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# What do you know about large numbers? Help the poor little sister in grade three!

background

Kathleen is a third-grade primary school teacher with 12 years of teaching experience in California County, USA. Her belief in mathematics teaching is that exploratory learning can make students really understand mathematics, and teachers should provide students with opportunities to explore and inspire their imagination of mathematics. There are 32 students in the class. This class lasts 45 minutes.

Lesson example

Teacher Catherine first told the students the purpose of this class: "Students, we often encounter many big numbers in our lives. For example, the loan for your house, the number of spectators in the football field, the weight of our planet and the daily trading volume of Wall Street stocks. In today's class, we will discuss the meaning of large numbers. "

Miss Catherine's class begins with a question:

Catherine: Students, please tell me how many students are there in our classroom.

The students count the students in the classroom. )

Student: 32.

Catherine: Very good. Let me ask you again: please discuss with the students next to you and estimate how many students can our classroom accommodate if each student has a desk.

(Students discuss)

Tammy: I think it can accommodate 64 students.

Catherine: Why?

Tammy: I think this room can accommodate twice as many students.

Catherine: Good. Attention, class. She said it twice. Where are the other students?

Nick: I think it can accommodate 100 students.

Catherine: Please explain.

Nick: I think we only have a small number of 32 students now, so I estimate that the whole classroom can accommodate 100 students.

Catherine: Good. Students, please note that he said the word "estimate". Now, let's continue our question.

Catherine: If there are three classes in each grade in our school, how many people are there in our school? Why?

(Students discuss)

Lubida: I think there are about 600 students, because there are about 100 students in each grade and about 600 students in six grades.

Catherine: Good. Students, please note that Rubida used "about" several times, which is a very good estimation technique. Do other students have different ideas?

Eddie: I think there are about 700 people. Because there are 600 students, we have about 100 teachers, principals and other staff, so there are 700 people in total.

Catherine: Eddie has a good imagination. But our staff is not 100, so there are about 600 students in our school. If we increase the staff, we should have about 650 students. Even so, I thank Eddie for his wonderful imagination.

At the moment, Kathleen changed the teaching content to a large number like 100, 1000, 10000. She still asks questions.

Catherine: Students, can you give an example of life with the number 100? For example, if you have 100, and so on.

(Students discuss)

Jeff: I have 100 toy cars.

Chris: I have 100 basketball cards.

Teacher Catherine then asked: How much is 100 yuan worth?

(Students discuss)

Mark: My game machine is worth 100 yuan.

Susan: My brother's bike is worth 100 yuan.

Miss Catherine continued to ask the students questions about the meaning of numbers. These questions include examples related to large numbers in students' daily life. In order to let students have a deep understanding of large numbers, Teacher Catherine gave an example of combining large numbers with daily life. She asked her classmates to guess how long it would take to count 1 1,000 (1,000) if a number was counted every second. How long does it take to count 1 million (one million)? How long does it take to count 1 000.000,000 (one billion)? Teacher Catherine further explained that one minute equals 60 seconds, one hour equals 3600 seconds (60 minutes), one day equals 86400 seconds (24 hours), one month equals 2592000 seconds (30 days), and one year equals 3 1, 654,38+004000. So 1 0,000 (one thousand) takes about 17 minutes (because1000 ≈17); 1 000,000 (one million) takes about 12 days (because 1 000,000 ≈ 86,400 ≈12); The number 1 000,000,000 takes about 32 years (because 1 000,000,000 ≈ 31,104,000 ≈ 32). She repeated this figure to impress the students: it takes about 1 7 minutes to count 1 0,000, and it takes about 12 days to count10,000,000; And 1 000,000,000 takes about 32 years.

After confirming that students have a certain understanding of large numbers, Teacher Catherine began to let them participate in mathematics activities to further understand and apply large numbers. She divided the students into four groups according to the order of their seats, and asked each group to choose a five-digit number, such as 23,456,34,567. And tell each group of students to discuss the following questions. Each student should play a different role and report to the class.

(1) Reorder these five numbers to make them the maximum number, and tell how many tens, thousands, hundreds, tens, ones and the difference between your maximum number and 100000.

(2) Reorder these five numbers to make them the smallest number, and tell the number of ten, thousand, hundred, ten and ten, and the difference between your smallest number and 10000.

(3) Reorder these five numbers into the intermediate number between the maximum number and the minimum number, and tell tens of thousands, thousands, hundreds and tens of thousands, and the difference between this number and 100000.

(4) Create the maximum number, minimum number and intermediate number used in actual situations.

During the students' discussion, Mr. Kathleen walked around the group, communicating with the students, answering their questions and questioning their mistakes in time. The students discussed for about 10 minutes. After teacher Kathleen confirmed the results of each group, she asked the students to report the results of their discussion.

1 The number selected by the group is 12345.

Students 1: The maximum number is 5432 1, and this number includes 50000, 4000, 300, 20, 1. The difference between this number and 100000 is 45679.

Student 2: The smallest number is 12345. There are 1 10, 2 thousand, 300, 40, 5 one. The difference between this number and 10000 is 2345.

Student 3: The median can be 2 1, 345.

Catherine: Wait a minute, Jamie, why did you say "yes"?

Student 3 (Jamie): Because there are many middle numbers.

Catherine: Thank you, students. Please note that there are many middle numbers. Jamie, please continue.

Student 3 (Jamie): The median can be 2 1, 345. This number is 2000 1000,300, 4 1 0 and 51. The difference between this number and 100000 is 78655.

Student 4: Softball spectator 5432 1, basketball spectator 12345, football spectator 2 1345.

Catherine: Good. The students in the first group obviously like sports. Although there is still a gap between their numbers and reality, they have a good understanding of large numbers. Generally speaking, there are about 60,000 spectators in softball field, 0.8 million spectators in basketball court and 70,000 spectators in football field.

The second group of choices 13579. Answer the question 1 to 3. For example, department stores in the city are busiest on Saturdays and Sundays, receiving 9753 1 person every day, busiest on Thursdays and Fridays, receiving 5 1 379 people every day, and not busy on Mondays and Wednesdays.

Catherine: Good. The students in the second group obviously have a lot of life experience. They look for clues from their daily lives, and students have the opportunity to go to department stores to check these data.

The number of group 3 is 56789, the number of group 4 and 6 is also 12345, and the number of group 5 is 23456. Can correctly answer 65,438+0 to 3 questions, and the example is very imaginative:

Group III: One bag can hold 98,765 pieces of rice, 56.789 pieces of soybeans and 78.956 pieces of corn.

Catherine: Good. The third group of students turned their eyes to the countryside. Thank you for your rich imagination. Students can count it themselves when they have the opportunity.

Group 4: The thickest book in the classroom is about 54.32 1 word, the thinnest book is about12,345 words, and the middle book is about 45,321word.

Catherine: Good. The fourth group of students are obviously imaginative. They found clues from the classroom.

Group 5: A book has 65,432 words, 23,456 lines and 43,256 words.

Catherine: Good. The fifth group of students gave an example of the same book, but their imagination was different from that of the fourth group.

The sixth group: Owen has 5432 1 household, 4 1 325 vehicles, and 12345 households have pets.

Catherine: Good. The sixth group of students gave an example of a city resident. You have a good imagination. However, there seems to be a little less cars. What do you think if it is changed to 4 1 and 325 households have Internet?

The students in the sixth group agree with Miss Catherine's suggestion.

Catherine: Through this lesson, I hope you have a profound concept of large numbers. Just as we talked about counting, we often use large numbers in our lives.

At the end of this class, Miss Catherine asked the students to go home and check newspapers, magazines and the Internet, and then gave examples to illustrate when to use millions, billions and trillions as the discussion to start tomorrow's class.

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