Tisch
Teaching purpose:
Make students know the cone, master its characteristics and see its plan.
Teaching aid preparation:
Let each student make a conical model with the patterns in the textbook, and let the students collect some conical objects. The teacher prepares a conical object, a flat plate (or glass) and a ruler.
Teaching process:
First, review.
1. Question: What is the formula for calculating the volume of a cylinder?
2. What are the characteristics of a cylinder?
Second, the introduction of new courses.
Teacher: We have learned about cylinders. Please take out the same object as the teacher you prepared, have a look and touch it. What do you think is the difference between it and the column?
Third, the new lesson
Understanding of 1 and cone.
Let the students observe and play with the cone model, and then specify several students to tell their observation results. Let the students realize that a cone has a curved surface, the vertex and the curved surface are circles, and so on.
The teacher pointed out that objects like this are called cones. In this lesson, we will learn this new three-dimensional figure.
The words on the blackboard: cone
Teacher: Most people only know conical objects. We draw these objects on the slide.
Show a slide with a conical object.
Teacher: Now we can draw lines along the contours of these conical objects, and we can get such figures.
Then the teacher pulls a slide to demonstrate the outline of a conical object.
Then it is pointed out that the figure obtained by this method is the geometric figure of a cone.
The teacher pointed out that the cone has a vertex and the bottom is a circle.
Then mark the vertex, bottom and its center o on the diagram.
At the same time, it should be pointed out that the cone we have learned is the abbreviation of straight cone.
Then let the students touch the surface around the cone with their hands and let them find that the cone has a curved surface. It is pointed out that this face of the cone is called the side face. Mark the outline on the picture. )
Ask the students to look at the conical object and point out that the distance from the apex of the cone to the center of the bottom is called height. Then mark the height on the map.
The teacher demonstrated on the bus. Q: Is this line the height of the cone?
After the roll call, the teacher should point out that the line along the surface is not the height of the cone.
Teacher: What is the height of the cone?
According to the definition of height, guide students to find that a cone has only one vertex, so it has only one height.
Then let the students take out their learning tools. Two students at the same table pointed out the bottom, edge and vertex of the cone, reminding students that the height of the cone should not be touched.
2. summary.
The characteristics of the cone (which can inspire students to summarize) emphasize the characteristics of the bottom and height, so that students can understand that the characteristics of the cone are that the bottom is round and the side is a surface with vertices and heights.
3. Measure the height of the cone.
Teacher: Because the height of the cone is inside, we can't measure its length directly, so we need a flat plate to measure it.
The teacher described the measurement process during the demonstration:
(1) Level the cone bottom first;
(2) horizontally placing a flat plate on the top of the cone;
(3) Measure the distance between the outer plate and the bottom surface vertically.
Attention must be paid to: (1) The bottom surface and flat plate of the cone should be placed horizontally; (2) When reading, be sure to read the value at the intersection of the lower edge of the flat plate and the ruler.
4. Teaching cone side development diagram.
Teacher: What is the side of the cone?
The teacher shows the cone model and asks the students to say the side parts.
Teacher: We have learned about cylinders. Who can tell us what the figure is when one side of the cylinder is unfolded?
After the student answered that the lateral spread of the cylinder is a rectangle, the teacher asked, well, please think about it. What is the shape of the side expansion of the cone? "
After giving the students a short time to think and discuss, the teacher pointed out: We will see what the shape of the side of the cone is after it is unfolded through experiments.
Then the teacher instructs the students to unfold the side of the cone model, so that the students can see that the side of the cone after unfolding is a sector. After unfolding, it can be folded again and restored to its original state, so that students can deepen their understanding of the side of the cone.
Fourth, classroom exercises.
1, do the topic of "doing".
Let the students take out the model patterns prepared before class. Make it into a cone first, and then let the students measure its base diameter independently. Teachers patrol the rows and give timely guidance to students with difficulties.
2. Do the 1 question in Exercise 9.
Let the students think freely. Anything close to a cone can be regarded as a cone.
3. Do the second question in Exercise 9.
extreme
Teaching content:
The content of the textbook P23-26, P24 "Do it", and complete the questions 1 and 2 in Exercise 4.
Teaching objectives:
1, know the cone, the height and side of the cone, master the characteristics of the cone, read the plan of the cone, measure the height of the cone correctly, and make the cone correctly according to the experimental materials.
2. Make and measure the height of the cone by hand, and cultivate students' hands-on operation ability and certain spatial imagination ability.
3. Cultivate students' awareness of independent exploration and stimulate students' strong desire for knowledge.
Teaching focus:
Master the characteristics of cones.
Teaching difficulties:
Correctly understand the composition of the cone.
Teaching aid preparation:
Everyone has a cone, and the teacher prepares a large cone model.
Teaching process:
First, review.
1. What is the formula for calculating the volume of a cylinder?
2. What are the characteristics of a cylinder?
Second, the new lesson
1, Understanding of Cone (Discussion Report on Intuitive Feeling Observation)
(1) Let students observe and fiddle with the cone model, and then specify several students to tell their observation results, so that students can realize that the cone has a curved surface, and the vertices and surfaces are round, and so on.
(2) A cone has a vertex and a bottom surface is a circle (mark the vertex, bottom surface and its center O on the diagram).
(3) A cone has a face, and this face of the cone is called a side face. (Mark the side on the drawing)
(4) Let the students look at the teaching AIDS and point out that the distance from the apex of the cone to the center of the bottom is called the height. (All lines along the surface are not the height of the cone, because the cone has only one vertex, so the cone has only one height. )
2. Summary
The characteristics of the cone (which can inspire students to summarize) emphasize the characteristics of the bottom and height, so that students can understand that the characteristics of the cone are: the bottom is round, and the side is a surface with vertices and heights.
3. Measure the height of the cone (organize students to measure in groups)
Because the height of the cone is inside, we can't measure its length directly, so we need to measure it with a flat plate.
(1) Level the cone bottom first;
(2) horizontally placing a flat plate on the top of the cone;
(3) Measure the distance between the flat plate and the bottom surface vertically.
4. Teaching cone side development diagram.
(1) What figure will the students guess when one side of the cone is unfolded?
(2) Experiments show that the side of the cone is fan-shaped after being unfolded.
Third, classroom exercises.
1, do the topic "Do it" on page 24.
Ask the students to take out the model pattern prepared before class, make a cone first, and then ask the students to try to measure its base diameter independently. Teachers will patrol all walks of life and give timely guidance to students who have difficulties.
2. Exercise 4, Question 1.
(1) Let students observe freely and point out anything close to a cylinder or cone.
(2) Let the students talk about what other objects around them are made up of cylinders and cones.
3. Complete the second question in Exercise 4.
Supplementary exercises
1 displays a set of graphs and identifies which ones are cones.
Show a set of numbers to indicate which is the height of the cone.
Show a group of combined graphics and point out which graphics are combined.
Fourth, summary.
What do you know about cones? Can you introduce the cone in your hand to your classmates?
Teaching reflection:
Through observation and perception, we can know and master the characteristics of the cone, experience and explore the process of measuring the height of the cone, and deepen our understanding of the height of the cone. In the process of rotation comparison between cylinder and cone, we can deepen our understanding of the characteristics of cone and develop students' thinking.
Tisso
Teaching objectives:
Knowledge and skills: 1. Make students understand and master the characteristics of the cone and the names of its parts.
2. Let students master the method of measuring the height of cone.
3. Cultivate students' observation ability, operation ability and thinking ability, and develop students' spatial concept.
Process method: create scenarios, students ask questions by themselves, and students actively participate in the process of knowledge formation through independent exploration, cooperation and exchange with their mouths, hands and brains.
Emotional attitude: cultivate students' autonomous learning spirit of active participation and courage to explore and innovate, develop students' thinking ability and cultivate students' interest in learning mathematics.
Teaching process:
First, review and strengthen.
Courseware demonstration: show a cylindrical pencil.
The teacher asked: What shape is this pencil? Can you tell me what features it has?
Health: It's a cylinder. It is characterized in that a cylinder has three faces, an upper bottom face and a lower bottom face, which are two identical circles, one side face is a curved surface, and the distance between the two bottom faces is called the height of the cylinder, and there are countless heights. The side of the cylinder is rectangular.
Second, create a situation and introduce passion
Teacher: The students have mastered the characteristics of cylinders well. Today we are going to learn a new geometric figure. Please look at the screen carefully.
Courseware: Sharpen a pencil with a pencil sharpener and cut the sharpened nib (cone) vertically.
Q: Is this still a cylinder? What geometry is it cut into?
Health: No. It is a cone.
The teacher revealed the topic: We call this geometric shape a cone, or cone for short. All the cones we have learned are straight cones. Today, we are going to learn "Understanding of Cones". Theme of blackboard writing
Third, explore the experience.
1, list questions.
Students, think about it. In daily life and productive labor, which objects are conical? You can also show the conical objects collected after class.
Health 1: The shape of the ice cream shell is conical.
Health 2: Some hats are conical.
Health 3: The funnel is conical.
Health 4: The plumb hammer used to build a house is conical.
……
The students are very observant. Please take out the cone model, have a look and think about it. What do you want to know about cones?
Students can ask:
1, want to know the characteristics of the cone.
2. I wonder how high the cone is? What does its height mean?
3. I wonder what the profile of the cone is?
I want to know how to calculate the volume of the cone.
I want to know how to calculate the surface area of the cone.
2. Explore and solve problems independently.
Teacher: Please take out the cone model, have a look, touch it, play with it, or guess what you can find.
Student: Observing and thinking with a cone model in hand.
Teacher: Tell the students in your group what you have observed and felt, and the students in the group will discuss the questions raised by everyone just now.
Group communication and discussion. The teacher went deep into the group to discuss with the students.
Teacher: Which group is willing to show your research results to everyone?
Health Report: (Default Presentation Process)
First, the characteristics of the cone.
We found that the top of the cone is thin and the bottom is thick.
The cone has a sharp part and feels very prickly. We call it the vertex.
A cone has a curved and smooth surface, which we call the side. This surface is a surface.
A cone has a circular surface, which we can call the bottom.
⑤ We also found that the bottom of the cone stands downward, and the top does not stand downward.
When the cone rolls on the table, it never goes forward or backward, but always draws a circle around a point.
B, the height of the cone
We find that the height of a cone is the distance from the top to the bottom.
② The height of the cone is the distance from the apex of the cone to the center of the bottom. We think that the cone has only one height.
③ The height of the cone is the length of the line segment from the bottom of the cone to the apex.
We don't think what they said is accurate. The height of a cone is the distance from the top to the bottom of the cone. It should be countless heights. Because you can draw a line parallel to the bottom from the vertex of the cone, you can make countless heights.
Teacher: Students have several different views on the height of the cone. Who is right? Please discuss in groups.
Student: Discuss in groups.
Teacher: Which students agree with XXX? The teacher also agreed with this classmate. Please look at the screen carefully. (The courseware demonstrates the height of the cone)
Teacher: This black dotted line is the height of the cone. Who wants to talk about the height of the cone?
Try to say the height of the cone:
The height of a cone is the distance from the apex of the cone to the center of the bottom. The cone has only one height. Because a cone has only one vertex and one bottom center.
Teacher: Please open page 42 and read the last sentence of the third paragraph. Who will read it?
(Definition of Named Pronunciation and Different Pronunciation)
Teacher: Which group did you find?
C, the side of the cone is unfolded.
We find that the lateral expansion of the cone is fan-shaped (Show the students, a student sticks the unfolded figure on the blackboard. )
The teacher demonstrated the process of lateral expansion with courseware.
Teacher: Through the study just now, we have mastered the names of the parts of the cone. Please pick up the cone model, and the group members tell each other the names of the parts of the cone.
Each group tells each other the names of the parts of the cone.
Teacher: Who wants to talk about the names of the parts of the front cone?
Two students went to the front and said
3. Abstractgeometric figures from objects.
Teacher: The students speak very well! Teacher, here are three pictures of cones. Please look at them. (Courseware demonstration) What is the geometry of a cone? Please watch carefully (courseware demonstration) how to draw the invisible part when drawing. (Courseware demonstration)
This is the geometry of a cone.
Health: Draw with a dotted line.
Teacher: Look at the blackboard, class. This is the geometry of the cone. Who can come to the front and tell me what you know about the cone by comparing it with the geometry of the cone?
The students came to the front and said
Teacher: Please close your eyes and think about what a cone looks like.
4. Explore the method of measuring cone height.
Teacher: Through the study just now, we have mastered the characteristics of the cone and the names of its parts. We know that the height of a cone is the distance from the top of the cone to the center of the bottom. How can we measure the height of the cone? Think about it first, and then use the materials prepared by everyone after class to explore the measurement method of cone height.
Student report:
Health 1: This is how our group measured it. First, put the bottom of the cone flat, put it horizontally on the apex of the cone with a ruler, and measure the height of the cone vertically with a triangular plate.
Health 2: Our group's method is similar to theirs, except that a small ruler is erected on the desktop, and then a triangle passing through the vertex is perpendicular to the ruler.
S3: I think this method is more accurate than the first measurement. Because the triangle is placed on the vertex of the cone, it can be kept perpendicular to the ruler and the height can be measured accurately.
Health 4: This is the way we measure it. We put the bottom of the cone upside down on the table, put the ruler on the bottom of the cone, and then measure the distance between the vertex and the bottom vertically with a triangular plate.
Health 5: I don't think this method is very good because it can't be used for all cones, such as a lot of wheat. Can you measure its height upside down?
Health 6: We think that no matter what method is used, we should pay attention to starting from the "0" scale when measuring small scales.
Fourth, reading questions.
Verb (abbreviation of verb) classroom practice
1. Find the cone in the picture below.
Textbook exercise 12 1
2. Judges. (gesturing)
The side of a (1) cone is a curved surface. ( )
(2) The cylinder side expansion is rectangular, and the cone side expansion is also rectangular. ( )
(3) The line segment from the apex of the cone to any point on the bottom surface is called the height of the cone. ( )
(4) The bottom of the cone is round. ( )
3. Exercise 12 and 2 questions
Sixth, class summary.
What did we learn in this class? What did you learn from this lesson?
Seven, homework.
Go outside and find some sand or mud to make a cone and try to measure its height, so that two people can cooperate.