2. Understand the decimal relationship between bit values and numbers, and the significance of the position of 0 in counting.
3. Through observation, comparison, experience, estimation and other activities, further cultivate students' sense of numbers.
4. On the basis of knowing the number within 100, according to the experience of knowing the number, make students know clearly "from which aspects to know the larger natural number and how to know the number from these aspects", help students establish the dimension and structure of knowing the larger natural number as a whole, and prepare thinking methods for knowing the number above 1000.
The relationship between value system and decimal system, and the establishment of digital cognitive structure.
Comment on "Let students learn some mathematical knowledge and learn the general structure of learning this mathematical knowledge" is the basic proposition of the paradigm course of panoramic mathematics education. Teacher Zhang Chong made it clear to the students that "how to know more natural numbers from these aspects and how to know numbers from these aspects" was the key goal to design, carry out curriculum construction and teaching design, which reflected the pursuit of higher teaching value.
Counting at inflection points, as a whole, establishes a dimensional system and structural method to understand larger natural numbers.
① Pre-class preparation course
Study Task 1: Investigate before class where the numbers between 100- 1000 are used in life, communicate and share with classmates, and then choose a number you like to write on the card and bring it to class.
Study Task 2: Think about what to learn before class.
Study Task 3: When you enter the classroom, please write the numbers on the digital card on the blackboard.
Comment on panoramic mathematics education, advocate opening before class, during class and after class, and construct and design three stages of mathematics curriculum and teaching: romance, accuracy and comprehensiveness. The arrangement of this "pre-class preparation class" is to let students feel and know the number within 1000 in life as a whole and romantically, realize the value of the number and the significance of learning, and prepare for class from the aspects of material, emotion and cognition.
② Long-term courses
Teacher: You found a lot! Tell me where you found your number in your life.
Health 1: The price of my schoolbag is 186 yuan.
Health 2: I have taken the 700 bus.
Health 3: There are 230 books in my family.
Teacher: These numbers are used in different places and have different meanings. But are there any similarities between these figures?
Health: It's all three numbers, all three numbers. (blackboard writing: three digits)
Teacher: What three numbers do they have?
Health: one, ten, one hundred. (blackboard writing: unit, ten, hundred)
Teacher: What are the digits, tens and hundredths of this number? (The teacher randomly chooses a blackboard book: 234)
Health: 2%, 3/10, 1/4.
Teacher: What is the unit, ten and hundred?
Student: Digital. (blackboard writing: numbers)
Teacher: It's all composed of three digits. It's all three digits, so it's called three digits.
Teacher: Who can tell me what each number you write is?
Health: 4%, 6/10, 2 in 1.
Teacher: Tell your deskmate how many digits, tens and hundreds did you write? Two people at the same table communicate with each other.
Comment on the adjustment of the textbook arrangement of this lesson, first teach the understanding of three digits (Example 2), and then teach the understanding of 1000 (Example 1). First, 1000 is produced by 999+ 1, and the understanding of 1000 must be based on the understanding of 1 to 999; Secondly, based on the grasp of children's learning situation, through the feedback from students in the classroom, we can see that they have a fairly full understanding of the three-digit number, so this adjustment is correct and necessary. Another unique feature of this issue is that it is completely based on the romantic understanding of life (the figures used in this class are all investigated by the children themselves from life) and the understanding of the numbers within 100. First, let students know what these numbers are and what they are. Numbers are the basis and key of other knowledge, and grasp the "bull nose" of knowing numbers.
Teacher: Teacher Zhang brought this number that each of you picked up today. Can you believe it? (dubious students)
Teacher: Look! There is a long axis on the floor, marked with the number 0- 1000, and the curved red arrows indicate 10 and 100 (showing courseware). Let's count and play together, shall we?
Health: Good!
Teacher: In order to play, you must obey the rules of the activity:
Take a look at it for the first time: from 0 to 1000. Look at the axis carefully and see where the numbers you write.
The second pass: start from 0 and count as you walk. Your number will go through hundreds, tens and ones. Circle the number you wrote on the number axis with a pen. (After completing the learning task, students stand in the circle number position)
Teacher: What's your number? How many hundred yuan, ten yuan and one yuan did you spend?
Health 1: I wrote the number 234, and I passed 200, three tens and four ones.
Teacher: Who is 234? After the students answer, the teacher writes the following on the blackboard according to the students:
Composition: 234 consists of two hundred dollars, three tens and four Zhang Yiyuan.
Teacher: Can you write the addition formula?
Health 1: 234 = 200+30+4.
Teacher: Please talk about your composition in this way. What is the addition formula?
Health 2: 459 consists of four hundred, five tens and nine ones, and the addition formula is 459=400+50+9.
Teacher: Talk to your deskmate about the composition and addition formula of the numbers you choose (students communicate briefly).
Teacher: 1000 Which number is closer to 0? Individual students report.
Health 3: My number is 234, which is close to 0.
Health 4: My number is 450, which is close to 0.
Health 5: My number is 999, close to 1000.
Teacher: Is your number greater than 500 or less than 500? Students under 500, please raise your digital card. (blackboard writing: size)
Teacher: Where is 500?
Health 1: in the middle, it is half of the number axis. The teacher asked a student to find 500 and stand there. )
Teacher: Look, are these students who raised their hands right?
Teacher: Guess how the students who didn't raise their hands compared with 500?
Health: More than 500.
Teacher: I asked three students to stand up. Guess how many these three students have? Tell me your reasons.
Health 1: I guess 1 this number is greater than 100, and she is close to 0.
Health 2: I estimate that the number 2 is more than 500, a little far from 500.
Health 3: I estimate that the number 3 is over 900, almost 1000.
The teacher asked three students to hold up their number plates (1No. 125, No.2 567, No.3 9 14) to praise them: You guessed it, you can estimate their numbers according to the distance. Who can continue to give three numbers from childhood to Dalian?
Health: 125 less than 567 less than 9 14.
Teacher: What do you think?
Health: The same digit ratio, from the hundred digits, 9 is the largest, 1 the smallest.
Teacher: We can write 125 < 567 < 9 14 or 9 14 > 567 > 125 in mathematical notation. (blackboard writing)
Teacher: We will not only compare the sizes on the axis of numbers, but also know that comparing the sizes of a number depends on this number. The teacher uses arrows on the blackboard to associate numbers with sizes. )
Teacher: Everybody close your eyes. The teacher chooses three numbers. Compare these three numbers. (The teacher picked out110,234 and 682)
Health: 1 10 is the largest and 682 is the smallest.
Teacher: Who is closer to 234?
Health: 1 10, they are far apart.
Teacher: Please go back to your positions and hold up the digital card to see if it is correct.
All the students answered: correct.
Teacher: Please count the seats larger than 600; Number of seats less than 500; Number of seats greater than 500 and less than 600.
It is another innovation and highlight of this class to evaluate the design and introduce the trajectory of several axes into the classroom. The sermon integrates the establishment of size, composition, operation and number sense, making the comparison, composition, addition and subtraction of mathematics concrete, intuitive and visible, which is a high integration of numbers and shapes. In addition, the huge trail has a strong sense of freshness and impact, and at the same time, it realizes the operation, activity and gamification of digital understanding, so that every student can participate in it personally and achieve very good results.
four
Synthesis of Cognitive Numbers in Different Representations
Teacher: Just now we learned the number, composition, size and number on the number axis. What else do you want to learn? (The teacher is writing on the blackboard)
1: Count.
Student 2: read and write.
Health 3: addition and subtraction ......
Teacher: Just now, we used the number axis to study the composition of numbers. There is not only one way to study any problem. Can you prove in other ways that 234 is made up of two hundred, three tens and four ones? There are learning tools in the small basket. After you finish, talk to the group members about how you proved it, and then communicate with the class.
Health 1: We use money, two hundred dollars for two hundred dollars, three tens for three tens, and four Zhang Yiyuan for four ones. (teacher map)
Health: We use sticks, two sticks represent two hundred, three sticks represent three tens, and four sticks represent four ones. (teacher map)
Health 3: We use wooden blocks, two for two hundred, three for three tens, and four for four ones. (teacher map)
Health 4: We use the counter. Two hundred dollars out of one hundred dollars dial two beads, three tens out of ten dollars dial three beads, and four digits dial four beads in one dollar.
Teacher: So many different methods look different. Are there any similarities?
Health: All of them are two hundred, three tens and four ones.
The teacher circled: 200 yuan, two bundles of sticks, two building blocks and two beads with hundreds of counters.
Health 1: This all means 200, which means 200.
Health 2: three tens, three small bundles of sticks, three building blocks and three tens of beads all represent three tens, which is 30;
Health 3: Four ones, four sticks, four building blocks, and four beads in a unit all represent four ones, which is 4.
Teacher: You see, the addition formula just written is actually 200 plus 30 plus 41. Let's challenge the knowledge of the fourth grade and change it to multiplication formula. Would you?
The teacher posted a wall chart 234 = () × ()+()× () × ().
Health: 234 = 2× (100)+(3 )× (10)+(4 )× (1)
Teachers guide students to get through again: addition formula, multiplication and division formula, money, building blocks, sticks and counters (omitted).
Teacher: 2,3,4 in 234, who is older and who is younger?
Birth 1: 2 older and 4 younger.
Teacher: All the children in kindergarten know that 4 is bigger than 2. How do you say 2 big and 4 small?
Student 2: Different positions.
Health 3: They represent different numbers. 2 means two hundred digits of one hundred and 4 means four digits of one, so 2 is greater than 4.
Teacher: Numbers, with different numbers, represent the size of numerical values?
Health: It's different.
Teacher: Look at this number again. Just like a triplet, all three numbers of 999 are the same. What is the difference? (The teacher draws a circle on the blackboard)
Student: Different numbers represent different sizes. A unit's 9 means nine ones, a decimal 9 means nine tens, and a hundred's 9 means nine hundred.
Teacher: You find that what must be clarified when studying the composition of a number?
All sentient beings: numbers (the teacher associates "numbers" with "composition")
Comment on this is another highlight of this class! We provide students with a variety of learning tools, sufficient time and space, so that students can express the composition, digits and counting units of three digits in various ways. More importantly, on this basis, guide students to compare various representations vertically and horizontally, so that students can understand and abstract the similarities and differences of various representations, get through various representations, and deeply understand the nature of the composition of numbers from many directions. This is a highlight of this class.
1 reading
(1) is not pronounced as 0.
Teacher: Not only writing depends on the number of digits, but also reading depends on the number of digits. (Blackboard: Reading) Can everyone read the number 234?
All students read: 234. (blackboard writing: reading: 234 (pieces))
Teacher: Why did you read 200 in 2? Instead of reading twenty?
Health 1: Because 2 is hundreds, I read 200. (blackboard writing: one hundred)
Teacher: Why don't you read 324?
Student 2: I read from a hundred schools.
Teacher: The way to read is to connect the number with its digits from the highest to the lowest.
Teacher: Let's try to read some numbers on the blackboard again.
Students read together: 286,563,894.
(2) How to pronounce the number with 0 at the end and 0 in the middle.
Teacher: I circle the number with 0 at the end with a red pen and the number with 0 in the middle with yellow. Try to read it yourself. What do you find the difference between the last 0 and the middle 0?
Health: Don't read the last 0, read the middle 0.
Teacher: Can you not write without reading the last 0? (The teacher erases two zeros of 300)
Health 1: No, you have to write without reading. If you don't write 0, 3 becomes a unit, not a hundred.
Teacher: What is the purpose of writing two zeros?
Health 2: Let 3 be in hundreds.
Health 3: Only by using two zeros to occupy digits and digits can we squeeze 3 to hundreds.
Teacher: The word "squeeze" is used well.
Teacher writes on the blackboard: 3 is now in one place, followed by a 0, occupying one place. Squeeze 3 into ten places, add 1 zero, and occupy ten places, so 3 becomes one hundred places.
The analysis of this link reveals the essence of reading: read a number together with its digits, laying the foundation for future multi-digit reading and writing. The reading method of 0 comes from students' own numbers, and the strategy of classification and comparative analysis is adopted to change teaching into discovery-students discover the reading law of 0 in different positions in numbers themselves. In the process of instructing students to demonstrate whether 800 zeros can be read or not with "midwifery", the students' arguments are very wonderful, and the word "squeeze" vividly expresses the occupying function of zeros and the position significance of numbers.
2 Write times
Teacher: Not only reading is inseparable from numbers, but also writing is inseparable from numbers. (Write numbers on the blackboard)
Teacher: Write 234. After reading it, you will immediately know where to write what. 200 is to write 2 on the hundred yuan; Thirty, ten people write 3; Four, write four in one place.
Teacher (choose three students): Please read out the number of your digital card (356,450,204) loudly, and the other students will write this number on the study task card.
Teacher: Please hold up the number plate and check the answer.
Teacher: Besides reading and writing numbers, the important knowledge of logarithm is counting (writing on the blackboard: counting and drawing big arrows), because numbers all come from numbers.
Teacher: Let's count down from 234, one by one.
Branch dial counter, student number: 235-244. It is difficult to stop and study the method of calculating inflection point. )
Teacher: Let's find another number from the blackboard and count from 367 to 5.
Coincidence number: 367,368,369,370,371.
Teacher: This is a list of thousands of people. The first page is the number within 100 that we have studied. Look at page two again. What's the number after 199?
Health: 200.
Teacher: How do you count it?
Health: 199+ 1 is 200. (Dial by counter)
Teacher: Counting the corners is the most difficult. Look at the screen This is a digital table. From page three to page ten, the last corner of 1 is empty. Let's count them together.
In the pre-school survey, we found that it is difficult for children to count from □99 to several hundred. We skillfully use thousands of tables to make students understand the reading method of turning over nine times in a row and the origin of the whole hundred: □99+ 1, effectively break through the difficulties, fully understand the decimal system, and fully understand the development law of natural number n+ 1. This design is very exquisite.
Teacher: What's the number after 999?
Health: 1000.
Teacher: How to calculate 1000?
Evaluation number comes from number, and the understanding of 1000 must be based on the expansion law of natural number n+ 1, and then count on the basis of 999. This is the most basic and necessary way to know 1000.
1 Millennium generation
Health: 999 plus 1 is 1000.
Teacher: Please take out your counters and dial 999. Fast and good teams will be rewarded.
Teacher: How much is 999 plus 1? Please dial the number on the counter.
Teacher: The teacher found that some groups still have some difficulties in dialing numbers.
Teacher: All the students sit down and dial with the teacher. (The teacher dials the counter to demonstrate)
Teacher: Where is 999 plus 1, 1? Why?
Health: 1 means 1, plus one.
Teacher: The unit used to be 9 ones, and it was increased by 1 one, and increased to 10 one. (PPT: 10 one)
Teacher: Is it past ten?
Health: Ten into one.
Teacher: Does the tenth bead stand for 1?
Health: Ten.
Teacher: 1 10 means 10 one. (PPT: 1 ten digits)
Teacher: It turns out that nine ten plus ten plus 1 ten is 10 ten. (PPT: 10 ten digits)
Teacher: Ten into ten, one into a hundred. 10 is 1 100, (PPT: 1 100) 1 100 represents 10.
Teacher: It used to be nine hundred plus 1 one hundred, that is 10 one hundred. (PPT: 10)
Teacher: When one hundred people reach ten people, they will advance to one thousand people.
Teacher: 1 1000 is 1 000,1000 is11000. (PPT: 1 thousands) This produces a new number, thousands.
Finally, ppt forms the following schema:
Comment: We also innovatively designed the presentation form of digital relations, unifying numbers, shapes and positions: First, relationships correspond to numbers; Second, the size of the counting unit corresponds to the height, and the image is vivid, which helps to deepen the impression of students and promote their understanding and understanding.
2 reading and writing
Teacher: One thousandth is 1 thousand. 1 thousand, what number is written?
Health: 1000. (blackboard writing: 1000)
Teacher: How do you pronounce this number?
Health: One thousand.
3 digits
Teacher: How many digits is 1000?
Health: four digits.
Teacher: What is the highest rank?
Health: The highest grade is thousand.
4 Restore life
Teacher: For teamwork, please take out 1000 yuan, 1000 sticks and 1000 small building blocks.
Teacher: Who can tell me how many 100 Yuan You has counted? Health 1: I want one hundred yuan.
Teacher: 1000. How many big bags did you count? Health 2: I take ten bundles 100.
Teacher: 1000 yuan. How many blocks did you count? Health 3: I take ten building blocks.
Teacher: 10. One hundred is one thousand. In this lesson, we learned the numbers between 1000 and 1000. (blackboard title: understanding numbers within 1000)
Comment on the expression of 1000 in various learning tools, deepen students' understanding that 1000 is one hundred, and better establish the sense of 1000.
Teacher: You investigated the numbers in your life before class, which shows that you need numbers in your life. This is the application of numbers (blackboard writing: application). In the future, I will learn the operation between numbers (blackboard writing: operation). To tell you a little secret, the operation of numbers is also related to numbers. (The teacher drew a red arrow)
Teacher: Students, today we are going to learn how to know a number.
Students: counting, counting, reading and writing, composition, size, application and operation. .......
Teacher: What did we learn first? What did we learn? Tell me. (Students' answers are abbreviated)
Teacher: We should also learn from these aspects when studying numbers above 10,000 in the future. What are they? Close your eyes and think about it.
Teacher: Open your eyes. Which of these projects is the most important? Why?
Student: Numbers, because they are inseparable.
Teacher: Circle the numbers and emphasize: Yes! You catch the number, you catch the bull's nose that knows the number.
Review the learning process and sort out all aspects of the research number. Students fully understand the numbers within 1000, and at the same time help children to construct the general structure of numbers, which provides a whole and portable paradigm for understanding the large numbers within 10000, above 10000 or even other numbers.