teaching program
Teaching content: problem-solving strategies, the first volume of the third grade of Jiangsu Education Press, 7 1-73 pages.
Teaching objectives:
1. In the process of solving practical problems, students can initially learn to think, analyze and solve related problems based on conditions.
2. Make students feel the value of problem-solving strategies and develop the ability of analysis, induction and simple reasoning in the process of constantly reflecting on solving practical problems.
3. Enable students to further accumulate experience in solving problems, enhance their awareness of problem-solving strategies, gain successful experience in solving problems, and improve their confidence in learning mathematics well.
Teaching preparation: multimedia courseware, related exhibition boards and stickers.
Teaching process:
Communication before class:
Nine children want to cross the river. There is only one boat by the river. There is no boatman on board. Only five people can sit on the boat at a time. How many times will it take to get all nine people across the river?
Can you think of a good way to help them cross the river?
First, enter a new lesson
Just now, the students solved the problem of life with what we have learned. In fact, solving math problems also requires strategy. Today, let's learn the strategies to solve the problem.
Second, learning guidance and exploration
Understand the meaning of the problem
1, showing the conditions: "The little monkey helped his mother pick peaches, picking 30 on the first day, and picking 5 more on the second day than on the first day."
What information did you learn from the topic? Mathematically, known information is called conditions. With these two conditions, you can ask questions. Let me see the question: How many did you choose on the third day?
Students answer orally.
Point out: The teacher just set a trap. According to these two conditions, we can only find out what we picked the next day, but not how much we picked the third day!
2. If I change one of the conditions, it shows that the modified condition is "five more than the previous day", can I forget it now?
It seems that this condition is quite magical? Let's have a look. Pick five more than the day before. What do you mean?
Default 1: the second day is more than the first day, and the third day is more than the second day. ...
The student sees that this condition looks simple, but he can find so many implied conditions from it and express them in an orderly way. Awesome! Who can speak in an orderly way like him?
Through roll call and multimedia presentation: the next day, five more than the first day ... the fifth day, five more than the fourth day.
Follow-up: Can you continue? Let me see: the sixth day is more than the fifth day ... can we continue? There are too many conditions, so many conditions can be summarized in one sentence. Let's talk about multimedia transformation together, and all the contents will be integrated into "five more than the day before".
Transition: Students really think. Can this sentence be thought from another angle?
Introduction and statement: +5 the first day = the second day. Can you understand what he means when demonstrating the courseware? The teacher understood that he was thinking backwards. Picking five more than the day before is the day after. You got it? Who can continue? Combined with the answers, it shows +5 the next day = the third day. ...
So many conditions actually mean the same thing. All conditions are hidden and converted into "+5 picked the day before = picked the day after". Let's read it together.
Default 2:
No one can say for sure. Can every day in the future be the second day? If it's the second day, choose five more than the first day. Stick your fingers on the board, that is to say, pick five more than the first day the next day. Can every day in the future be the third day? If it is the third day, then-on the third day, pick five more boards than the second day.
Default 3:
Students answer 30+5.
When was 30 chosen? What do you need five for? That is to say, the +5 picked on the first day is equal to the next day. Can you understand what he means when you show the courseware?
……
Transition: Students really think. Stay on the big screen: pick five more than the day before. Can you still think about this sentence from different angles? Default 1 before transition
Summary: a seemingly simple condition for everyone to explore, but found so many continuous implicit conditions, which is the charm of mathematics.
Second, analyze the quantitative relationship.
Can so many conditions solve our problems? What are you going to say? Think first, then talk to your deskmate.
Three-column calculation
1, is there any way? Write down your ideas in the exercise book.
1 Students practice by themselves.
2 communication:
Show the formula of 1: Tell me what you think.
Combined with the introduction of students, the formula of camera blackboard writing is calculated. What does 35 mean? What about these five? What do you want? You see, the result of the first step, as the condition of the second step, helps us solve the next problem. Mathematics is like this, constantly changing between the known and the unknown. Is the problem solved? Answer it together.
Exhibit 2 Presentation Form: Can you understand this classmate's method? Somebody tell me. The student said that he made a list and wrote down the daily picks in turn. How about this method?
2. Show me the question: How many did you choose on the fifth day?
Requirements of 1: No discussion, independent solution. Think about how to do it first, have you thought about it? Take out the homework paper, the first question, you can fill in the form or calculate it in a list, the time is 1 minute, and go.
The students finish the calculation and the teacher makes a tour.
3 show communication.
Show 1: Watch the big screen together. He chose to fill in the form. Take a look. Is that correct?
Evidence 2: He answered continuously. I picked 50 on the fifth day, right? On the fourth day, what two conditions did you use to test you and make demands? According to what you picked on the third day, you can calculate what you picked on the fourth day. With what you selected on the fourth day, you can calculate. ...
Exhibit 3: Display mode: 5×4=20, 20+30=50.
A classmate did this. Is this correct? How is 5×4 calculated?
Do you think it makes sense to assume that the teacher does this? How is 5×4 calculated?
The fifth day is 20 more than the first day, right? what do you think?
I didn't watch it on the first day, and then I got one more five every day than the day before. On the fifth day, there were several fives more than on the first day. That's twenty. Knowing that this extra 20, plus the first day's, is even the fifth day. How about the method? Not bad, huh?
Fourth, reflection and summary.
1, induction.
Just now, we thought of three methods and showed them with multimedia. The two of them have the same way of solving problems. Did you find them? How do they calculate it?
Summary: It all comes from the conditions of picking on the first day, picking more on the second day than on the first day, and picking on the second day. If there is a second day, you can work out what to pick on the third day according to this condition. In this way, you can work out the fourth and fifth days in turn. Students, thinking from such conditions and calculating the method to solve the problem step by step is the strategy to solve the problem. Show arrows.
Let's look at the third method. According to these conditions, we found that the fifth day picked four fives more than the first day, and then added the first day to solve the problem. Although this method has different ideas, it is also a strategy derived from conditions.
2. Looking back.
Students, we have solved a complicated problem together. Let's review the process of solving problems. What are the steps?
① Health: We should think from the conditions.
Teacher: Yes, thinking from the conditions is the strategy to solve the problem. Determine what counts first, and then determine what counts according to the corresponding conditions. This step is called-analyzing quantitative relations.
② Health: I know that I can fill out forms or do columns.
Teacher: Well, this step is to calculate the answer sheet. There are many ways to answer questions, such as filling out a form or enumerating.
③ Preset 1: Health: Find the conditions before solving the problem.
Teacher: We should look for both conditions and problems. For more complicated conditions, it is necessary to understand the meaning of each condition. This step is to understand the meaning of the question, which is the basis of other steps.
Preset 2: Health: Find conditions and problems.
Teacher: Yes, we must first make clear the conditions and problems. For more complex conditions, we must also find out the meaning of each condition. This step is to understand the meaning of the question, which is the basis of other steps.
Premise 3: Students can't figure out the problem. Teacher: No? I have always felt that one step is also very important, that is, to understand the meaning of the problem and show it. Do you know what it means to understand the meaning of the topic? Yes, it means to see clearly the conditions and problems in the topic, and to understand the meaning of each condition for more complicated conditions. This step is the basis of other steps, don't forget it.
Summary: To solve a math problem well, there must be at least three steps: understanding the meaning of the problem, analyzing the quantitative relationship, and calculating and solving.
Third, guide application and enhance understanding.
It seems that the students really gained a lot. In particular, mastering the strategy of conditional memory is a new skill. Want to use this skill? All right, give it a try.
Do what you want 1 topic.
1, 1.
1 Show the first picture. This is a kind of balance. What conditions do you see? Anything else? That is-display: four apples weigh 400 grams.
It is not easy. I found two conditions. What can I ask? Can you answer that?
Show the second picture and look carefully. What conditions do you see? So according to these two conditions, what can be found?
3 Show two pictures Just now, let's calculate the average weight of each apple according to the weight of four 400g apples. According to the fact that oranges are 20 grams heavier than apples, the quality of oranges is calculated. This problem-solving strategy is also based on conditions.
2. The second little question. There are three conditions for raising a topic. Can I ask questions according to these conditions?
1 Students ask questions, and the camera shows.
Which question do you think is the easiest? According to which two conditions? How to calculate? Show me the formula and get the number of pens. Now we can get the number of ballpoint pens. How to calculate?
I know the number of ballpoint pens, and this problem can be solved. Who will come?
Second, finish the second question "Think about it and do it".
The teacher 1 took out a ball, interacted with the teacher and students, and felt the ball fall and bounce many times.
2 show the questions and understand the conditions. "A ball falls from a height of 16 meters, if the height of each rebound is always half of its falling height."
There are two conditions, which do you think is more complicated? After the students say it, the multimedia will underline it.
The height of each rebound is always half of its falling height.
Students answer orally.
Combined picture: If this is 16 meters, where is the height of the first rebound? Who wants some?
Where is the height of the second rebound?
Show me the question: the third time ...: Understand the meaning of the question, can you analyze the quantitative relationship and solve the problem by yourself? Take out your homework paper and finish the second question.
Communicate and report. The first rebound. What about the second?
Reflection: What is the height of the third bounce? If you don't have the first two results, can you get the third result directly? Then with the result of the third time, we can further infer the height of the fourth bounce. Mathematics is like this, round and round.
Fourth, practice independently, enlighten and improve.
1, complete the "Want to Do" question 3.
1 name reading
Can anyone do this topic?
3 Show the circle. A circle means 1 child, so 18 circles mean ... Please find out the location of Fangfang and Bingbing according to the requirements of the topic, and then answer.
Who will report it? How many people are there between Fangfang and Bingbing?
Health: This is Fangfang's position?
Follow-up: What do you think? Where is Fangfang's position? What terms have you set? Where are the soldiers?
Considering the conditions, we solved the problem smoothly. Do you think drawing is helpful to solve this problem?
Point out: Sometimes the problem is difficult to understand, so drawing becomes easy to understand.
2. Expansion and extension
Transition: The students are great. The teacher wants to give you a present. Do you want it? I will give this gift to whoever solves my problem first. Are you ready? I have a question. Let's go
Display: Mom bought 3 boxes of apples, 5 kg each; I bought 4 boxes of pears, 40 kilograms more than apples. How many boxes of pears and apples did you buy?
Organize communication.
Follow-up: There are so many conditions, why only use two conditions?
It is pointed out that it is not necessary to think about the problem from the conditions, and sometimes it is also quick to think about the problem, depending on the specific analysis of the specific problem.
Verb (abbreviation of verb) class summary
Today we learned problem-solving strategies together. Did you get anything?
Blackboard design:
deprive
I picked 30 on the first day.
The key part of solving the problem was selected five times the next day, five times the third day, five times the fourth day, and five times more on the fifth day than on the fourth day ... How many did you pick on the third day? How many did you pick on the fifth day?