Studying Classroom Teaching as a Medium for Professional Development Proceedings of a U.S.-Japan Workshop (2002) / Chapter Skim
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Appendix F: A Study Lesson: Large Numbers at Fourth Grade
Appendix F: A Study Lesson: Large Numbers at Fourth Grade
Pages 177-214
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From page 177... ...
Background Lesson Plan Hiroshi Nakano Lesson Plan Transcript Blackboard , Teacher, Tokyo Gak~gei University, Setagaya Elementary School Postlesson Discussion Transcript 178 ~3 191 205 207
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From page 178... ...
Thus, 16532 is read as ichi man rokku sen go hyaku san jug nit This translates as one man (ten thousand) , six sen (thousan(ls)
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z (1 hundred miBion) yen if you use 1-man yen bills?
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Hint: lO-man liters would fill half a classroom. Answer: 500 classrooms.
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w'll it take to make 1-ok? z (~1 hundred miBion)
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Hint: If you line up I-man Daraemon comic books in a row, it wall be 150 meters long. Answer: lOO-man meters.
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Mathematical Thinking C Using previously learned knowledge of the number system of the numbers up to one thousand, a student can think about the system of large numbers that reach up to "okay (100 million)
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In this unit, the students wall learn that all whole numbers are expressed using the numbers O though 9 based on the previously learned principles mentioned above. Japanese numerations were invented for showing a large number using the small number of units.
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. Sen Hyaku Juu Ichi Sen Hyaku Juu Ichi I Man I Man I Man I Man l l l l By presenting this kind of chart, the students (even the students who do not know the unit "oku")
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The Goal of This Lesson: · Based on the previously learned knowledge of the principles of the Japanese numeration system up to 1000 man (10 million) , the students think about what kind of unit names might be logical to use.
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clarify the unit/position per? hildren + Tell the students that the rule for adding "O" at the end of a number means multiplying the number by 10 was previously learned knowledge.
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3. To know what quantity the number + ~ oku represents T: The height of a stack of ~ man yen bills for 100 man yen is ~ centimeter.
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C: ~ man comic books equals 150 meters. 10 man books is 10 times it so 1500 meters.
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· Did the students figure out the length of ~ oku comic books using the acquired knowledge of relative quantity for the number ~ oku? · Did the students develop interest in the number ~ oku?
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. 3 sensei means teacher APPE N DIX F
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S'70 6 ~ S ~ S S Teacher: Now, you can see that the number shikeJ one position so a number sticks out further than the units we studied previously. The next step is to think about how we can read the number.
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You must have heard the word somewhere before, haven't your Bitt the word eke veneers in this sih~otion . ~ - i- err -a Well, this is the first time for us to learn oku formally andbecause there were two students who did not know oku when I asked before this is called ichi-oku (1 hundred-million)
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From page 194... ...
If you stack 1 -man yen bills for 1 OO-man yen, the height of the bills will be 1 centimeter. Students: I got itI got it Student: Why does it become 1 centimeters Teacher: I wish I can take out real bills for 1 OO-man yen as evidence.
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So the value is also 100 times bigger. Okay, now Okay, we will go on to the second question.
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Students suggested possible answers. After four minutes, Nakano-sensei stated that 500 classrooms filled with water would be approximately ~ okay liters about 1000 times the given hint.
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From page 197... ...
Students suggested possible answers. After four minutes, Nakano-sensei stated that 500 classrooms filled with water would be approximately ~ okay liters about 1000 times the given hint.
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the radio said that it has been 30 years since Doraemon was born. It said that the Doraemon comic book series reached sales of 1 -oku (,1 hundred-million)
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Well, I will give you a hint, because if you think about the problem as it is, you may not go forward. Actually, a person actually lined up some books Students: Wow Teacher: It said that the person lined up 1-man books.
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The students worked independently while Nakano-sensei walked among them, looking at their work and stopping to talk briefly with some about their solutions. The observers from the lesson study team also moved among the students, watching how they approached the problem and taking notes.
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... One, two, three, four, five, six, seven, eight, (counting zeros)
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~ fork /0~o = /~ _ _ ~ Teacher: Well, now Matsumoto-kun, Hayashi-kun, and Maho-san got 1 50 man, and only Shirai-kun's was 1500 man. Well, what is going one Could Shirai-kun explain in front of the class how you thought about your solutions Okay, everybody.
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From page 203... ...
Do you have any questions Teacher: If you Jon't have any questions, Joes that mean it's okay with your Did you understand Shirai-kun's explanations Okay, you can ask. Student: Could you explain it one more timed Teacher: Could you explain it slowly Shirai: From here, the number of zeros increased one by one so Teacher: Wait a second, so this one has So this one has two zeros (times 1001.
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From page 204... ...
Then during tomorrow's lesson, we will look at Matsumoto-kun, Hayashi kun, and Maho-san's answers, and think about how long a row will be if we had 1 -oku Doraemon books. Nakano-sensei ended the class by asking students to write down their thoughts about the lesson in their notebooks and to turn them in.
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By having the students work on several problems to help their thinking about the relative size of the number ~ oku (100 million) using a quiz show format, ~ thought they could use the newly acquired concept (the relative size of numbers)
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So while ~ was watching the lesson, ~ thought that if the students can not conceptualize the size of ~ okay, it is very difficult for the students to know the relative size of ~ oku. ~ know that you cannot bring actual I-man yen bills to show the height differences between lOO-man yen and I-oku yen, but the teacher needed to show the height of both cases so that the students feel how much these numbers are different.
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~ hope that we can make the students understand that the numbers that they are learning now are very large numbers. F·~e UJ11: ~ thought if the teacher went over the relationship of numbers such as "Coke liter equals 500 classrooms" and "Coke kilogram equals 500-man children" then the students could gain a better image of the number ~ oku.
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B: ~ have a comment on the students' answers for those problems. When the students were working on the second problem that used liters, one of the students said "~-oku liters equals 12 classrooms" although the students worked on the first problem, ~ oku is 100 times 100 man.
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From page 211... ...
Although the students had already learned some parts of concept of the decimal positional notation system using the chart in the third grade, ~ thought the content that was introduced in today's lesson was a little bit difficult for the students to learn. ~ thought the content that was taught in today's lesson should have moved to the third lesson of this unit.
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Therefore, ~ thought the teacher needled to go over the clecimal positional notation system using the chart that was mentioned by someone before. In aciclition, the students learned four problems tociay, but ~ thought the teacher needled to go over the problems more carefully and unify the relationship in them.
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In many cases, students do not know how far apart Tokyo is from Osaka. ~ think using such numbers for the two cities could provide a clearer image of large numbers.
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In many cases, students do not know how far apart Tokyo is from Osaka. ~ think using such numbers for the two cities could provide a clearer image of large numbers.
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