The teaching content of the first volume of mathematics teaching plan (1) in the sixth grade of primary school by Education for All Press:
Do the exercises on page xx of the textbook.
Teaching objectives:
1, master the basic properties of the ratio, and simplify the ratio according to the basic properties of the ratio.
2. The invariable nature of the connection quotient and the basic nature of the fraction are transferred to the basic nature of the ratio.
Teaching focus:
Basic properties of comprehension rate.
Teaching difficulties:
The basic properties of ratio can be applied to simplify the ratio.
Teaching process:
First, exciting calibration.
1、20÷5=(20× 10)÷( × )=( )
2. think about it: what is the constant law of business? What are the basic properties of fractions?
3. We studied the invariable law of quotient, the basic properties of fraction, and the relationship between connection ratio and division and fraction. Think about it: what kind of laws are there in the proportion? We will study this problem in this class.
Second, self-study interaction, timely inspiration
Basic properties of activity ratio
Learning style: teamwork, reporting and communication.
Learning tasks.
1, inspired and induced, found the problem: 6: 8 and 12: 16 are different, but their ratio is the same. What is the law? .
6:8=6÷8=6/8=3/4 12: 16= 12÷ 16= 12/ 16=3/4
2. Observe and compare, and find the law.
(1) Use the relationship between ratio and division to study the law of ratio. (Law of Constant Quotient)
(2) Using the relationship between ratio and score to study the law of ratio.
3. Summarize the law of induction.
(1) Summary: The first term and the last term of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged, which is called the basic property of the ratio.
(2) Question: Why should the "same number" here emphasize the exception of 0?
Activity-based simplified ratio
Learning style: try to train, report and communicate.
Learning tasks.
1, know the simplest integer ratio.
(1) Question: Who knows what kind of ratio can be called the simplest integer ratio?
(2) Induction: The simplest integer ratio must meet two conditions. One is that the front and rear terms of the ratio are integers, and the other is that the common factor of the front and rear terms of the ratio is only 1.
(3) Point out several simplest integer ratios.
2. Use nature and master the method of simplification.
(1) Write down the aspect ratio of two United Nations flags.
(2) Thinking: Are these two ratios the simplest integer ratio? Why? (There are other common factors besides 1 before and after the term. )
(3) try to simplify.
(4) Reporting communication: Just divide the front and back terms of the ratio by their common factors.
(5) think about it: these two are the same after simplification. What does this mean? The two flags are different in size and the same in shape.
(6) Show examples and organize exchanges.
① Least common multiple of denominator:1/6: 2/9 = (1/6×18): (2/9×18) = 3: 4.
(2) First, the front and back terms are converted into integers, and then simplified as: 0.75: 2 = (0.75×100): (2×100) = 75: 200 = 3: 8.
③ Calculated by fractional division:1/6÷ 2/9 =1/6× 2/9 = 3/4.
(7) Abstract: If both the front and rear terms of a ratio are fractions, then multiply the front and rear terms by the least common multiple of the denominator at the same time; If the front and back terms of a ratio are decimals, praise them first, and then simplify them.
Third, the standard evaluation
1. Complete the "do" on page xx of the textbook and make collective revision.
2. Complete the exercises X, X, X on page xx of the textbook.
Fourth, class summary.
What did we learn in this class? What did you get?
The first volume of mathematics teaching plan for the sixth grade of primary school by Education for All Press (2) Teaching content:
Related contents and exercises on pages xx and xx of the textbook.
Teaching objectives:
Knowledge and skills:
1. Understand the application of positioning in life and the methods of positioning by solving problems.
2. Learn to describe the specific position of the object on the plan by measurement, and draw the specific position of the object on the plan according to the description.
Emotions, attitudes and values:
1. I realize that mathematics knowledge is closely related to real life, and I feel that there is mathematics everywhere in my life.
2. Cultivate students' ability of cooperation and communication, as well as their interest and self-confidence in learning mathematics.
Process and method: master the drawing method through group discussion.
Teaching emphases and difficulties:
Important: The position of an object can be determined according to any direction and distance.
Difficulty: Mark the specific position of the object on the plan according to the description.
Teaching methods:
Cooperation, communication and discussion.
Prepare teaching and learning tools:
Teacher: multimedia courseware, ruler, protractor, etc.
Student: Ruler and protractor.
Teaching process:
First, scene import
1. Exchange the news about typhoon in Example X.
Have the students ever heard of a typhoon? What's your impression of typhoons?
(2) Broadcast typhoon news: At present, the typhoon center is located on the ocean surface 30 southeast of City A, 600 kilometers away from City A, and is moving straight to City A at a speed of 20 kilometers per hour.
Teacher: How do you feel when you hear the news?
Inspire students to communicate and guide them to pay attention to the location and dynamics of typhoons.
2. Introduce new courses.
Where is the exact location of the typhoon now? In today's class, we will learn the knowledge of determining the position of an object.
[Blackboard Title: Position and Direction (1)]
The design intention is to guide students to pay attention to the mathematical knowledge of determining the location by exchanging information about typhoons, so as to stimulate students' interest in learning and pave the way for the development of teaching.
Second, explore new knowledge.
(1) Teaching examples 1
1. Projection display example 1.
Students observe the situation map and exchange information from it?
Inspire students to pay attention to the following information when observing: where are the four directions of east, west, north and south; Where is the observation point; Where are the individual locations of the typhoon center in the picture? )
2. Communicate the method of determining the specific location of typhoon center.
Ask the students to try to tell the specific location of the typhoon center.
⑵ Teachers should give guidance according to students' reports.
Question: What does 30 southeast mean?
(East-South 30 indicates the direction of the typhoon center position relative to City A, that is, the angle between the connecting line between the typhoon center position and City A and the due east direction is 30, that is, the due east yearns for South 30. )
⑶ Summarize the method of determining the position.
Question: If there is only one condition, can you determine the specific location of the typhoon center?
Guide the students to draw a conclusion: to determine the specific location of the typhoon center, we must know two conditions, that is, the direction of the object and the distance between the object and the observation point in this direction. Simply put, it is necessary to use the method of "direction+distance" to determine the specific position of the object.
3. Organize calculation.
Teacher: Now that we know the specific location of the typhoon center, how many hours will it take for the typhoon to reach City A?
Students calculate independently and organize communication.
600 ÷ 20 = 30 (hours)
(B) Teaching Example 2
1. Projection demonstration example 2.
Question: In the diagram of example 1, where should the specific locations of City B and City C be marked? Please mark the specific locations of city B and city C in the diagram of example 1.
2. Try drawing.
(1) Students think independently about how to mark the specific locations of cities B and C.
⑵ Group communication drawing method.
(3) Try to draw.
Teachers patrol and exchange, participate in some group discussions, and coach students with difficulties.
3. Organize class exchanges.
Projection shows students' finished works.
Organize exchanges and comments to learn how B and C mark their positions on the map.
City B: First determine the direction, and measure 30 northwest of City A with a protractor (the center point of protractor coincides with City A, and the 0 scale line of protractor coincides with the true north direction, measuring 30 west); Let's express the distance again. 1cm is 100km. City B is 200km away from City A, which is 2cm on the map.
City C: First determine the direction, directly find the north direction of City A on the map, and then indicate the distance. 1cm means 100km. City C is 300km away from City A, which is 3cm on the map.
4. Do the math.
After the typhoon arrived in city A, its moving speed became 40 km/h, and it arrived in city B several hours later.
200 ÷ 40 = 5 (hours)
5. Summarize the basic steps of drawing.
Communication: What do you think should be paid attention to when determining the position of an object on a map? How can we be sure?
Summary:
(1) Determine the east, west, south and north directions in the plan.
(2) Determine the observation point.
(3) Determine the direction of the painted object according to the given degree.
(4) According to the scale, determine the distance between the painted object and the observation point.
In the process of design intention teaching, we should pay attention to the cultivation of students' observation ability, give students enough time and space to explore and experience the method of determining the position on the map, and let students feel the value and charm that mathematics comes from life, is higher than life and is used in life.
Third, consolidate the practice.
1. "Do" on page 20 of the textbook.
The specific direction and distance of the object are not given directly in this question, so students need to measure and calculate it themselves.
(1) Let students measure, calculate and fill in the blanks independently.
(2) Organize communication.
Let the students talk about how to measure the direction and how to calculate the distance.
2. The textbook page 2 1 "Do it".
(1) Students draw independently.
2. Projection display, organization review.
(3) Exchange drawing methods.
Fourth, class summary.
In today's lesson, we know that to determine the position of an object, a key needs two conditions: direction and distance. The method of indicating the position of an object on the plan is to determine the direction first, then determine the distance according to the selected unit length, and finally draw the specific position of the object and mark the name.
The first volume of mathematics teaching plan for the sixth grade of primary school by Education for All Press (3) Teaching objectives:
1, understand the meaning of ratio, learn the reading and writing methods of ratio, master the names of each part of ratio and the methods of finding ratio.
2. Make clear the relationship between ratio and division and fraction, make clear that the latter term of ratio cannot be 0, and understand that things are interrelated.
3. Stimulate the sense of cooperation, cultivate the ability of comparison, analysis, abstraction, generalization and autonomous learning, and cultivate patriotic feelings through active discovery and discussion.
Teaching focus:
The significance of comparison.
Teaching preparation:
Multimedia courseware, three pieces of red chalk and five pieces of white chalk.
Teaching process:
First, create a situation and understand its meaning.
1, Teacher: Students, we just finished the National Day. Do you know how big the motherland was on June 10 this year? Xx years ago, on June 65438+1 October1,the five-star red flag was first raised in Tiananmen Square in Ran Ran, which made people all over China proud. But do you know that there are many interesting math problems hidden in our national flag?
Show me a national flag:
2. Judgment: Xiao Qiang's height 1 m, his father's height 173 cm, and the ratio of Xiao Qiang to his father's height is 1: 173.
Clear: the name of the same quantity is the same as the name of the unit.
Second, the whole class summarizes and unfolds.
1, last year's Olympic Games, the China women's volleyball team beat the United States 3-0 in the first game, playing the role of China women's volleyball team. What does 3: 0 mean here? Is it the same as what we learned today? Why?
Emphasis: 3∶0 here refers to how many games each team won, not the division relationship. The ratio learned today refers to the division relationship between two numbers.
2. What did you gain from today's study?
3. Do you know? In the 4th century AD, the Greek mathematician eudoxus used line segments to find the most beautiful geometric proportion in the world-the golden section. The ratio is about 0.6 18, and the ratio is about 2∶3.
Introduction: The golden section is widely used. The aspect ratio of the national flag is 2 to 3, which is close to the golden section. Now you know why the five-star red flag looks so good!
There are many places in life where the golden section is used:
Choosing a model on the runway also requires that the ratio of the length of the model to the length of the leg conforms to the golden section.
Barbers also apply the golden section to hairstyle design.
……
Students can also investigate after class.
The first volume of mathematics teaching plan for the sixth grade of primary school by Education for All Press (4) Teaching objectives:
1. In specific cases, explore the method of determining the position, and several pairs can be used to represent the position of the object.
2. Ask the students to determine the position on the square paper in pairs.
Teaching focus:
The position of an object can be represented by several pairs.
Teaching difficulties:
The position of an object can be represented by several pairs, which can correctly distinguish the order of columns and rows.
First, import
1. There are xx students in our class, but most students and teachers don't know each other. If I want to invite one of you to speak, can you help me think about how to express it simply and accurately?
2. Students express their opinions and discuss how to use the method of "which column and which row".
Second, new funding.
1, teaching example 1
(1) If the teacher uses the second column and the third row to indicate the position of XX, can he also indicate the position of other students in this way?
(2) Students practice showing other students' positions in this way. (pay attention to the column first and then the emphasis of the lines)
(3) Teaching writing: the position of XX is in the second column and the third line, which we can express as: (2, 3).
Can you write down your position according to this method? (Students write down their positions in their exercise books and name their answers)
2. Summary example 1:
(1) How much data did you use to locate a classmate? (2)
(2) We are used to saying columns before rows, so the first data represents columns and the second data represents rows.
If the order of these two data is different, then the position of the representation is different.
Step 3 practice:
(1) The teacher reads the name of a classmate in the class, and the students write his exact position in the exercise book.
(2) When do you need to locate yourself in your life? Talk about the way they determine their position.
4. Teaching Example 2
(1) We just learned how to express the position of our classmates. Now let's see how to show the location of the venue on such a schematic diagram.
(2) According to the method of example 1, the whole class discussed how to display the gate position. (3,0)
(3) Discuss and tell the location of other venues at the same table, and answer by name.
(4) Students mark the positions of "Bird House", "Orangutan House" and "Lion Tiger Mountain" on the map according to the data given in the book. (Projection Review)
Third, practice.
1, exercise 1, question X.
(1) Students independently find out where the letters in the picture are and tell the answers.
(2) Students mark the positions of letters according to the given data, and connect them into figures in turn, and check them at the same table.
2. Exercise 1, Question X: Guide the students to know how to read the page number first, and then find the corresponding position according to the data.
3. Exercise 1, question X.
(1) Write the position of each vertex on the graph independently.
(2) Vertex A is translated 5 units to the right. Where is it? What data has changed? Point a is further shifted upward by 5 units. Where is it? What data has also changed?
(3) Translate point B and point C according to the method of point A, and get a complete triangle after translation.
(4) Observe the pictures before and after translation and tell me what you found. (The graph remains the same, the column, that is, the first data changes when moving to the right, and the row, that is, the second data changes when moving up).
Fourth, summary.
What did we learn today? What do you think of your present situation?
Verb (short for verb) homework
Practice x questions x, x, x.
The first volume of mathematics teaching plan for the sixth grade of primary school of Education for All Press (5) Teaching content:
Nine-year compulsory education and six-year primary school mathematics textbook Volume 11 "The Significance of Comparison".
Teaching objectives:
1. Mastering the meaning of comparison is helpful for reading and writing correctly.
Remember the names of the parts of the ratio, and you will find the ratio correctly.
3. Understand the relationship between ratio, division and fraction, make it clear that the latter term of ratio cannot be 0, and understand the relationship between things at the same time.
4. Through self-study discussion, stimulate students' interest in cooperative learning and cultivate students' ability of analysis, comparison, abstraction, generalization and self-study.
First, create situations and induce participation.
1, Teacher: What is the relationship between two cups of juice and three cups of milk? What method would you use to express their relationship? What questions can I ask and how to answer them?
Raw 1: More milk than juice 1 cup.
Health 2: Fruit juice is less than milk 1 cup.
Health 3: The number of cups of juice is equivalent to that of milk.
Health 4: The number of cups of milk is equivalent to that of juice.
Teacher: Which quantity is compared with which quantity?
Health: Compare the number of cups of juice and milk.
Teacher: What is seeking? what can I say?
Health: Compare the number of cups of milk with the number of cups of juice.
2. Teacher's statement: With the new mathematical comparison method, it can be said that the ratio of cups of juice to milk is 2 to 3. Today, in this lesson, we learn to compare two quantities in a new way. (blackboard writing: proportion)
3. Teacher: What do you want to learn in this course?
(What do you mean, who is better than who ...)
Second, self-study to explore new knowledge.
1. Explore the concept of ratio.
The teacher pointed to the blackboard and asked, What do you want? Which quantity is the ratio of which quantity?
Health: What we want is the score of juice and milk, and the ratio of juice and milk.
Teacher: Yes! 2÷3 is the score of juice and milk, or it can be said that the ratio of juice and milk is 2 to 3.
(Blackboard: The ratio of juice to milk is 2: 3. Read it all. )
Teacher: In this way, milk is a fraction of juice, which can also be said to be the ratio of milk to juice.
Health: Milk is a part of fruit juice. It can also be said that the ratio of milk to juice is 3 to 2.
(blackboard writing: the ratio of milk to juice is 3 to 2)
Teacher: It's all a comparison between juice and milk. Why is one 2 to 3 and the other 3 to 2?
Health: Because 2 to 3 is the ratio of juice to milk, and 3 to 2 is the ratio of milk to juice.
Teacher: Yes, the comparison of two quantities, who is in front and who is behind, cannot be reversed.
Try it out.
Teacher: What does 1: 8 mean?
Health: 1 and 8 stand for 1 cleaning solution and 8 parts water respectively.
Teacher: How to express the relationship between the washing liquid and the amount of water in the container?
Health: Find the volume first and then compare it.
Courseware presentation: Xiaojun 15 minutes, Xiao Wei, 20 minutes, 900 meters long mountain road. Ask the students to fill in the form.
Teacher: How did Xiaojun and Xiao Wei get their speed? What does 900: 15 mean? What does 900: 20 mean?
Teacher: Talk about the significance of 900m15min.
Health: 900 meters 15 minutes is the distance and time for Xiaojun to walk.
Teacher: What is the speed ratio of the small army?
Health: The speed of a small army can be said to be the ratio of distance and time.
Teacher: What do you mean by comparison? Talk to each other at the same table and report the situation. )
Life 1: division is called ratio.
Health 2: The division of two numbers is called ratio.
The division of two numbers used to be called division, but today it is called ratio. There is another name. Do you think it is more appropriate to add a word before the word "than"?
Health 1: add "OK".
Student 2: Add the word "you".
Division of two numbers is also called the ratio of two numbers. Think about what relationship this ratio represents between two numbers.
(With the students' answers, the teacher shot a bullet under "Division" and the students read the concept of comparison together. )
2. Self-study the names of each part and inquire the proportion.
Teacher: Please teach yourself 68-69 pages. Draw the knowledge that you think is important, and after the self-study, talk to each other at the same table about "What I have taught myself".
(After talking to each other, students at the same table report and explore collectively. )
Health: I learned how to write comparisons.
The teacher points to 2: 3 and asks the students to write 2: 3 on the blackboard. )
Teacher: What is the ":"symbol in 2 and 3?
Health: This is a comparative number. (blackboard writing: comparison number)
Teacher: When writing comparison numbers, the upper and lower points should be aligned and placed in the middle. Let the students at the same table look at each other to see if the comparison figures are correct, and then report. )
Health: I know that the number before the comparison symbol is called the first item of comparison, and the number after the comparison symbol is called the last item of comparison.
The teacher (pointing to 2: 3) asked: What is the entry after the first paragraph? (Students answer and then report. )
Health: I know how to pronounce Bibi.
(The teacher points to 2: 3 and calls the students to try to read 2: 3, and then the students read 2: 3 together. )
Teacher: We already know the pronunciation, writing and the names of the parts. Think about it. What else did you learn?
The first volume of mathematics teaching plan for the sixth grade of primary school by Education for All Press (6) Teaching objectives:
1. Knowledge and skills: Connecting with the actual life, guide students to know some common percentages, understand the meaning of these percentages, and master the general method of finding percentages through independent inquiry, so as to correctly find the common percentages in life. According to the internal relationship between scores and percentage application problems, students' transfer and analogy ability and mathematics application consciousness are cultivated.
2. Process and method: guide students to experience colorful mathematical activities such as exploration, discovery and communication, construct knowledge independently, and summarize the method of calculating percentage.
3. Mathematical thinking: enable students to learn to understand the world from a mathematical perspective and gradually form the habit of "mathematical thinking".
4. Emotion, attitude and values: Let students realize the usefulness and necessity of percentage. Perceived percentage comes from life, and the applied value of experienced percentage.
Teaching focus:
Understand the meaning of percentage and master the method of calculating percentage.
Teaching difficulties:
Explore the meaning of percentage.
Teaching tools:
Ppt courseware
Teaching process:
First, review the import (X points)
1, show oral calculation questions, x minutes, correct the wrong questions.
2. Summarize the questions raised by the students and say them orally.
3. Change "a few percent" in the question to "a few percent" to guide students to analyze and answer.
4. Summary: The algorithm is the same, but the expression of the calculation results is different.
5. Description: We call the percentage of correct questions to the total number of questions the correct rate; Then a few percent of the total number of wrong questions is called the error rate. These are collectively referred to as percentages. Introduce new courses and reveal goals.
6. Oral arithmetic contest: (1 min) (see courseware)
7, according to the oral calculation, put forward mathematical problems. What percentage of the total number of questions did you answer correctly? What percentage of the total number of questions is wrong? )
8. Try to answer the revised question.
9. Comparison: How to solve the similarities and differences between "what percentage of a number is another number" and "what percentage of a number is another number"?
10, give some percentages in life, make clear the goal, and enter the new curriculum: (1) Know the meaning of percentages such as compliance rate, germination rate and qualified rate. (2) Learn the method of calculating percentage, and the problem of calculating percentage will be solved.
Second, question guidance (X points)
1, explaining the meaning of the compliance rate.
2. The formula for calculating the compliance rate of blackboard writing, and explain why the division is written in the form of fractions.
3. Organize students to discuss in groups of four.
4, the tour guide writing format. Read the examples and think about the following questions.
(1) What is the compliance rate?
(2) How to calculate the compliance rate?
(3) Thinking: Why is there "× 100%" in the formula?
(4) The success rate of the trial example 1.
Three. Query and inquiry (X mark)
1. Show the percentage calculation formula written by students on the display platform.
2. Ask students to be careful and carry out ideological education.
What percentage does (1) occupy in life? What do they mean? How to find these percentages?
② Find the germination rate in 1(2).
Four, consolidate the exercise (xx points)
1, ask questions by name, organize collective evaluation, and lead students to consolidate the meaning of percentage again.
2. Let the students make a thorough analysis and understanding of each question and find out the reasons for the mistakes.
3. Show the questions, guide students to write the format, and emphasize
4. Pay attention to solving problems: see clearly what rate is sought? Find the corresponding quantity.
5. Ask students to compare and find out: What are these percentages compared with 100%? What percentage may exceed 100%?
6. Lead students to observe and find that: attendance rate+truancy rate = 1.
Verb (abbreviation of verb) strengthens consolidation.
1, tell me what the following percentage means. (1 star)
(1) The school planted 200 seedlings with a survival rate of 90%.
(2) The myopia rate of students in Class Six (1) reached 14%.
(3) The salt yield of seawater is 20%.
2. Judges. (2 stars)
(1) All the 105 saplings planted in our school last semester survived, and the survival rate of these saplings was 105%. ()
(2) There are 54 students in Grade 6 * *, all of whom arrived at school today. The attendance rate of grade six students today is 54%. ()
(3) Put 25g of salt into100g of water, and the salt content of salt water is 25%. ()
(4) The qualified rate of a batch of parts is 85%, so the unqualified rate of this batch of parts must be 15%. ()
3, solve the problem (3 stars)
(1) There are 27 students in our class. Last semester's final exam, 24 were excellent. Then what is the excellent rate of our class? All 27 students are qualified. What's the pass rate?
(2) Class 6 (1) has 48 students at school today, and 2 students are absent from class, seeking attendance.
(3) Ask two people to check each other in groups, and each person will practice a question and make an oral statement. 1. Uncle Wang planted trees on the barren hills, planted 125 trees and survived 1 15 trees. What is the survival rate of these trees?
(4) Of the 300 parts processed by Master Wang, 298 were qualified. What's the pass rate?