"Multiplying two numbers by two numbers" is based on students' learning the written calculation of multiplying two numbers by one number and the oral calculation of multiplying two numbers by integer ten. Teachers can pay attention to three issues when watching:
1. What do students really understand about their computing power? What else do you need to learn in class?
2. In computing teaching, how to use intuitive means to solve the problems that the algorithm is easy to learn and the arithmetic is difficult to go deep.
3. In computing teaching, how to use intuitive means to solve the problems that the algorithm is easy to learn and the arithmetic is difficult to go deep?
Estimation is widely used in daily life, so that students can "choose the right unit to make a simple estimation in combination with the specific situation and realize the role of estimation in life" at the first stage of study. In the second period, "experiencing the process of communicating one's own algorithm with others, and being able to express one's own ideas" and "being able to choose appropriate methods for estimation in the process of solving problems" are the requirements of mathematics curriculum standards for estimation teaching. Teachers have encountered many puzzles in the teaching and evaluation of estimation. Front-line teachers (especially rural teachers) often ask: "Curriculum standards enhance the weight of estimation in decimal teaching. Is it necessary to learn the estimation for such a long time? " "Is estimation really important for students?" "What should we pay attention to when evaluating teaching priorities?" "How to cultivate students' awareness of estimation?" Some teachers also asked: "Is there a unified evaluation standard for estimation? "... in the face of the confusion of front-line teachers in the teaching of Estimation, we * * * share the lesson of Estimation by Mr. Wu, hoping that teachers will think with the following questions:
1. What is the value of estimating teaching?
2. In the process of solving problems, how to choose an appropriate estimation method?
3. How to cultivate students' estimation consciousness and ability, and how to cultivate students' sense of numbers?
case presentation
Case 1: Multiply two numbers.
Case information
Name of case: Book 6 "Double Numbers Multiplying Double Numbers" in the textbook of People's Education Press.
Lecturer: Shi Dongmei (Senior Middle School Teacher, Huangchenggen Primary School, Xicheng District, Beijing)
Teaching design
Teaching objectives
1. Understand the operation of two-digit multiplication, master the algorithm and be able to calculate correctly.
2. In the process of guiding students to experience the calculation method of multiplying two digits by two digits, experience the diversity of algorithms and help students understand the calculation reasons with the idea of infiltrating the combination of numbers and shapes.
3. Stimulate students' desire to explore problems in learning, so that students can deepen their understanding of knowledge through continuous exploration and communication.
Teaching process:
First, before teaching, master the algorithm in communication.
1. Get mathematical information from life situations
Teacher: What information do you know from the picture below?
Students look at the theme map to get information: each 12 yuan, 14, one * * *, how much is it?
Continuous problem solving
Teacher: How to find * * * How much does it cost? Why use multiplication?
Student: The price of each book is 12 yuan, and 12 is each book. Buying the same book 14 means that there are 14 copies. how much is it? That is,141what is 2 yuan?
3. Learn vertical calculation
The teacher asked the students to try to calculate vertically. (Single performance, teachers patrol to find different algorithms)
Students introduce the vertical calculation method on the blackboard.
Teacher: During the calculation she said, I heard several multiplication formulas. Who knows which formula she is talking about? The first sentence, the second sentence, the third sentence, the fourth sentence, the fifth sentence, and finally he said, add up 168 (the teacher draws arrows to guide the students to make gestures and write them on the blackboard).
Then the teacher shows the mistakes made by the students: for example,12×14 = 60; 12× 14= 188; 12× 14= 1248。 Questioning "Who did the right thing?"
4. Students use estimates to eliminate incorrect results.
Student: 12× 14 can't get 60 because the product of 12× 10= 120, 12× 14 must be greater than14.
Student: 12× 14 can't be 1248, because12×100 = 1200,12×1. Obviously 1248 is wrong.
Some students questioned12×14 =118, which proved that this answer was wrong.
The teacher suggested using a calculator to verify the calculation result of 12× 14.
Teacher: We used a calculator to verify that the calculation result of 12× 14 is 168. We listened to the students' speeches just now. Do you have any questions? . (The teacher waits for the students' response) Now that everyone agrees, can we finish the class? Students report that they can't finish the class, indicating that they need to study the problem. ) What else do you want to know after class?
Second, with the help of the model, guide students to experience the whole process of discovering the multiplication method of two digits.
1. Let the students say their questions.
Student: I can work out this problem a long time ago, but I don't know why I wrote the calculation process like this.
Teacher: Good question. We should not only pay attention to the results, but also pay attention to the process.
Student: How did mathematicians find this calculation? Who invented it?
Teacher: You not only know the method, but also understand the reason behind it. If you want to know why, you should know why.
Student: Is there any other way to verify the correctness of the results besides the calculator?
Teacher: You think very carefully. You need other methods to prove whether the calculation method is correct or not.
Student: ...
Teacher: You have asked so many valuable questions, which reminds me of one thing. What was wrong with the wrong question just now? What should I pay attention to when calculating? Are worthy of our in-depth study. Then we will use this schematic diagram to further study and see what new gains will be made.
2. Transform new knowledge into old knowledge by point diagram.
(1) Research the algorithm with the help of the dot graph.
Teacher: Think of a dollar as a point. There is such a dot diagram. Divide a point on the bitmap, calculate it, and then use it to find the reason for the calculation. Communicate with each other at the same table.
(2) Students report and explain problems with conceptual drawings.
The following situations will occur:
12×7×2; 14×6×2; 14×4×3; 14×2×6; 12× 10+ 12×4;
12×5+ 12×5+ 12×2
Teacher: So many solutions have verified that the result is correct. Although these methods are different, they still have a common feature. Did you find it?
(3) organize ideas
Teachers help students organize their speeches;
12×7×2, 14×6×2, 14×4×3 and 14×2×6 are calculated by dividing 12 or 14 into several parts. For example, 12×7×2 means that 12 is regarded as each copy. First, seven such shares are 84, then 84 is regarded as each share, and then two such shares are 168. There is a general relationship here.
12×10+12× 4 and 12 × 5+ 12 × 2, find several numbers respectively (full relation), and finally add the products (full relation). Either way, break up first and then merge. The purpose of dividing the big into the small, the complex into the simple, and the new knowledge into the old knowledge is actually to multiply two digits by two digits by one digit.
Summary: Looking back at the process of learning with mind map just now, using calculator is not the only verification method. You can also use the method of dividing first and then combining to transform new knowledge into old knowledge to verify.
Third, a variety of algorithms are connected vertically to further understand arithmetic.
1. Establish horizontal and vertical connections.
Students' thinking: 12×7×2, 14×6×2, 14×4×3, 14×2×6,12×/0+.
Find the answer:12×10+12× 4 is related to the vertical type. The first product in the vertical form is 12×4, and the second product is 12× 10. The sum of the two products is 168.
2. Use the train of thought to talk about the basis of each step of vertical calculation.
Teacher: In the longitudinal calculation, the results of four formulas are used. Can these four formulas be found in the diagram? Students look for answers in mind maps with questions. (Students talk while demonstrating the courseware)
Students find the basis of each step of calculation in the picture.
There are two points in each row, so there are four rows, which is 2×4=8. Each line has 10, so there are four lines, that is 10×4=40. There are two in each row, and there are 10 rows, which is 2× 10=20. Each line has 10 lines. If there is 10 × 10 = 100, it will add up to 8+40+ 100+20= 168.
Summary: Looking back at the learning process just now, although we agree with the calculation result of 10 minutes, we are not satisfied with finding only the calculation result, but keep asking why. Let's use bitmap to calculate in various ways, which not only verifies the correctness of the results, but also enables us to find the reasons behind the calculation method.
3. Study the generation of errors
Let's see where these students are wrong and what to pay attention to when calculating.
Conclusion: In fact, these students' mistakes have provided us with good learning resources. Analysis together will definitely attract everyone's attention.
Fourth, different forms of exercises meet the needs of different students.
1. Longitudinal calculation: 23× 12, feedback students' knowledge.
2. Guess the calculation game
3. The result of choosing the big answer: □2×□4 is:
a、586 B、390 C、8 D、8
Tell me the reason for your choice (verified by a calculator). Why are ten digits different? All available products are eight digits.
4. Choose the value range of the product: 1□× 1□ What is the possible result?
Tell me your reasons; For example, when verifying, the teacher gives the results directly, which surprises the students. Let students have the desire to find tricks.
Teacher's explanation: the secret of fast calculation is actually hidden in the train of thought. Today, our research coincides with that of mathematicians thousands of years ago. Let's take a look.
Courseware playing and recording: The Unity of Arithmetic in Ming Dynasty tells a calculation method of "tapestry" multiplication, which is calculated by grid. For example, to calculate 12× 14, first write two multipliers on the top and right of the grid, and then multiply each digit of one multiplier by each digit of another multiplier, for example, 2× 4. 1×4=8, just write 04 in the lower left box, and complete it in turn, and then add the diagonal numbers respectively to get the product of 12× 14, that is, 168.