1. Math Courseware for Grade Six in Primary School
Teaching content:
Example 7 on page 36 of the textbook, "Practice", Exercise 6 on page 39, question type 16 ~ 2 1, thinking problem.
Teaching objectives:
1. Make students go through the process of "finding the product of two numbers as 1" and "finding the reciprocal of a number", know and understand the meaning of reciprocal, and master the method of finding the reciprocal of a number.
2. Make students develop their thinking ability of observation, comparison, abstraction and generalization in the process of understanding the characteristics of the two reciprocal.
Teaching emphases and difficulties:
Understand the meaning of reciprocal and learn to find the reciprocal of a number.
Teaching process:
First, the introduction of new courses.
Dialogue: Students, the word "friend" is familiar to us. Can you tell us which students in the classroom are your friends?
Answer by roll call.
Talk: In the study and life of the sixth grade, many students have established deep friendship. A "friend" is a relationship between two people. In mathematics, there are also some relationships between numbers. For example, the product of two numbers is 1, which can be said to be a relationship between these two numbers. What numbers have this relationship? How to find such two numbers? This is what we are going to study today.
Second, learn new knowledge.
1, understand the meaning of reciprocal.
(1) Example 7, students do it by themselves.
(2) Introduce concepts.
Two numbers whose product is 1 are reciprocal. For example, and are reciprocal. It can be said to be a countdown, and it is a countdown.
Guide: Please observe carefully. What are the characteristics of these formulas that we have just discovered?
Through student communication, it is clear that the product of two numbers in these formulas is 1.
It is pointed out that two numbers whose product is 1 are reciprocal.
(3) Take students as an example. Make timely comments.
(4) Question: What are the reciprocal numbers? Why do you say "reciprocity?"
Summary: The reciprocal is not a specific number, but the relationship between two numbers. When the product of two numbers is 1, the two numbers are reciprocal.
2. Induction
(1) Question: We already know that two numbers whose product is 1 are reciprocal. Can you find the reciprocal of the sum separately?
Question: Observe the reciprocal groups above, what changes have taken place in their numerator and denominator positions, and share your findings with your deskmate.
Group discussion: guide and observe the relationship between the reciprocal and the original number, and think about what changes have taken place in the position of numerator and denominator compared with the original number.
Roll call answer: To find the reciprocal of a fraction, just exchange the positions of numerator and denominator.
Follow-up: Does 0 have a reciprocal? Why? 1
It is pointed out that there is no reciprocal of 0 because the product of 0 multiplied by any number will not be 1. The reciprocal of 1 is 1.
To find the reciprocal of a number except 0, just switch the numerator and denominator of the number.
Third, consolidate practice.
1, do exercise 6, question 17.
Students say the reciprocal of each number separately, and choose a few numbers to say what they think.
2. Do Exercise 6, 18.
Students become independent and then communicate collectively. Choose two questions and let the students talk about the process of thinking.
3. Do Exercise 6, 19.
Before practice, it is explicitly required to observe what the three numbers in each group have in common and what the reciprocal has in common. Write and observe with questions.
The whole class exchanges the results, and the reciprocal of each group of numbers on the blackboard.
Question: Have you found the characteristics of each group number and its reciprocal? Share your findings with everyone.
It is pointed out that from these four groups of numbers, the reciprocal of true score is false score, and the reciprocal of false score greater than 1 is true score; What is the reciprocal of the score? What is the reciprocal of the score?
4. do thinking questions.
Revelation: Think about the meaning of reciprocity. What is the condition that the product of three fractions is 1 [blackboard writing: ()× ()× () =1]?
Introduction: We know from crosstalk that the product of three scores is 1, in which the product of two scores and the third score are reciprocal. Can you find these three scores from these seven scores? Try to find it.
Students try to practice first, then communicate in groups.
Fourth, the class summary
What did you learn in this class? What is reciprocal? How to find the reciprocal of a number?
Verb (short for verb) homework
Supplementary exercises.
Blackboard writing plan:
Understanding of reciprocity
Two numbers whose product is 1 are reciprocal.
To ask for the reciprocal of a number, just switch the numerator and denominator of this number.
2. Mathematics courseware for the sixth grade of primary school
Teaching objectives:
1, so that students can use two data to determine the position on the grid paper and determine the position on the grid paper according to the given data.
2, through learning activities, enhance students' ability to use what they have learned to solve practical problems and improve their awareness of application.
Teaching focus:
Determine the position of a point on a square paper with several pairs.
Teaching difficulties:
Correctly represent columns and rows with grid paper.
Teaching preparation:
Teacher preparation: projector.
Student Preparation: Square Paper
teaching process
First, review and consolidate.
Mark the positions of the students in the following classes (sketch)
{With the help of the teacher's operation of the student seat map on the platform, the actual specific situation can be quickly mathematized}
Second, explore new knowledge.
(A) 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 example 1, the whole class discussed how to show the position of the gate. (3,0)
In the teaching process, teachers should pay special attention to the 0 th column and 0 th line to guide students to find it correctly. )
3. Discuss the location of other venues at the same table and answer by name.
4. According to the data given in the book, students mark the positions of "Bird House", "Orangutan House" and "Lion Tiger Mountain" on the map. (Projection Review)
Make full use of students' existing life experience and knowledge, and encourage students to explore independently and cooperate and exchange. In teaching, we should make full use of these experiences and knowledge to provide students with exploration space, so that students can describe the position from life experience to determine the position by mathematical methods, develop mathematical thinking and cultivate spatial concepts through observation, analysis, independent thinking and cooperative communication.
Classroom improvement
Exercise 1, question 6
(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. Talk to each other in groups.
(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).
Let the students see the method of expressing the position of points on the plane with number pairs, build a bridge between number and shape, and strengthen the mutual connection between knowledge.
Third, in-class evaluation
Exercise 1, question 4
Students finish independently, and then students check and communicate with each other. Finally, the teacher shows the students' works and the students evaluate them.
Exercise 1, question 5
(1) Students draw a simple polygon on paper. Each vertex is represented by two data.
(2) Work at the same table, with one person describing and one drawing.
Continue to infiltrate the idea of combining numbers with shapes.
Fourth, classroom self-evaluation.
What do you think of your performance in this class? What areas need to continue to work hard?
Verb (abbreviation of verb) Design intention:
In this section, I make full use of students' existing life experience and knowledge, starting from familiar seating positions, and let students subtly establish the concept of "which column and which line" in the practice of dictation, and cultivate the habit of saying "column" before "line" from habit. Then use the grid diagram to show the position, so that students can know how to find the corresponding position from the grid coordinates. This is from intuition to abstraction, from easy to difficult, in line with children's learning characteristics.
3. Mathematics courseware for the sixth grade of primary school
The teaching objectives of this book:
The teaching goal of this textbook is to enable students to:
1. Understand the significance of fractional multiplication and division, master the calculation method of fractional multiplication and division, skillfully calculate simple fractional multiplication and division, and perform simple fractional elementary arithmetic.
2. Understand the meaning of reciprocal and master the method of finding reciprocal.
3. Understanding the meaning and nature of ratio, seeking ratio and transforming ratio can solve simple practical problems about ratio.
4. Master the characteristics of the circle and draw the circle with compasses; Exploring and mastering the formula of the circumference and area of a circle can correctly calculate the circumference and area of a circle.
5. Know that the circle is an axisymmetric figure, and further understand the axisymmetric figure; Translation, axial symmetry and rotation can be used to design simple patterns.
6. Be able to express the position with several pairs on the grid paper, and get a preliminary understanding of the idea of coordinates.
7. Understanding the meaning of percentage and calculating skillfully can solve simple practical problems about percentage.
8. Understand the fan chart, and choose the appropriate chart to represent the data as needed.
9. Experience the process of finding, asking and solving problems in real life, understand the role of mathematics in daily life, and initially form the ability to solve problems by comprehensively applying mathematical knowledge.
10. Experience the diversity of problem-solving strategies and the effectiveness of using hypothetical mathematical thinking methods to solve problems, and feel the charm of mathematics. Form the consciousness of discovering mathematics in life, and initially form the ability of observation, analysis and reasoning.
1 1. Experience the fun of learning mathematics, improve the interest in learning mathematics, and build confidence in learning mathematics well.
12. Develop the good habit of working hard and writing neatly.
First unit position
Unit 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. Be able to use several pairs on a square paper to determine the position.
Orientation of Teaching Content (1) New Teaching and New Teaching
Teaching objectives 1. In specific cases, to explore the method of determining the position, 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.
The focus of teaching can be expressed by number pairs.
Difficulties in teaching can be expressed by number pairs, and the order of columns and rows can be correctly distinguished.
training/teaching aid
Teaching process 1. introduce
1. There are 53 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 4
(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 3: 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 6
(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
Exercise 1: Question 1, 2,5,7,8.
4. Mathematics courseware for the sixth grade of primary school
Teaching objectives:
1. Through the investigation and statistics of practical problems, let students experience the whole process of collecting, sorting and analyzing data and realize the significance of statistics.
2. Make students learn to simply collect and sort out data, fill in simple statistical tables, draw simple statistical charts, and analyze the statistical results simply.
3. Cultivate students' ability to analyze and solve some practical problems, and realize the truth that "mathematics comes from life and serves life".
Teaching focus:
Collect and sort out data, fill in simple statistical tables and draw simple bar charts.
Teaching difficulties:
Be able to extract mathematical information, ask mathematical questions and make decisions according to statistical tables and charts.
Teaching preparation:
courseware
Teaching process:
First, introduce dialogue to ask questions
Teacher: Students, have you ever heard of the word "statistics"? Blackboard: Statistics What do you want to know about statistics?
What is statistics? How to make statistics? What's the use of learning statistics? )
Transition: Students have raised valuable questions. In this class, we will learn and understand "statistics" together.
Second, explore the problem
Understanding statistics
1. Show courseware and extract mathematical information. There are four kinds of drinks, 5 boxes of peach juice; 10 box of pear juice; 9 boxes of apple juice; Five cases of orange juice.
2. Students fill in the number of boxes of drinks in the statistical table on the exercise paper.
3. Report: How did you fill it out?
Understand the meaning of "total".
4. Compare the beverage chart with the statistical table.
Teacher: If we can find more mathematical information in a short time, should we look at the picture below (at sixes and sevens) or the statistics above? Why? (The number of boxes of each beverage is clear at a glance)
Teacher: A table like this is called a statistical table.
Blackboard writing: statistical tables
It is precisely because of this advantage that statistical tables are used in many places. Where have you seen statistical tables?
5. Look at the statistical table to extract mathematical information.
(2) Understand statistical charts
1. Courseware: Show the drink map.
2. Students put forward suggestions for placement.
Follow-up: What are the benefits of classified delivery? (easy to get; The number of boxes is clear at a glance)
3. The courseware shows the classified drinks.
Teacher: It's a good idea for uncle workers to arrange drinks. We can draw a statistical chart according to this method.
Blackboard writing: statistical charts
4. Understand statistical charts
Courseware demonstration: square paper → numbers on the left → names of drinks below.
Teacher: How do you intend to express the number of boxes of peach juice?
freedom of speech
Mathematically, it is represented by a vertical line. (blackboard writing: right)
Draw a statistical chart
Students take out their favorite colored pens and indicate the number of other drinks with horizontal bars.
6. Look at the statistics, extract information and ask math questions.
(3) Learn to read statistical charts.
1. The courseware shows the statistical chart of the existing drinks in the supermarket after two days. Look at the statistical chart and answer the questions.
2. Make decisions according to the statistical chart.
Teacher: Look at this chart. If you were the store manager, what decision would you make?
(4) Summary
Third, practical application.
1. Try it in the math book 128.
2.XX Olympic gold medal list
Fill in statistics, draw statistics and answer questions.
Teacher: Look at this chart. What did you find? The number of gold medals has increased. )
Forecast the number of gold medals in the 2xx Olympic Games held in Beijing in 2008.
Fourth, expand the query.
1. What did you gain from this class? Is there a problem?
2. Teacher's summary: We have only studied statistical charts initially today, and we will study statistics in depth in the future.
Verb (abbreviation for verb) assigns homework.
Choose the content you are interested in, find the data yourself, make statistical tables and draw bar charts.
5. Mathematics courseware for the sixth grade of primary school
Teaching material analysis:
This part of the content is based on students' understanding of the concept of circle and the basic characteristics of circle, guiding students to explore the relationship between the circumference and diameter of a circle through experiments in the form of group cooperation, and learning pi by themselves, so as to summarize and explore the formula for finding the circle. On the other hand, it can improve students' ability to use formulas to solve practical problems and realize the close connection between mathematics and real life.
Teaching objectives:
1. Let students experience the exploration process of pi, understand the meaning of pi, master the formula of pi, and use the formula of pi to solve some simple practical problems.
2. Cultivate students' abilities of observation, comparison, analysis, synthesis and hands-on operation, and develop students' concept of space.
3. Let students understand the meaning of pi, remember the approximate value of pi, and combine the teaching of pi to feel the mathematical culture and stimulate patriotic enthusiasm.
Teaching focus:
The formula of circumference is deduced through various mathematical activities, and the circumference can be calculated correctly.
Teaching difficulties:
Discussion on the relationship between circumference and diameter of a circle.
Teaching preparation:
Multimedia courseware, lines, rulers, circles with different diameters cut from plastic plates, experimental reports, calculators, etc.
Teaching process:
First, quasi-cognitive conflict, stimulate the desire to learn.
1. Talk: Students, I know everyone likes to watch the cartoon Pleasant Goat and Big Big Big Wolf. Today, the teacher brought them to our class. Listen: (Courseware plays the story: On a sunny day, Pleasant Goat and Big Big Wolf held a running race. Pleasant goat runs along a square route, and Big Wolf runs along a circular route. After a lap, the two returned to the starting point at the same time. At this time, they are arguing over who will travel long distances. Students, what do you think? (Students guess)
2. How can we determine which of them runs a long distance? (Student: Find the perimeter of a square and a circle first, and then compare them. )
3. Name a lifetime and talk about the calculation method of the circumference of a square: (Student: side length ×4= circumference) Today, let's study the circumference of a circle together. (revealing topic: circumference)
Second, experience the whole process of inquiry and verify the conjecture.
(1) Understand the meaning of perimeter and preliminarily perceive the relationship between perimeter and diameter.
1. Dialogue: What is a circle? (Courseware shows 3 wheels)
2. Teacher: What do the above three numbers mean? What does "inch" mean? (Students read and answer)
3. Three wheels roll once each. Guess who rolls the longest distance? What did you find out from it? (health: the length of a wheel rolling once is the circumference of the wheel; The longer the diameter, the longer the circumference, the shorter the diameter and the shorter the circumference)
Ac method for measuring circumference
1. Students take out the circles cut before class and point out their perimeters.
2. How to measure their circumference? (deskmate communication mode)
3. Name the front projection to show the method of measuring perimeter.
① Rolling method. Remember clearly: make a mark and scroll from the zero scale until the mark points here again. The length of a circle rolling is the circumference of the circle.
(2) circle method. Clear: the line is close to the circumference, the redundant part is removed and the line is straightened. The length of the straight line between these two points is the circumference of the circle.
③ Measure with a soft ruler. Clear: Measure with the side with centimeter scale on the soft ruler. Start with the zero scale, draw a circle and see which scale is aligned.
4. Summary: These methods have a common feature: (Student: Turn a curve into a straight line) This is the method of "turning a curve into a straight line" in mathematics.
5. (There are pictures of ferris wheel in the courseware) Q: Can you measure its circumference by the method just now? (Health: No, it's inconvenient) Q: What should I do? Inspire students to explore the relationship between the circumference and diameter of a circle.
(3) Know pi.
1. Talk: Next, divide the students into four groups, choose their favorite method, measure the circumference and diameter of these circles around them, and complete the table. (Students complete the form in the book in groups) (Show the form in the courseware)
2. The team leader reports the measurement results. (Students say grades, teachers improve courseware)
Let the students observe the data in the table and tell them what they have found. (Students report in groups: the circumference of a circle is always more than 3 times the diameter)
4. (Courseware demonstration) Introduce the book Weekly Parallel Computing and the significance of "Path One on Wednesday". The circumference of a circle is about three times the diameter.
5. Introduce Zu Chongzhi's contribution to the calculation of pi, so that students can imagine the process of Zu Chongzhi's exploration of pi and realize the hardships and difficulties of scientific discovery. (Courseware plays data, students learn by themselves)
6. What did the students learn from the introduction of the materials? (Students exchange learning)
7. Teacher's summary: Zu Chongzhi is the pride of our nation, precisely because he is outstanding.
Achievements: There is a crater on the moon called Mount Zu Chongzhi, and the 1888 asteroid in the universe is also named after him. I hope my classmates can study as hard as him in the future and be an extraordinary person in the future.
(4) Derive the formula
1. When students understand the relationship between the circumference and diameter of a circle, let them talk about how to calculate the circumference of a circle. (Student: circumference = pi × diameter)
2. Dialogue: If the capital letter C is used to represent the circumference of a circle, how is this formula represented by letters?
3. Talk: What other conditions can be known to find the circumference? (health: radius) why? (Health: In the same circle, the diameter of the circle is twice the radius) Then how to change this formula?
4. Read the formula together to deepen the impression.
Third, refresh the application ability and summarize and consolidate new knowledge.
1. (The courseware shows the question 1) Students answer the perimeter of two circles.
2. What are the circumference of three bicycle wheels in Example 4? (Courseware shows three wheels) Through calculation, who has the longest circumference? What does this mean? (health: the circumference of a circle is related to its diameter)
(The courseware shows a fountain) The circumference of the circular fountain is12m. What's its circumference? Students finish their exercise books independently, and the projector displays the answers. )
4. (The courseware shows the schematic diagram of the Ferris wheel) Its radius is 10 meter. If you sit on it for a week, how many meters will it turn in the air? Students finish their exercise books independently and then communicate with each other in class.
Fourth, exchange learning gains and expand after class.
1. What have you gained from learning the circle in this lesson? (Students communicate with the whole class)
2. Dialogue: Now if the teacher asks Pleasant Goat and Big Big Wolf, who walks longer? What can students do? (Students finish independently, and then the whole class communicates) Is there any other way? (Students can solve problems by calculation, or they can directly observe the contrast between two pictures. )
3. Teacher: Various methods can help us determine who walked this long distance, so when Pleasant Goat learned the result, he shouted that the race was unfair, so the old village head redesigned a new race route for them: Q: If Pleasant Goat and Big Big Big Wolf race along this route, who will walk the longer distance? Students think after class and communicate in the next class. )
Teaching reflection:
First, the two main threads of "situation" and "knowledge" blend with each other.
Combined with the teaching content of this class and the age characteristics of students, teachers grasp the two main lines of "situation" and "knowledge" in teaching situations, and strive to create a lively, harmonious and harmonious learning atmosphere for students. As we all know, "Pleasant Goat and Big Big Wolf" is an animated film deeply loved by students. Students are very interested in this and have a certain understanding. Taking this as the learning background and the starting point of the learning circle, the "situational clues" and "knowledge clues" of this lesson are organically integrated to form a complete unity, which stimulates students' interest in learning and actively participates in learning activities.
Second, hands-on operation allows students to experience the formation process of knowledge.
Hands-on operation is an important way for students to acquire knowledge. Based on students' life experience and existing knowledge background, this course provides them with rich operational materials and open operational space, so that students can experience the derivation process of the formula for calculating the circle. In this process, teachers participate in students' learning activities as organizers, guides and collaborators, so that students' operational activities are purposeful, ideological, selective and creative, and students can do, watch and create.
Thirdly, mathematics reading makes students feel a strong mathematical culture.
In the process of mathematics learning, introducing some knowledge of mathematics discovery and history can enrich students' overall understanding of mathematics development and play a certain incentive role in subsequent learning. Combined with the teaching content of this lesson, the teacher introduced the knowledge of pi to the students. The introduction here is from "One Way of Three Weeks" and "Calculation and Preparation" by Zu Chongzhi in Zhoubian Suanjing, to the application of pi in modern life and the computer calculation of pi, so that students can have a complete understanding of the history of pi, feel the wisdom of our ancestors, and appreciate the close relationship between mathematical knowledge and human life experience and actual needs.