Understanding parallelogram lecture notes 1 1. Teaching materials
Understanding parallelogram is the second volume of the fourth grade mathematics textbook published by Jiangsu Education Publishing House. Before this, students have intuitively understood parallelogram, preliminarily mastered the characteristics of rectangle, square and triangle, and understood parallelism and intersection, which has paved the way for the transition to this lesson. At the same time, this part lays the foundation for understanding trapezoid and exploring the area formula of parallelogram in the future.
Specifically, this lesson includes two examples, 1 give it a try, six questions to think about and do, and "Do you know?" .
Example 1 present three pictures of life scenes. Let students find and tell where there is a parallelogram according to their existing life experience and knowledge, so that students can fully perceive the parallelogram. Then the textbook requires students to make a parallelogram and communicate with each other, so that students can explore the basic characteristics of the parallelogram in these specific operations and communication, such as swinging with a small stick, surrounding a nail board, drawing on square paper or drawing along the edge of a ruler. On this basis, the textbook abstracts the figure of parallelogram, guides students to discover and summarize the characteristics of each side of parallelogram independently through observation, measurement and other activities, and develops students' spatial concept.
Example 2 By asking students to measure the distance between two opposite sides of a parallelogram, students are guided to know the base and height of the parallelogram and reveal the meaning of the base and height.
The following "Try it" asks students to measure the base and height of each parallelogram to understand the interdependence between the base and height.
In addition, "Want to Do" arranges practical exercises, so that students can consolidate their understanding of parallelogram through observation, operation, comparison and communication.
Finally, "Do you know" introduces the deformable characteristics of parallelogram and its application, which helps students feel the application value of parallelogram and cultivate their awareness of mathematical application.
Teaching objectives:
1. Knowledge goal: Explore the basic features of parallelogram with real life, know the base and height of parallelogram, and draw or measure its height correctly.
2. Ability goal: to develop students' spatial concept and mathematical thinking ability in activities such as observation, operation, analysis, generalization and judgment.
3. Emotional goal: to feel the close connection between mathematics and life, accumulate experience in understanding graphics, cultivate mathematics application consciousness and develop students' interest in learning geometry knowledge.
Teaching emphases and difficulties:
According to the important position of teaching content in the whole textbook and the difficulty of students' learning, I will focus on understanding the basic characteristics of parallelogram, correctly judging parallelogram and understanding the bottom and height of parallelogram. It is difficult to measure or draw the height of parallelogram correctly.
Second, teaching methods.
The ancients emphasized: "A good seducer is a good guide." According to the characteristics of the teaching content and students' thinking activities, I adopt teaching methods such as dialogue, explanation, experiment and practice.
Instruct students and choose teaching methods reasonably. Students should not only learn, but also learn. Therefore, students' learning methods mainly include listening carefully, hands-on operation, independent inquiry and cooperative communication.
Third, teaching preparation.
Prepare sticks, nail boards, square paper, rulers, triangular rulers, puzzles, straws, etc. Group and multimedia courseware.
Fourth, talk about the teaching process
Based on the understanding of the new curriculum standards and the teaching materials of this course, I designed the following teaching process:
(A) contact life, the introduction of new courses
Bloom, an American psychologist, said: "The greatest motivation for learning is the interest in learning materials." So at the beginning of the class, we first show three life scenes in the textbook with multimedia and say, "Students, please enjoy some pictures first. What do you see in the picture? " Can you find the parallelogram? "Guide the students to find out the parallelogram in each picture, and then let them tell where they can see the parallelogram in their lives. On the basis of students' full perception of parallelograms, they said, "Students know a lot about parallelograms, and today we will continue to learn about parallelograms. (blackboard writing: knowing parallelogram) "
(B) independent exploration, learning new knowledge
Curriculum standards point out that students should not only master the results of mathematics, but also understand the formation process of mathematical results and mathematical thinking methods. So I will divide this link into three levels for teaching.
The first level: hands-on operation, perceptual characteristics. Let the students make a parallelogram with the materials in their hands, and then discuss in groups. In student activities, teachers should participate in activities and give necessary guidance. Finally, according to the students' report, the teacher showed four methods through multimedia: throwing sticks, nailing boards, drawing on square paper and drawing along the ruler. Using multimedia technology, the wooden stick, nail board, square paper and ruler are hidden one by one, and the parallelogram figure is abstracted, which runs through the process from concrete to abstract.
The second level: conjecture verification, summarizing characteristics. The teacher performed a standard parallelogram figure on the basis of the parallelogram figure just abstracted, and asked, "Can you think about the characteristics of each side of the parallelogram in combination with the previous operation process?" Students may have two sets of conjectures: the opposite sides are equal and the opposite sides are parallel. Then the teacher encouraged the students to verify their guesses through measurement and comparison, and summed up the basic characteristics of parallelogram: two groups of opposite sides are parallel and equal respectively. After that, the first question of "think and do" is displayed, so that students can use this basic feature to judge the parallelogram, and explain why the second quadrilateral is not a parallelogram, reveal the extension of the parallelogram through counterexamples, and further understand the essential attributes of the parallelogram; Three or four figures change the position of parallelogram, and reveal the essential attributes of parallelogram through variant figures.
The third level: on the basis of a preliminary understanding of the characteristics of the parallelogram, know the base and height of the parallelogram. First, show a parallelogram through the courseware. Q: What is the distance between the upper and lower sides of this parallelogram? Can you measure energy? Let the students demonstrate how to measure the distance between a set of opposite sides of a parallelogram and draw the corresponding line segments. The teacher's lens tells the students that the vertical line segment from a point on one side of the parallelogram to its opposite side is the height of the parallelogram, and this opposite side is the bottom of the parallelogram. (The teacher writes on the blackboard and marks the bottom and height.) Then he teaches "Try it" and instructs the students to point to the line segment to be measured in the picture, and then measure the bottom and height of the three parallelograms respectively. Later, he asked one of the parallelograms, "If you take the other side as the bottom, will you still measure its height?" How many different values do you think the height of parallelogram has at most? "Let students consolidate their understanding of the bottom and top and realize their interdependence. Finally, show the fifth question of "think and do" and ask the students to draw the height on the bottom of each parallelogram. Teachers should properly guide the drawing method according to the actual situation, reminding students to draw the height as a dotted line and mark it at right angles.
(3) Consolidate practice and improve application.
The new curriculum standard emphasizes that the formation of basic skills needs some training. So I help students to consolidate their knowledge and improve in time through "thinking and doing".
Question 2 asks students to explore how to spell out a parallelogram with two and four identical triangular rulers. After the group cooperation is completed, the whole class reports different spellings to further internalize the characteristics of parallelogram.
The third problem is the hands-on problem. Ask the students to cooperate with their deskmates first, and then report the methods. Finally, the teacher's courseware demonstrates the spelling method, in order to let students feel that parallelogram can be transformed into rectangle.
Question 4 asks students to cut a parallelogram paper into two parts and make it into a rectangle. After the students think independently, the group communicates how they cut and spell. Let the students know that a rectangle can be made by cutting a parallelogram along a height and then translating one of the figures in the right direction. In order to explore the area formula of parallelogram independently in the future.
Question 6 can be completed by the student group, and then the group can send representatives to report the results. Finally, summarize the similarities and differences between rectangle and parallelogram, and guide students to find out what has changed and what has not (the angle has changed, the edge has not changed, so the perimeter has not changed) in the process of drawing the rectangle made of beverage tubes into parallelogram. Then it is concluded that parallelogram has the characteristics of easy deformation.
On this basis, ask students to read "Do you know?" Perceive the deformable characteristics of parallelogram through examples in life. It is helpful for students to feel the application value of parallelogram and cultivate their sense of mathematics application.
(4) class summary
At the end of the course, ask the students, "What did we learn today? What's new? " Guide them to summarize the main contents of this lesson and cultivate their ability of generalization and evaluation.
(5) Blackboard design
Good blackboard writing is a lever to pry open students' wisdom. This lesson adopts the outline blackboard design, which has the function of outlining and highlighting the key points.
Understanding parallelogram lecture notes 2 I. Talking about teaching materials
1, teaching material analysis
This part of the content is based on students' intuitive understanding of parallelogram, preliminary understanding of the characteristics of rectangle and square, and understanding of verticality and parallelism. Learning this part well is conducive to improving students' practical ability, enhancing their innovative consciousness and further developing their interest in "space and graphics". So this lesson plays a vital role in primary school mathematics.
2. Teaching objectives
"Mathematics Curriculum Standard" emphasizes: let students experience the process of abstracting objects into mathematical models and explaining and applying them, so that they can truly master mathematical knowledge and skills, understand mathematical ideas and methods, and gain rich experience in mathematical activities. Therefore, I have determined the teaching objectives of this class as follows:
(1) Make students master the meaning and characteristics of parallelogram and draw the height corresponding to the bottom correctly.
(3) Through observation and hands-on operation, cultivate students' abstract generalization ability and preliminary spatial concept.
3. Emphasis and difficulty in teaching
According to the students' existing life experience and knowledge base, I have determined that the teaching focus of this course is to understand and master the definition of parallelogram and the names of its parts.
It is a teaching difficulty to draw the corresponding height of the bottom correctly.
Second, talk about learning.
This lesson is based on students' understanding of parallelogram and the relationship between vertical and parallel, as well as their preliminary understanding of parallelogram. However, students' thinking level is in the transition period from image thinking to abstract thinking, and they have a strong thirst for knowledge and curiosity, which is the internal motivation of students' learning. Therefore, in this course, students are often used to intuitively perceive the source of knowledge and deeply understand the characteristics of parallelogram and trapezoid.
Second, oral teaching methods and learning guidance.
The design concept of this lesson is:
1, classroom teaching is the process of emotional growth first, and then the process of knowledge growth.
2. Students' learning process is a process of active construction and dynamic generation. Teachers should activate students' original experience, stimulate students' enthusiasm for learning, and let students truly understand new knowledge through experience, experience and application.
3. Mathematics learning should be a process in which students enjoy the service of teachers.
Based on the above ideas, in teaching, I follow the teaching reform idea of "guiding inquiry learning and promoting active development" and adopt the following teaching methods:
(1) Guide students to carry out inquiry learning activities by means of "observation and operation".
(2) Organize students to carry out conscious group cooperation, exchange and study.
(3) timely use of multimedia teaching, give full play to the advantages of modern teaching methods.
Learning methods: Students experience the occurrence, development and formation of knowledge through practical operation, hands-on experiments, independent exploration and cooperative exploration, and then experience the characteristics of graphics in communication, making their learning activities a vivid, lively and personalized process.
Third, talk about the teaching process
(1) Review old knowledge.
1. What are parallel lines?
2. Draw a set of parallel lines.
[Design intention: The task of teaching is to solve the contradiction between students' existing knowledge level and educational requirements. We must attach importance to students' existing life experience and knowledge base to pave the way for expanding new knowledge. ]
(B) create a situation, a preliminary perception.
1, the courseware shows the theme map. Tell me what you have learned from the map.
Please observe carefully again. Where is the quadrangle in the picture used? (Group discussion and exchange)
[Design Intention: Create a realistic situation that students are familiar with and interested in, stimulate students' interest, and let students devote themselves to inquiry with full enthusiasm. ]
(3) Understand the characteristics and clarify the relationship.
The new curriculum requires students to know parallelogram and trapezoid through observation and operation. According to this requirement, I arranged seven levels of inquiry activities in an orderly way.
1, draw a quadrilateral.
Students, just now we observed that there are many quadrangles in the picture. You may have observed more than that in your life. Ask the students to draw the quadrangle you have just observed or the quadrangle you have observed elsewhere on your drawing paper, ok?
[Design intention: arouse students' existing knowledge of quadrangles through the process of watching, thinking and drawing. ]
2. Exhibition of works.
(paste the representative works on the blackboard)
[Design intention: to stimulate students' desire to express themselves, enjoy the joy of success, and stimulate students' desire to explore new knowledge. ]
3. Classification of works.
For the convenience of narration, the works are numbered. )
(1) Observe these numbers. What are their similarities?
(2) What figures do you know? Say their names.
(3) Please work in groups to classify these quadrangles and tell me why. (Teachers patrol and guide)
(4) According to the classification of students, teachers guide students to know parallelogram.
(And random blackboard writing: parallelogram)
4. Observe the chart.
(1) Think about it: What are the characteristics of the sides and corners of a parallelogram (students talk and discuss with each other)
(2) communication summary
Parallelogram: two groups of opposite sides are parallel and equal, and the diagonal lines are equal.
Design Intention: Under the guidance of teachers, students use their existing life experience to observe, think, explore and question, and cultivate and improve their analytical and comprehensive abilities. ]
5. Verify the conclusion.
(1) Please open the book on page 64, find the parallelogram, and guide the students to verify the conclusion just observed with a ruler, triangle and protractor.
(2) Check your own parallelogram.
(4) Reveal the concept. The students' guess was proved to be correct.
[Design intention: To provide students with sufficient opportunities to engage in mathematical activities, explore new knowledge in hands-on practice, exchange and discussion, master the characteristics of graphics, reorganize teaching materials mechanically, and guide students to master the meaning and characteristics of parallelogram. ]
(5) Practice (done on page 64). Show courseware: Which of the following figures is a parallelogram? )
Design Intention: Timely feedback not only helps students to consolidate new knowledge, internalize new knowledge and experience the joy of success in practice, but also helps teachers to understand the learning situation and regulate the teaching progress, thus ensuring the teaching quality and improving the classroom teaching efficiency. ]
6. Application in life.
(1) Tell me what objects around us have parallelograms.
(2) Courseware shows parallelogram which is common in life.
[Design Intention: Mathematics originates from life, and the parallelogram is understood by contacting the physical objects around us, so that students can feel that mathematics is around them and there is mathematics everywhere in life. Mathematics always serves life, arousing their enthusiasm for life and strong desire to explore, and cultivating good observation habits. ]
7. The base and height of a planar quadrilateral.
(1) demonstrate with ppt: draw a vertical line from one point on one side of the parallelogram to the opposite side. The line segment between this point and the vertical foot is called the height of the parallelogram, and the side where the vertical foot is located is called the bottom of the parallelogram.
(2) Continue the ppt presentation and find out the corresponding bottom and height.
(3) Do: Draw the height of each quadrilateral, and the teacher will patrol and guide.
(4) Let the students discuss: How high can a flat quadrilateral be?
[Design intention: Through watching, watching, doing and discussing, let students see the height of a parallelogram more intuitively, and master that a vertex of a parallelogram can be made into two heights with different lengths, and a parallelogram has countless heights, which easily breaks through the difficulties in this lesson]
(4) Guide reading and consolidate practice.
1, free reading, encourage students to question and ask difficult questions.
Design intention: After hands-on practice, cooperative communication and feedback practice, students have basically achieved the teaching objectives of this lesson. Then, through reading and discussion, students are guided to sort out and summarize the fragmentary, incomplete and vague information they have learned before, so that students can clearly and correctly understand and master new knowledge. ]
2. do: put a parallelogram with a small stick.
Design intention: Through group practice, it not only cultivates students' hands-on operation ability, but also improves the level of cooperative inquiry among students and deepens their understanding of parallelogram characteristics, which can be described as "killing two birds with one stone". ]
(5) Summing up reflection and evaluating experience.
1. class summary: talk about your own gains and feelings.
2. Collective evaluation: Students evaluate their own and each other's performance in this class.
3. Teacher evaluation. Students' classroom learning, representative behavior, etc.
[Design intention: Through summary and evaluation, help students sort out the context of knowledge, reflect on their own learning process, understand learning methods, and gain mathematics learning experience. ]
(6) Arrange homework and expand application.
1, handy
(1) Can you cut a parallelogram into two completely equal figures?
[Design intention: expand basic knowledge, improve application requirements, give students room for thinking development, encourage students to innovate, and achieve the purpose of cultivating ability and developing personality. ]
Step 2 stand out
Understanding the draft of parallelogram handout 3- a textbook
1, teaching content analysis
The area of parallelogram is students' understanding of quadrilateral, triangle and trapezoid after mastering the characteristics of parallelogram and calculating the area of rectangle and square. Teaching on the basis of knowing the base and height of parallelogram, mastering the formula on the basis of understanding, and applying the transfer assimilation theory to bring the new knowledge of parallelogram area calculation formula into the existing cognitive structure will help students learn the derivation method and prepare for the derivation of triangle and trapezoid area formulas.
2. Teaching emphases and difficulties:
Teaching emphasis: understand and master the calculation formula of parallelogram area and calculate the area of parallelogram correctly.
Teaching difficulties: understanding the derivation method and process of parallelogram area formula.
Bidirectional teaching method
The whole teaching consists of review and introduction, inquiry experience and practical application. In the introductory stage, students feel that there is an internal connection between rectangle and parallelogram, and review the characteristics of rectangle and parallelogram and the calculation formula of rectangle area. Lay a foundation for learning new knowledge in the future.
In the exploration and experience stage, it is divided into three levels. The first level is counting squares. It is too much trouble for students to experience the method of counting squares alone, so we must find a simpler method to calculate the area of parallelogram. By "Why are different graphics equal in area?" Find out the relationship between parallelogram and rectangle, and then boldly guess what the area of parallelogram may be equal to? The second level, explore the calculation formula of parallelogram area. In this process, I first assigned two tasks:
1. How to transform a parallelogram into a learned figure?
2. What is the relationship between the parallelogram and the converted graph? Fill in the experimental report, so that students can have a clearer purpose in the process of operation. Then in the process of students' operation, the teacher pays attention to the operation and methods of patrolling students, gives guidance and lists typical methods. I have considered several situations in advance. Then, in the process of students' reporting, teachers pay more attention to the accuracy of students' language and emphasize "translation". Finally, there is a teacher's question: "What has changed and what has not changed in the process of transformation". Students combined with the report form to draw the following conclusions: the area has not changed, the shape has changed, the base of the parallelogram is equal to the length of the rectangle, and the height of the parallelogram is higher than the width of the rectangle, thus successfully concluding that the area of the rectangle is equal to the length * width, so the area of the parallelogram is equal to the bottom * height. In this way, the students summed up the calculation formula of parallelogram area by cutting, moving, spelling, observing, comparing and summarizing. Let the students really move and experience the derivation process of the formula. The third level is the letter expression of self-study formula to cultivate students' autonomous learning ability.
In the practical application stage, it is divided into basic contact and expansion exercises. In the basic exercise, first complete the example 1 and use the formula to directly calculate the area. Then pay attention to let the students measure by hand, let the students actively find the necessary conditions for calculating the area, and find the area according to these conditions. Finally, change the posture of the parallelogram, so that students can accurately find the bottom and height, and calculate the area to complete 1 and 2 questions. Through this part of exercises, students' understanding and application of area formula will be further consolidated.
In the outward bound training, first of all, we arranged judgment questions and multiple-choice questions. Through discrimination and selection, students can further understand that the area of parallelogram is related to two factors: base and height. Calculating the area in units of area requires a set of corresponding foundations and higher-level knowledge. Then an open topic appeared: "The area of parallelogram is 24 square centimeters. What is its base and height? " ? (base and height are integers). What if there is no limit to decimals? It not only enlivens students' thinking, but also pushes this class to a climax. Finally, a rectangular box for thinking appeared, with length 15 cm and height 10 cm. What are the perimeter and area respectively? What about the perimeter and area of parallelogram? Through this part of practice, students can deepen their understanding and application of parallelogram area formula, and achieve the purpose of mastering and using it flexibly.
Understanding parallelogram lecture notes 4 I. Talking about teaching materials
Lecture content: Jiangsu education publishing house, fourth grade, second volume, 43~45 pages.
Second, the position, function and significance of teaching content.
Understanding parallelogram This course is based on students' intuitive understanding of parallelogram, their preliminary understanding of the characteristics of rectangle, square and triangle, and their understanding of parallelism and intersection. Through a series of exploration and practice activities, they constantly know the characteristics of parallelogram, parallel equilateral, the base and height of parallelogram. This part is the basis of studying parallelogram area in the future, which is conducive to improving students' practical ability, enhancing their sense of innovation and further developing their interest in "space and graphics".
Third, say the goal.
1, knowledge and skills target
(1) Understand the concept and characteristics of parallelogram.
(2) Knowing the base and height of the parallelogram, we can draw the height.
(3) Cultivate students' practical ability, observation ability and analysis ability.
2, process and method objectives
Let students explore new knowledge through hands-on operation, eye movement observation, verbal expression and brain thinking.
3. Emotional attitudes and values goals
Let students feel the close connection between graphics and life, and feel the joy of successful exploration.
Fourth, talk about the difficulties in teaching.
Key point: Understand the characteristics of parallelogram. Know the base and height of the parallelogram.
Difficulties: Make the height of parallelogram, and understand the corresponding relationship between base and height.
5. Teaching and learning methods.
(A) teaching methods:
According to the characteristics of the textbook of this course, in order to highlight the key points and break through the difficulties more effectively, according to the students' cognitive rules, and following the guiding ideology of "teacher-oriented, student-oriented and training-oriented", the observation and discovery method is adopted as the main method, supplemented by the multimedia demonstration method. In teaching, design inspiring thinking questions, create problem situations and guide students to think. The timely use of audio-visual media in teaching can stimulate students' desire to explore knowledge and gradually draw conclusions, so that students are always in a positive state of actively exploring problems, thus cultivating students' thinking ability.
(2) Speaking and learning methods
1, according to the principle of autonomy and difference, let students participate in the occurrence, development and formation of knowledge independently in the learning process of "observation → guess → generalization → verification → communication → application", so that students can master knowledge.
2. Students can solve more than one problem, guide students to sum up methods in time and overcome the mindset. The example explanation adopts the method of decomposing graphics, so that students can experience and learn the "transformed" mathematical thought.
3. Use the graphics in real life to make the process of acquiring new knowledge natural, enhance students' sense of accomplishment and self-confidence, and thus cultivate a strong interest in learning.
Six, said the preparation of teaching AIDS and learning tools
Teaching AIDS: teaching courseware, triangle, parallelogram paper, rectangular movable frame, nail board,
Learning tools: prepare sticks, rulers, triangles, watercolor pens, square paper, colored paper, scissors, protractor, parallelogram paper, etc. In droves
Seven, talk about the teaching process.
First, guess the map game to stimulate the introduction of interest.
Talk: Students, do you like playing games? Let's play a guessing game.
(Design intention: Through the guessing game, let students initially perceive the characteristics of parallelogram and the difference between rectangle and square, so as to pave the way for subsequent study. )
Second, contact with life, preliminary perception
Where is the parallelogram on the wall chart?
(Design Intention: "Mathematics Curriculum Standard" points out: "Students' mathematics learning content should be realistic, meaningful and challenging. "Choose materials that students are familiar with and interested in, attract students' attention, stimulate students' enthusiasm for actively participating in learning activities, and let students initially perceive parallelograms. )
Third, students' independent inquiry
1, make a parallelogram with the materials in your hand.
Draw on the nail board, on the square paper, and draw along the edge of the ruler with a wave of a stick.
(Design intention: The design of this link is student-centered, dare to let go, let students' various senses participate in the activity, and let students experience some characteristics of parallelogram in operation. )
2. Study the characteristics of parallelogram with the help of hand data.
Observe the parallelogram in groups and study the relationship between its position and length.
Judging whether a quadrilateral is a parallelogram according to its features. Show the question "Want to do" 1 Let the students judge. Question: Why is the second figure not a parallelogram?
(Design intention: The design of this link provides students with sufficient space for independent exploration, guides students to use the materials in their hands to choose interesting ones for discovery and communication, and enables students to draw conclusions in the collision and communication of thinking. )
3. Teaching the height and bottom of parallelogram.
Teachers and students work together to break through the difficulties.
Let the students follow the teacher with parallelogram paper in their hands. The teacher talks about folding while doing it. Then the crease is the height of the parallelogram. Explain that the edge perpendicular to the height is the bottom. Please draw the height with a pen and triangle and mark it. Fold several heights in the same way and observe the characteristics of heights. Then teachers and students write down the definition and characteristics of high and low on the summary board.
(Design intention: In this link, it not only reflects the guidance for teachers and students to learn, but also cultivates the ability to use their hands and brains. The difficulty has been well broken through. )
Fourth, consolidate practice.
(A) to consolidate the basic simple application
(B) Examples illustrate the use of knowledge
(C) comprehensive training to improve their ability
(4) Summarize and reflect, and improve.
Verb (abbreviation for verb) Read "Do you know"
This paper introduces the deformable characteristics of parallelogram and its application in real life, which helps students feel the application value of parallelogram.
Sixth, the class summary (design intent: let students develop the habit of summarizing, sorting out and summarizing what they have learned from an early age)
Seven, expand and extend
Let the students compare and analyze the rectangles, squares and parallelograms they have learned, and find out the similarities and differences.
Design intention: let students understand the relationship between old and new knowledge and the endless truth of learning. )