Mathematics teaching plan for the sixth grade of Beijing Normal University 1

Teaching objectives:

1. Explore the length-width relationship of a rectangle by drawing, and further understand the meaning of inverse proportion.

2. Experience the exploration activities and understand the characteristics of the inverse proportion curve.

Teaching focus:

Explore the relationship between length and width when the rectangular area is constant.

Teaching difficulties:

Find the feature that represents the inverse ratio curve.

Teaching process:

First, old knowledge paves the way.

1, what is the significance of the proportional relationship? How to express this relationship in letters? What about the scale image?

2. Do you remember the diagram of the relationship between two multipliers when the product is constant? Circle the square with the product of 12. What line can you connect?

3. Tell me about it.

(1) The change of two multipliers.

(2) What is the relationship between the two multipliers?

What is your guess?

Second, explore new knowledge.

X and Y represent the lengths of two adjacent sides of a rectangle with an area of 24 square centimeters, and their changing relationships are shown in the following table.

x/cm 1 2 3 4 6 8 12 24

y/cm 24 12 8 6 4 3 2 1

1, talk about the change of length and width. (Group communication)

2. Which quantity is definite here?

3. What is the relationship between the length and width of a rectangle when the area is fixed? (group discussion)

Blackboard writing: length× width = rectangular area (certain)

4. According to the above data, draw 8 rectangles on the grid paper. (Each unit represents 1 cm2)

Process requirements

(1) Show the grid paper and mark the numbers on the X and Y axes.

(2) The teacher explains and draws a rectangle.

(3) Students continue to draw. (Complete directly in the textbook)

5. Connection points A, B, C and D ...

(1) Guess: The points are A, B, C, D ... in a straight line?

(2) Teachers and students are linked together to verify their guesses.

Third, the class summary

Let's talk about the difference between an image representing a direct proportional relationship and an image representing an inverse proportional relationship.

Fourth, consolidate practice.

The total amount of bread remains the same. The number of each bag and the number of bags are as follows.

Number of bags 2 3 4 6 8 12 24

Number of bags 12 8 6 4 3 2 1

(1) What is the relationship between the number of bags per bag and the number of bags? Explain why.

(2) Chart the above data.

Beijing normal university sixth grade mathematics teaching plan ii

first kind

Teaching goal: to make students know the characteristics of the cylinder and the development diagram of the side of the cylinder.

Teaching preparation: teachers and students each bring a cylinder, and teachers give students a paper tube in groups of four. Every student is ready to make cylindrical materials.

Teaching emphasis: let students understand the characteristics of cylinders.

Difficulties in teaching: understanding that the lateral expansion of a cylinder is a rectangle, and understanding the relationship between the length, width and cylinder.

Teaching process:

First, review.

We know cuboids and cubes.

Who can talk about the characteristics of cuboids? A cuboid is surrounded by six rectangles, two opposite rectangles are exactly the same, and the height of a cuboid is countless. What about the cube?

Who can tell us what we have learned about cuboids and cubes?

Second, new funding.

Teacher: Today, the teacher will learn a new three-dimensional figure with you: cylinder, or cylinder for short.

1, initial impression

Teacher: Students, please look with your eyes and touch with your hands. Tell me the difference between a cylinder and a cuboid.

A cylinder is surrounded by two circles and 1 face. )

2. Group study: What are the characteristics of these faces of a cylinder? What's the connection between noodles and noodles?

3. Communication and reporting

(1) With regard to two circles, it is concluded that the upper and lower circles are completely equal circles, both of which are the bottom surfaces of cylinders. (2) As for the curved surface, it is concluded that it is the side of the cylinder. If you expand along the height, you can get a rectangle or a square, and if you expand along the diagonal, you can get a parallelogram. The length of the unfolded rectangle is equivalent to the circumference of the bottom of the cylinder, and the width of the rectangle is equivalent to the height of the cylinder.

(3) About the height of the cylinder: The distance between the two bottom surfaces is called the height of the cylinder. There are countless heights. Height can sometimes be replaced by length, thickness and depth.

4. Give examples to further clarify the characteristics.

Teacher: Now everyone has a better understanding of cylinders. What objects are cylinders in life?

(Students give examples, and then let the students judge for themselves. When the students say that chalk is a cylinder, the teacher can let the students discuss it. )

Step 5 judge by knowledge

Which of the following figures is a cylinder? Which ones are not? Explain why.

6, making a cylinder

Third, practice.

1, judged by knowledge.

Which of the following figures is a cylinder? Which ones are not? Explain why.

Beijing normal university sixth grade mathematics teaching plan 3

? course content

Unit 3, page 34 of the sixth grade experimental textbook published by Beijing Normal University, the curriculum standard of compulsory education "graphic transformation".

? Teaching objectives

1. Through observation, operation and imagination, we can make complex graphics by translation or rotation, thus experiencing the transformation of a simple graphic and developing the concept of space.

2. With the help of calculation and analysis on grid paper, the transformation process of graphic translation or rotation is expressed in an orderly way.

3. Use jigsaw puzzles to transform various figures on square paper to further improve students' imagination.

? Emphasis and difficulty in teaching

Through observation and operation activities, the transformation process of graphic translation or rotation is described.

? Prepare teaching AIDS and learning tools

Triangular ruler, ruler, crayons, compasses, one piece of square paper for each person, four isosceles right-angled triangles (hard paper) with the same size, and a set of puzzles, which can be modified individually.

Difficulties:

1 lies in students' understanding of axial symmetry. Axisymmetry is a method of graphic transformation.

2. Students' mastery of rotation.

? Teaching design

Teaching and learning process

First, create a situation

Teacher: In the previous study, we had a preliminary understanding of translation and rotation. Let the students draw a triangle on the grid paper and say what translation and rotation are. Students communicate on their own square paper, and then ask some students to show them.

Teacher: Students, when we analyze the transformation of a figure, we should not only talk about how it translates or rotates, but also how it translates or rotates, so that we can clearly know its transformation process.

Teacher: Students communicate well. Let two students at the same table cooperate with each other, design a figure by themselves with two triangles, then transform it and talk about its transformation process. (Students design and operate by themselves, and teachers patrol and guide)

Teacher: The students did a good job. Let's invite some students to come up and demonstrate the graphics they designed and talk about how it changes the graphics. If it is a rotating pattern, what figure should be said to rotate around which point every time it rotates?

Second, try to practice:

Teacher: Next, please observe the picture below, think while observing, and take out the square paper and triangles prepared before class, and mark the four triangles with A, B, C and D respectively. Put them on yourself, move them, turn them, and change the graphics. Then, according to the following four questions raised by the teacher, communicate with your deskmate.

(1) How to transform the four triangles A, B, C and D to get the "windmill" figure?

(2) How can the four triangles in the "windmill" figure be transformed into rectangles?

(3) How do four triangles in a rectangle turn into squares?

(4) How do the four triangles in the square transform back to the original figure?

Students operate by themselves, exchange the method of graphic transformation at the same table, and the teacher visits and guides.

Teacher: The students did it very seriously just now. Now let's talk together and let the students say their different methods. As long as the method is correct, the teacher should give affirmation.

Third, expand the practice.

Teacher: Students, what have we learned in this class? (graphic conversion). What school tools did you use to set the numbers just now? (triangle). Just now, the students only used two or four triangles to determine the graphics, and the transformed graphics were few and simple. Do you want to transform more and more beautiful graphics? (thinking). Next, please observe the graphics transformed by the teacher first. (Teacher shows pictures)

Teacher: Let the students start swinging, and then talk about how the puzzle on the left translates or rotates to get the picture on the right.

Students operate and answer the transformation process.

Teacher: Please take out your favorite jigsaw puzzle, work in groups of four, put it on a square piece of paper, and then change it to see which group of students changes the most beautiful figure. Remember, whoever changes a graphic, talk to the students in the group about how you changed the graphic.

Students are in groups of four. They use puzzles to change the shapes on the square paper. The teacher will patrol and guide them.

Teacher: Class is over. Many students haven't had time to transform their own graphics. It doesn't matter. After returning, we can continue to show, change and communicate with our classmates.

Fourth, the class summary:

1. Students, you learn from each other and cooperate with each other in this class. Tell us what you learned in this class. How do you feel?

2. Teachers inspire students and arouse hope.

For each step of graphic transformation, let students talk about how to translate or rotate, which can further consolidate the concept of translation or rotation and facilitate students to form a correct thinking method.

This activity is mainly for students to operate and experience the process of graphic transformation through their operations. In the change of graphics, graphics have also been transformed, but different thinking angles often lead to different operation processes. So whether it is changed to (1) or (2), or changed to (3) or (4), there are various operation methods. Therefore, when organizing students to carry out activities, students can try first and then communicate.

Graphic transformation is a comprehensive exercise of translation and rotation knowledge, and it is also an important basis for students to design graphics in the future. Through a large number of students' operation activities, it is of great help to improve students' spatial imagination.

There are many transformations in the jigsaw puzzle, only one of which is shown in the picture. When carrying out this activity, you can choose some figures in the puzzle to transform according to the actual situation of students. When students are more skilled, they can operate some complicated graphic transformations. )

Summarize the requirements of rotation:

direction

The degree of rotation around a point.

Beijing normal university sixth grade mathematics teaching plan 4

Teaching content:

Beijing normal university printing plate elementary school mathematics volume 11 unit 5 p58 "double bar graph"

Teaching objectives:

1. Understand the characteristics of the composite bar chart, understand the similarities and differences between the simple chart and the composite chart, and be able to use the composite bar chart to represent the corresponding data on the vertical and horizontal axis charts.

2. Enable students to understand the composite bar chart and make simple analysis, judgment and prediction according to the relevant data in the composite bar chart.

Teaching focus:

Knowing the characteristics of the composite bar graph, we can get as much information as possible from the composite bar graph.

Teaching aid preparation:

Cai courseware

Learning aid preparation:

Draw a picture.

Teaching process:

First, stimulate interest, introduce new ideas, explore enlightenment

1. Introduction: Here are two clips that I want to show to my classmates. Play videos about Liu Xiang and Yao Ming. Q: What do you see? How much do you know about Liu Xiang and Yao Ming? (Students narrate and teachers summarize. )

2. Tell everyone a good news. In a few days, our school's annual "Autumn Sports Meeting" will be held. This sports meeting is different from the past! In order to improve the popularity of our school's "Autumn Sports Meeting", our school wants to use one of them as the image ambassador of this sports meeting. Who do you prefer to represent our school as the image ambassador of this sports meeting? Students express their opinions and produce opinions. )

It seems that all students have their own ideas, so what methods are used to decide who to recommend? (Hands up, statistics) Yes! We can collect and sort out everyone's ideas on the spot. So what's the situation in our class? (Raise your hand) Please raise your hand if you support Liu Xiang; Those who support Yao Ming, please raise your hand. (Know the statistics on the spot and be aware of them. )

Just now, it was just the collection and arrangement of our class, and it can't represent the opinions of the whole grade students. So the teacher collected and sorted out the statistical data of the other six classes in grade six before class. (Show the statistics of Liu Xiang and Yao Ming recommended by each class in Grade 6), and fill in the data just collected from our class. Question: Can you compare the results in the table? Yes, but it is more difficult. )

5. In order to reflect your opinion more clearly, do you think it would be better for us to show these data? (Histogram) The teacher also thinks that the histogram is very good, because it can express the statistical data of each class intuitively. But how to use histogram to represent the above two sets of data? (Students express their opinions)

6. Show the composite bar chart made according to the class statistics. What can you see from the chart? (Title, date, unit, horizontal axis and vertical axis, different bar charts, legends and unit sizes indicated by vertical axis, etc. ), why choose two colors of bars? How is this different from the bar chart we have learned before? We call this kind of bar graph "composite bar graph".

7. Can we continue to draw our statistical chart according to the statistical data of other classes? (Students supplement the complete statistical map)

8. Comments: Look for three types:

(1) Bar chart with few numbers;

(2) The drawn straight line is not standardized;

(3) more correct and beautiful. Let the students comment.

9. Look at the picture. Which class likes Liu Xiang and Yao Ming, and there is a big difference? Which class likes Liu Xiang and Yao Ming, the difference is relatively small? What information can you get from the picture? According to the survey of grade six, who do you think is more likely to be the image ambassador of our sports meeting?

Second, cooperation and interaction, * * * and exploration

Our sports meeting will be held soon. Do you want to be a sports star in our school like Liu Xiang and Yao Ming? So what sports do you usually do? (Student narrator) I didn't expect students to love sports so much. The teacher is very happy that everyone can take an active part in exercise!

2. Look at the picture and analyze it

In ball games, when serving from the sideline, there are both one-handed and two-handed pitches. According to your experience, do you think one-handed or two-handed pitching is far? (Students express their opinions)

Show the statistics and composite bar chart on page 58 of the textbook and evaluate the pitching distance of the two pitching methods. Which is more convenient to compare?

How many meters does the vertical axis in each grid represent? Why does the bottom grid use polylines? Guide students to communicate with each other after careful observation and thinking.

Each unit of the vertical axis represents 0.5 meters, and the bottom unit is omitted with dotted lines. )

What information do you get from the composite bar chart above? (Students draw a reasonable conclusion according to the statistical chart)

Review and summarize, show personality

1. What did we learn in this class today? What are your thoughts and experiences?

In order to carry out this sports meeting better, there are a lot of data about sports activities that need to be collected and sorted out. We only counted some sports activities just now. Please collect and sort out the relevant data after class and during the sports meeting, draw and design a statistical chart to see who designed it beautifully and correctly. Create a problem situation that is convenient for statistics, stimulate students' interest in learning, let students go through the process of collecting data, sorting out data and analyzing data, and gradually form statistical concepts.

In the process of describing data with statistical chart, guide students to discuss what statistical chart is suitable to describe this group of data, and then think about whether one bar statistical chart can represent two groups of data, and realize the necessity of compound bar statistical chart. This expands students' thinking and ability to solve practical problems by comprehensively applying what they have learned.

Encourage students to get as much information as possible from statistical charts and realize that data contains information. At the same time, develop a rigorous and serious study habit and make clear every detail in the statistical chart.

Comprehensively apply what you have learned to solve practical problems.

Give appropriate guidance to the teachers of statistical projects.

Teaching reflection:

By creating a relaxed and lively learning atmosphere, students' interest in participating in statistical activities is stimulated. Through the process of sorting out and describing the data, and in mutual evaluation and communication, we constantly improve and perfect our respective statistical charts, and gradually clarify the characteristics of composite bar statistical charts, so as to guide students to find problems from statistical charts, express their ideas, verify their guesses and experience the role of data.

Beijing normal university sixth grade mathematics teaching plan 5

Teaching content:

The textbook is 8788 pages.

Teaching objectives:

1, knowledge and skills: explore the hidden laws or changing trends in a given thing.

2. Mathematical thinking and problem solving: Understand the basic process and methods of problem solving and improve the ability of problem solving.

3. Emotional attitude: explore the laws between numbers and figures.

Teaching focus:

A way to explore the law

Teaching difficulties:

How the law is alphabetized is how to express the law with alphabet formula.

Teaching aid preparation:

A long piece of paper and a rope.

Teaching rules:

Autonomous learning, group cooperation, explanation and discussion.

Teaching process:

First, scenario creation, import review

Teacher: What mathematical laws exist in our life?

Second, review and organize, and build a network.

1, show me the multiplication table.

Teacher: There are many rules in our multiplication table, too. Please fill in this multiplication table first.

Can you fill it out? The teacher instructed how to fill it out. The students wrote it on page 66 of the book.

Observe carefully after filling in the form and see what interesting rules you can find. Talk to your classmates about the speech.

2, find the law, fill in.

Teacher: Let's compare who has done the most in two minutes.

( 1) 2,4,6,8, _____, 12, 14,

(2) 1,3,5,7, _____, 1 1,

(3) 8, 1 1, 14, 17,_____,23,26,

(4) 1,8,27,64, _____,2 16,

(5) 1,4,9, 16,25, _____,49,

(6) 3,6,9, 12,_____, 18,2 1,

(7) 1,3,6, 10, 15,_____,28,

(8) 6, 1, 8, 3, 10, 5, 12, 7, ( ) , ( ),

Students should explain the reasons and basis when answering questions.

Teacher: What's the number? Why?

Teacher: What do you think are the general rules for a series like this?

Third, pay attention to review and strengthen improvement.

Show the mathematical rules in life and share them with your classmates (courseware)

Teacher: If it were not a series but a graph, would you still observe their arrangement?

On Children's Day, students in Class/kloc-0 and Class 6 (2) hang balloons in the classroom according to the following rules.

What color is the 20th balloon? Where is 48th Street?

Beijing normal university sixth grade mathematics teaching plan 6

Teaching content:

Pages 4-5 of the textbook: Examples 2 and 3 and Exercise and Exercise 1.

Teaching requirements:

1. Make students understand and master the calculation method of cylinder surface area, calculate correctly according to the actual situation, and cultivate students' ability to solve simple practical problems. Let the students know the step-by-step method of approximation.

2. Further cultivate students' thinking ability of observation, analysis and reasoning, and develop students' spatial concept.

Prepare teaching AIDS and learning tools:

The teacher prepares a cylindrical model (with a layer of paper on the surface that can remove all parts); Students prepare a cylinder.

Teaching focus:

Master the calculation method of cylindrical side area.

Teaching difficulties:

Can calculate correctly according to the actual situation.

Teaching process:

First, pave the way for pregnancy:

1. Review the characteristics of the cylinder. Question: What are the characteristics of a cylinder?

2. Calculate the transverse area of the following cylinders (orally):

(1) The circumference of the bottom surface is 4.2 cm and the height is 2 cm.

(2) The bottom surface is 3 cm in diameter and 4 cm in height.

(3) The radius of the bottom surface is 1 cm and the height is 3.5 cm. ..

3. Q: How to calculate the area of the bottom of a cylinder?

4. Introduce new courses.

We have calculated the lateral area of the cylinder, so how do we calculate the surface area of the cylinder? In this lesson, we will learn the calculation of cylinder surface area (blackboard writing topic)

Second, independent research:

1. Calculation method of cognitive surface area.

(1) Please take out the cylinder and have a look. Think about what parts the surface of a cylinder includes, and then tell everyone. Name the students and take out the cylinder. Point out and explain which parts of its surface include.

(2) Teacher demonstration.

Show me the teaching aid, explain that the surface is completely unfolded, see what graphics you can get, and tell everyone if it is right. Take the paper off the surface of the cylinder and stick it on the blackboard. Then compare it with the cylinder and explain each part. Obviously, the surface of a cylinder includes a side and two equal circles.

(3) Get the formula.

Please look at the figure on the surface and say, how should the surface area of a cylinder be calculated? (blackboard writing: the surface area of a cylinder: lateral area+two bottom areas) Ask: How to calculate the lateral area of a cylinder? How to calculate the bottom area of a cylinder?

2. Teaching example 2.

Example 2, students' reading problems. Question: How many steps does this question take? Can you do it? Name one person who is performing on the blackboard, and the rest of the students are performing in the exercise books. Ask the students to talk about the specific meaning of each step and how to calculate it.

3. Organize exercises.

Do some exercises. Name two people performing on the blackboard and the rest of the students performing in the exercise books. Collective correction, talk about the difference between these two problems, why? Points out the conditions that should be paid attention to in calculating the surface area of cylinder, and lists the formulas correctly.

4. Teaching example 3.

Example 3, students' reading problems. Question: What exactly is this question about? What is the difference between the surface area calculated here and Example 2? Why? (Only use lateral area plus a bottom area) Name the students and perform on the blackboard. The rest of the students do it in their exercise books. Collective revision, ask why only one bottom area is added.

5. Organize exercises.

(1) Page 7, Question 4 (2). Group discussion first, then written practice, and then collective revision.

Beijing normal university sixth grade mathematics teaching plan 7

Teaching objectives:

1, can master translation, rotation and axial symmetry for pattern design.

2. Be able to flexibly use various methods to design patterns.

3. Appreciate all kinds of beautiful patterns and feel the magic of the graphic world.

Teaching emphases and difficulties:

1 can systematically express the process of translation, rotation and axisymmetric graphics of a simple graphic.

2, can flexibly use translation, rotation and axial symmetry to design patterns on grid paper.

Teaching aid preparation:

Multimedia courseware.

Teaching process:

First of all, exciting introduction:

1, enjoy the beautiful patterns in life.

2. What do you want to say when you see these beautiful patterns in your life?

3. Reveal the theme: pattern design

Second, explore new knowledge.

The courseware shows the petal pattern in the textbook.

1. Question: How does this petal pattern pass through Figure A?

2. Group discussion and cooperation.

3, the group report, show their own methods and results. (which basic map has transformed the petal pattern? )

4. Encourage innovation.

Do you have any other methods?

5. Summary:

This beautiful petal pattern was originally obtained by translation, rotation and axisymmetric transformation of the basic figure A.

6. Question: How did Xiao Xiao change the number 1 into the number 2? Do you know how she did it?

Third, hands-on experiments.

1, exercises 1 and 2.

2. Grouping design mode.

(1) Exhibition of Works.

(2) Student evaluation.

Fourth, the class summary: What new gains have you made through this class?

Beijing normal university sixth grade mathematics teaching plan 8

First, teaching materials:

The textbook introduces the yield of common rice and hybrid rice in an experimental field, leads to the practical problem of "increasing yield by a few percent" through the boy's "what does it mean to increase yield by a few percent", and guides students to analyze the quantitative relationship and re-recognize the meaning of percentage. The calculation in the textbook provides two different solutions. This arrangement will broaden students' thinking and develop their flexibility of thinking.

Teachers can guide students to draw line segments to understand. After students have made clear the meaning of "increasing production by a few percent", they can ask them to answer independently. It should be noted that students should be encouraged to solve problems according to the quantitative relationship in practical problems and the significance of increasing production by several percent, rather than relying on rote memorization and application methods.

Second, student analysis

Before learning this content, students have learned the definition of percentage, reading and writing, percentage and fraction, reciprocity of decimals, simple application of percentage, and solving simple percentage problems with equations. On this basis, the application of percentage is further studied. Teaching objectives:

1. Understand the meaning of "increase by a few percent" or "decrease by a few percent" under specific circumstances, and deepen the understanding of the meaning of percentage.

2, can solve the practical problems about "increase by a few percent" or "decrease by a few percent", improve the ability to solve practical problems by using mathematics, and realize the close relationship between percentage and real life. teaching process

First, import

Line graph is one of the important methods to grasp the quantitative relationship. Can you express the following quantitative relationship with a line graph?

In the second classroom activities carried out by the school, 32 people took part in the Go class, and the number of people who took part in the model airplane class was 25% more than that who took part in the Go class.

Students finish line drawing independently.

Show students' grades

3. The teacher evaluates the students' works.

Guide students to analyze the quantitative relationship and re-understand the meaning of percentage. Guide students to analyze the quantitative relationship from review.

Second, the application of percentage

1. Show the problems in the textbook p23.

2. Thinking: What do you mean by "increasing production by a few percent"? Students are free to express their views, and teachers will evaluate them.

The yield of hybrid rice is several percentage points higher than that of common rice.

Students answer their own questions, introduce the yield of common rice and hybrid rice in an experimental field, and lead to the practical problem of "how much increase in yield"

3. Intra-class communication

Method 1:

7-5.6 = 1.4 (ton) 1.4 ÷ 5.6 = 0.25= 25%

Method 2:

7 ÷ 5.6 = 1.25= 125%

125%- 100% = 25% Guide students to answer in two different ways, broaden students' thinking and develop their thinking flexibility.

Third, give it a try.

1. Show the questions below the textbook p23.

2. What do you mean by "what percentage"?

The percentage is mainly used for agricultural harvest, and a few percent is a few tenths.

The grade is110, that is, 10%, and 25% is 2.5%, that is, 25% focuses on understanding the meaning of "what percentage". Let students communicate independently and develop their thinking.

3. Students solve problems independently (2.61-2.25) ÷ 2.25 = 0.36 ÷ 2.25 = 0.16 =16%.

Fourth, practice.

1, textbook p24, exercise 1.

2. Practice the second question in the textbook p24

3. Practice the third question in the textbook p24.

Verb (abbreviation of verb) course summary

What did you gain from today's study?

Teaching reflection: after the whole class is finished, it can be said that it is deeply touched. This lesson is the concrete application of percentage. Further improve students' ability to use percentages to solve problems. Throughout the whole class, because the materials collected by students in the pre-class investigation are fully prepared, students are interested in the introduction and have a good atmosphere.