The first is the organic combination of "three calculations"
Oral calculation, estimation and pen calculation are inseparable organic unity in computing teaching. However, in actual teaching, some teachers are used to strictly distinguish between oral calculation, estimation and written calculation. The topic requires oral calculation, estimation and written calculation, and it is taught in isolation, which is not conducive to the cultivation of students' computing ability and good sense of numbers. In teaching, we should seize the opportunity to explore the internal relationship between oral calculation, estimation and written calculation, organically combine them, skillfully use their relationship to pave the way for students' thinking, realize the harmony and unity of various algorithms, and make the combination of arithmetic and algorithms reach a vivid situation.
Teaching clip 1
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Teacher: Kid, the teacher brought you some boxes of watercolor pens. (Show an example) How many watercolor pens are there in 3 boxes? How to arrange them?
Teacher: Tell me what you think. (simple answer)
Teacher: Estimate, how many sticks are there in three boxes?
Health 2: 48 is less than 50, so it must be less than 150.
At 3: 48, there are nearly 50 branches, 50×3= 150, about 150 branches.
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Teacher: Through estimation, we all know that there are about 150 markers in three boxes. How many are there? Try to find out.
The students explored the calculation method independently, and the teacher made a careful inspection and found that most students tried to use vertical calculation, but a particularly active student in the class wrote the answer directly.
Teacher: How do you calculate it?
Health 1: My oral calculations are: 8×3=24, 40×3= 120, 120+24= 144.
Teacher: This is a very good method. He is a good boy who loves thinking.
In group communication, the teacher writes the children's methods on the blackboard first.
Teacher: Can you understand his algorithm?
At this time, many students have raised their hands.
Health 2: I can understand. He divided 48 into 40 and 8. Multiply 8 by 3 times 24, then multiply 40 by 3 times 120, and then add their results.
Teacher: It's clever to think of dividing to solve new problems.
Student 3: Teacher, I calculated with a pen and got 144.
Teacher: Oh, please come up and write down the process on the blackboard.
Born on the blackboard:
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Teacher: Why should 14 in 1 4 be written in hundreds and ten digits respectively? (simple answer)
Teacher: Is there any calculation error? Who wants to share it with you?
Health 4 (embarrassedly): Teacher, I did it by hand, but I forgot to add two tens. The result is 124.
Teacher: I wish I could find my own mistakes! I hope you don't forget to "carry" when you calculate in the future.
Health 5: Teacher, I just added four tens and two tens, and forgot to multiply four times three times ten.
Teacher: Oh, would you like to show everyone your homework?
Show students' mistakes:
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Health 6: Teacher, in fact, we just estimated that it was 150, and he got 64, which must be wrong.
Teacher: Considering the estimation, you are very clever. Because of this, people are used to estimating before or after written calculation, which can help us grasp the results quickly.
Teacher: Just now, the children thought of oral calculation and written calculation. Is there any connection between these two methods?
After the students thought independently for a moment, a pair of small hands raised.
1: I found that 8×3=24 in oral arithmetic is the number of units multiplied by a vertical number:
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According to the students' answers, the teacher writes on the blackboard and adds arrows.
40×3= 120, that is, the number in the tenth place is multiplied by one place.
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Teacher: Oh? But there is no 120 in the vertical position?
Health 2: That's because it keeps 120 in mind and directly adds 24 to get 144.
Health 3 (interrupted): It's just two steps.
Teacher: You see, oral calculation and written calculation are different, but when you think about it carefully, it turns out to be the same.
In fact, oral calculation, written calculation and estimation are inseparable. Proper use of them can bring us great convenience. For the teaching of example 48×3, let students estimate the approximate figures first, which will help students to grasp the results and feel the value of estimation before accurate calculation. After accurate calculation, the accurate result is compared with the estimated value to test whether the result is reasonable and provide support for determining the calculation result. It can be seen that estimation can serve oral and written calculations, and it has a certain monitoring and inspection effect on oral and written calculations. For the accurate calculation of this problem, the author does not require students to use vertical calculation according to the requirements of the textbook, but gives them more open space for independent exploration, so there are two forms of oral calculation and written calculation. I think oral calculation is more helpful for students to understand arithmetic than vertical calculation. Some students with learning difficulties often know why vertical calculation is too standardized and programmed, so the author thinks that oral calculation should be emphasized first, and then vertical calculation should be introduced, which can make the algorithm and calculation more intuitive and natural. Finally, organize students to find the connection between oral calculation and written calculation, so that students can see the evolution process more clearly, so as to achieve students' deep understanding of arithmetic and practical mastery of the algorithm.
Second, flexible use of "three calculations"
Learning mathematics knowledge should be applied to specific problems in real life, which is the practical value of learning mathematics. Oral calculation estimation is simple, fast, flexible and convenient, which has a wide range of application values in real life, and sometimes accurate calculation can not be separated from written calculation, so the three have different values. If the algorithm can be flexibly selected when solving practical problems, the cultivation of students' computing ability and good sense of numbers will certainly develop in practical application.
Teaching clip 2
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After the students answer independently, communicate in groups.
Teacher: Who wants to share your method with everyone?
Health 1: I listed it this way, 69×4=276 (one), and a * * * needs 276 wheels, which is enough.
Teacher: If you do this, please raise your hand.
More than half of the class raised their hands.
Student 2 (can't wait): Teacher, this is too much trouble!
Teacher: Tell me about your method.
Health 2: My formula is the same as his, but it is too much trouble to calculate 69×4. Actually, you can tell by an estimate.
Teacher: Oh? what do you think?
Health 2: I regard 69 as 70, 70×4=280 (pieces). 280 wheels can hold 70 cars, which is enough.
The teacher took the lead in applauding, and the students all gave him a approving look.
Teacher: Yes! It is very convenient to use estimation for such a topic that does not require accurate calculation results.
The teacher didn't stop there, but waited quietly. After a while, several students raised their hands.
Student 3: Teacher, I use division and can compare directly with my mouth.
Teacher: Oh? Tell me.
Health 3: 280 ÷ 4 = 70 (cars), that is, 280 wheels can hold 70 cars, which is enough.
Teacher: It's smart to think from different angles. In this way, you can make a verbal comparison, which is very simple!
Many students couldn't help applauding his method, and applause rang out again in the classroom.
Teacher: So when you meet different types of questions, you should not only understand the meaning of the questions, but also learn to observe the characteristics of the data and choose the methods flexibly.
Solving the question "Is 280 wheels enough?" What most students think of is the comparison of the writing methods of the column multiplication formula. At this time, they don't try, but leave enough time for students to think deeply. They find that multiplication with pen is not the only way to solve this problem, and it is easier to do oral calculation directly with multiplication estimation or column division formula. Therefore, students can realize that oral calculation, estimation and written calculation all exist around us, and feel that flexible selection of methods according to the meaning of the problem and the characteristics of the data can bring great convenience to our study and life.
Improving students' computing ability is a meticulous and long-term teaching work. Therefore, we must do more practical research, grasp the true meaning of oral calculation, estimation and written calculation teaching, and strive to infiltrate, combine, support and promote the "three calculations" so as to continuously improve students' computing ability and gradually enhance their mathematical literacy.
(Editor: Li Xuehong)