The area calculation of triangle is the content of Page 75-78 of Book 9 of Primary School Mathematics by People's Education Press. This content is based on the understanding of triangles in Volume 8. Volume 9 will calculate the areas of rectangles and parallelograms. 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. The textbook first calculates the area of a triangle by counting squares, and then transforms two identical right-angle, acute-angle and obtuse-angle triangles into rectangles or parallelograms by swinging, rotating and translating, and obtains that the area of a triangle is equal to half that of a rectangle or parallelogram, and then summarizes the calculation formula of the triangle area. According to the arrangement characteristics of teaching materials and the age psychological characteristics of fifth-grade students, I have determined the teaching objectives, teaching emphases, difficulties and emphases of this course.
Teaching objectives:
1, so that students can master the formula for calculating the area of triangle and use the formula to calculate the area of triangle.
2. Cultivate students' operational ability, spatial imagination ability and logical thinking ability through teaching methods such as graphic editing, graphic splicing and graphic transformation.
Teaching emphasis: master the calculation formula of triangle area, and use the formula to calculate the area of triangle.
Teaching difficulty: understanding the derivation method of triangle area calculation formula.
Teaching key: guide students to understand the meaning of dividing by 2 in the formula of triangle area calculation.
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.
First, the introduction of new courses.
The introduction of the new curriculum is to guide students to enter the learning state quickly. Good lead-in can ignite the spark of students' thinking and activate students' thinking. I introduce new lessons in an intuitive way. First of all, I guide students to observe the flag of the Young Pioneers Brigade and tell them that the length of the flag is 120 cm and the width is 90 cm. Let the students use the old knowledge to calculate the area of the flag and sum up the formula for calculating the rectangular area. Then show the red scarf and guide the students to say that calculating the area of the red scarf is to find the triangle area, thus playing the role of knowledge transfer, stimulating students' strong desire for knowledge and strong interest in learning, enabling students to enter a good learning realm and create a good start for the whole teaching process.
Second, expose the topic.
According to students' psychological characteristics, I used the method of stimulating interest to reveal the topic, so as to arouse students' attention and interest, stimulate their enthusiasm for learning, and play a connecting role. I will write the topic "Calculation of Triangle Area" directly on the blackboard, and then ask the question "What should I learn in this class?" Let the students discuss with each other and say three questions. What is the formula for calculating the area of (1) triangle? (2) How is the formula for calculating the triangle area derived? (3) How to calculate the area of a triangle with a formula? In this way, let students skillfully put forward the learning objectives of this course, turn the objectives into their own learning needs, and make students change from "I want to learn mathematics" to "I want to learn mathematics".
Third, deduce the formula.
The derivation process of formula is the formation process of students' knowledge. According to students' cognitive rules, I asked students to move their eyes purposefully and step by step, think with their brains, operate with their hands, and tell with their mouths. Through experiments, I deduced the formula for calculating the triangle area. Teaching is divided into four steps. (1) Guide to guess: I ask students to count the area of the triangle with square paper according to the method on page 75 of the textbook, and guide students to observe how many centimeters the bottom of the triangle is. How many centimeters wide is it? What is the relationship between the length and area of the bottom and the height? Let the students observe and analyze, and get that the base of the triangle is 6cm, the height is 4cm, and the area is 12cm2 (Figure 1).
The bottom is 6 cm, the height is 4 cm, and the area is 12 cm.
Figure 1
Then lead the students to guess that the area of a triangle is half the product of the base and the height.
(2) Try to operate: When students have psychological doubts and need the teacher's explanation and verification urgently, the teacher asks the students to recall how the parallelogram area calculation formula is derived. As the students speak, I demonstrate the deduction method of transforming a parallelogram into a rectangle (cut a triangle along the height of the parallelogram and put the cut triangle on the other side to become a rectangle, as shown in Figure 2).
Figure 2
In order to arouse students' memory and promote the transfer of knowledge. Then ask students to imitate the derivation method of parallelogram area formula, convert triangles into other figures, and take out the rectangle learning tools prepared before class to measure the length and width of rectangles. (length 10 cm, width 6 cm), calculate its area as 10×6=60 cm2, then cut along the diagonal of the rectangle and divide it into two triangles with the same size and shape, and calculate the area of a triangle as 10×6÷2=30 cm2 (as shown below). Look carefully, students.
This triangle is half of the original rectangle. Make students understand that the derivation of triangle area calculation formula follows the development law from image thinking to abstract thinking. Then let the students take out the paper of the parallelogram, measure its base and height as 10 cm and 6 cm respectively, and calculate the area of the parallelogram of 10×6 as 60cm 2, and then cut it along the diagonal of the parallelogram, which can be divided into two triangles with the same size and shape to calculate a10× 6 ÷. Students once again see that this triangle is half of the original parallelogram, and observe that the base and height of the parallelogram are consistent with the base and height of the cut triangle, which breaks through the difficulties in teaching. (3) Inductive formula: Through two experiments, the students discussed it one after another, and came to the conclusion that the formula for calculating the triangle area is base × height ÷2, written in letters as S=ah÷2, and pointed out that the base and height of the triangle must be known when calculating the triangle area, and the base and height cannot be divided by 2 when calculating the triangle area, which makes the students' knowledge more systematic and perfect. (4) Reading query: After students come to a conclusion naturally through their own experimental operations, I will ask students to carefully read the contents on pages 75 to 77 of the textbook, and compare the similarities and differences of their own deduction methods, highlighting that the textbook uses the method of "combination" to verify the formula, while we use the method of "division" to verify the formula. Both methods are derived by transforming triangles into rectangles or parallelograms, and both methods can be tried successfully. After that, I will leave some time for students to ask questions, and then I will give targeted explanations, create a cordial and harmonious classroom atmosphere, make students dare to ask questions, and further organically combine the leading role of teachers, the main role of students, the demonstration role of teaching materials and the complementary role among students, thus improving classroom efficiency.
Fourth, practical application.
After the students deduced the formula for calculating the triangle area, I showed an attempt similar to the textbook example: the bottom of a red scarf is 100 cm and the height is 32 cm. What is its area? Let the students answer independently and act out three types of students: good, medium and poor. I made a patrol inspection to get information feedback and found out two estimated situations: (1)100× 32 ÷ 2 =1600 cm2; (2) 100×32=3200 square centimeters, and organize students to discuss and explain according to the feedback information, emphasizing that when applying the triangle area calculation formula, don't forget to divide the base and height by 2, otherwise the area of rectangle or parallelogram will be calculated, so as to ensure that students can master knowledge systematically.
Verb (abbreviation for verb) consolidation exercise
Practice is a necessary way for students to master knowledge and form skills, and an important means to check the implementation of teaching objectives. In order to improve the efficiency of practice, I designed three exercises reasonably.
Question 1: Calculate the area below. This is the topic to be done on page 77 of the textbook, which belongs to a single exercise and is used to consolidate new knowledge.
Question 2: The area of parallelogram is12cm2. Find the area of colored triangle.
This is the topic of exercise 18 on page 78 of the textbook, which is a comprehensive exercise. This paper not only reviewed the relationship between the triangle area formula and the parallelogram area formula, but also further consolidated the calculation of the triangle area to prevent students from drawing gourds as usual.
Question 3: Who has the simplest solution to calculate the area of the team flag in the Young Pioneers? This topic is a creative exercise, which can not only stimulate students' interest in learning, but also promote their thinking.
Sixth, the class summary
Summary is an important part of classroom teaching, which enables students to further clarify specific teaching tasks, grasp key points and form systematic knowledge. I ask students to contact the student goals put forward at the beginning of this class and summarize what they have learned in this class. The formula for calculating the triangle area is: (1) base × height ÷ 2; (2) After the base and height of the triangle are determined, the area of the triangle is also determined; (3) When calculating, don't forget to multiply the base and the height and then divide by 2. In this way, by sorting out and summarizing, it plays the role of making the finishing point and making the arrangement of the whole class good from beginning to end.