Mathematics optimization teaching plan for the fourth grade 1 1. Teaching objectives
1. Combined with the specific situation, it can correctly calculate the decimal addition and subtraction, and can choose a simple method to calculate.
2. It can solve the practical problem of simple decimal addition, subtraction and mixing.
Second, teaching material analysis
The teaching content of this lesson is based on the addition and subtraction of decimals. The textbook asks, "Who has the highest total score?" How much higher? Then, two commonly used calculation methods are introduced, one is step-by-step calculation, the other is comprehensive calculation. The key point is to let students understand the order of decimal addition and subtraction mixed operations. In the process of research, the study of calculation methods is closely combined with problem solving, which makes students feel that mathematics comes from life. In the process of inquiry, students are required to estimate the results before solving problems, which permeates the idea of estimation.
I want to explain some special terms involved in the situation, such as "professional score" and "comprehensive quality score" After students understand the situation, they can make their own estimates first, and then organize students to explore independently and communicate with the whole class.
In the design of exercises, "shopping" is based on the real life that students are familiar with, which has certain openness and flexibility and is helpful to the development and improvement of students' abilities in all aspects.
Third, the analysis of the situation of schools and students.
Our school is a rural primary school. Most students have a good foundation and have a strong interest in learning mathematics. After studying the new textbook for several years, students have initially developed good study habits and cooperative consciousness, dared to question, and initially possessed the ability to explore and solve practical problems independently. However, some students have poor study habits, so the design of teaching process needs to pay attention to all students and the development of each child.
Fourth, the teaching process
(A) create a situation
Play live video.
(Play the live video of Tian Haiyan, a teacher from our school, taking part in the whole town vocal competition. The students are very involved. They clapped their hands and said, "Our music teacher sings well!" " "Like a famous star!" "Where did she get it?" "It must be a champion!" )
Teacher: Students, tian teacher's outstanding performance in this competition has been well received by the judges. After the preliminary and semi-finals, she finally competed with Jia of kindergarten for the championship. Do you want to see their final grades?
Health: (eager) "Yes!"
(Multimedia shows the pictures and achievements of two contestants, and the form is basically the same as the teaching material. Player No.5 becomes tian teacher and Player No.9 becomes Teacher Jia.)
Teacher: What did you find, class? What questions can I ask?
Health 1: Who can win the first prize?
S2: Teacher Jia won the first prize because his professional score was higher than that of tian teacher.
Student 3: No, tian teacher's comprehensive quality score is higher than Mr Jia's, so tian teacher can get the first place.
Health 4: I don't understand what "professional score" and "comprehensive quality score" mean. Which grade will determine their performance?
Health 5: (confident) I know! I have seen on TV that the major is singing and the comprehensive quality is music theory knowledge. Add up everyone's two scores and decide who is the champion.
Teacher: You are such a careful boy! As you said, people usually add up two scores to judge who has better grades. We use this method to judge who performs better.
Independent investigation
1. Teacher: Who can estimate their total score?
Health 1: (thinking) Their grades are almost the same, both exceeding 9 points.
Health 2: Their grades are very close, so we should make a concrete comparison.
Teacher: How to calculate? Please have a try and see whose method is popular! (Students act at once)
Teacher: Who wants to introduce their own methods to everyone?
The total score of player 1: 5 is already known. I ask for the total score of player 9 and compare it with the score of player 5. My formula is: 8.65+0.40=9.05 (minutes) and 9.43-9.05=0.38 (minutes). Tian teacher is the champion, 0.38 points higher than Mr Jia.
Health 2: I have the same idea as him, but I have combined two formulas, and the formula is: 9.43-(8.65+0.40).
Teacher: Why are there brackets?
S3: Because we have to work out the total score of contestant No.9 first.
Teacher: Can students work out the numbers of mixed addition and subtraction questions step by step like this? Have a try.
(Student feedback after independent calculation)
Health: 9.43-(8.65+0.40)
=9.43-9.05
=0.38 (minimum)
Teacher: What should I pay attention to when calculating decimal addition and subtraction?
Health: When columns are arranged, add and subtract decimal points to align.
(3) Expand the application
The teacher showed the shopping list.
Shopping list of supermarkets in the new century
20xx . 09. 15 15:4 1
Subtotal of commodity name, quantity and unit price
Bread 2 2.70 Yuan 5.40 Yuan
Soy sauce 1 4.85 yuan 4.85 yuan
Accounts receivable: 10.25 yuan
Guest Payment: 20 yuan.
Small change: 9.75 yuan
Teacher: What math questions can you ask from this shopping list?
Health 1: I want to check the total price of two loaves of bread and a bottle of soy sauce, right?
Health 2: I want to help my aunt check it and see if the money is right.
……
Teacher: It seems that students can ask questions from different angles, so let's use what we have learned to solve these problems!
(Report after students' activities)
Student 1: the first question: 2.70+2.70+4.85= 10.25 (RMB), which is the same as the shopping receipt.
Health 2: Question 2: 20- 10.25= 10.75 (yuan).
S3: The second question is wrong. The result should be 9.75 yuan. He forgot to abdicate! Because the minuend is an integer, the decimal point is after one digit, so when I use the vertical type, I put the decimal point after 20 and then add two zeros to calculate.
Health 4: We think so, so it is not easy to make mistakes when abdicating.
Health 5: Teacher, we didn't write 0, but we kept it in mind.
Teacher: The students have good ideas. When the decimal place of the minuend is less than that of the minuend, when the column is vertical, 0 should be added at the end of the minuend. If you reach a certain level of proficiency, you don't have to write 0.
2. Self-editing and self-calculation
Display data 4. 12 12.3 5.08
Teacher: Can you use these numbers to write a formula of addition, subtraction or a mixture of addition and subtraction?
(student's formula, communication)
Health1:4.12+12.3+5.08
Health 2: 4. 12- 12.3-5.08
S3: We can't calculate the question he made up now. It should be changed to 12.3-4. 12-5.08.
Health 4:12.3-(4.12+5.08)
Teacher: Now let's calculate the three questions we made up, and pay attention to the questions reminded by our classmates when calculating.
Reflection on the Teaching of verb (abbreviation of verb)
"Mathematics comes from life and is applied to life." In the teaching of this class, I created a life situation closely related to it and full of interest, which fully mobilized the students' inquiry and made them devote themselves to the inquiry of new knowledge with full enthusiasm. Tian teacher is a teacher in our class, and the students are very concerned about whether tian teacher can win the championship. This kind of psychology makes students eager to know Mr. Jia's total score, so as to devote themselves to the exploration of new knowledge.
I try to be close to the students in the design of exercises. Students not only feel interesting in the process of solving problems, but also feel the application value of mathematics. I organize my own calculations to make boring calculations interesting, so that students can fully appreciate the joy of success in a democratic and harmonious atmosphere and receive good teaching results.
VI. Case Review
Instructional design teachers of this course pay attention to creating real life situations for students, giving full play to students' main role, guiding students to think independently and communicate in groups, realizing autonomous learning and embodying the basic ideas of the new curriculum.
1. Closely linked with real life.
From the introduction of topics to the teaching process, this course pays attention to excavating teaching materials from familiar cases around students. For example, we created a scene for students in which our school teachers participated in the competition. Students care about the teacher's grades, and their interest in learning arises spontaneously, which makes the classroom full of interest, and makes students truly feel that mathematics is around and that mathematics comes from life.
2. Provide students with time and space for independent exploration.
The teaching of this lesson is not only the exploration of new knowledge, but also the application of knowledge. Teachers can boldly let go and provide students with enough time and space to independently calculate, think and discover. Students inspire and complement each other in cooperation and exchange, and a good interactive space is formed between students.
3. Pay attention to the cultivation of the ability to solve practical problems.
In teaching, teachers pay attention to the idea of "applying what they have learned". From creating situation-exploring algorithm-improving application, the teaching concept of "from life to life" is fully embodied. In particular, the design of exercises such as "shopping" and "self-editing and self-calculation" is not only close to the actual life of students, but also has certain openness and flexibility, which stimulates students' interest in learning. In this process, students not only exercise the ability to solve practical problems, but also gain a good emotional experience.
The teaching goal of the fourth grade mathematics optimization teaching plan 2;
Knowledge and skills:
1. Let students experience the application of operational research in solving practical problems through simple examples.
2. Make students realize the diversity of problem-solving strategies and form the consciousness of finding the best solution to the problem. Process and method:
Make students understand the idea of optimization, form the consciousness of finding the best scheme from various schemes, and improve students' ability to solve problems.
Emotions, attitudes and values:
Let students feel the extensive application of mathematics in daily life, and try to solve simple problems in life with mathematical methods.
Key points:
The idea of experience optimization.
Difficulties:
Find the best solution to the problem and improve students' ability to solve problems.
Teaching process:
First, situational introduction
Do students like pancakes? Who has baked a cake, or has seen my parents bake it? Can you tell us about the process of making pancakes?
2. There is also math knowledge in pancakes. In this class, we will go to the wide angle of mathematics to learn about pancakes.
Second, explore new knowledge.
1, teaching example 1.
Show guests making tea at home.
Xiao Ming, pour a pot of water for mom and make a cup of tea for aunt Li. How can I get the guests to drink tea as soon as possible? Observe and understand the situation diagram. What would you do if you were Xiao Ming? How long will it take? Discuss with your classmates and see whose plan is more reasonable. Design the scheme in groups and think about it: which things should be done first in these processes? What can I do at the same time? Comparison: whose scheme takes the least time? Whose scheme is the most reasonable?
2. Teaching example 2.
Picture showing the situation: Mom is baking a cake. She can only bake two cakes at a time for three minutes on each side. The little girl said: Mom and Dad, I am alone, and asked: How can I eat the cake as soon as possible?
Think independently first, then discuss and communicate in groups. How did you arrange it? How long will it take for your plan to be branded?
Q: How many minutes does it take to bake a cake? How about flipping two? One * * * needs to bake three cakes. How can I bake for the least time?
Q: How else can you build a brand? Which method is more reasonable?
Inspiration and guidance: When baking the third cake in the second method, only one cake is baked in the pot that can bake two cakes at a time, which may waste time. Think about it, will there be a better way? Enlighten students to find that if you bake two cakes in the pot every time, you won't waste time. Q: You have to bake the front and back of the cake for 3 minutes. How to arrange to bake two cakes at a time?
Students began to use coins and textbooks to represent cakes.
Q: If you want to bake 4 cakes and 5 cakes ... 10 cake?
How to arrange the most time-saving? Discuss in groups and talk about your findings.
3. Complete the method used by Tian Ji in horse racing.
Third, consolidate new knowledge.
Math game:
1, two people take turns to report, only 1 or 2 at a time. Add up the figures reported by two people, and whoever reported 10 will win.
Think about it: if you were allowed to count first, how much should you count for the first time to ensure victory? What should I report next?
2. If two people report in turn, they must report a natural number not greater than 5, and the numbers reported by two people in turn are added. Whoever reported the number, the sum is 100, wins.
If you were allowed to count first, what would you count the first time to win? How to report it later.
The teaching goal of the fourth grade mathematics optimization teaching plan 3;
1, through the cooperative exploration of life optimization problems, understand reasonable and rapid problem-solving strategies and improve students' problem-solving ability.
2. Feel the application of the idea of overall planning in daily life, and try to solve practical problems with the method of overall planning.
3. Make students accumulate experience in mathematics activities in independent exploration and cooperation and exchange, and gradually form a good habit of arranging time scientifically and reasonably.
Teaching emphases and difficulties:
Focus: Try the process of reasonable time arrangement and realize the importance of reasonable time arrangement.
Difficulty: master the method of reasonable time arrangement.
Teaching method: heuristic method
Learning method: practice method
Teaching aid preparation:
multimedia courseware
Teaching process:
First, contact life and talk about getting started.
Students, have you ever done housework? Who can tell me what housework they have done? (Students speak)
Xiaoming also takes the initiative to help his mother do housework on weekends. Listen, what did he do? (Courseware demonstration)
Sweep the floor, clean the table and boil water.
Time 8 minutes 2 minutes 10 minutes
He also recorded the time of doing housework. Guess: How many minutes does it take Xiao Ming to finish these chores?
Today we are going to study science and reasonable time arrangement. (Show the topic)
Second, create situations and explore new knowledge.
1, tea making problem
Who made the tea? Raise your hands, please. What do you usually do when making tea? What will you do first? What should I do after that? Estimate how long it will take you to do these things
Between? (Name)
(2) Take a look. How many things did naughty tea make? (Show the courseware) What information did you get from the picture?
If you are naughty, how long will it take to finish them one by one? But Xiao Ming is a good boy who loves thinking. What's he thinking? (Show courseware), how can we do it as soon as possible?
Let the guests drink tea quietly? How to understand the word "as soon as possible"
Clever Xiaoming wants to compare with everyone to see who can design the best tea-making scheme. Show courseware.
Xiao Ming also sent us a warm message: When designing, we should consider: 1, what should we do first? Do what again? What can I do at the same time? 2. available
The arrow → indicates the order of doing things. 3. After your reasonable arrangement, how long will it take to work out a * * *? How much time was saved? Next, take the group as a single.
Bit, cooperative exploration, and Xiao Ming. Blackboard demonstration.
(3) Communicate with each other to see whose design scheme is reasonable and time-saving.
(3) Students show and explain the design scheme, and students observe collectively.
Scheme A: Wash the pot 1 min → take water 1 min → boil water for 8 minutes → make tea 1 min.
Wash the teacup for 2 minutes.
Looking for tea 1 min
1+1+8+1=11(minutes)
Scheme B: Wash pot 1 min → take water 1 min → boil water for 8 minutes → make tea 1 min.
Looking for tea 1 min
Wash the teacup for 2 minutes.
1+1+8+1=11(minutes)
Scheme C: Wash the pot 1 min → take water 1 min → boil water for 8 minutes → find tea 1 min → wash the teacup for 2 minutes → make tea 1 min.
1+1+8+1+2+1=14 (minutes)
Which of these schemes do you think is the most reasonable and time-saving? Why (at the same time) students say that the teacher writes on the blackboard. Show courseware and guide students to read.
Flowchart.
At this point, the naughty plan also came out. (Show the courseware), can you understand his tea-making plan?
Please think again, what else can you do at that time? (Student says) How long can it be kept? How many more things did you do? (reveal: things done at the same time
The more love you have, the more time you save.
As Xiao Ming wrote this chart, we call it a "flow chart"
Third, solve problems with knowledge.
1, guide the students to finish the pancakes on page 82 of the textbook. Group report and communication.
Fourth, in-class training.
1. Judgment: Is this a reasonable arrangement of time? Why? (Courseware demonstration)
A, Xiao Dongdong watches TV while eating.
B, ride a bike while talking on the phone.
C. walk and watch.
D, playing football on the road.
Five, talk about the harvest, the class summary.
What other things in life can be improved through reasonable arrangements?
Summarize the class: What did you gain from today's study?
Finally, the teacher gave everyone a sentence from the great writer Lu Xun, encouraging everyone (courseware): "Time, every day is 24 hours, but one day."
Time brings wisdom and strength to diligent people, leaving only regret to lazy people. "
Sixth, homework
Blackboard design:
Arrange the time as a whole
Scientific, reasonable, orderly and synchronous completion.
The best scheme: washing the pot → receiving water → boiling water → making tea.
Wash the teacups together
Shizhan tea
Reflection after class:
The fourth grade mathematics optimization teaching plan 4 teaching content:
People's Education Edition, the first volume of mathematics in the fourth grade of primary school, page 1113, example1and example 2, page 1 14, do it.
Teaching objectives:
1. Let students experience the application of operational research and game theory in solving practical problems through simple examples.
2. Make students realize the diversity of problem-solving strategies and form the consciousness of finding the best solution to the problem.
3. Let students learn to arrange their time reasonably.
Teaching emphases and difficulties:
We can find the best solution from various solutions to this problem.
Teaching aid preparation:
Multimedia courseware, group self-study outline, process diagram.
Teaching process:
First, create a situation
Teacher: When I was reading a book last night, I suddenly (voice-activated door: doorbell rang) to see who came. (Demonstration courseware)
Teacher: What else do you see from the picture? (Miss Xiao is making tea for the guests) What do you do when making tea?
Second, explore example 2
1, read it
Teacher: What does a teacher do? How long will it take? (Courseware gives example 2) Free reading.
2, put a pendulum
Teacher: Which of these things should be done first and which can be done at the same time? Work in groups and put a flowchart. Let's go
Step 3 talk about it
Teacher: Which group will tell you about it?
Teacher: How many minutes does this arrangement take? How to calculate? Why only add "8"? (Because you can do other things while boiling water, saving time) Is there a faster way?
Step 4 draw a picture
Teacher: In order to show the process of making tea more clearly, we are used to drawing arrows. This is called flow chart (blackboard writing: flow chart). Please draw the process of boiling water in groups.
5. Summary
Teacher: What inspiration did you get from solving the problem of boiling water? Try to do things at the same time, which can save time.
6. Exercise: This book 1 14 pages (2).
Teacher: Teacher Wu told me a message: Li Xiaoqing was ill. How to arrange these things? Please show it in the exercise book with a flow chart. Teacher: (showing individual methods) Is this a reasonable arrangement? Why? This arrangement can save time, so you can have more rest. )
7, lead to the topic
Teacher: Problems like this are called "optimization problems" (chessboard problems). "Optimization" requires choosing the best solution.
Three. Query case 1
1, example 1 theme map
Teacher: Xiaoqing likes pancakes. Shall we prepare some for her? What information do you learn from the picture? (Students casually say)
Teacher: How long does it take to bake only one cake? How to brand?
2, independently explore the situation of flipping 2 and 3 cakes.
Teacher: How long does it take to bake two or three cakes? How to brand? Work in groups and draw a circle on it to complete the first study outline.
(Group activities)
Teacher: How many minutes can two cakes be used at the earliest? How to brand? Teacher: How about three? Ask individual students to demonstrate on the platform in order to find the best method. Teacher: Show me again, teacher. (Demonstrate while talking) Bake the cake 1 and the front of cake 2 first.
It takes 3 minutes; Bake the reverse side of cake 1 and the front side of cake 3 for 3 minutes. Finally, it takes 3 minutes for the reverse side of pancake 2 and pancake 3, and 9 minutes for a pancake. What did you find from the demonstration? There are two cakes in the pot at a time, which saves time. ) Teacher: This is the best way to bake three cakes. Take out your three round cakes and put them out.
Say it.
3. Turn over 4 or 5 cakes.
Teacher: Can you bake four cakes in the way you learned before? (Yes, divide it into 2 +2 brands) How many minutes does it take? How about five cakes?
4. There are many cakes.
Teacher: There are too many cakes. How to bake them quickly? How many minutes per person? After group discussion, complete the self-study outline II.
5. Summary:
When the number of cakes is even, two cakes are branded; When the number of cakes is odd, two cakes are branded first, and the last three cakes are branded by the best method. This is the most time-saving.
Fourth, life examples.
1, reading questions.
2. What do you get from these questions? Reasonable arrangement of things can save time and improve efficiency.
3. What other things in life can be improved through coexistence? Let's discuss in groups.
Verb (abbreviation of verb) practical application.
1, dining topic: book 1 14 page (1) topic.
Teacher: It's getting late. I will take Mr. Wu to a delicious restaurant for dinner. (Courseware demonstration topic) Group exchange opinions.
Summary: Try to take care of one guest and cook for one more guest.
2. Amusement park problem
Complete the following things in groups to see which group is faster and better: 1) Copy 4 word cards, 2) Complete 5 mouth cards, 3) Give the mouth cards to the teacher for wholesale, 4) Stop handing in word cards and mouth cards and replace the admission ticket.
3. Summary
Teacher: Looking back on today's study, what have you gained or learned? What do you think of your performance? What about the team members? What about the teacher?
Six, evaluation and analysis table.
Fourth grade mathematics optimization teaching plan 5 teaching material analysis:
Before the fourth grade, students have already known the figures such as cuboid, cube, cylinder, rectangle, square, triangle and circle, which are scattered in their minds. On the basis of students' existing knowledge, this lesson is to guide students to sort out and summarize these learned graphics, conduct comprehensive exercises on these graphics, build a preliminary graphic knowledge system, and cultivate students' ability of comparison, classification, induction and generalization. At the same time, through students' hands-on operation, we can find the stability of triangle and the instability of quadrilateral, and make students realize the application of triangle stability and quadrilateral instability in life with life examples.
Teaching objectives:
Knowledge goal: Organize graphics and understand the characteristics of different types of graphics through specific classification activities. Through practical operation, I realized the instability of quadrilateral and the stability of triangle, and realized the application of these characteristics in daily life.
Emotional goal: pay attention to cultivating students' ability to solve problems by using mathematical knowledge in graphic understanding activities. Experience the process of exploration in practice and improve the ability of independent exploration, cooperation and communication.
Skill goal: According to the characteristics of graphics, graphics can be classified according to certain standards.
Teaching focus:
Be able to classify graphics according to certain standards.
Teaching difficulties:
Understand the instability of quadrilateral and the stability of triangle.
Teaching preparation:
All kinds of plane figures and three-dimensional models made of cardboard, such as cuboids, cubes, cylinders and spheres.
Teaching process:
First, review the questions and introduce new lessons.
Show the courseware and ask: What graphics have we learned before?
The teacher draws or finds out the corresponding graphic model according to the students' answers.
Think about it: can you classify each figure according to its characteristics? Title of teacher's blackboard writing: graphic classification
(1) is divided into one point: let students try to classify independently and use the method of labeling. (You can also draw a picture to classify). And communicate the classification method with the deskmate.
The reasons for the classification of group reports.
Three-dimensional graphics and plane graphics
(1) three-dimensional graphics;
(2) Plane figures of rectangles, squares, triangles and parallelograms (surrounded by line segments).
Teacher: Can the plane figures we just separated be reclassified? Have a try.
1. Plan (according to whether the line segment is closed or not)
Rectangular, square, triangular, parallelogram,
(Pentagon ...) Circle
2. Plane graphics (according to the number of corners or according to the number of edges)
Rectangular, square, triangle, parallelogram triangle
3. Plane graphics (according to whether there is a right angle)
Rectangular, square. Triangle, parallelogram.
Teachers and students are classified by the same summary.
Second, practical activities: (exploring the characteristics of quadrangles and triangles)
1. Students take out the prepared movable quadrangles and triangles.
Teacher: Laura, what did you find? Communicate at the same table.
2. Report and write it on the blackboard.
Summary: parallelogram is easy to deform and has no stability. Triangles are stable.
3. Show the courseware. Watch the application of these graphics in life.
Third, consolidate the application.
It's time for us to say goodbye.
1. Trapezoids and parallelograms are quadrilaterals. ( )
2. Both triangles and parallelograms are stable. ( )
3. The figure composed of four sides is a quadrilateral. ( )
Draw a picture
1. Please use a line segment to divide a square into two identical triangles.
Please divide the picture below into triangles and parallelograms.
Fourth, class summary.
What did we learn in this class?
You can take it out and answer. Or take a collective answer.
Verb (short for verb) homework
1. Draw a graphic classification table in your own way.
2. Complete the 13 page campus workbook.
Blackboard design:
Graphic classification
Stereographic figure
Graph: a graph surrounded by curves.
plane graph
A figure surrounded by line segments.
We find that quadrilateral is unstable and triangle is stable.