Optimizing Teaching Design Part I: Teaching Objectives;
1, so that students can realize the diversity of problem-solving strategies through simple examples such as "making tea" and "pancakes", initially realize the application of optimization ideas in solving practical problems, and form the consciousness of finding the best solution.
2. Feel the application of the thought of overall planning in daily life, and try to solve the problem 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 scientific and reasonable time arrangement.
Teaching emphases and difficulties:
Focus: Try the process of reasonable time arrangement and realize the importance of reasonable time arrangement.
Difficulties: master the method of reasonable time arrangement, and enhance the consciousness of using mathematical knowledge to solve practical problems in life.
Teaching process:
First, talk to stimulate interest and introduce new lessons
Students, we all know that life is the most precious thing for people, and time is the most important thing to cherish. To cherish time, we must learn to arrange time reasonably. Today, let's use the idea of optimization to learn how to arrange time reasonably.
Second, create situations and explore new knowledge
Situation 1: the problem of making tea
1, question introduction: What do you usually need to do when making tea?
What will you do first? What to do after that? Estimate how long it will take you to do these things.
2. The courseware shows the situation map. What information do you get from the picture? How to arrange can save time?
3. Let the students communicate at the same table first, then guide them, arrange the time reasonably, and consider the order of things. Think about what can be done at the same time.
4, deskmate cooperation, design scheme.
5. Communicate with each other and show the scheme.
Show the flow chart of courseware:
Option a: do it one by one:
Option B: Do several things at the same time:
6. Which of these schemes do you think is the most reasonable and time-saving?
Summary: It seems that to arrange the time reasonably, we should not only consider the sequence, but also consider the things that can be done at the same time, so as to save time. We call this scheme of making tea in the shortest time the "optimal scheme", and this idea is the "optimization" idea.
Situation 2: pancake problem
1, show situational pictures: guide students to observe and find the key mathematical information: you can only bake two cakes at a time, both sides should be baked, and each side takes 3 minutes.
2. Organize activities: Next, have a pancake contest to see who is the smartest pancake maker.
Guide the students to put a pendulum with coins or pieces of paper, and then show the process by drawing. The teacher will patrol for guidance.
Name the process of showing pancakes on stage and say how long it took.
The courseware shows the schematic diagram of pancakes:
3. Summary: This arrangement takes the least time, which is the optimal method.
Third, consolidate the use, expand and upgrade
Explore the law of the time it takes to bake 4 cakes and 5 cakes.
Knowing the optimization method of baking three cakes, what is the optimization scheme of baking four cakes and five cakes?
Ask the students to work as a group, discuss the operation and find the optimal method, and record the process.
The whole class reported the exchange and came to the conclusion:
Fourth, contact life and train in class
Is this a reasonable arrangement of time? Why?
A, Xiao Dongdong watches TV while eating.
B, ride a bike while talking on the phone.
C. read while walking.
D, playing football on the road.
Five, talk about the harvest, the whole class summary
What other things in life can be improved by reasonable arrangement?
Summarize the whole class: What have you gained from today's study?
Optimizing Teaching Design Part II: Learning Content: Compulsory Education Beijing Normal University Edition Primary School Mathematics Grade Four Volume II Page 8 1-82
Core Literacy: Cultivating Students' Application Consciousness
Curriculum standard requirements: solving simple practical problems from the perspective of optimization
Teaching material analysis:
Optimization problem is a common mathematical problem in life. This lesson takes "making tea" and "pancakes" as the background, and encourages students to try to find the best solution among various solutions to problems. "Making tea" first presents the things and time needed to make tea in an illustrated way, and then gradually guides students to try to solve how to save time in making tea with three questions; By discussing what can be done at the same time, optimizing the program saves time; By calculating the time required by different programs, we can further understand the optimization idea. "Pancake" clarifies two contents through the situation map: first, the tasks of this pancake activity-each of dad, mom and me 1 cake; The second is the basic method of pancake. In this regard, the textbook puts forward three questions: the question 1 is to let students try to solve the problem of how to eat cakes as soon as possible; Question 2 is to understand the methods that are difficult to learn by reading mom's practice; The third problem is to continue to solve a large number of pancake problems by using methods, and explore its time-saving law to further understand the optimization idea.
Learning situation analysis
The fourth-grade students are in the transition period from concrete thinking to abstract thinking. Based on the existing experience of mathematical interpretation, operation, calculation, comparison and diversification of methods, they can express mathematical problems and solving processes in different ways and methods, understand the extensive application of mathematics in daily life, solve practical problems in life with mathematical knowledge, and have the consciousness of mathematical application and reasonable time arrangement.
learning target
1. Experienced the process of solving simple practical problems from the perspective of optimization, and initially realized the application of operational thinking in solving problems.
2. Feel the extensive application of mathematics in daily life, and cultivate students' awareness of application and reasonable arrangement of time.
3. In the process of solving problems, realize the significance of optimization, stimulate students' interest in learning mathematics, and establish the concept of cooperative learning.
Learning focus
Through the process of solving simple practical problems from the perspective of optimization, I have a preliminary understanding of the application of operational thinking in solving problems.
Learning difficulties
Find the best solution from a variety of solutions to simple problems in life.
learning process
First, the introduction of interest, preliminary understanding and optimization
Brain teaser: It takes 5 minutes to cook 1 egg, and how long does it take to cook 4 eggs?
Default1:20 minutes (how to cook? )
The default is 2: 5 (how to cook? )
Which scheme would you choose? What do you think?
In life, we can choose a more reasonable plan according to the actual situation. For example, considering saving time, cooking four eggs together is an optimal plan. Today, we will explore and solve the optimization problem in life.
(blackboard writing topic: optimization)
Diagnostic evaluation: test students' life experience and common sense through their answers.
Design intention: Interesting math activities can effectively stimulate students' interest in learning and mobilize the classroom atmosphere. In the process of thinking, students realize that doing some things at the same time can save time and understand the significance and purpose of optimization.
Second, make tea reasonably and gradually understand and optimize.
(Show the situation map)
Just now, everyone will think especially and praise you! In order to praise everyone, the teacher brought a picture. Please observe it carefully and describe the mathematical information in the picture with mathematical stories.
Please think:
What should I do first to make tea? What will be done later? How long will it take?
Students report and show.
Preset 1: washing kettle-washing teacup-looking for tea-receiving water-boiling water-making tea1+2+1+8+1=14 (minutes)
Preset 2: Wash the teacup-find the tea-wash the kettle-receive water-boil water-make tea 2+1+1+8+1=14 (minutes)
Preset 3: Wash the kettle-receive water-boil water (wash the teacup, find tea)-make tea? 1+1+8+1=11(points)
Everyone used their brains and worked out different plans for making tea. Which plan saves time?
Do you have any questions about making tea?
Summary: Although the 3 minutes saved by the optimized scheme is very short, we can read a math story, run 500 meters and do a good deed.
Communicative evaluation: Test the achievement of learning goal 1 through students' answers.
Design intention: Students should list the workflow first, and then consider how to optimize it; By discussing what can be done at the same time and going through the optimization process, we can describe the order of making tea in words and flow charts; Compare the time required by different schemes, further feel the value of optimization, and deepen the understanding of reasonable and overall arrangement.
Third, skillfully pancakes, in-depth exploration and optimization
After drinking the naughty tea, my mother was warm and ready to make his favorite pancakes.
(Show the situation map)
Talk about the mathematical information in the picture.
How many cakes does mom need to bake? How many minutes does it take to bake 1 cake to bake 2 cakes?
It takes the same time to bake 1 cake as it does to bake 2 cakes. Why?
Two cakes can be baked in the pot at the same time, which can save time. This is the optimization in the cake baking problem.
1, cooperative learning: How can three naughty families eat cakes as soon as possible?
Requirements:
Replace the cake with a wafer, operate it by hand, and make a reasonable pancake scheme.
Default 1: one pancake takes 6 minutes, and three pancakes take 18 minutes.
Preset 2: It takes 6 minutes to bake two cakes together, 6 minutes to bake the third cake, and 1 * * * takes 12 minutes.
Preset 3: bake the front of 1 and the front of No.2 cake first, which takes 3 minutes; It takes 3 minutes to re-bake the reverse side of 1 and the front side of No.3 cake; Finally, it takes 3 minutes to bake the reverse side of the No.2 cake and the reverse side of the No.3 cake, and 9 minutes for one * * *.
Summary: There are two cakes in the pot every time, which saves time, and mom saves more time and effort.
Communicative evaluation: Test the achievement of learning goal 1 through students' answers.
Design intention: Based on the existing experience, students can think about the reasonable operation scheme, which can be branded one by one, two before one, or two pots every time. They try to use the front and back of textbooks and other items instead of the front and back of the cake for experimental operation, and further understand the optimization scheme through interpretation, operation, calculation and other ways, and gradually optimize the thinking process.
2. How long does it take to bake 4 cakes and 5 cakes?
3. What did you find?
Default 1: add 3 minutes each time.
Preset 2: Starting from 2 cakes, the number of cakes multiplied by 3 is the required time.
Presupposition 3: No mathematical law is found, and the teacher points out the law (if the number of cakes to be baked is even, you can bake two cakes; if the number of cakes to be baked is odd, you can bake two cakes first, and then bake the last three cakes in an optimal way, so as to achieve the overall optimization).
It turns out that there are mathematical laws in the pancake problem, which is really wonderful!
4. Do you have any questions about pancakes?
Summary: Optimization is a common problem in life. Optimization scheme can help us save time and solve problems efficiently. Please study optimization seriously.
Interactive evaluation: through the students' answers, the achievement of learning goal 2 is detected.
Design intention: In the process of solving four or five cakes, guide students to discuss the methods of exchanging four or five cakes, encourage students to explore and discover the law, and infiltrate the connection between knowledge.
Third, arrange homework, consolidate and expand optimization
In mathematics learning, there are not only time optimization, but also combination optimization. For example, the problem of graph coloring-in the map of China, two neighboring provinces are painted with different colors, and at least several colors are needed.
There are many examples of optimization in life. Please pay attention to them and record them with math diary, math stories or math picture books as today's math homework.
Interactive evaluation: through the students' answers, the achievement of learning goal 3 is detected.
Design intention: Mathematical culture is helpful to cultivate students' rational thinking and creative thinking. Through the understanding of mathematical operations research, mathematical culture can be infiltrated and the quality of mathematical culture can be improved.
Fourth, learning summary, mutual evaluation of classroom performance
What did you learn in this class? Any questions? What do you think of your performance? What about classmates? What about the teacher? Please complete the classroom evaluation form and make a process evaluation.