Textbook training speech
I. Status of teaching materials
This unit is based on students' knowledge of circles, cuboids and cubes. It is the last part of primary school geometry knowledge learning and the basis for further learning geometry knowledge in the future.
Volume geometry, three views). Cylinders and cones (cylinders in textbooks refer to straight cylinders, referred to as cylinders for short; The side of a cone is a curved surface. The study of this unit will enable students to understand three-dimensional graphics.
Deeper and more comprehensive, which is conducive to further developing students' concept of space.
Two. Teaching objectives of this unit
1. In real situations, through observation, operation, comparison and other activities, we can understand cylinders and cones and master their characteristics.
2. Combined with the specific situation, through exploration and discovery, we can understand and master the calculation methods of lateral area, surface area of cylinder and volume of cylinder and cone, and solve simple practical problems.
3. Experience the process of exploring the knowledge of cylinders and cones, and further develop the concept of space.
4. In the activities of observation and experiment, guessing and verification, communication and reflection, we can initially understand the process of the generation, formation and development of mathematical knowledge. Experiential mathematics activities are full of exploration and creation, and we have a preliminary understanding of some mathematical thinking methods.
Three. Unit teaching content
Information window topic knowledge points
Information window-ice cream box cylinder and cone
Side area and surface area of cylindrical paper tube made of information window 2
Information Window III Volume of Ice Cream Packaging Box Volume of Cylinder and Cone
Four. Outstanding characteristics of module preparation
1. It breaks the traditional knowledge arrangement order and strengthens the contrast and connection between cylinder and cone.
The textbook of this unit arranges three information windows, namely, the understanding of cylinder and cone, the surface area of cylinder and the volume of cylinder and cone. In the information window 1, the understanding of cylinder and cone is arranged at the same time. Students can
Through the observation, operation and comparison of cylinder and cone models, the relationship and difference between them are more clearly understood, and the characteristics of cylinder and cone are discovered and mastered. In the information window 3, after learning the volume of the cone, it appears in pairs again.
The form of the word shows the students' guess that the volume of the cone is related to the cylinder. Guide students to explore the relationship between cone and cylinder volume through experiments. In this way, cylinders and cones are arranged together for teaching, which breaks the tradition.
The mode of learning one by one strengthens the contrast between cylinder and cone, which is more conducive to students to understand and master the relevant knowledge of cylinder and cone through discovery and exploration.
2. Reflect the learning process from conjecture to verification, and infiltrate the ideas and methods of studying mathematical problems.
The compilation of this unit's teaching material pays attention to the guidance of mathematical thinking methods, such as the exploration of the calculation method of the cylinder volume of the third information window, which embodies this point well. The textbook provides such an idea: from the memory circle
The deduction method of area formula is the breakthrough point (turning a circle into a square), which realizes the transfer of thinking. It is speculated that the volume formula of cylinder may be derived from transforming cylinder into cuboid. This kind of writing helps students to understand the research.
The ideas and methods of studying mathematical problems can improve students' ability to study mathematical problems.
Verb (abbreviation of verb) the overall planning of unit class hours
Information window: one information window, two information windows, three views and arrangements.
Comprehension and practice of cylinder and cone: 1 exploration of surface area of cylinder; Basic exercise: 1 volume exploration of cylinder; Basic exercise: 1 class review; Exercise: 1
Consolidation exercise: 2 class hours cylindrical volume consolidation exercise: 1 class hours comprehensive exercise: 1 class hours.
Cone volume exploration and basic exercises: 1 class hour.
Volume consolidation exercise for cylinders and cones: 2 class hours.
Suggestions on teaching intransitive verbs
Information window 1: ice cream box
1, teaching content:. Characteristics of cylinders and cones.
2. Information window introduction: The picture provides us with two ice cream packaging boxes with different shapes.
Sample settings:
The first red dot: the preliminary understanding of cylinder and cone.
The second red dot: Learn the characteristics of cylinders and cones.
3, information window teaching suggestions:
First, teachers should pay attention to students' existing life experiences.
Cylinders and cones are no strangers to students. How to make senior students make full use of the existing knowledge and experience, synthesize the skills they have mastered, have a profound perceptual understanding of the characteristics of cylinders, and establish a "circle"
The appearance of "column" is what teachers should consider when preparing lessons. Therefore, in the teaching process, the teacher should let the students look for cylindrical and conical objects that they often see in life, and at the same time, they can let the students go back and make one themselves in advance.
Cylinders, in class, let students talk about their understanding of these two forms in combination with their own graphics.
Second, give students more hands-on opportunities.
The key to learning solid geometric figures is that students should have a sense of space, and the best way to cultivate students' sense of space is to operate by hands. Therefore, in class, students should repeatedly touch, measure and compare, thus summarizing the characteristics of cylindrical cones.
Third, pay attention to the application of multimedia and cultivate students' spatial concept.
Let the students abstract the objects in their eyes into geometry and let them know the height of the cylinder cone. There are certain difficulties, and teachers can make full use of the media to resolve them. In particular, multimedia should be used to help students distinguish between buses and buses. Schools that do not have the conditions should use teaching AIDS to let students observe carefully and fully expand their imagination to achieve the above goals.
4. Practice analysis:
In practice, we should pay attention to let students cultivate their own spatial concept on the basis of hands-on operation.
The third question of autonomous exercise is to cultivate students' imagination and establish the concept of space, which also paves the way for students to further study surface area. When practicing, students can think first and then contact. It can also be used as
Ask the students to find some objects according to the pictures and cut them along the height to get a preliminary understanding of the sides of cylinders and cones. In fact, it is to pave the way for the next window to learn lateral area column, combined with students
For students who have difficulty in understanding, the teacher should let the students operate by themselves to deepen their understanding. Many questions in this part need to be practiced, such as the fourth question in the exercise, which students should do by themselves.
Question 5 is also the topic of further cultivating students' spatial concept. In practice, students can imagine first, then let them experiment when their imagination is not clear, and then shelve the experiment to further imagine and deepen their understanding step by step.
Question 6 should make students understand two points: one is the relationship between the length of ribbon and the diameter and height of the cylinder, and the other is to let students find that there are ribbons at the bottom of the cylinder that are repeated with the above.
"Extracurricular practice" is to let students find cylindrical and conical objects in their lives and measure the diameter and height of the bottom. Teachers should pay attention to guide students to master the correct measurement method for measuring the height of cone: (1) First of all,
Level the bottom of the cone; (2) horizontally placing a wooden board at the top of the cone; (3) Measure the distance between the flat plate and the bottom surface vertically. The page number mentioned in the teaching reference is wrong, it is 49 pages. )
Information Window 2: Making cylindrical paper tubes
1. Teaching content: lateral area and surface area of cylinder.
2. Introduction to the information window: On the left is the paper tube produced by the cylindrical paper tube workshop, and the paper tube on the right indicates the diameter and height of the bottom surface.
3, information window teaching suggestions:
First, strengthen the intuitive operation, so that students can intuitively understand the surface area and lateral area of the cylinder.
The operation mentioned here should be two points. One is the operation before class. Before class, the teacher asked the students to make a cylindrical paper tube by themselves, and combined with the process of making a paper tube by themselves, exchanged how they did it. It is understood that
The student's answer courseware shows the process of making paper tubes in the paper tube making workshop. Let students clearly understand the process of making paper tubes. Let the students realize that the surface area of a cylinder is the area of two circles and one side. In the second-hand finger class
Operation, focusing on solving lateral area's calculation method, the teacher asked the students to realize that the edge of a cylinder is actually a rectangle, and the length and width of this rectangle should be the circumference of the bottom respectively.
High, this is difficult for students to understand. Repeated operations and multimedia courseware should be used here to help students understand. Therefore, the lateral area should be the perimeter x height of the bottom surface.
Second, pay attention to the distinction between several concepts.
This window involves several concepts, such as lateral area, surface area, bottom area, bottom perimeter and so on. Many teachers who have taught fifth grade feel this way. When learning this part of knowledge, a knowledge point is one.
Students have a good grasp of knowledge points, but when all the knowledge points are put together, students are very confused. Why? The main reason is that students understand these concepts. What bottom circumference should I use?
Dragon, ask what is used in the tail area so that students can have a clearer mind.
4. Practice analysis:
The second problem of autonomous exercise is that the teacher should let the students know that the area of a trademark is actually a lateral area of a cylinder, and at the same time, pay attention to the fact that the result of this problem is approximated by "one step".
Question 3 is difficult for students to understand. Therefore, in practice, students should rotate the front of the drum into a cylinder, so that students can understand through demonstration that what the drum rotates once is a rectangle, and finding the length of the drum rotation is actually finding the lateral area of the drum. If students can't understand, they can use courseware to further strengthen their understanding of this life phenomenon.
Question 5 is actually an in-depth understanding of the surface area of a cylinder. The teacher should let the students understand the train of thought: first, how should I enclose the rectangle when I see it? Who made the circumference after enclosing the bottom? The perimeter of the second bottom surface is known, so how to calculate its bottom surface diameter? Therefore, according to the diameter of the bottom surface, the following bottom surface is selected accordingly.
Questions 8~ 10 are all about solving practical problems in life. In practice, it is suggested that Question 8 or Question 9 should be treated as a semi-example, and Question 10 should remind students of the change of their unit. Through practice, further consolidate
The calculation method of lateral area and surface area of cylinder can improve students' ability to solve practical problems. First, according to the characteristics of practical problems, let students know what fields they are seeking, and then solve specific problems flexibly to prevent them from being moved around mechanically.
Settings.
The question 12 is a thinking question. According to the actual situation of the class, students can finish it independently first, and then communicate and give feedback. Students can also experience it and then answer it. Through communication, students know that every time they cut, the surface area will increase the area of the two bottom surfaces. Wood is cut into four sections and needs to be cut three times, covering an area of 36 square meters.
Information window 3: Ice cream packaging box volume
1, teaching content: volume of cylinder and cone
2. Introduction to the information window: This picture shows cylindrical and conical ice cream boxes, with their bottom diameter and height marked respectively.
The setting of the example. There are two red dots here. The first red dot is the volume of the learning cylinder. The second red dot is the volume of the learning cone.
3, information window teaching suggestions:
1. Enlighten and induce students to recall the ideas and methods of solving mathematical problems in the past, find the calculation method of cylindrical volume through guessing and operation, and guide students to realize the transfer of methods.
How to find the volume of a cylinder is hard for students to imagine. At this time, the teacher can let the students recall the previous methods to solve mathematical problems and let them have the idea of transforming a cylinder. unite
I thought of the derivation of the formula of circle area, and the derivation method of circle area appeared in my mind, which transformed a circle into a cuboid. There are similarities between a cylinder and a circle. I thought it might be to transform a cylinder into a cuboid. With this guess, I will go.
Further verification.
Second, let students understand the volumes of cylinders and cones in operation.
When teaching the volume of cylinders, teachers can prepare some cylindrical objects, such as radishes, so that students can try in groups, and how to transform cylinders into cuboids, combined with students' exercises.
Teachers can also use multimedia or teaching AIDS to reproduce this process, so that students can see this transformation process more vividly and intuitively. Through this operation, students can further understand the transformed mathematical ideas, and should pay attention to guiding students to understand dragons.
The relationship between cube and cylinder, and then the volume formula of cylinder is deduced. Explain why the volume of cubic centimeters in textbooks should be converted into milliliters.
It is not difficult for students to understand the volume of a cone. Teachers should first guide students to guess according to the ideas provided in the textbook. What might the volume of a cone be related to? What does it matter? Second, let
Students design experiments to operate and draw conclusions through verification. Third, in the process of operation, let students experience one-third for themselves. In the process of application, the mistake that students easily make is to omit writing 1/3. In order to solve this difficulty,
In the teaching process, teachers should try their best to let students understand the relationship between a cone and a cylinder with equal bottom and height through experiments, so that students can experience this process personally and deepen their impressions. The experiment in the textbook is just an ordinary teaching experiment.
Other experiments can be designed during class hours. (You can add questions and ideas during the discussion)
4. Practical analysis
When the volumes of cylinder and cone are put together, students are sometimes easily confused, so they should strengthen basic exercises repeatedly.
In the exercise of 12, first let the students clearly knead the cylinder into a cone, and the volume will not change. After the volume of the cone and its base radius are obtained, the cone can be obtained by arithmetic formula or equation.
Height. Students can also find the height relationship between cylinder and cone by further observation. This allows students to further study the relationship between equal volume, equal height and base diameter.
13 is more difficult. Students must have a sense of space and know in their minds how my cylinder is folded, where the bottom circumference is made and where the height is made, in order to work out the correct result. If students can't imagine it, they must fold it with paper themselves to further clarify the bottom circumference and height of the cylinder. Strengthen the concept of space.
※ 14 is a difficult comprehensive topic. In practice, students should first make it clear that the volume of three figures can be calculated by "bottom area × height", because their heights are equal, so
Just compare the size of the bottom area Then further guide students to think: when the perimeter is equal, who has the largest area, a circle, a square or a rectangle? This question. Ask the students to assume that their perimeter is concrete.
Number (such as: 3 1.4), and then calculate the size of the comparison area; You can also provide students with a rope. Surround, measure and calculate, and you can find the answer: when the perimeters are equal, the area of the circle is the largest, which is a square.
A rectangle has the smallest area. The final answer is that the cylinder has the largest volume. (Calculator can be used for calculation)
The problem of "smart house" is to let students know the surface area. In the teaching process, teachers should make full use of learning tools to make students understand. In order to make students fully understand that the so-called surface area is the surface area, so we should
This is the surface area of a cuboid minus the areas of two bottom circles. Plus the cylindrical side area. It is difficult for students to understand, so they can further understand with the help of physical objects. At the same time, you can show other shapes for your classmates to come.
Talk about their surface area and volume.
The review is divided into two parts. The first part is to sort out the knowledge learned in this unit. Cylinders and cones are in the form of tables for students to review their characteristics and volume formulas. The second half is the method of sorting out the research problems.
The first type: autonomous retrospective arrangement.
Qingdao version of the textbook pays more attention to reviewing and sorting from middle and lower grades. In senior grades, students are fully capable of reviewing and sorting independently. Students can communicate independently or in groups, and review what they have learned in this unit during the communication.
Second, when reviewing and sorting out, teachers can focus on the process and methods of studying problems.
Students are not familiar with the comprehensive exercise of question 3 because they don't know much about rain gauges. So first of all, students should combine pictures to understand the structure of rain gauge and the problems to be solved.
Students understand the first question. How many square centimeters of material does it take to make a rain gauge shell? This is the surface area of the rain gauge (only one bottom surface). The second question is how much rain did a * * collect in the water storage bottle? this is
Find the volume of a cylinder. Let the students do their own calculations after figuring this out.
In the sixth question in the comprehensive exercise, the teacher should let the students understand that the bottom area of the largest cylinder and cone is the inscribed circle of the bottom area of the cube. Height is the side length of a cube.
Students will also find it difficult to practice question 8 comprehensively. Guide the students to practice according to the following steps: first, let the students know that the extruded toothpaste is a small cylinder, the bottom area of this cylinder is the area of the nozzle, and the height is the length of extrusion. Second, let students pay attention to the unity of units when calculating.
Did I learn? Attention should be paid to guiding students to learn to analyze and understand pictures, especially the second question, which contains more information. Before completing this problem, the teacher should let the students understand the pictures and exchange the information they found.
Comprehensive application
This can be achieved from the following aspects:
First of all, let students investigate before class to understand how water turns into ice and how its volume changes, and collect some natural phenomena by themselves.
Second, according to the students' communication, discuss the methods and steps of the experiment and prepare the experimental materials.
Third, experiment. Pay attention to the following points when doing experiments. First, the shape of ice cubes should be regular, otherwise it is difficult to measure the volume. It may be difficult to find ice in this season.
Try using ordinary ice cubes or ice cream instead of ice. Second, you can experiment in groups and consider whether the team members have the conditions to experiment. Teachers should try their best to help students overcome difficulties and complete experiments. )
Fourthly, by calculating and exchanging experimental results, students' comprehensive learning and research ability can be improved. When calculating, pay attention to the calculation method of how much you have learned and how much you have lost. This may be the difficulty of students' calculation)