Beijing Normal University Edition, Unit 3, Lesson 1 (page 30-32).

Textbook analysis

The content of this unit is further expanded on the basis of double-digit multiplication in grade three. This lesson is the first lesson in this unit. Combined with the situation of "satellite running time", the textbook leads to the time for a satellite to orbit the earth once, and puts forward the mathematical problem of "how long does it take to orbit the earth 2 1". In the process of solving practical problems, help students understand the meaning of operation. Before accurate calculation, the textbook arranges an estimation link to organize students to estimate and communicate. Then, explore and master the calculation methods of two-digit and three-digit multiplication with students to encourage the diversification of algorithms. The textbook provides several different methods, such as oral calculation, table algorithm, vertical calculation and so on. It aims to cultivate students' awareness of trying to use various methods to calculate, but it does not require every student to master several different calculation methods. The key point is to discuss the longitudinal calculation and clarify the algorithm. Try it after class, which is intended to let students transplant the existing calculation method of multiplication with zero at the middle and end of the multiplier to the multiplication of two digits multiplied by multiple digits, and consolidate it in practice. Then, apply what you have learned to solve the problems around you, so as to expand and improve. This lesson also laid the foundation for later learning division calculation.

Student analysis

In the first stage, students have learned the multiplication of two digits. This lesson is to transfer the existing knowledge to the calculation learning of multiplication of two or three digits. The calculation is not very difficult, so students should explore the calculation method independently.

Because of students' different knowledge backgrounds and personality differences, their methods will be varied in the face of the same topic. Therefore, in teaching, we should create specific situations, combine students' existing life experience, carry out meaningful mathematical thinking and communication, and promote the understanding of mathematics. While learning calculation, we should infiltrate mathematical thinking methods such as migration and transformation.

Teaching objectives

1. It can estimate the range of the product of two-digit or three-digit multiplication in combination with specific conditions.

2. Explore the calculation methods of two-digit and three-digit multiplication, be able to calculate correctly, and be willing to exchange algorithms with peers.

3. Cultivate positive interest in calculation and good calculation habits, and improve the ability to solve some practical problems by multiplication.

Teaching focus

Explore the calculation method of two-digit and three-digit multiplication.

Teaching difficulties

In-depth understanding of arithmetic in effective communication.

training/teaching aid

courseware

teaching process

First, create situations and ask questions. (about 5 points)

Teacher: watch a video first, listen while watching it, and pay attention to collecting information.

[Modification intention: The purpose of creating this situation is to stimulate students' interest in learning, provide information, find problems from it, and let all students participate. So there is no need to beat around the bush and watch the video directly. ]

(Video playback, video dubbing:1970 On April 24th, China's first artificial earth satellite was successfully launched, marking a historic breakthrough in space technology research. It takes about 1 14 minutes for the satellite to orbit the earth once. )

Teacher: What information have you collected?

Forecast:

(1)1April 24, 970, satellite launch.

This is China's first artificial earth satellite, and its name is "Dongfanghong-1".

③ It takes 1 14 points to circle the earth.

The teacher commented in time (the teacher posted it). In fact, there is still a lot of information about satellites. Interested students can continue to collect after class. In this lesson, we only study the problem of satellite running time. (main title of bulletin board-satellite running time)

Teacher: Can you ask math questions based on this information?

Forecast:

① How long does it take to circle the earth twice (the number of laps is one digit)? How long does it take to circle the earth half a circle? ..... can be solved `.

Teacher: Your good question shows that you study well! Who can solve this problem? What do you think of multiplication?

Students ask questions and point out the answers. Guide the students to tell how many times the artificial earth satellite goes around the earth, that is, how many times is 1 14, multiplied by 1 14.

Teacher: That's reasonable. Can you work out the result orally? How accurate your calculation is! It seems that the students have a good grasp of the calculation of multiplying three digits by one digit!

(2) How many times a day? ..... cannot be solved or is not suitable for the class to solve.

Teacher: It takes some time and a lot of information to solve this problem. Put it in the problem bank for the time being.

(3) If students don't ask the question that laps are double digits, the teacher will ask:

Teacher: The teacher also wants to ask a question. Read it. How to solve this problem?

[Review intention: Let students ask questions first, and cultivate students' awareness and ability to ask questions. Because the questions raised by students are unpredictable, there are several different schemes. According to the editor's intention and considering the students' learning level, it is decided that the teacher will put forward the examples in the textbook and explore the calculation method by solving them. ]

Student formula, the teacher writes on the blackboard: 1 14×2 1.

Teacher: Is this a multiplication of several numbers? (Three digits multiplied by two digits) Let's discuss the calculation method of three digits multiplied by two digits by solving this problem. (Checkerboard Subtitle-Multiplication of Two or Three Numbers)

Second, explore the algorithm to solve the problem. (about 20 points)

1, combined with the situation to estimate. (about 3 points)

Teacher: Please estimate it first. How long does it take to go around the earth 2 1?

After giving the students about half a minute to think independently, exchange the estimation process, and the teacher will assist in writing on the blackboard.

Forecast:

① Take 1 14 as10, 2 1 as 20,1/0× 20 = 2200, which is approximately equal to 2200;

Teacher: Will the actual calculation result be more than 2,200 or less? what do you think? Good idea!

[Review intention: Students have the basis of estimation and master some estimation strategies. The estimation focus of this lesson is to estimate the range of three-digit multiplied by two-digit product. Therefore, teachers consciously guide students to think, master the method of estimating the scope, and form habits. ]

I will estimate that both multipliers are very small, so the estimated result will be less than the exact result, that is, the calculated result will be greater than 2200.

② Let 1 14 be 120, 2 1 20, 120× 20 = 2400, which is about equal to 2400.

Teacher: That's very clear! This estimate is ok! How does the actual calculation result compare with 2400? More or less? Not so good. Are you sure?

Help students feel that a multiplier estimate is large and a multiplier estimate is small, so it is difficult to determine the range of results. Close to 2400, almost.

2. Exploration of concrete calculation and calculation method. (about 15)

(1) independent calculation. (about 3 points)

Teacher: What is the result of 1 14×2 1? Please think about how to calculate first, then write down your calculation process in your notebook and start.

Students calculate independently and write the calculation process in a prepared notebook. Teachers patrol, understand the students' situation, guide and help individual students, and ask students with different methods to perform at predetermined positions.

Teacher: If you have finished it, you can think of other calculation methods and try to write it down.

(2) AC algorithm. (about 2 points)

Teacher: I found that some students in our class have good methods. Now, please look at each other at the same table. If you don't understand, you can speak softly, and you will get something!

Students communicate at the same table.

(3) The whole class enjoys the algorithm. (about 10)

Teacher: Please sit down first and see who sits most straight. Please introduce XXX first. Look at the difference between his method and yours, and think about what is good about his method.

Guide students to introduce algorithms and organize students to listen and evaluate each other.

Predicting students may have the following algorithms:

① Oral calculation (using multiplication and division)114× 20 = 228014×1=142280+14 =

Teacher: Who has the same method as him? Your method is very popular!

② Table oral calculation

Teacher: (If it is not convenient for blackboard writing performance, you can show the students' books on the physical projection. Have you ever seen this method of tabular calculation before? Your method is really valuable!

③ Vertical pen calculation

According to the students' introduction, the teacher assisted the blackboard writing. What is the first step (1 14× 1 or so) and the second step (114× 20,20 or so)? Why only write 228 here? (0 does not affect the calculation result, so it is unnecessary to write, which means 228 10). What is the final calculation (1 14+2280, the sum of the two numbers is about 2 1).

Teacher: Your writing is really good, and your oral English is also good! Who else uses vertical calculation? would you please say that again.

④ Oral calculation (decomposition multiplier)114× 21=14× 7× 3 = 798× 23 = 2394.

Teacher: It is difficult to multiply three digits directly by two digits. Just decompose 2 1 into 7×3. This method is different! Students have a good habit of listening to lectures. This method belongs to you! But can this oral calculation method be used in all multiplication problems? (No) It seems that we should choose the appropriate algorithm according to the actual situation.

Forecast:

(1) If the four methods proposed in the textbook do not all appear, students should be guided to read the textbook by themselves, and the treatment is as follows:

Teacher: Write the calculation results and answers completely in the book, and then look at the four calculation methods in the textbook to see which one we didn't expect. Can you understand it yourself?

Students read the textbooks by themselves, and the teachers guide them individually.

Teacher: Which students understand? Let's introduce it!

According to the students, the most likely method is list method or multiplier decomposition method.

Teacher: You are really good at reading, which is also an important way for you to learn!

3. Compare summary methods. (about 2 points)

Teacher: So many different calculation methods are really a wonderful sharing! What methods are relevant? How are they calculated?

Guide the students to state that 1 algorithm, table algorithm and vertical algorithm all calculate the time of 1 and 20 laps respectively, and then add up the numbers.

Teacher: awesome! You have discovered the mystery between them!

[Revision intention: In the second draft, when exchanging algorithms, let students discuss the relationship between these methods. During the trial, I found that the teacher was too heavy and the links were not clear enough. So the original design was adopted. After exchanging all the algorithms, compare different algorithms to further understand them. ]

Teacher: The result is 2394. Let's answer together. (The blackboard says: 2394 (minutes) and the answer-Around the Earth 2 1 needs 2394 points. )

Teacher: Compare the calculated result with the previous estimated result, which is almost the same. Which is closer to 2394? How to estimate more accurately?

Students express their ideas and teachers guide them appropriately. In general, when estimating, one multiplier is estimated to be large, and the other multiplier is estimated to be small, so the figure is closer to the accurate result.

Teacher: Actually, either way, the calculation of multiplying three digits by two digits is converted into the calculation we have already learned. Similarly, can the multiplication of three digits by three digits, four digits or even more be calculated? I'm sure you can all do well.

Third, consolidate practice and apply it. (about 13)

1. Do the math. A test on page 34 of this book. (about 5 points)

Teacher: By solving the problem just now, we found the calculation method of multiplying three digits by two digits. Please solve this problem in the way you like.

54×3 12 (the correct answers are 16848 respectively)

Encourage students to choose different methods to calculate, then show the calculation process and guide other students to listen to the judgment. Choose a different presentation method.

Show the vertical calculation. When the vertical calculation is 54×3 12, write three digits first and then two digits, which is more convenient for calculation.

2. Vertical calculation (problem in the book 1). (about 3 points)

Teacher: In the calculation just now, most students chose vertical calculation. Let's try again. Look at the last two questions in the 1 question on page 34, and calculate them directly in the book to see who is right!

203632×32×54 (answer: 649634 128)

Teacher: After you finish writing, point to the book and tell your deskmate how you worked it out.

Feedback: Show examples of mistakes. If there are no typical mistakes, show two questions about forest doctors.

Teacher: Look at this question carefully. What should students pay attention to when calculating vertically by multiplication?

Students express their ideas.

Teacher: I believe that with your reminder, students can calculate more carefully!

Fourth, sum up the harvest and expand the extension. (about 2 points)

Teacher: What have you gained from this class?

Students sum up their gains.

Teacher: Where do you think you master it better? Where does it need to be strengthened?

Guide students to evaluate themselves.

Teacher: What homework do you want to leave for yourself?

Students may mention: vertical calculation exercises, problem-solving exercises, etc.

Teacher: It's amazing! You can leave homework for yourself! As you said, let's use the knowledge we have today to solve the problems around us.