The third grade mathematics courseware of primary school: subtraction tower
Teaching objectives:
1. Knowledge goal: guide students to construct three digits and cultivate their ability of inquiry and induction.
2. Ability goal: know the method of constructing three digits and the minimum three digits; Master the difference and minimum difference between two three-digit numbers.
3. Emotional goal: to cultivate students' oral expression ability and thinking ability.
Teaching focus:
Master the difference and minimum difference between two three-digit numbers.
Teaching difficulties:
Minimum difference between two three-digit numbers
Teaching preparation:
number card
Teaching process:
First, migration and perception.
1. Introduction
Teacher: Son, we learned how to do numbers before. Now let's review how to make three digits with a digital card and see who does it more correctly.
2. Students do three figures.
Ac feedback
Teacher: What are you thinking when you have three figures? What is the number made of? What is the minimum quantity?
Organize students to recall mathematical methods, clarify learning tasks, enhance the pertinence and effectiveness of learning activities, and pave the way for learning new knowledge. 〗
Second, independent inquiry, building new knowledge
(a) Explore new calculation methods
Observe and think
Teacher: For example 1, how can you make those three digits with a digital card? (Students answer orally)
Operation and perception
Teacher: Next, let's have a little competition.
(1) Two people cooperate: use these six number cards to make three digits and the smallest three digits, and calculate their difference. (Check after doing)
(2) Make two three-digit numbers independently and calculate their difference. (Cross-check)
(3) Exchange two of the three digits just made and calculate their difference. (Cross-check)
(4) Inductive evaluation.
Students who are experienced in building three digits, such as 1, focus on calculating the difference of three digits, so the teacher regards it as a "warm-up match" for each child, so that they can feel and experience it in calculation. 〗
(2) Calculate the difference and the minimum difference.
Example 2: Choose six cards from the number card 123456⑦ ⑧ ⑨, put in three digits, and find the difference between the two numbers.
1. Calculate variance
(1) Think about it, how can we get the difference?
(2) Try independently and exchange feedback.
Blackboard: 987- 123=864
(3) Guide students to summarize the difference that can be obtained by subtracting the smallest three digits from three digits.
Cultivate students' self-study ability and independent thinking ability by trying to calculate and exchange feedback; Guiding students to summarize by themselves can cultivate students' language expression ability and generalization ability. 〗
2. Explore and calculate the smallest difference
Group work
A, how can we get the smallest difference? (looking for ways)
B, you can find several groups of numbers and try to calculate them.
Discuss whether the smallest difference has been found.
(2) Collective communication: How did you get the smallest difference?
Write on the blackboard according to the students.
3 12-298= 14、4 12-398= 14、5 12-498= 14、6 12-598= 14、7 12-698= 148 12-792= 14
(3) What are the characteristics of each formula? Irregular calculation of minimum difference?
(4) Demonstrate several rays.
(5) induction training for teachers and students
These two numbers must consist of six different numbers.
(2) The two numbers must be as close as possible in the number of rays to produce as little difference as possible.
Finding the minimum difference is a difficult point in teaching. Teachers should give students enough time and space to think and try to find ways, but teachers should make reasonable adjustments and give hints and guidance when necessary to avoid wasting too much time. In addition, in teaching, we should help students find and analyze the laws between numbers with the help of number rays, so as to use knowledge flexibly. 〗
(3) The difference is 45 1.
1. Students independently put out two three-digit numbers with digital cards, so their difference is 45 1.
2. Communication: the difference is 45 1. How did you find the minuend and the minuend?
Blackboard: 968-5 17=45 1, 876-425=45 1.
3. Teacher-student induction: You can assume that a three-digit number is greater than the difference, subtract the difference from the minuend to find out the reduction, and then check whether it meets the requirements.
Third, internalize new knowledge, integrate and extend.
1. Use the digital card 1245⑧ ⑨ to output two three-digit numbers and calculate their difference.
(1) Output two three-digit numbers and calculate their difference.
(2) Exchange two digital cards and calculate their differences.
2. Put out two three-digit numbers with a digital card and calculate their difference.
(1) Output two three-digit numbers and calculate their difference.
(2) Put out two three-digit numbers and calculate their minimum difference.
(3) Output two three-digit numbers so that their difference is 175.
Did you encounter any problems in the calculation?
In practice, let students develop the ability of independent thinking and independent calculation, cultivate the habit of asking questions and asking difficult questions, and let students go hand in hand in oral expression and thinking ability. 〗
Fourth, experience the harvest and make a fierce evaluation.
Reflections on the Teaching of Subtraction Tower in Mathematics of Grade Three in Primary School (I)
According to the content arrangement of the textbook, the first sub-item of the example 1 requires the three digits and the minimum three digits of the six cards 1, 2, 3, 5, 7 and 9, and calculates the difference between them. The second problem is to form the difference of two other three digits, and then calculate the difference after exchanging the position of the digital card. Example 2 requires that six cards and nine cards in 1, 2, 3, 4, 5, 6, 7 and 8 be placed in two three-digit numbers, and the difference, minimum difference and formula based on fixed difference are found.
Personally, it is not difficult to find the difference between students by setting three digits with a number card. Last semester, students learned to construct three numbers-addition and subtraction-in a mathematical square, but in Example 2, it was difficult for students to choose six numbers from multiple digital cards and get the difference and the minimum difference to set the formula. The focus of this lesson should be to understand the law that differences become bigger and smaller. Therefore, in the teaching example 1, students can initially understand the law that the difference becomes bigger and smaller by changing the bit value of the number card, so as to get the business trip and the minimum difference according to the law. On the basis of understanding, learn Example 2 again, and choose from multiple number cards, which reduces the difficulty and also plays a consolidation role. Flowchart provides abundant information resources for students to make numbers. In this session, I let students make full use of the existing knowledge and experience, explore new knowledge independently through observation, thinking and discussion, learn to read the flow chart, and initially build a subtraction tower, so that students' learning activities can become a learning process to gain successful experience. This link also helps students to further consolidate the structure of the subtraction tower, clarify their thinking and pave the way for the next level of exploration of the law.
Students are very interested in building subtraction towers, so they master them quickly. At this level, I let students explore independently, encourage them to discover the laws themselves and further develop their thinking. At the same time, this link is also difficult. I can guide it appropriately so that students can feel it initially. Through observation, thinking and comparison, students can learn to sum up and improve their thinking ability and generalization ability. Then I transformed the subtraction tower into a simple vertical one and told the students the story of Gaussian mathematics. Let students realize that mathematics knowledge is around us while listening to the story.
At the beginning of the class, I asked the students to talk about which towers you have seen in your life and what they were built with, so as to stimulate students' interest in learning. So what is the subtraction tower today, to guide students to explore.
Secondly, I ask students to read the flow chart of the subtraction tower and clear their minds. I use computer examples and teachers' blackboard writing to deepen students' impression: Start-Select Numbers-Count-Minimum Numbers-Difference-Whether the Numbers Are Same-Yes (End), No (Again). Then the students try to practice and choose any questions in the book. Some errors can be found through operation and projector display. For example, the first time is to choose three from three numbers and subtract the smallest three; The second time is to select the number of three numbers in the first difference and subtract it from the minimum number.
Third, students will find the rules through their own operations. For example, the difference of ten digits in subtraction is 9; Hundreds and units add up to 9; The result of building the last tower is 495, and the subtraction tower can be built with up to 5 floors. The situation of my three classes is different, so we can discuss it in depth according to the class situation.
Finally, ask the students to summarize. What have you gained from this course? The students mentioned the significance of subtraction tower, the composition of subtraction tower, the law of subtraction check and so on. Teachers can give different levels of guidance according to the actual situation of the class.
I hope students can learn knowledge well, build today's subtraction tower and build more beautiful towers for the motherland in the future.
Reflections on the teaching of subtraction tower in the second grade mathematics of primary school
The teaching objectives of this course are
1. If three digits are constructed as required, the number and the minimum number in the three digits are released.
2. Be able to read and use the flow chart as a subtraction tower.
For students, although they have been exposed to the knowledge of "flow chart" in the second grade, they still rely on the teacher's enumeration and explanation in understanding and specific application. So, at first, I asked students to try to understand the flow chart and put it on the table with their own digital cards. Taking an example as an example, I let students really understand the meaning of the flow chart and sweep away the possible problems in understanding.
At the same time, in the concrete calculation of the subtraction tower, I first let the students try to construct the subtraction tower with the numbers 5, 8 and 7. The students found that it was a four-story tower, and then tried to find that the numbers 6, 7 and 8 built a five-story tower. This is what I asked the students to choose three numbers by themselves. Try it and think about what you find through the structure of these three subtraction towers.
Sure enough, the children made the following discovery.
1, every calculation, the number on the tenth place must be 9, and the three numbers of the last tower must be 9, 5 and 4, and the result is 495;
2. It seems that the subtraction tower constructed by three numbers has at most five floors;
3. The sum of each number of each calculation result must be 18.
The first one found that they also found the truth under the timely guidance of the teacher. That is, given three numbers, to divide them into numbers and minimum numbers, then the numbers in the ten digits must be the same; Moreover, the single digits of the smallest number must be greater than the single digits of the number, so abdication will definitely occur in the process of subtraction, so the ten digits of the difference must be 9.
For students in Grade Three, it is often necessary to find the rules in the process of trying, discussing, trying and discussing, and use the rules to answer practical questions creatively. Therefore, I definitely think it is necessary to give children enough time and space to think.
So far, this course seems to have achieved the teaching purpose, but I am puzzled: "You know, as long as you quote three numbers, I know it will be a grass-roots tower!" " "The students are very excited and eagerly holding numbers. I will answer them one by one. This is fast and verified. Although they are very excited, they all seem to know the secret. Then I told them
1, in fact, the number of layers of the subtraction tower is related to the split of 9. Namely;
9(8- 1) (five-story tower)
9(7-2) (four-story tower)
9(6-3) (three-story tower)
9(5-4) (Tower on the second floor)
9, 5, 4, these three numbers are a tower.
In the calculation, the number of three numbers-minimum number-1 is equivalent to its corresponding number of layers.
2. Three figures is five floors at most. Three-digit and four-digit have the characteristics revealed by the flow chart in the book, while five-digit has no such characteristics.
In the teaching of this course, I feel that it is far more meaningful for students to discover the rules themselves in games and trying activities than to tell them directly; Secondly, when teaching such teaching content, the most important thing is to let students develop the habit of being diligent and good at thinking, so that they can feel the interesting and useful mathematics. However, we don't need to know everything about some knowledge involving number theory. But teachers can consciously tell them some interesting rules, so that they can enjoy the happiness of takenism. But the solution of this contradiction depends on teachers' better research on teaching materials.