Mathematics, compulsory education curriculum standard experimental textbook (People's Education Edition), the first volume of grade five, 88~9 1 page.

Learning Situation and teaching material analysis

"Trapezoidal area" is taught on the basis of students' understanding of trapezoidal characteristics, mastering the calculation of parallelogram and triangle areas and forming a certain spatial concept. Therefore, the textbook does not arrange to calculate the area of a trapezoid by counting squares, but directly gives a trapezoid. By imitating the method of calculating the area of a triangle, it guides students to think about how to convert the trapezoid into a learned figure to calculate its area. Let students discover and master the calculation method of trapezoidal area in the process of independent participation in exploration, and let students realize the meaning construction of new knowledge, solve new problems and obtain new development in the process of mathematical recreation.

Teaching objectives

1. Through independent exploration and cooperative communication, we have experienced the derivation process of trapezoidal area formula, mastered the calculation method of trapezoidal area, and used the formula flexibly to solve related mathematical problems.

2. By observing, guessing, calculating and other mathematical activities, we can develop our spatial concept and reasoning ability, so as to obtain various strategies to solve problems and feel the inner charm of mathematical methods.

3. Experience the fun of "re-creation" in mathematics and get personalized development.

Emphasis and difficulty in teaching

Teaching emphasis: master the trapezoid area formula and calculate the trapezoid area correctly.

Teaching difficulty: understanding the derivation process of trapezoidal area formula.

Teaching preparation

Trapezoidal learning tools, computer courseware.

teaching process

First of all, pave the way for pregnancy and trade in the old for the new.

Teacher: Students, we learned a very important learning method when we were studying the calculation of parallelogram and triangle area. Do you remember what it is? Who can tell us how the areas of parallelogram and triangle are derived?

According to the students' feedback, the teacher demonstrated the derivation process of parallelogram and triangle area formulas with computer. )

Teacher: When deducing the area formulas of parallelogram and triangle, we always use the transformation method to transform the graph we want to study into the graph we have learned, find out the relationship between them, and then deduce the area calculation formula.

Design intention: Using multimedia demonstration, the derivation process of parallelogram and triangle area formulas is intuitively reproduced to attract students' attention. At the same time, arouse students' memory, communicate the connection between old and new knowledge, and prepare for the transmission of new knowledge.

Second, set the situation and ask questions.

1, situation creation. (Computer demonstration)

Teacher: There is a manufacturer who wants to make some desks and chairs for the kindergarten. The desktop is trapezoidal, with an upper bottom of 80cm, a lower bottom of 120cm and a height of 70cm. What do you need to make such a desktop?

Students will say "trapezoidal area" in unison, and the teacher will demonstrate how to abstract the ladder diagram from the physical diagram simultaneously. )

(Teacher writes on the blackboard: the area of trapezoid)

Design intention: Mathematics knowledge is connected with students' real life, so that students can easily feel and appreciate the practical significance and usefulness of mathematics knowledge. Therefore, starting from students' life experience, the actual situation of trapezoid is presented, so that students can feel the necessity of calculating the trapezoid area.

Step 2 ask questions.

Teacher: There are many such trapeziums in our life, and we need to calculate their areas, but we haven't learned the calculation method of trapezium area. What do you think the trapezoidal area may be related to? How do you want to deduce the calculation method of trapezoidal area?

Presupposition of learning situation: Students will judge that the area of trapezoid may be related to its upper bottom, lower bottom and height according to their existing knowledge and experience, and guess that the calculation formula of trapezoid area should be converted into learned figures. Students may say parallelogram, rectangle or even triangle. Teachers should give positive comments on students' various conjectures here.

Teacher: The students all have a preliminary idea of deducing the formula. No matter what figure you turn into, the general idea is to turn the trapezoid into the figure we have learned, find the relationship between the figures, and deduce the area formula of the trapezoid. Any conjecture must be verified before it can be determined whether it is correct. Do you want to have a try at once?

Design intention: The process of conjecture verification is also the process of students' active participation in mathematical knowledge exploration. Inspire students to apply what they have learned, make bold guesses, stimulate students' desire to explore new knowledge, and make students clear the goal and direction of exploration, that is, conduct research in a scientific way. Only by embodying students' dominant position can students truly experience the formation process of knowledge.

Third, provide materials and explore independently.

1, introduction of learning tools.

Teacher: The teacher has prepared a general trapezoid, a right-angled trapezoid and an isosceles trapezoid for each student. Think about it, can you complete the verification task with these trapeziums? If not, what should I do?

Design intention: To prepare a set of such learning tools for students is to stimulate their learning enthusiasm, activate their experience reserves and ignite the spark of innovative thinking. Students can't complete the puzzle only by their own trapezoid. We need to find another identical trapezoid in the hands of students to complete the task.

2. Research suggestions.

Teacher: Before you start the operation, the teacher should make the following three suggestions: (1) Choose the trapezoid you like, think independently about what you can transform it into the graph you have learned, and then study it according to the idea of "transform-find the connection-deduce the formula"; (2) Communicate your method with team members and verify it; (3) Choose an appropriate way to communicate and report. Let's compare which group has more ideas and moves faster.

Design intention: from providing students with operational requirements to giving students research suggestions, it reflects the change of teachers' role. In practical research, teachers let students think independently first, and each student has his own personalized understanding of the problem, and then guide students to cooperate and communicate. Let students realize the independent generation and construction of knowledge in activities such as observation, comparison, judgment, communication and reflection. At the same time, there will be many different strategies and solutions for students to learn to listen in communication and expand their thinking in listening.

3. Cooperative learning.

Students discuss and practice in groups, and teachers patrol to understand the situation.

Presupposition of learning situation: in the operation experiment, students' different thinking levels and different learning tools may lead to a variety of problem-solving strategies, including segmentation and spelling; Some are converted into parallelograms, others into triangles. Teachers should leave enough time and space for students to operate and communicate, and at the same time, they should withdraw and guide them in time.