Pages 22 and 23 of the fourth grade of primary school mathematics published by Beijing Normal University.
second, teaching material analysis
? The content of this lesson is to further understand the triangle, which is of great significance to the students behind to deeply understand the characteristics of the sides and angles of the triangle.
? This lesson is conducted on the basis of students learning the classification of known angles.
? This lesson mainly studies two methods to classify triangles. Because students have learned acute angle, right angle and obtuse angle, and know the characteristics of these three angles, as long as they classify triangles according to the characteristics of these three angles, they can complete the first method of classification by angles. The second classification is based on the characteristics of whether the three sides are equal, and students can also carry out various activities such as observation, folding and measurement.
? Through the study of this lesson, let students master two methods of triangle classification through "dichotomy" and cultivate students' orderly thinking.
third, the analysis of academic situation
1. Through the students' previous homework, it is found that the students' diagonal judgment is more accurate.
2. Students' awareness of group cooperation is constantly improving.
Fourth, teaching objectives:
(1) Grasp the classification standards and methods of triangles through practical operation, understand the characteristics of each type of triangle, and be able to identify right triangles, acute triangles, obtuse triangles, isosceles triangles, equilateral triangles and arbitrary triangles.
(2) Through observation, comparison, classification and other operations, students' exploration spirit, inductive generalization ability and logical thinking ability are cultivated, and students' spatial imagination ability is developed.
(3) Let students feel the joy of learning mathematics and experience the joy of success in the process of inquiry, so as to stimulate students' enthusiasm for learning mathematics well and understand that cooperation can improve efficiency.
(4) Set diagram will be used to represent the relationship between different kinds of triangles, which permeates the idea of set. Cultivate students' classification ability.
5. Emphasis and difficulty in teaching:
Emphasis: Through thinking, independent exploration and cooperative communication, triangles are accurately classified according to their angles and sides.
difficulty: being able to master the characteristics of various triangles and the internal relations among them.
VI. Preparation of teaching AIDS and learning tools
Teacher: PPT courseware, triangles
Student: triangle, protractor, scissors, triangles
VII. Teaching process
(1) Scene introduction:
1. Students, can you name this figure? (Show the Pentagon)
2. How many triangles can this Pentagon be divided into? (three)
3. Are these three triangles the same? What is the difference? (writing on the blackboard: edges and corners)
4. What different angles can you find in these triangles?
ask: what kind of angle is a right angle? What kind of angle is obtuse? What kind of angle is acute?
5. These different triangles make up beautiful patterns to decorate our lives. Let's look at a set of pictures. Please tell the patterns you see
(boats, peacocks, pigeons, birds, houses, people and horses) while observing and using your imagination.
(2), inquiry activities
1, the students are great! Be good at observing and thinking rationally. (Multimedia shows the pattern of a ship made up of triangles) Look at this image again.
2. What kinds of triangles are this sailboat pattern made of? We will classify these triangles in this lesson.
blackboard writing: the classification of triangles.
3. Before class, we prepared such a small triangle. Before classifying, let's look at the requirements of group activities:
Activity 1:
Requirements of group activities:
(1) Think about what criteria you are going to classify.
(2) I think it can be divided into several categories.
(3) After the division, observe what features each triangle has, and give each triangle a name.
students communicate in groups and report their conclusions.
Teachers guide students according to their reports: What are the characteristics of triangle angles as classification criteria? How to divide it?
* For the first time, according to the standard of "whether there is a right angle", we divided these triangles into two categories, those with right angles and those without right angles. Think about it, can we continue to divide this category without right angles?
* for the second time, we divided the remaining triangles into two categories according to the standard of "whether there is obtuse angle", one with obtuse angle and the other without obtuse angle. Can we continue to divide it?
* Every time like this, we divide triangles with the same characteristics into one category, and triangles without this characteristic into another category. This is the most basic classification method-dichotomy. (writing on the blackboard: dichotomy)
* Based on the above two dichotomies, we finally divided triangles into three categories.
Teacher's guidance: Observe the first category. What are their characteristics in common? There is a triangle with a right angle like this. What shall we name it?
triangles with right angles are classified into one category, called right triangles (blackboard writing: right triangles)
triangles with obtuse angles are classified into one category, called obtuse triangles (blackboard writing: obtuse triangles)
triangles without right angles and obtuse angles are classified into one category, and all three angles in this category are acute angles.
* choice: which diagram do you think best reflects the relationship among right triangle, obtuse triangle and acute triangle? And tell me your reasons.
Summary: None of them is included in anyone, and they are in a parallel relationship.
* Can a triangle have two right angles? Can there be two corners? (group communication)
summary: (courseware presentation) A triangle is a closed figure, and two right angles or two obtuse angles cannot form a triangle.
7. Math game:
Can you guess what triangle is in this envelope? Please provide a justification for the answer.
A, revealing a right angle-right triangle
B, revealing an obtuse angle-obtuse triangle?
C, show an acute angle-can you guess exactly what kind of triangle it is now? Why? Summary: It seems that if we want to quickly judge what triangle this triangle is, we only need to know what the largest angle of this triangle is. If the largest angle is a right angle, it is a right triangle. If the largest angle is obtuse, it is an obtuse triangle; If the largest angle is acute, it is an acute triangle.
Just now, we divided triangles into three categories according to their different characteristics. Are there any different classification methods? Which group is willing to exchange your views?
8, students report, teacher's camera guide:
Student 1: "Divide triangles according to whether their sides are equal or not." We divide triangles into three triangles with equal sides, two triangles with equal sides and three triangles with unequal sides.
Health 2: Our group thinks that triangles with three equal sides should be included in triangles with two equal sides, so we divide triangles into two categories.
9. teacher: are there any different ideas? Raise your hand if you agree with the first classmate, and raise your hand if you agree with the second classmate?
teacher: do you think an equilateral triangle is an isosceles triangle? (equilateral triangle is a special isosceles triangle)
11. The two equal sides of isosceles triangle are called "waist" and the two equal angles are called "bottom angle".
what are the characteristics of an equilateral triangle? The three sides of an equilateral triangle are equal and the three angles are equal
12. Teacher: If Wayne diagram is used to represent the relationship among equilateral triangle, isosceles triangle and triangle, how should we fill in the blanks?
(show isosceles triangle and equilateral triangle) Introduce the names of each part.
(3) Hands-on operation:
? You all have a square in your hand. What kind of triangle will you get if you fold its diagonal in half? This triangle is divided by sides. What triangle is it? What triangle is it by angle? There is such a triangle in the triangle board. Take it out and have a look. We will call it an isosceles right triangle.
students show their achievements.
(4) Classroom extension: Are there any other classification criteria? In fact, there are other classification criteria for triangles. For example, triangles can be divided according to whether they are axisymmetric figures or not. An axisymmetrical triangle is an isosceles triangle and a non-axisymmetrical triangle is an equilateral triangle. If it is an axisymmetrical triangle (isosceles triangle), it can be divided into two categories according to whether there is only one axis of symmetry: one is an isosceles triangle with only one axis of symmetry, and the other is an equilateral triangle with three axes of symmetry. In short, in the classification activities, we should choose appropriate classification standards to form classification strategies, and learn to describe classification activities in an orderly and orderly manner, so as not to miss or repeat them.
(5), Summary
This lesson I know ... I know ... I have learned ... (Perfect the assembly diagram-there are only words, no circles)
Classification is very important in our daily life, because using the classification method, our life becomes orderly, and our life will be more comfortable and exciting.