Lines, rays and angles
New Teaching of "Line, Ray and Angle"
Standard knowledge and skills:
1. Make students know ray and straight line, and identify the relationship and difference between the three concepts of ray, straight line and line segment.
2. Let the students know the angle and the representation of the angle, and know the names of each part of the angle.
3. Cultivate students' preliminary ability of observation, comparison and generalization. 4. Cultivate students' spatial concepts about ray, straight line, line segment and angle.
Process and method
By observing and operating learning activities, students can experience the formation process of straight line, ray and angle representation.
Emotional attitudes and values:
I realize that mathematics knowledge is closely related to real life, and I can feel learning everywhere in my life.
Importance of key angles
Relationship among Difficulty Ray, Straight Line and Line Segment
Teaching aid courseware, activity angle, ruler or triangle
Supplementary instructions for teachers to guide students' activities
A, understanding the ray, straight line
1, review the line segment characteristics.
Display line segment: What are the characteristics?
2. Know Ray.
Courseware (1) shows that students get a ray when they perceive that one end of a line segment extends indefinitely.
(2) What are the characteristics of rays?
(3) Have you ever seen rays in your life?
Instruct students to draw rays with a ruler or triangle.
3. Know the straight line.
Courseware (1) shows that students get a straight line when they perceive the infinite extension of both ends of a line segment.
Students try to draw a straight line.
(4) What is the relationship between a line segment and a straight line?
4. The connection and difference between line segments, rays and straight lines.
Show the form: fill in the form in groups.
Names, graphic connections and differences
line segment
ray
straight line
Group report
5. practice. Which of the following figures is a line segment, a ray and a straight line? (P39、 1)
Guide imagination
Courseware shows that countless rays can be drawn from one point, paving the way for learning.
Second, understanding angle.
Leave two rays from one point and ask: Do you know this figure?
What is a horn? What symbol should be used to represent the angle? Let's study the angle.
1, can you give an example of a corner you have seen?
Students give examples. Teachers use students' examples to show objects and abstract them into corners of various shapes, so that students can perceive the existence of corners in life.
2. Establish the concept of angle.
(1) Summarize the steps of drawing corners according to the students' speeches: ① Draw a point and draw a ray from it; (2) from this point leads to another ray; (3) Write the names of each part. It is represented by ∠ 1
(2) Q: What exactly is an angle? Summarize the concept of angle.
The figure composed of two rays from a point to the exit is called an angle. This point is called the vertex of the sum angle, and these two rays are called the edges of the angle. The sign of the angle is "∞".
Third, consolidate the exercises:
1, P36 "Do it"
2、P39、2、
Fourth, class summary.
Q: What have we learned today? Do you think it's weird?
In this lesson, we learned about straight lines, rays and angles (blackboard topic: straight lines, rays and angles)
Homework after class: P40,8 Student report: Straight board with two halls, which can be tested.
Students report after observing and thinking.
A ray has only one endpoint and extends to one end indefinitely.
Through practice, we can consolidate and review what we have learned in time.
blackboard-writing design
Lines, rays and angles
Angle measurement
Knowledge and skills:
1. If you know the protractor and the unit of measurement of angles, you will find angles of different sizes on the protractor and know its degree. You will use a protractor to measure the angle.
2. Cultivate students' hands-on operation ability through some operation activities.
3. Let students understand the significance of angle measurement by connecting with life.
Process and method:
By observing and operating learning activities, students can form the skills of measuring angles, and at the same time, students can experience and appreciate the formation process of knowledge.
Emotional attitudes and values:
In the process of learning, feel the close connection between mathematics and life, and stimulate students' interest in learning mathematics. .
Focus on the protractor and use it to measure the angle.
It is difficult to understand the protractor, so you can measure the angle with the protractor.
Teaching aid protractor, ruler or triangle
Supplementary instructions for teachers to guide students' activities
First, create situations and introduce topics.
Show the following three kinds of chairs and ask the students: What kind of chair do you like to sit in and why?
After the students answered, they made the following summary: According to the communication of the students just now, it seems that different angles of the chair backrest have different functions. For example, the second kind of chair is specially designed for astronauts who landed on the moon. To build such a chair, you must know the angle of the backrest. Is there any way to know its angle? (According to the students' answers to the blackboard topic: Angle measurement)
Second, explore independently and know the protractor.
1, know the center of the protractor, 0 scale line, internal and external circle scale.
(1) Teacher: What tools are used to measure angles?
Teacher: Please observe your protractor carefully, study it carefully and see what you find.
(2) Group cooperative learning protractor.
(3) Students report the research results. Pay attention to let students express their ideas as much as possible here. Some questions can be answered by students.
According to the students' answers, the teacher should explain where the center of the protractor is, where the 0-degree scale line is, where the internal scale and the external scale are, and the protractor divides the semicircle into 180 equally. Write on the blackboard according to the answer: center, 0-degree scale line,
Internal scale and external scale. (If the students can't answer that the protractor divides the semicircle into 180 equal parts, the teacher can ask the following questions for inspiration: According to the scales and numbers on the protractor, how many equal parts do you think the protractor divides the semicircle into? )
2. Establish the concept of 1.
(1) Let the students divide the protractor into 180 equally. How big is the angle of a thin wire game stick (cut from a plastic broom) on the desk?
(2) Discuss with the students * * *, and come to the conclusion that the angle the students just posed is 1.
3. Know the temperature.
(1) Show the following angles on the protractor and ask the students what the angle is and why.
Draw an angle of 20 on the protractor, in which each scale is marked with a dotted line, and then
Tell the students why it is 20.
(2) Display the angles of 60 and120 on the protractor (draw the angles printed on paper on the protractor). Discuss with the students why one scale means 60 and the other means 120. So let the students talk about what they should pay attention to when reading angles on a protractor. Break through the difficulty of reading the scale of inner and outer circles.
(3) Find the angles of 30, 100 and 135 on the protractor.
Third, try to measure the angle and explore the method of measuring the angle.
1. Show the following angle (P37) and ask: Can you read the degree of this angle? Because there is no marked degree, students can't understand it. Then ask: what should I do to read the degree of this angle? Guide students to practice and measure angles step by step.
The first step is to make the central point of the protractor coincide with the vertex of the angle; Step 2, making the zero scale line of the protractor coincide with one side of the angle; The third step is to look at the scale on the protractor on the other side of the angle, which is the degree of this angle. The teacher demonstrated while explaining and guided the tour.
2. Measure the degrees of the following angles (P39,3). (If the side of the second corner is not long enough, you can extend the side to measure. Ask the students why they can extend the edge to measure. ).
Fourth, compare the angles.
Measure the following two groups of angles with a protractor and compare their sizes. (P38 case 1)
Discussion: What does the angle have to do with it?
Conclusion: The size of the angle has nothing to do with the length drawn on both sides of the angle. The size of the angle depends on the size of both sides. The bigger the fork, the bigger the angle.
Verb (abbreviation for verb) consolidation exercise:
1, P38 "Do it"
2.P39 and P4 estimate the degree of each angle first, and then verify it.
3. P40,6 Spell out angles of the following degrees with a set of triangles.
75 105 120 135 150 180
Sixth, the class summary
Q: What have we learned today? What did you get?
Homework: P40, 5 and 7 Students report after thinking.
Students are free to express their views.
extensor
Students observe the protractor and study in groups.
The whole class communicates and reports, and students express their opinions. After the students make independent judgments, the whole class corrects them.
The student replied: it's a horn.
Student report. The protractor divides the semicircle into 180 equally.
The students put a pendulum on the table.
Student discussion
After reading the book, the students point out the vertex and both sides of the angle of 1 on the protractor.
The angle of students' speaking and its reasons
Students' reading angle
What should students pay attention to when reading angles on a protractor?
Students find the angles on the protractor and point out the vertices and two sides of these angles.
Students' cooperation is completed, and let students give feedback after completion)
Students try to measure and then demonstrate.
Explain how it was measured while measuring.
Then the students use a protractor to measure two angles in the book.
Let the students talk about their feelings after measurement.
Make students realize that the size of the angle has nothing to do with the length of the pictures on both sides of the angle.
Through practice, we can consolidate and review what we have learned in time.
Classification of angles
Knowledge and skills:
1. Let the students draw angles according to the prescribed degrees with a protractor, and further consolidate their knowledge about angles through practice.
2. Cultivate students' hands-on operation ability and analytical reasoning ability.
3. Cultivate students' self-study ability.
Process and method
Through learning, students can experience the whole process of drawing and practicing corners, and further consolidate the relevant knowledge of corners.
Emotional attitudes and values:
Make Xu feel the close connection between mathematics knowledge and real life, and experience the fun of learning mathematics.
Emphasis will be placed on drawing angles according to the specified degrees with a protractor.
Difficulties in cultivating students' hands-on operation ability
Teaching aid protractor, movable square, ruler or triangle
Supplementary instructions for teachers to guide students' activities
First, import:
Teacher: What have you talked about recently? (knowledge of horns)
Who wants to talk about what horns are?
T Open a pocket with various angles:
Teacher: We have prepared many speakers for each group. How are you going to study these horns? (classification)
Second, explore new knowledge:
1. Group the corners of each group.
Teacher: How to divide it? Why do you want to divide it like this? Do you know what an angle greater than a right angle and less than a right angle is called?
Students sum up what are right angles, acute angles and obtuse angles.
Blackboard writing: acute angle: less than 90; Right angle: equal to 90; Oblique angle: greater than 90 degrees.
2. Do you classify according to the degree of angle?
Teacher: Have you measured it? Measure it. What are the characteristics of these angles? Which of these three angles is more special? (Right angles) Can you tell which ones are right angles around you?
Please choose the right learning tool and draw a right angle for everyone.
What school tools did you choose to report by name? How did you draw it?
Draw an acute angle and an obtuse angle with the fastest speed.
Point out how you check for your classmates. (blackboard writing: visual, quantitative and comparative triangle)
5. Summary: The right angle of 90 is used as the standard to judge acute angle and obtuse angle, so the right angle is very important. (Stick on the blackboard at right angles)
6. Know boxers and rounded corners.
Teacher: Besides these horns, what other horns do you know? What do you know about boxers and rounded corners? Open the book P4 1 and teach yourself Example 2.
(2) Please take out the movable corner and start to fold out straight corners and rounded corners.
Blackboard writing: flat angle: equal to 180 fillet = 360.
Teacher: What other angles did you find are the relationship between boxers and rounded corners? Blackboard writing supplement: 1 right angle = 2 right angles
1 fillet = 2 right angles = 4 right angles.
Teacher: Then let's look at the obtuse angle. Just say more than 90, okay? How to make up?
Blackboard writing: obtuse angle: greater than 90, less than 180 III. Consolidate understanding:
1, first judge what angle it is, and then compare the two angles. Think about it, how do you do your research? (short article)
2, P4 1, thinking about the problem
3.P43 and P44 fill in the picture.
4.P43 and 1 First estimate and then measure the degree of each angle in the diagram.
Fourth, class summary.
What did we learn in this class? (blackboard writing: classification of horns) Tell me what you have gained.
5. Homework after class: P43, 3, 5. Student report: corner knowledge.
The concept of students' answering angle
Hands-on operation to fold right angles and rounded corners.
Report to the class after group discussion and exchange.
Students supplement the concept of obtuse angle.
Students judge and compare independently, and the whole class corrects.
Review the relevant knowledge of the corner to prepare for learning new knowledge.
Through the classification of angles, we can deepen our understanding of diagonal lines.
Corner drawing and corner consolidation exercises
Knowledge and skills: 1. Let the students draw the angle according to the prescribed degree with a protractor, and further consolidate the knowledge about the angle through practice. 2. Cultivate students' hands-on operation ability and analytical reasoning ability. 3. Cultivate students' self-study ability.
Process and method
Through learning, students can experience the whole process of drawing and practicing corners, and further consolidate the relevant knowledge of corners.
Emotional attitudes and values:
Make Xu feel the close connection between mathematics knowledge and real life, and experience the fun of learning mathematics.
Emphasis will be placed on drawing angles according to the specified degrees with a protractor.
Difficulties in cultivating students' hands-on operation ability
Teaching aid protractor, movable square, ruler or triangle
Supplementary instructions for teachers to guide students' activities
First, review and check.
1, tell me what the following angles are.
2. We already know the angle. We can measure the angle with a protractor and classify the angle. How to draw the angle? Today we are going to learn to draw corners.
Write on the blackboard: draw corners
Second, explore new knowledge.
1, the drawing method of teaching angle
Q: What is the tool for measuring angles?
Explain that you have to draw an angle of a specified degree and draw it with a protractor.
For example, draw an angle of 65.
(1) Please teach yourself how to draw corners.
(2) Give it a try
Let the students take out the protractor, pencil and exercise book and draw a picture step by step according to the steps in the book.
Say it.
Please tell the students how you draw. Students said that the teacher demonstrated on the blackboard, and finally the teacher explained the instructions.
2. Do it (P42,2)
Draw angles of 75 and105 respectively.
Let a better student act it out and the rest draw it in the exercise book. The teacher visited and paid attention to the steps of drawing.
The second class, consolidation exercises.
1, p43,2 Choose a suitable method to draw the following angles and tell them what kind of angles they are.
10 45 60 90 105 120
2.P44 and P6 use a pair of triangular rulers to draw the angles of 15, 75, 150 165 respectively.
Fourth, class summary.
What did we learn in this class? What do you have? Tell me.
V. Homework:
P44、7
Students draw an angle with a specified degree, and the deskmate uses a protractor to help check whether the degree is accurate.
Let's talk about the steps of drawing corners after painting.
Draw a corner and judge what it is.
Curriculum revision
Students draw the designated corners, check and review each other's knowledge about corners, and prepare for learning new knowledge.
Make students master the method of drawing corners and cultivate their drawing ability.
Strengthen the communication and contact between angle measurement and drawing angle
Through practice, we can consolidate and review what we have learned in time.