Pay attention to the infiltration of mathematical thinking methods in teaching, so that students can "know mathematics" So how to design the teaching design of mathematics in the sixth grade of primary school in the last semester? Next, I will bring you a sixth-grade math teaching plan of People's Education Press for your reference.
People's education press sixth grade mathematics teaching plan 1 teaching goal of the first volume.
Make students understand the meaning of directions such as north (south) in the Middle East and south (north) in the west in specific situations, describe the position of objects with directions and distances, and initially feel the scientificity and rationality of determining the position of objects with directions and distances. Further cultivate students' ability to observe, read pictures and express in order, and develop the concept of space.
Emphasis and difficulty in teaching
Key points: by solving practical problems, let students know the application of positioning in life and the methods of positioning; In the situation, students can determine the position of objects according to the direction and distance, and describe a simple road map.
Difficulties: By solving practical problems, students can determine the position of objects according to the direction and distance, and can draw a simple road map.
teaching process
First, set the scene and introduce a new course.
Students, have you seen the story of the race between the tortoise and the hare? I've seen it. Who knows who won the game? Say tortoise together. Why did the tortoise win? The student said: Because the rabbit is asleep. The rabbit knows that he is wrong. I'm going to race the tortoise again today;
Please see "The Tortoise and Rabbit Race Sequel"
Look at the pictures of the tortoise and rabbit race and introduce the topic.
Why did the rabbit lose again? Sheng smiled and said that it was because the rabbit ran in the wrong direction. How can we reach the finish line? What are the factors that determine it? What we are going to learn today is: in what direction is the starting point and the end point? How far is the end point from the starting point?
With these two questions,
Let's learn today's new lesson: location.
Students, what direction have we learned? Health: East, South, West and North. What else is there? Health: southeast, southwest, northeast, northwest. We have learned eight directions. Show courseware
Second, independent exploration, cooperation and exchanges
Every year, the coastal areas of China are hit by typhoons. Look, this is a map of a strong typhoon in a certain year. Please calculate it.
(1) Teaching examples 1
1. Current position of typhoon center. (Courseware demonstration)
At present, the typhoon center is located on the ocean surface 30 southeast of A city, 600 kilometers away from A city, and is moving straight to A city at a speed of 20 kilometers per hour. ..
How many hours will the typhoon arrive in city A?
2. What do you mean by 30 east by south? If this is the only condition, can you determine the specific location of the typhoon center?
3. What will happen if this is predicted? Is this accurate in determining the direction? How to predict more accurately?
4. Is there anything else to announce? (distance)
(600 kilometers away) What if there is no distance?
5. Summary: When forecasting a typhoon, we should say both the direction and the distance. Key point: how to express 30 east by southeast? It can also be said that it is 60 east of the south, but in life, we usually say that it is closer to the direction of the object (the angle is smaller). 6. Oral answer: How many hours will the typhoon arrive in City A?
7. Exercise: Complete the exercise on page 20 of the textbook.
Let the students finish it independently, let the students experience the process of knowledge formation in operation, and then correct it collectively.
(B) Teaching Example 2
1. Courseware shows that after the typhoon arrives in City A, it changes direction and moves to City B ... Affected by the typhoon, there will also be heavy rain in City C. City B is located 30 degrees northwest of City A, 200 kilometers away from City A. City C is just north of City A, 300 kilometers away from City A. Please mark the locations of City B and City C in the icon of example 1.
2. How to express distance?
First determine the direction on the floor plan, and then determine the distance of each building. If the students don't say anything, the teacher can guide them: How are you going to show 200km on the map? So as to help students determine the scale and distance on the map. 1cm is more suitable to represent 100km.
3. Students independently complete and collectively revise.
4. Modified communication: What do you think your group should pay attention to when determining the location of this point on the map? How can we be sure?
How do you think to determine the position of an object through the study just now?
Teacher's summary: Generally, when drawing a plan, the angle is determined first, and then the distance on the plan is determined.
According to the direction and distance, the position of the object can be determined.
5. Oral answer: After the typhoon arrives in City A, its moving speed becomes 40km/ h, and how many hours will it arrive in City B?
6. Exercise: Complete the exercise on page 2 1 of the textbook and open the exercise on page 2 1 of the textbook:
(1) Get information:
The teaching building is in the north of the school gate150m.
The library is 35 degrees northeast of the school gate150m. The gymnasium is 200 meters north of the school gate at 40 degrees.
(2) Teacher: What aspects do you think should be considered to accurately mark the location of a place on the floor plan? (3) Teachers and students * * * comb together: a. First determine the center of the plan. B. determine the direction and distance.
(4) independent operation, independent drawing plan.
(5) Improve the drawing process through name display and communication.
Students show drawings and demonstrate the process, and other students comment and supplement them.
It seems that the painting process is a bit complicated. Let's review the whole process again. Is the process and method of drawing clear? Did you just draw it like this?
Third, knowledge feedback, consolidate application.
It seems that the students have a good understanding of this section. Do you have the courage to challenge yourself now?
Courseware demonstration:
1. The police station received the schematic diagram sent by undercover.
(1) The criminal 1 is in the () direction of the police station, with a distance of () meters.
(2) The distance between criminal 2 and the police station is ().
() meters.
(3) The distance between criminal 3 and the police station is ().
() meters.
2, do, show the courseware, and modify it after independent completion.
Fourth, class summary.
What is your greatest achievement in this course? What else don't you understand?
Location and direction are often encountered in life.
If you want to set a position, remember two things:
Direction first, distance is indispensable.
Verb (abbreviation of verb) students who have expanded their enrollment have gained a lot. Can you create a school building plan with what you have learned today? Try it yourself!
Teaching objectives of the first volume of the sixth grade mathematics teaching plan 2 of People's Education Press
1. On the basis of students' existing fractional addition and the basic meaning of fractions, combined with life examples, students can understand the meaning of fractional multiplication by integers, master the calculation method of fractional multiplication by integers, and skillfully use the calculation rules of fractional multiplication by integers to calculate.
2. Through observation and comparison, guide students to sum up the calculation law of fractional multiplication by integer through experience, and cultivate students' abstract generalization ability.
3. Guide students to explore the internal relationship of knowledge and stimulate students' interest in learning. Through demonstration, students can have a preliminary understanding of arithmetic, and feel the charm and beauty of mathematical knowledge in this process.
Emphasis and difficulty in teaching
Teaching emphasis: make students understand the meaning of fractional multiplication by integer and master the calculation method of fractional multiplication by integer.
Teaching difficulties: guide students to summarize the calculation rules of fractional multiplication by integer.
teaching process
First, review.
Show the review questions.
1. List the formulas according to the meaning of the question:
What is five 12?
How much is three 14?
2. Which of the following sentences can be regarded as the unit 1?
The speed of a cheetah is three-seventh that of a lion.
The students who take part in the chorus account for one-fifth of the class.
Red flowers are half of yellow flowers.
October saves three quarters compared with September.
3. Calculation: 3/10+3/10+3/10 =
3/10+3/10+3/10 How can we calculate this problem?
Today we are going to learn fractional multiplication.
Second, new funding.
1, multiply the teaching score by 3/10+3//kloc-0+3/10.
(1) What are the addends in this addition formula? (All 3/ 10)
(2) What other methods can be used to calculate the sum of several identical addends? How to go public? (Multiplication, 3/ 10 ×3)
(3) 3/10+3/10+3/10 = 9, then 3/10+3/10 = 3.
So 3/10× 3 = _ _ _ _ _ _ = 9. Think about it, class. What is the calculation process of 3/ 10 ×3=9?
Who can finish it?
2. Example 1,
(1) Understand the meaning of the question:
Guide the students to look at the pictures and understand that "the distance of a person running one step is equivalent to 2/ 1 1", that is, the distance of a kangaroo jumping, that is, the whole line segment is regarded as the unit "1". Divide this line segment into 1 1, where two represent the distance that people run one step.
(2) guide students to understand according to the line diagram,
What does it mean that the distance a person runs is equivalent to 2/ 1 1 of a kangaroo's jump? How to understand "equivalence"? Then help to understand through the line segment diagram. Draw a line segment to indicate the jumping distance of kangaroos. "People run as far as kangaroos.
If you jump 2/ 1 1 ",you should regard this line segment as the unit" 1 ",and divide this line segment into 1 1 parts on average, of which 2 parts represent the distance of one step. When a man runs three steps, how much does the kangaroo jump? Is to find three 2/ 1 1. What is this?
(Formula: 2/11× 3 = 6/11)
Is there a simpler calculation method? Done independently. The innate properties of fingers. Show courseware demonstration.
3. Combining the above two problems, the calculation rules of fractional multiplication by integer are summarized: fractional multiplication by integer, the product of fractional numerator multiplied by integer is numerator, and the denominator remains unchanged.
4. Practice: Practice the second question of "doing".
5. Teaching Example 2
(1) shows 3/8×6, and students can calculate independently.
(2) According to the calculation results, students observe and discuss: Is the product of multiplication simplest fraction? What should I do?
(3) Students divide by their own ideas: a, divide first and then calculate; B, first calculate the product and then drop the score. (4) Contrast, let students understand that the method of dividing first and then calculating is relatively simple, and explain the writing format of dividing first and then calculating to students.
6. Practice, show the courseware, and students can calculate independently. Then modify it.
Third, consolidate the practice.
Competition:
Previous single wheel
1, complete the first question of "doing". Remind students to observe whether the denominator and integer of a score can be simplified before calculation, thus forming the habit of simplifying the score before calculation.
Second round
2. "Do it" question 3. Remind students to observe whether the denominator and integer of a score can be simplified before calculation, thus forming the habit of simplifying the score before calculation.
Fourth, the class summary:
What did you buy today?
Homework: Exercise 2, Question 1, 2, 4.
Teaching objectives of the sixth grade mathematics teaching plan 3 of People's Education Press
1. Let the students know the circle and know the names of its parts.
2. Through hands-on operation and experimental observation, explore the characteristics of a circle and the relationship between radius and diameter in the same circle.
3. Initially learn to draw circles with compasses to cultivate students' drawing ability.
4. Cultivate students' thinking ability of observation, analysis, abstraction and generalization.
Emphasis and difficulty in teaching
Teaching focus
Grasp the characteristics of circles in hands-on operation and learn how to draw circles with compasses.
Teaching difficulties
Understand the concepts on the circle and summarize the characteristics of the circle.
teaching tool
courseware
teaching process
Activity 1: Demonstrate the operation and reveal the topic.
The courseware shows, "Everyone is the referee!"
Demonstrate the animation of two people riding bicycles. One person's bicycle wheel is round, while another person's bicycle wheel is of other shapes.
Let students perceive the application of circle in life.
Activity 2: Hands-on operation, exploring new knowledge
(1) The teacher asked the students to illustrate which objects around them have circles.
(2) Know the name of the part of the circle and the characteristics of the circle.
1. Students take out round learning tools.
2. Teacher: Touch the edge of the circle. Is it straight or curved?
The teacher explained that a circle is a curved figure on a plane.
3. Understand the names of various parts of the circle and the characteristics of the circle through specific operations.
(1) First, fold the circle in half, open it, change the direction, fold it again, open it again ... Repeat several times.
Teacher's question: What did you find after folding it several times?
Look carefully, where do these creases always intersect in the circle?
The teacher pointed out: we call this point of the center of the circle the center of the circle. The center of the circle is generally represented by the letter o.
Teacher's blackboard writing: the center of the circle
(2) Measure the distance from the center of the circle to any point on the circle with a ruler and have a look. What can you find?
The teacher pointed out: We call the line segment connecting the center of the circle and any point on the circle as radius, and the radius is generally represented by the letter R: radius.
The teacher asked: According to the concept of radius, what conditions should students have to think about a radius?
How many radii can a circle draw?
Are all radii equal in length?
Teacher's blackboard writing: The same circle has countless radii, all of which are equal in length.
(3) Students continue to observe: When the circle was folded in half just now, where did each crease pass through the circle? Where are the two ends of the circle?
The teacher pointed out: we call it a line segment passing through the center of the circle with both ends on the diameter of the circle. Diameter is generally represented by the letter D.
Teacher's question: According to the concept of diameter, students think about it. What conditions should a diameter have?
How many diameters can a circle be drawn?
Measure several diameters in the same circle with a ruler and have a look. Are all diameters equal in length?
Teacher's blackboard writing: The same circle has countless diameters, and all the diameters are equal in length.
(4) Teacher's summary: We know from the study just now that the same circle has countless radii, and all the radii are equal in length; There are countless diameters, all of which are equal in length.
(5) Discussion: What is the relationship between the length of the inner diameter and the length of the radius of the same circle?
How to express this relationship in letters?
Conversely, in the same circle, the length of the radius is a fraction of the diameter.
Teacher's blackboard writing: In the same circle, the diameter is twice the radius.
(3) feedback exercises.
1, P58' s "Do it" question 1, 3 and 4
2. Exercise 2 and 3 in Question 14
(4) the drawing of the circle.
1, students learn by themselves, reading 57 pages.
2. The students try to draw.
3. Students draw a circle with compasses and pay attention to the problem by summarizing the trial drawing.
4. The teacher summarizes the blackboard: 1. Fixed radius; 2. fix the center of the circle; 3. Rotate once.
The teacher stressed: when drawing a circle, the distance between the two feet of the compass should not be changed, the foot with a needle tip should not move, and the center of gravity should be placed on the foot with a needle tip when rotating.
5. Students practice
P58' s "hands-on" question 2
(5) Teachers ask questions
Why do students draw different circles? What determines the size of a circle? What determines the position of the circle?
Teacher writes on the blackboard: the radius determines the size of the circle, and the center of the circle determines the position of the circle.
(6) Thinking: In physical education class, the teacher wants to draw a big circle on the playground to play games. What if there are no compasses this big?
Third, the class summarizes.
What did we learn in this class? What did you get from this lesson?
Fourth, homework
Exercise 14, question 1
Teaching objectives of the first volume of the sixth grade mathematics teaching plan 4 of People's Education Press
1. Make students learn the calculation method of circular area and the related calculation method of circular and rectangular mixed graphics.
2. Learn to use the existing knowledge and mathematical thinking methods to derive the formula for calculating the area of a circular ring, including the application of circles and squares.
3. Cultivate students' abilities of observation, analysis, reasoning and generalization, and develop students' spatial concepts.
Emphasis and difficulty in teaching
The teaching emphasis of 1
Can use circle and other related knowledge to solve practical problems.
2 Teaching difficulties
Mixed use of circle and other graphic calculation formulas.
teaching tool
PPT card
teaching process
1 Review and consolidate previous knowledge and introduce new lessons.
2 New knowledge exploration
2. 1 ring zone
First, the introduction of the problem
Do students know what CDs can be used for? Who can describe the appearance of a CD?
Answer (abbreviated).
Today we will do some math problems related to CD.
Second, the ring zone solution
Example 2. The silver part of the CD is a ring with an inner radius of 50px and an outer radius of 150px. What is the area of this ring?
Steps:
Teacher: What do you need to find the area of a circle first?
Health: area of inner ring and outer ring
Teacher: Students can do it themselves and communicate solutions in groups.
Teacher: Give the calculation process and results:
Third, the application of knowledge
Do the second question:
The diameter of the circular island is 50m, with a circular flower bed with a diameter of 10m in the middle and lawns in other places. What is the area of the lawn?
Teacher: This is a typical round area application problem. It is very simple to get the radius from the diameter and substitute it into the formula of ring area.
2.2 Round and Square
First, the introduction of the problem
Teacher: The students know the gardens in Suzhou. Have you ever observed the windows of garden buildings? It has many beautiful designs and many common graphics, such as pentagon, hexagon, octagon and so on. Among them, the inside of the outer circle or the outside of the inner circle is a very common design.
Teacher: Not only in gardens, but also in China's architecture and other designs, you can often see "the inside of the outer circle" and "the inside of the outer circle", such as this Fiona Fang Building in Shenyang, trademarks and so on. Let's get to know this figure consisting of a circle and a square.
Second, knowledge points
Example 3: The radius of two circles in the figure is1m. Can you find the area between a square and a circle?
Steps:
Teacher: What does this topic tell us?
Health: the radius of the left circle = half the side length of a square =1m; The area of the right circle = half of the diagonal of the square =1m.
Teacher: What are the requirements?
Health: the area of a square is greater than that of a circle, and the area of a circle is greater than that of a square.
Teacher: What should I do?
Inductive summary
If the radii of two circles are both R, what is the result?
When r= 1, it is completely consistent with the previous results.
Fourth, knowledge application.
On page 70, do:
The picture below shows the bronze mirror inside the outer ring of China in the Tang Dynasty. The diameter of the bronze mirror is 600px. What is the area between the outer circle and the inner side?
Teacher: Students, please use what we have just learned to solve this problem.
Solution: The radius of bronze mirror is 300px.
5.3 Classroom exercises
If you have enough time, practice 5/6/7 exercises in class.
(Students can be invited to write the problem-solving process on the blackboard.)
6 abstract
1. What did we learn today?
Today, under the premise of knowing the area formulas of circles and squares, this paper discusses the area calculation method of rings and figures inside the outer circle and outside the inner circle. This is not to ask students to remember these derived formulas, but to hope that students can understand the derivation method and use what they have learned to solve similar problems in the future.
2. In our daily life, we often need to find the area of a circle. For example, yurts are round, because the living area can be used to the maximum extent, and the cross section of plant roots is round, because it can absorb water to the maximum extent. We can also give some other examples, such as why do plates and wheels have to be round? Everyone needs to think more!
7 blackboard writing
Example 2 Solution Steps
Teaching objectives of the first volume of the sixth grade mathematics teaching plan 5 of People's Education Press
(1) You can measure the circumference of a circle with the tools around you.
(2) Be able to master various methods of measuring and calculating the circumference.
(3) be able to say seven digits after the decimal point of pi.
(4) Being able to understand Zu Chongzhi.
(5) The formula for calculating the circumference can be used flexibly for calculation.
(6) Cultivate students' logical reasoning ability
(7) Educate students in patriotism.
(8) Cultivate students' abilities of observation, comparison, generalization and hands-on operation.
Emphasis and difficulty in teaching
Key point: the meaning of the circumference and pi of a circle.
Difficulty: the derivation process of the formula of circle circumference
teaching tool
Ppt courseware, video, basketball, coins, bottle caps.
teaching process
First, discuss the introduction of exploration activities.
1, showing real basketball, bottle caps and coins.
Reveal the theme: circumference
2. Question: The side length of a square and a rectangle is the circumference of four sides. Is the circumference of the circle the same as theirs?
3. Guide students to measure the circumference of basketball with tools around them (group discussion and exploration)
4. Question: A circle has no side length, it is just a curve. Can you measure the circumference of a circle with the tool in your hand? How many ways can you think of?
5. Share measurement methods
Methods: Turn the curve into a straight line, roll it up, measure it with a soft tape, and wrap the rope around it.
Second, understand pi.
1. Question: Look at the diameter and circumference of basketball and coins. What's your conclusion?
Conclusion:
The circumference of a circle is related to its diameter. The greater the diameter, the greater the circumference.
The circumference of a circle is always a little more than three times its diameter.
2. Question: Does anyone know what pi is?
Pi 3. 14 15926535
Can you guess how many decimal points pi has?
(Show pictures of Zu Chongzhi and the development history of pi)
Zu Chongzhi, an ancient mathematician in China, first made the value of pi accurate to 7 decimal places, which was 1000 years earlier than that of foreign countries.
Pi is the ratio of the circumference of any circle to its diameter. This diameter is a fixed number, represented by the letter π, which is an infinite acyclic decimal. π=3. 14 15926535 ... Take the approximate value π=3. 14.
3. Play the video: song title 3. 14 15.
Third, use the formula to calculate the circumference of the circle.
1. According to the relationship between the circumference and diameter of a circle, a formula for calculating the circumference of a circle can be derived. Tell me what's in the book.
Formula: C=πd or c = 2 π r.
2. Question: What conditions do you need to know to find the circle?
Condition: diameter or radius, π=3. 14.
3. Examples
The example on page 64 of this book.
Step 4 do exercises
(show ppt)
Summary after class
The circumference of a circle is related to its diameter. The greater the diameter, the greater the circumference.
Pi π is an infinite acyclic decimal, π=3. 14 15926535 ... Take the approximate value π=3. 14.
The circumference formula of a circle: C=πd or c = 2 π r.
homework
Members of the same group measure the circumference of a school circle and cooperate in groups.