, students' observation ability, communication ability and cooperative inquiry ability are initially cultivated, which effectively promotes the development of individual thinking.
Emotional goals:
Let students fully feel the close relationship between mathematics and life, stimulate students' positive and happy mathematical emotions, and make them gain successful experience in solving problems with knowledge. The initial score comes from life and is applied to life.
Teaching emphasis: understand that only "average score" can produce scores.
Teaching difficulties: the formation of the concept of "fraction" Understand the meaning of denominator and numerator.
Teaching preparation: teaching aid preparation: multimedia courseware, rectangle, square, circle, equilateral triangle and other graphics.
Teaching process: First, create situations and lead to questions.
Students, have you ever shared anything in your life? Now, the teacher wants you to help me score a point, okay?
There are four moon cakes now. How to divide between the two children? How much is each person divided?
How can two children divide two moon cakes fairly? How much is each person divided?
In this way, we will share each share equally. What division did we learn before?
Let's see how two children share a piece of moon cake. How much does everyone get?
Can half be expressed by the numbers learned before?
Then, the teacher introduces you to a new friend-score.
In this lesson, let's learn the preliminary understanding of fractions together.
Revealing the theme: a preliminary understanding of scores (blackboard writing)
Second, hands-on operation, inquiry and communication (1), understanding 1/2, understanding1/2.
Think about it, how do we divide this moon cake? How much does everyone get?
Take a look. Are the two and a half moon cakes the same size?
Two cakes are exactly the same size, that is, the cake is divided into two parts on average. This half moon cake is 1/2 of the whole moon cake.
In other words, a moon cake is divided into two parts on average, one of which is 1/2 of its size.
Can you find another 1/2 in this moon cake?
2. Write a score of 1/2.
Let's write it down.
Who will read this music score and say what the name of each part means? What does 1/2 mean?
Show courseware. If so, can it be expressed in half?
Exercise: Can the colored parts in the picture be represented by 1/2? Why?
Summary: Only the average score can guarantee the fairness of the score and get the score.
Courseware, each person gets 1/2 moon cakes. Are they the same size? Why?
So when we describe it, we must make it clear who it is.
Is it possible to get half of the mooncakes? Is there any other way to get half?
3, origami activities
Take out a picture at random, fold it first and show its 1/2.
Obviously, the folding method is different. Why are all the colored parts 1/2?
We use these three folding methods to fold the rectangle 1/2, so is the size of 1/2 of the same figure equal? Why?
Summary: A moon cake, rectangle and square, as long as it is divided into two parts on average, each part is its 1/2.
(2) Discovery score
1. If a moon cake is divided into four portions on average, how much is each portion? How to express it? Who will write it? What does 1/4 mean?
Please fold it with a square to show a quarter of it.
These figures have different shapes. Why are all the colored parts a quarter?
2. Divide a circle into three parts equally. How much is each part? How to write? What does 1/3 mean?
Divide a rectangle into five equal parts, point out one fifth of it and color it. What does 1/5 mean?
Summary: Numbers such as 1/2, 1/3, 1/4, 1/5 are all called scores. Divide it into eight parts on average. How much is one part? 100 average share? Can you name more such scores?
Third, consolidate the practice.
1. Please tick if the following points are not equal.
2. Can the scores below represent the colored parts in each picture? The painting that can be expressed is "√", and the painting that cannot be expressed is "×". Tell me why.
Do you know that the colored part accounts for a small part of the whole figure? Tell me why.
4. True or false
5. Which of the following pictures is colored 1/4, tick ().
Why are the same squares represented by different fractions?
Summary: The same shape may mean different scores, and different shapes may mean the same score.
6. Square that will change: What numbers are used to represent squares in different graphs?
8. think about it
Summary: What did you get from this lesson? Blackboard design:
A preliminary understanding of scores
1 ... average molecular fraction
-... the score line says: Who owns half?
2 ... denominator
The second part: the teaching goal of the teaching design of "preliminary understanding of scores" in junior high school mathematics;
1. Guide students to get a preliminary understanding of scores in familiar life cases, intuitive graphic and physical discussion and research, establish a preliminary concept of scores, read and write scores, and clarify the meaning of scores with the help of graphics.
2. Compare the molecular score of 1 with the help of objects or intuition.
3. Cultivate students' cooperative consciousness, mathematical thinking and language expression ability through group cooperative learning activities.
4. In the hands-on operation, observation and comparison, cultivate students' courage and self-study spirit, so that they can gain successful experience in using knowledge to solve problems.
Teaching emphases and difficulties:
The preliminary construction of the concept of fraction and some points to be understood. Compare the molecular fraction of 1 by physical objects or intuition.
Teaching philosophy:
The teaching of "fraction" belongs to concept teaching. Concept teaching should pay attention to the process of teaching activities, that is, the teaching of thinking activities in the teaching field, not just the result of mathematical activities-the teaching of mathematical knowledge. Its occurrence and development have a process. Only by letting students know the "ins and outs" of scores can learning be full of interest and motivation. In the teaching design of this course, I tried to make several attempts:
First of all, create rich mathematics learning situations to help students learn scores.
From integer to fraction, it is a cognitive breakthrough for students. In order to build a breakthrough stage for students, I have designed a wealth of realistic situations that are close to students' reality and are of interest to students, such as "dividing moon cakes". On the basis of highlighting the average score, I help students understand and understand the meaning of scores in familiar situations, thus introducing new lessons. Students experience the generation process of time markers in positive thinking and trying, and initially perceive the concept of time markers under the guidance of teachers.
Second, strengthen mathematical practice activities, so that students can actively construct mathematical knowledge.
Students' learning of mathematics knowledge is not passive acceptance, but active construction, and hands-on operation has a positive role in promoting students' construction. Therefore, in this class, I fully provide students with opportunities to practice, and let students understand the meaning of scores in the process of hands-on, brains and mouth-opening through the situation of "folding and folding". For example, when you know the score, ask students to fold out one-half and one-quarter of a square piece of paper to further understand the meaning of the score.
Third, innovative exercises make concept learning open to some extent.
Concept learning is not boring, and the charm of scores can make concept learning open to some extent. Therefore, I designed activities such as finding scores from graphs, comparing scores by origami and comparing scores by graphs, which not only permeated the idea of combining numbers with shapes, but also helped students understand the connection between scores and life and experience the happiness brought by successful learning.
Teaching process: 1. Create situations, set questions to stimulate interest, experience the process of generating scores 1, and stimulate interest introduction.
The teacher took out four moon cakes and asked the students to help the teacher think about it. If these four mooncakes are given to two students, how should they be distributed fairly? How much does everyone get? Give two pieces to two people. How can we divide it fairly? Give a piece to two students. How to divide it fairly? (The teacher demonstrates how to divide the mooncakes), which leads to the new lesson "Divide". Teacher's blackboard "score.
2. The scores of writing, reading (1) and writing teaching achievement.
The teacher demonstrated the process of dividing moon cakes. (Emphasis on average score) How to express half by score? Divide the moon cake of 1 into two parts on average, where 1 is 1/2 of this moon cake.
(Teaching Writing Score "1/2")
Teacher: Just now we know the score "1/2", and each part of the score has its own name. Taking "1/2" as an example, the teacher summed up the meaning and wrote on the blackboard:
Teacher: Please raise your right hand and read after the teacher: First, draw a short horizontal line to indicate the average score. This line is called the fractional line. (The teacher said while writing on the blackboard) Divide it into two parts on average and write "2" at the bottom of the score line. We call it the denominator (the teacher's blackboard book). Assign each person two parts of 1 and write "1" on the score line. It's called a molecule. (Teacher writes on the blackboard)
1 ...
-... the score line says: half.
2 ... denominator
2, born on the table, the writing of "half" is empty. Tell each other the names of the parts of the musical score at the same table.
3. The teacher should write the fractional line first, then the denominator, and finally the numerator. When reading fractions, read the denominator first, then the numerator. Students read together. Students practice speaking and writing, and the teacher says several scores at the same time. The students write them in their exercise books and instruct them to perform.
(4) Practice of saying the name of the music score and reading the music score: The teacher shows the music score, says the names of each part, and reads the music score.
(Design intention: This link is mainly to let students start from the existing knowledge and experience, as well as the practical significance of the score. Through the introduction of the daily life situation of "dividing moon cakes", students draw the conclusion that "a moon cake" is divided into two parts on average, and each person gets half. With the help of physical demonstration, the "half" is abstracted from a specific quantity to a number, and the concept of score is preliminarily understood to establish a new cognitive balance. At the same time, on the basis of students' understanding of music score, the names of various parts of music score are introduced to further guide students to understand the meaning of music score. )
Second, strengthen mathematical practice activities and let students construct mathematical concepts independently.
1, half done
① Take a square piece of paper, fold out its 1/2 and color it.
(Life and death teachers patrol)
(2) The report shows that
(3) Solve the question "What can 1/2 represent for colored parts with different folding modes?" problem
Reports and presentations.
2. Exercise: Can the colored part in the picture below be represented by half? Explain why. (Multimedia demonstration) Students' exercises
3. Students associate a quarter of the new scores with half of their studies. (A quarter of the teacher's blackboard) If we continue to divide the square equally, how many more may appear?
Correlate and report
(Design intention: This link is mainly for students to initially establish half of the concepts and representations. Guide students to grasp the essence and make a moderate abstract summary. "As long as the object or figure is divided into two parts on average, 1 is half." Then, it further moved Lenovo by one-fifth, one-sixth, one-seventh, one-eighth and one-tenth ... It subtly guided students to think deeply and effectively cultivated their abstract thinking ability. )
4, hands-on fold a quarter
(1), students take a square piece of paper, fold out a quarter of this paper and color it with your favorite color. After folding, let's talk in the group and see if there are different folding methods. (Life and death teachers patrol)
(2) Exchange report
③ Solution: "Look carefully at the different folding ways of these figures. Why are all the colored parts represented by a quarter? " problem (Student answers)
(4) The teacher summarizes the same figure and expresses the same score with different folding methods.
(Design intention: This link is mainly to let students know more scores independently, and transfer and expand their knowledge appropriately through independent thinking, hands-on operation and group communication. Students show the formation process of knowledge from their respective interests, needs and cognitive starting points. Under the question of "Why can different folding methods be expressed by a quarter", guide students to gradually understand that the different folding methods are not the essential attributes of music scores, but the essential attributes of music scores are "how many copies are divided equally" and "only one copy can be used to express this 1 share". )
5. Compare scores.
1. Take out the square that has just been folded, and compare it with one-half and one-quarter. Whoever is bigger is smaller. Compare the folded pictures in your hand and tell the reason in the group. (health report)
2. Teacher's summary: the molecule is 1. The method of comparing scores: "The numerator of a score is 1, and the larger the denominator, the smaller the score; The smaller the denominator, the greater the score. "
(Design intention: This link is mainly to explore the score as the attribute of numbers and compare the scores intuitively. Guide students to organically combine operational activities with language expression and developing thinking, compare the scores expressed by students, skillfully use the generated learning resources, and deepen their understanding of the scores through comparison. )
Third, consolidate the application and deepen the understanding and application of the meaning of fractions.
1, the courseware shows a five-pointed star and a windmill. What grades do these things remind you of? answer
2. Courseware display book 1, 93 pages with 2 questions, 96 pages with 3 questions, which the students completed independently. (Teachers and students * * * revise together)
3. Let the students talk about what things around them have found the shadow of the score. (Student answers)
4. Teacher's summary: Students really talk less. Yes, scores are everywhere in our lives and are closely related to our lives. In today's class, we have got to know each other a little. In the future study, we will continue to approach the music score, understand the music score and explore more mysteries about the music score.
Teaching reflection
The textbook "Preliminary Understanding of Fractions" is based on students' knowledge of integers. From integer to fraction is an extension of the concept of number, which is a qualitative leap for students to understand the concept of number. Because there are great differences in meaning, reading and writing methods and calculation methods. The concept of score is abstract, which is difficult for students to accept and learn well at once. Therefore, the knowledge of fractions is taught in stages, and this unit is just "a fraction that was first recognized". Cognitive score is the first stage of cognitive score, the "core" of the unit textbook, and the first lesson of the whole unit, which plays a vital role in future learning.
New courses are often introduced from old knowledge. The key is to firmly grasp the breakthrough point of old knowledge and new knowledge, and "preliminary understanding of scores" must be based on the concept of "average score" So at the beginning of teaching, I asked the students to answer, "How to divide four moon cakes between two students? How many pieces will each student get? " Students quickly answer "average score", and each student is divided into 2 pieces, which is fair. Then I asked, "How can two students divide two moon cakes fairly? How many pieces each?" Students also quickly answered the "average score", each 1. Then I struck the iron while it was hot and asked, "1 How can I share the moon cakes with two students?" How many pieces are divided? " Let the students feel that when the number of divided items is non-integer, it can be expressed by a new number-score, which leads to dividing a moon cake into two parts on average, and everyone gets half, which is half of the moon cake. This leads to the new lesson "score".
"Mathematics Curriculum Standards" points out that "effective mathematics learning activities cannot rely solely on imitation and memory, and hands-on practice, independent exploration and cooperative communication are the most important ways for students to learn mathematics." Therefore, in teaching, I pay attention to guiding students to experience the process of knowledge formation independently, and let students feel that a square is divided into two parts on average, one of which is half of a square; Divide a square into four parts, and take one part as a quarter of the square. Let students experience the formation process of scores, and make the original complex and abstract things simple and intuitive, which is convenient for students to understand and master.
Learning is active and perception is profound. When I guide students to talk about their life scores, the students' speeches are very positive, accurate and wonderful, and I can't help applauding them. When students are asked to express their scores on learning tools, they are full of interest. Some students even express 1/7,112, 1/24. ...
In order to let students further understand the concept and improve each student's thinking, I designed exercises to help students further understand the importance of "average score" in the process of forming scores, and how to use scores on the basis of average score to deepen students' understanding of the concept of "average score". The design of exercises takes into account all students and individual students with strong ability, so we arrange expansion exercises to promote their thinking development, and use mathematical methods such as rotation and reasoning to solve problems, so that students' learning activities can become a learning process of independent exploration and successful experience.
Of course, my teaching also has some shortcomings. For example, when I teach the names of various parts, I regard students as passive recipients, ignoring students' dominant position and their experience of "doing mathematics". The teaching time is too long, and the time allocation of each teaching link is not very reasonable. In the future teaching work, I will constantly sum up experience, improve the teaching level, and strive to become a new research-oriented teacher driven by the new curriculum reform.
The third part: the description of the teaching design textbook of "Preliminary Understanding of Fractions";
"Cognition Score" is the initial course of "Preliminary Cognition Score". It is an extension of the concept of number from integer to fraction on the basis that students have mastered some integer knowledge. Fractions and integers are quite different in meaning, reading and writing methods and calculation methods. Students will find it difficult to get good grades. Therefore, at the beginning of this class, we will arouse students' curiosity and desire to explore through the outing that students are interested in and the math problems they encounter when dividing food. Let students feel the meaning of fractions while living and contextualizing mathematics, so as to lay a good foundation for further study of fractions. In order to help students establish the meaning of scores. In teaching design, attention should be paid to showing the formation process of fractional meaning, intuitive operation and experience in various activities. Understand the score first, then summarize the meaning of the score, and then use the meaning to solve practical problems in life. The teaching methods and learning methods we choose are;
Activity teaching method: that is, taking intuitive experience activities as the main line, combining examples, creating mathematical situations and putting forward mathematical problems. Students experience learning in activities, establish correct representations, master mathematical methods and solve problems. Follow the teaching principles from life to mathematics and from concrete to abstract. Intuitive demonstration and hands-on operation: In the teaching of number and algebra, providing intuition is the starting point of cognition. In the design, we pay attention to intuitive demonstration and hands-on activities. Let students learn by using learning tools, intuitive operation and cooperative inquiry, and get real direct experience in real feelings.
Teaching content:
Page 92 ~ 93 of the first volume of the third grade of People's Education Press: Example 1, Example 2, Example 3 and related exercises.
Teaching objectives:
1, get a preliminary understanding of a score combined with specific conditions, which can be expressed by the results of actual operation, and learn to compare the sizes of such scores with intuitive methods.
2. Know the names of each part of the score and read and write a score of this simple score correctly.
3. Combine observation, calculation, comparison and other mathematical activities to guide students to learn to communicate the results of mathematical thinking with their peers and gain positive emotional experience.
4. Understand that mathematics comes from the actual needs of life, feel the connection between mathematics and life, and further cultivate curiosity and interest in mathematics.
Teaching focus:
1, know a little, read and write a little.
2. The molecular fraction of 1 can be compared.
Learning aid preparation:
Rectangular, square, circular
Teaching process: 1. Introduction to the conversation.
Do you like going for an outing, children? In fact, there are math problems in outings. Let's go and have a look.
1. Divide items (courseware shows: 4 apples, 2 bottles of water, 1 cake)
Teacher: Can you help them divide it? How to divide it so that everyone can get the same amount? Four apples, who comes first?
Raw 1: Divide four apples into two equal parts, each with two bottles of water. 2: Divide the two bottles into two equal parts, one bottle for each part.
Teacher: In mathematics, divide each share equally. What is this called? (blackboard writing: average score)
What are the benefits of an average score? (Fairness)
But there is only one cake. Can two people share it equally? Board: (divide a cake into two parts equally), how much does each person take?
Health: Half.
Teacher: If you are allowed to divide it, how?
Health: halved.
Teacher: Let's have a try, shall we? Health: Everyone gets the same amount.
Teacher: Come on! Point with your finger. Where is the half of the cake? Is it this half? Is it this half? It seems that a cake is divided into two parts on average, and each part is half of the cake, but what numbers should be used to represent this half?
Health: Half.
Teacher: Have you heard of it? Numbers like half are fractions. Let's get to know the scores together in this class. (blackboard writing topic)
Design intent
Curriculum standards emphasize: starting from students' existing knowledge and life experience, let students experience and abstract practical problems into mathematical models. In this link, students' existing experience in understanding "integers" was triggered by dividing apples, mineral water and cakes, and naturally experienced a leap from "integers" to "fractions", which led to the learning of "recognizing fractions". In the observation and comparison, students also initially perceived the difference between "integer and fraction", which paved the way for the meaning of learning fractions below.
Second, compare operations and explore new knowledge.
1, reading and writing scores
Divide the cake into two equal parts. (Demonstrate the writing of fraction, fractional line, denominator and numerator) What do "2" and "1" mean respectively?
Health: 2 means two copies, 1 means one copy.
Teacher: What did he say?
Student: Evaluate classmates.
Teacher: Can you write? Let's write one together. The teacher teaches writing and reading scores. This is 1/2 of this cake. What about the other one? Who does (also 1/2 of this cake) mean?
The teacher concluded: It seems that a cake is divided into two parts on average, and each part is half of the cake. Now, can you tell us how the 1/2 of this cake came from?
Communicate with each other at the same table and give feedback; The student said.
2. Take a rectangle, fold it first and color its 1/2.
This is half the cake. Teacher, here is a rectangular piece of paper. How to express it?
Please see the requirements: take a rectangular piece of paper, fold it in half first, and color half with diagonal lines.
Students' coloring works
Teacher: Obviously, the folding method is different. Why are all the colored parts of this rectangular piece of paper 1/2?
Health 1: It's all half.
Health 2: The rectangle is divided into two parts on average, and one part is colored.
Summary: It doesn't matter if the folding method is different, as long as it is half of this rectangle, each copy is its 1/2.
3. Judgment: The colored part in the figure below is 1/2, so put a "tick" in ().
Summary: As long as both cakes and graphics are divided into two parts on average, each part is its 1/2.
4. Fractional teaching
(1) How much do you want to know?
Health:
1/4,1/8,1/3,1/6 ...
(2) Take a piece of paper and fold it in half, and indicate its score with diagonal lines.
Report: How many parts do you divide this figure into and how many parts are colored?
Health 1: I divided it into 8 parts, and the colored part was its 1/8.
Health 2: Divide a rectangular piece of paper into four parts, draw one part, and each part is its 1/4.
Intra-group communication
Display works:
1/4 is represented by rectangles, squares and circles.
(3) Different shapes. Why is the painted part of it 1/4?
Health: Because they are divided into four parts on average, and one of them is colored.
(4) Display other scores
Design intent
Constructivism holds that students' construction is not the result of teachers' teaching, but through personal experience and interaction with learning environment. What is the meaning of the score? I'm not sure, but as long as I start "folding", "drawing" and "drawing", the students will know fairly well. In a large number of intuitive, practical and experiential activities, students can really feel what "the meaning of music score" is, and then sum up the meaning of music score, and organically combine "number and shape". By choosing different types of representative works to display on the blackboard (some ... whatever kind of figure, as long as it is divided into four parts on average, one of them is a quarter of this figure. Make students understand the meaning of fractions further.
5. Compare scores.
(1) Exhibition works: 1/2 and 1/4 represented by rectangles.
Compare their respective color parts, can you see which one has the higher score?
Health 1: 1/4
Health 2: 1/2
What part does 1/2 stand for? 1/4? What symbol is used in the middle? (Less than sign)
(2) Use the same circle to represent its ratios 1/8 to 1/2 and 1/4. Imagine? (small)
Verified by students' works.
(3) Can rectangles and squares of the same size show different scores? The teacher gave each group the same size of graphics. Who represents the big score? Who said the score was small? Intra-group comparison.
Third, application integration, expansion and extension.
1, can you use fractions to represent the colored parts in each picture below? (Practice in the book)
Report:1/31/61/91/8
2. Look at the picture and estimate (the title in the book)
Rectangular 1
1/3 estimates, courseware moves 1/3, and the validation rectangle is divided into three parts on average.
1/6 estimates that the courseware has been moved by 1/6, and the rectangle is divided into six parts on average.
How did it get done all at once? What's the trick?
Health 1: 1/3 is twice as high as the following.
Through observation and comparison, it is estimated that this is a good learning method.
Further down, how many points may appear?
Summary: When the average number of shares is increasing, the size of each share will become smaller and smaller.
3. How much does the picture below remind you of?
Photo: French flag (1/3)
Each part is 1/3 of this graph.
Chocolate (1/6), one for each person, how many people can you give?
How many times can you think of it?
Student: 1/2 teacher: everyone has one. How many people can you eat?
Student: 1/3 teacher: everyone has one. How many people can you eat?
Teacher: Different observation angles will lead to different scores for the same piece of chocolate.
4. Play: Dumex 1+ 1 milk powder advertisement.
Dongdong invited three children to eat cake. When he divided the cake into four parts,
At first glance, four more people came. Just after solving this problem, another person came. what should he do ？
How many points can you associate with watching advertisements?
Health: I can think of 1/4.
Teacher: Which picture did you think of 1/4?
Health: In the first picture, the cake is divided into four parts on average, one for each person.
Health: I can think of 1/8.
Teacher: Which painting do you associate with 1/8?
Health: In the third picture, a cake is divided into eight parts on average, one for each person.
Health: I can think of 1/2.
Is 1/2 here the 1/2 of the whole cake?
Student: No, it's the cake in the boy's hand 1/2.
Teacher: What did Dongdong gain in the process of dividing the cake?
Health: I have gained friendship.
Design intent
In the design of exercises, we should follow the principle of going from shallow to deep, further consolidate the understanding of the meaning of fractions in painting, writing and association, and carry out emotional education for students in combination with real life, so that students can experience that mathematics comes from mathematics and serves life.
Fourth, the whole class summarizes and talks about the gains.
What did you learn from this course?