The area of triangle 1 handout I. Teaching materials:
This topic is the teaching content of the first lesson of Unit 5 in the first volume of the fifth grade of People's Education Press. The area calculation of triangle is studied by students on the basis of mastering its characteristics, and it is one of the basic knowledge for further learning the circular area and the surface area of three-dimensional graphics. Therefore, it is an important basic skill and knowledge for students to experience and perceive the exploration process of triangle area calculation and master the formula of triangle area calculation. The arrangement of teaching materials is based on the areas of rectangles and parallelograms that students have learned.
Second, tell the teaching objectives:
1, knowledge and skills
(1) Make students experience the exploration process of the triangle area calculation formula and understand the triangle area calculation formula. Let the students experience the process of exploring and obtaining the triangle area formula, instead of letting the teacher directly explain the calculation method of the triangle area to the students, so that the students are in an acceptable state. This design conforms to the modern learning concept of new curriculum students.
(2) Through various learning activities, cultivate students' practical ability, abstract, generalization and reasoning ability, and cultivate students' cooperative consciousness and exploration spirit.
(3) Cultivate students' ability to apply what they have learned to solve practical problems in life.
2. Process and method
Let students experience mathematics learning activities such as operation, observation, discussion and induction. Through the arrangement, cutting and folding of graphics, the mathematical idea of graphic transformation is infiltrated, and the connection between mathematics and life is experienced in the process of exploring learning and solving practical problems.
3. Emotions, attitudes and values
Let students get positive and happy emotional experience in exploration activities, and further cultivate students' interest in learning mathematics.
Third, talk about the key points and difficulties in teaching:
The key point is to understand the derivation process of triangle area calculation and calculate according to the formula. The difficulty is to understand the relationship between the base, height and area of triangle and the base, height and area of assembled parallelogram.
Fourth, preach the law:
"Hands-on practice, independent inquiry and cooperative communication" is an important way for students to learn mathematics. Therefore, in the teaching of this course:
1, experimental method
Students learn new knowledge through their own hands-on operation, which is more memorable and interesting than listening to teachers explain new knowledge. Therefore, when teaching the derivation process of triangle area calculation formula, let students operate and discuss, which embodies the teaching principle of taking students as the main body and teachers as the leading factor.
2. Courseware demonstration is enlightening.
Students do experiments, exchange reports, and then watch the courseware demonstration, and the teacher gives guidance, so that students can understand the calculation method of triangle area more intuitively and vividly.
Five, the teaching process theory:
(A) the creation of life situations, revealing the topic
1, please recall and tell the process of deducing the area calculation of parallelogram in the last lesson. Starting from solving a rectangular piece of land in Gaomiao Park, the landscape master wants to divide it into two halves, how to ask questions and reveal the theme respectively. Topic on the blackboard: area of triangle (design intention: students are familiar with knowledge and continue to infiltrate the mathematical idea of transformation, that is, transforming parallelogram into rectangle to calculate area, paving the way for learning new knowledge. For students whose expression is unclear and incomplete, the teacher shows courseware to inspire them to express completely and give encouragement. )
(2) Explore new knowledge
Show me the question: how to turn triangles into the figures we have learned?
1, work in groups and swing by hand. (Note: students prepare two right-angle, obtuse-angle and acute-angle triangles, and the shapes of the two right-angle, obtuse-angle and acute-angle triangles are exactly the same. Design intention: Teachers provide an open space for students to experience the process of independent exploration. Create problem scenarios to make students realize that "triangles with exactly the same shape" is the premise of putting them together. Through students' hands-on spelling, students' subjectivity in learning can be brought into full play, which is also helpful to the establishment of concepts such as "putting two triangles with the same shape into a parallelogram". )
2. Group representatives report the experimental results, demonstrate the operation process of pendulum and explain the method of pendulum. In the "My Discovery" column, teachers should encourage students to speak boldly and speak their own findings in the operation, and teachers should give encouragement. (Design intention: Let students report the experimental results, and the teachers will give them praise and affirmation, so that students can experience the joy of learning success, set up "my discovery" open questions, and cultivate students' divergent thinking ability. )
3. The courseware demonstrates the process of putting triangles into parallelograms. (Design intention: Let the students spell first, and then play the courseware demonstration. This order must be well grasped. Let students do experiments freely first, which is conducive to students' free play in the operation process and does not constrain students' imagination and thinking ability. After reporting the experimental results, students can watch the courseware demonstration, which is more vivid, intuitive and vivid, and is conducive to the cultivation of students' thinking ability in images. )
4. Do and discuss problems in groups.
Question: Can two identical triangles be put together?
The area of each triangle is equal to? The base of this parallelogram is equal to? What is the order of this parallelogram? What is the area formula of triangle? Students discuss problems with the help of pictures in their hands. Group representatives report and discuss the learning results.
(Design intention: Let students discuss and discover the relationship between the base, height and area of triangle and the base, height and area of parallelogram, and help students deduce the triangle area formula. Cultivate students' awareness of cooperative learning. )
(3) Consolidation and expansion
1, courseware shows how to solve the area of red scarf.
Students calculate independently, and the teacher calls the students to perform on the blackboard.
The beating process of courseware demonstration specification. (Design intention: The design of basic questions consolidates students' mastery of basic knowledge. Learning of infiltration estimation)
2. Practice solving problems with the corresponding base height in the same triangle.
3. Take life as an example, conduct safety education on traffic warning signs and calculate the area.
(4) class summary
Students, the formula for calculating the triangle area has been deduced through personal experiments in this class. It's amazing! But please think it over. Do you have any questions about this course? (Design intention: In the study of a class, don't let students have the illusion that all the problems have been solved in this class. Teachers should pay attention to cultivating students' problem consciousness, and students will actively explore when they have questions. )
In this lesson, we learn the calculation of triangle area. What knowledge have you gained?
Lecture 2 on "the area of triangle" talks about the learning content.
The area of triangle is the content of Page 84-86 of Book 9 of Primary School Mathematics published by People's Education Press. This content is taught on the basis of knowing triangles, learning to calculate rectangular areas and just learning parallelogram areas in Book 8. At the same time, it is related to the area of parallelogram and trapezoid, which paves the way for studying the area calculation of circle and combination figure in the future. By means of swing, rotation and translation, two identical right-angle, acute-angle and obtuse-angle triangles are transformed into rectangles or parallelograms respectively, and it is concluded that the area of triangles is equal to half that of rectangles or parallelograms, and then the calculation formula of triangle area is summarized.
Say the learning goal:
1. Understand the derivation of triangle area formula.
2, the correct use of triangle area calculation formula for calculation.
3. Apply formulas to solve simple practical problems.
Key points of study: Understand the formula for calculating the area of triangle and calculate the area of triangle correctly.
Difficulties in learning: Understand the derivation process of triangle area formula.
According to the above teaching objectives, teaching emphases and difficulties, I intend to adopt the following teaching methods:
1, develop the migration principle. Use the law of migration to guide students to learn new knowledge on the basis of sorting out old knowledge.
2. Strengthen students' hands-on operation. On the basis of students' simple pendulum experiment, through courseware demonstration, two identical triangles are combined into parallelogram by rotation and translation, which deepens students' experience and understanding of the source of triangle area formula.
I focus on the following points in my learning methods:
1, learn to bring forth the old and bring forth the new, and use knowledge transfer and learning method transfer to master learning methods.
2. Operate the experimental method. Students use two identical triangles to spell out the learned figures and find out the relationship between the triangle area and the parallelogram area.
3. Learn the discussion method. On the basis of operational experiments, the relationship between the base height of triangle and the base height of parallelogram is discussed, and the calculation formula of triangle area is summarized.
In view of the needs of the above contents, I designed the following teaching procedures:
Speaking of learning process
First, exciting calibration.
(A) stimulate the introduction of interest
1. Show me the parallelogram.
The area formula of (1) parallelogram. (blackboard writing: parallelogram area = bottom × height)
(2) The parallelogram has a base of 2cm and a height of 1.5cm. Find its area.
2. Since parallelogram can be calculated by formula, how to calculate the area of triangle? (revealing topic: calculation of triangle area)
Teacher: Today, we are going to learn "the area of a triangle" (blackboard writing).
learning target
1, understand the derivation of triangle area formula.
2, the correct use of triangle area calculation formula for calculation.
3. Apply formulas to solve simple practical problems.
On self-study interaction (timely guidance)
(1) Derive the formula of triangle area.
1. Spell with two identical right triangles.
(1) Teachers participate in students' spelling and give individual guidance.
(2) Students demonstrate mosaic graphics.
(3) Discussion
① Can two identical right triangles form a big triangle to help us deduce the triangle area formula? Why?
② Observe the spliced rectangles and parallelograms. What is the relationship between the area of each right triangle and the area of the spliced parallelogram?
2. Spell with two identical acute triangles.
(1) Organize students to try spelling with school tools. (Name demonstration)
(2) Students demonstrate pendulum patterns (highlighting rotation and translation)
The teacher asked: What is the relationship between the area of each triangle and the area of parallelogram?
3. Spell with two identical obtuse triangles.
(1) Students do it independently.
(2) Students demonstrate mosaic graphics.
Step 4 ask clever questions
(1) What can two identical triangles be transformed into?
(2) What is the relationship between the area of each triangle and the area of parallelogram?
(3) What is the formula for calculating the triangle area?
5, guide students to clear:
① Two identical triangles can be combined into a parallelogram.
(2) The area of each triangle is equal to half the area of the parallelogram. (Write it on the blackboard at the same time)
The base of this parallelogram is equal to the base of the triangle. (Write it on the blackboard at the same time)
The height of this parallelogram is higher than that of the triangle. (Write it on the blackboard at the same time)
(3) How is the formula for calculating the triangle area derived? Why add "divide by 2"? (Strengthen the understanding of the derivation process)
Blackboard writing: triangle area = base × height ÷2
(4) If S is used to represent the triangle area, and A and H are used to represent the base and height of the triangle, what can be written as the formula for calculating the triangle area?
(c) Correctly use the triangle area calculation formula for calculation.
1, teaching example 2
Red scarf. Bottom 100cm, height 33cm. How many square centimeters is it?
(1) Students answer independently.
(2) Revise the answer (the teacher writes on the blackboard)
(4) Applying formulas to solve simple practical problems.
Solving simple practical problems by using triangle area calculation formula can improve students' understanding of triangle area calculation formula and solve simple practical problems in life.
Third, evaluate training.
Through evaluation training, we can evaluate whether students have mastered new knowledge and improve their computing ability and speed.
Four. abstract
The students are great. It is found that two identical triangles can be used to make parallelograms or rectangles. By means of swing, rotation and translation, two identical right-angle, acute-angle and obtuse-angle triangles are transformed into rectangles or parallelograms respectively, and it is concluded that the area of triangles is equal to half that of rectangles or parallelograms, and then the calculation formula of triangle area is summarized.
Fifth, blackboard design,
This blackboard design makes students clear at a glance, neat, simple and clear.
Lecture notes on the Area of Triangle 3 I. Teaching materials:
1, lecture content:
I said that the content of the class is the fifth unit of the first volume of fifth grade mathematics of People's Education Press.
2, the status and role of teaching materials:
The area calculation of a triangle is the area of a graph (1). In the exploration activities in the second class, the calculation method of the area of a rectangle, a square and a parallelogram is mastered by students. Through this part of teaching, students can understand and master the calculation method of triangle area and solve practical problems related to triangle area calculation in real life; At the same time, it will deepen students' understanding of the internal relations among triangles, rectangles and parallelograms, and lay a foundation for students to further explore and master the area calculation methods of other plane graphics.
At the same time, the area derivation process of triangle contains the mathematical thought of transformation and migration. The learning of this course focuses on letting students go through the learning process, infiltrating preliminary mathematical ideas and methods while acquiring knowledge, and cultivating the spirit of scientific inquiry, so as to further improve students' ability to solve some practical problems by using the knowledge and skills they have learned. The most important feature of the content arrangement of this lesson is to strengthen the hands-on operation, so that students can discover the internal relations of various figures in the hands-on practice and experience the general strategy of triangle area calculation. Let students experience the process of discovering, exploring and solving problems, and cultivate their reasoning ability. This arrangement enables students to understand the ins and outs of the triangle area formula and exercise their mathematical reasoning ability, thus feeling the inherent charm of mathematical methods.
3. Teaching objectives:
(1) Knowledge and ability goal: Let students explore and master the triangle area calculation formula through translation and rotation, and correctly use the area formula to calculate the triangle area, so as to deepen students' understanding of the internal relationship between triangle and parallelogram area formula.
(2) Process and Method Objective: To enable students to experience mathematical activities such as group cooperation, hands-on operation, exchange and discussion, analysis and induction, experience transformed mathematical ideas, and develop spatial concepts and preliminary reasoning ability.
(3) Emotional attitude and values goal: to cultivate students' sense of unity and cooperation and the spirit of courage to explore, so that students can experience the joy of success in the process of learning mathematics.
4. Teaching emphases and difficulties:
(1) key point: if you master the formula of triangle area, you can use the formula to solve the practical problems about triangle area calculation in your life.
(2) Difficulties: Understand the derivation process of the triangle area calculation formula, and instill the mathematical method of migration and the mathematical idea of transformation.
(3) Focus: Guide students to understand the meaning of dividing by 2 in the formula for calculating the triangle area.
5. Prepare teaching AIDS and learning tools:
Teachers prepare courseware, and students prepare two identical triangles with acute angle, right angle and obtuse angle in groups.
Second, talk about teaching methods and learning methods.
In this class, according to the characteristics of fifth-grade students' wide knowledge and strong learning consciousness, I use teaching methods such as trying teaching method, experiment method and practice method to teach. On the basis of old knowledge, let students try to solve problems by teaching materials by themselves, working independently with learning tools, discussing and consolidating exercises with each other, and then teachers explain and choose according to the difficulties in students' trying exercises and the key points of teaching materials, giving full play to students' main role and teachers' leading role, which is conducive to cultivating students' exploration spirit and operational ability. When teaching, I follow six steps: introducing new lessons, revealing topics, deducing formulas, practical application, consolidating exercises and summarizing before class.
Third, talk about the teaching process.
1, introduce old knowledge and stimulate thinking:
In this section, I first ask students to recall the area calculation formulas of rectangle, square and parallelogram. Show me another triangular red scarf and ask, can you calculate the area of a triangle? (Most students will say that the area of a triangle = base × height ÷2), then the teacher asked: Why can the area of a triangle be obtained from base × height ÷2? So today let's study how to calculate the "triangle area". (blackboard title: area of triangle)
2. Recall old knowledge and guide migration:
Recalling the derivation process of the parallelogram area formula, Q: Can we convert triangles into previously learned figures like the derivation of the parallelogram area formula? (This part of the design is to learn new knowledge on the basis of connecting with old knowledge, transfer the derivation method of parallelogram area to the derivation of triangle area calculation formula, and instill the mathematical method of migration and the mathematical idea of reduction into students to pave the way for the derivation of triangle area calculation formula. )
3, teamwork, hands-on operation:
(1) Use learning tools for hands-on operation in groups. Let's see what shape a triangle can be transformed into.
(2) Group report: The result of the student report may be a rectangle, a square, a parallelogram or a larger triangle. At this time, the teacher will guide: the area of a triangle is not calculated for the time being, and it is also a special case to spell it into a rectangle or a square, while two identical right triangles, acute triangles and obtuse triangles can all spell it into a parallelogram, thus leading the calculation formula of triangle area to a parallelogram. Put the numbers spelled out by the students on the blackboard one by one.
4. Student report summary: First, discuss in groups: What is the relationship between the base of parallelogram and the base of original triangle? What is the relationship between the height of parallelogram and the height of original triangle? What is the relationship between the area of a triangle and the area of a parallelogram? Then representatives from each group talked about the relationship between parallelogram and triangle: the base of the combined parallelogram is equal to the base of the original triangle, higher than the height of the original triangle, and the area of a triangle is half that of the combined parallelogram.
Teachers and students sum up the derivation process together and draw various conclusions. Conclusion 1: Two identical triangles can be spliced into a parallelogram. The base of this parallelogram is the base of the original triangle, and the height is the height of the original triangle. Because the area of each triangle is equal to half of the area of the spliced parallelogram, the area of the triangle is equal to the base × height ÷2. Conclusion 2: Cut in the middle of the height and rotate the upper part into a parallelogram. The base of a parallelogram is the base of a triangle, its height is half that of a triangle, and the area of a parallelogram is the area of a triangle. Area of triangle = area of parallelogram = base of triangle × height, so the area of triangle is s = ah ÷ 2.
The teaching of examples is the focus of this lesson. For the examples in the book, I focus on letting students learn through group inquiry, and present the knowledge they should master one by one in communication. This knowledge is the key to this lesson. It is estimated that when students are operating, there may be spellings of parallelogram with only one triangle, examples and "Do you know?" We can strengthen the reason of "2" from many angles, and I think it is necessary to spend some time. Moreover, this practice is also based on students' learning practice and understanding of traditional mathematical culture.
5, simple application, highlight the key points:
(1) Verification conclusion: Calculate the area of the triangular red scarf in the first link through the formula.
(2) Consolidation exercise: Mathematics comes from life and is applied to life.
After learning the calculation formula of triangle area, I designed a set of exercises.
(1) oral calculation (proficient in triangle area calculation formula).
(2) Judgment (understanding meaning and breaking through difficulties).
(3) Select (understand the relationship between the area of triangle and the area of parallelogram).
(4) Application (solving practical problems in life).
The design of the exercise is mainly divided into the following links:
The first exercise is mainly to let students correctly apply the triangle area formula to calculate the area of each triangle. In the process of application, standardize students' writing and cultivate good homework habits.
The second link focuses on the difference between "∫2" and "×2". The main reason is that from the practice of students in the past, this is the wrong mainstream and students must pay attention to it.
The third link is expanding practice, and the data has more possibilities, mainly to stimulate students' desire to explore. Through this open exercise, students can once again understand the relationship between triangles and the corresponding parallelogram areas.
6. Class summary: What did you gain from this class? Let the students talk about their achievements in knowledge and group cooperation in this class, and the teacher will give them an encouraging evaluation.
Fourth, say the blackboard design:
Area of triangle
Area of triangle = area of parallelogram ÷2
Area of triangle = base × height ÷2
S=ah÷2
Example 1S=ah÷2
= 100×33÷2
= 1650 (square centimeter)
The area of triangle lecture note 4 What I am talking about today is the area of triangle, which is the teaching content of the second lesson of Unit 6 in the first volume of the fifth grade of People's Education Press, and belongs to the field of space and graphics.
First of all, the textbook: the content of this course is based on students' mastery of the relevant characteristics of triangles and the derivation of the area formulas of rectangles and parallelograms (learning premise). Mastering the calculation of triangle area is one of the basic knowledge (functions) for further learning circular area and surface area of three-dimensional graphics. Therefore, it is an important basic skill and knowledge (meaning) for students to experience and perceive the exploration process of triangle area calculation and master the formula of triangle area calculation. Therefore, it is of great significance to learn this lesson well.
Second, talk about learning.
Learning this lesson has a good knowledge reserve, a certain deduction experience and practical ability, and the fifth-grade students' strong curiosity and positive psychological characteristics are conducive to learning this lesson.
Third, talk about teaching objectives (including teaching methods with emphasis and difficulty)
Based on the above understanding of the teaching materials and the new curriculum concept, I have formulated the following teaching objectives.
1, knowledge and skills
Let students go through the process of exploring the formula of triangle area and master the calculation method of triangle area, which can solve the corresponding practical problems.
(Note: The "process" emphasized here is to let students experience the process of exploring and obtaining the triangle area formula, rather than requiring teachers to directly present it for students to passively accept. This design conforms to the modern learning concept under the curriculum standard. )
2. Process and method
By piecing together, observing, discussing and summarizing triangles, we can infiltrate and transform ideas, develop the concept of space and cultivate students' ability to analyze, summarize and solve problems.
3. Emotional attitudes and values
Let students get positive and happy emotional experience in exploration activities and cultivate students' interest in learning mathematics.
4, said the teaching emphasis and difficulty.
Focus: Explore and master the formula for calculating the triangle area.
Difficulties: Understand the derivation process of triangle area and experience the transformation idea.
5. Oral teaching methods and learning methods
Curriculum Standard points out that effective mathematics activities cannot rely solely on imitation and memory. The more effective way for primary school students to acquire geometry knowledge and form spatial concepts is hands-on operation, so I adopt the teaching method of "creating situations, independent inquiry and cooperative learning" to highlight the key points of this class. In the way of learning, I design "exactly the same triangle to spell out which graphics I have learned" as the starting point, organize students' practical activities such as operation → observation → discussion, integrate dynamic demonstration, help students understand the derivation process, infiltrate the transformation ideas, and break through the difficulties of this lesson.
Fourth, talk about the teaching process
On the basis of analyzing teaching materials and choosing teaching methods and learning methods reasonably, my preset teaching procedures are as follows.
(A) the creation of situations, the introduction of new courses
Situation 1: Ask the students to recall and tell the process that the students explained and deduced the area calculation of parallelogram in the last class.
Situation 2: What is the area of the red scarf that students are familiar with?
Design intention: Ask students to describe the derivation process of parallelogram area formula, continue to infiltrate the mathematical thought of transformation, and prepare for exploring the area of triangle. Understanding mathematics and life from the red scarf)
(2) Hands-on operation
Derived formula
This link first raises the question: how to transform triangles into the figures we have learned?
Then design a four-level query process of activity completion formula.
The first level: put them together and talk about methods.
In this link, I preset the results of students' independent inquiry. There are basically three methods (unit area measurement method, patchwork method, excavation and filling method) ***7 possibilities. Measurement method is suitable for estimation, and the derivation process of patchwork method is more intuitive and easier to understand than excavation and filling method. Therefore, three operations focusing on spelling are excavated in class, namely, a pair of acute triangles, a pair of right triangles and a pair of obtuse triangles are spliced into a parallelogram or rectangle, and the filling and excavation method is mainly based on self-study.
(Design intention: Let the students start to piece together and explore independently, so as to provide students with free space and not bind their imagination. Let students realize that "triangles with identical shapes" are the premise of pendulum, and establish the concept of "putting two triangles with identical shapes into a parallelogram".
The second level: communicate the results and demonstrate the process.
(Design intention: Let students report their grades, and the teacher will give them affirmation, so that students can experience the joy of learning success. After the report, organize students to watch the demonstration to show the process of graphic arrangement more vividly and intuitively, which is conducive to the cultivation of students' thinking ability in images. )
The third level: group discussion, observation and comparison
The teacher shows a set of triangles and corresponding parallelograms, and makes the students think: What did you find through observation? The group reported on the discussion.
(Design intention: Let students discuss and communicate in groups to find out the relationship between the base, height and area of triangle and the base, height and area of parallelogram, so as to help students deduce the triangle area formula. Cultivate students' awareness of cooperative learning)
The fourth level: summary
Derive the formula, so that students can accurately describe the area formula of triangle and express it with letter specification.
General idea: In the second part, I designed four levels of learning activities, step by step, interlocking, following the basic laws of learning, so that students can fully experience the derivation process and feel a meaningful inquiry learning.
Consolidate understanding
practical application
Combine 3 in the textbook
Classroom questioning is practiced at different levels to achieve students' learning goals of understanding and consolidation. Guide students to standardize their writing habits by demonstrating the process of writing on the blackboard.
Classroom summary
Rebate target
Let's talk about what students have gained by studying this lesson and improve their understanding of mathematics. Let students know mathematics thoughts and the significance of learning mathematics from learning activities: first, triangle → parallelogram realizes important transformation of thoughts; Secondly, from the size of the red scarf to the triangle area formula to the calculation of the red scarf area, help students understand the learning view that mathematics comes from life and is used for life.
Reflection on the Teaching of verb (abbreviation of verb)
Reflect on the completion of goals, the transformation of teaching methods and the application of information technology, so as to better carry out classroom teaching.
The above is the content of my lecture. Please correct me if there are any shortcomings. Thank you.