加载中…美国小学数学课教案 [双语]
(2009-07-21 17:01:58)
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美国小学数学课教案
Discovering Math: Concepts in Number Theory
Objectives
Students will
Understand Maya achievements in mathematics.
Understand the Maya calendar.
Learn how to convert Maya numbers to decimal numbers, and vice versa.
Learn basic Maya arithmetic: addition, subtraction, multiplication, and division.
Understand Maya achievements in mathematics.
Understand the Maya calendar.
Learn how to convert Maya numbers to decimal numbers, and vice versa.
Learn basic Maya arithmetic: addition, subtraction, multiplication, and division.
Materials
Discovering Math: Concepts in Number Theory video
Computer with Internet access
Print resources about the history of Maya mathematics
Computer with Internet access
Print resources about the history of Maya mathematics
Procedures
Have students research the Maya culture and create a time line
of Maya civilization using print and Web resources. The following
Web sites are a good starting point:
Civilization.ca - Mystery of the Maya - civilization timeline
http://www.civilization.ca/civil/maya/mmc09eng.html
Mayan World
http://www.mayan-world.com/time.htm
The Maya Civilization, The Time-Line
http://www.mexconnect.com/
mex_/travel/ldumois/maya/ldmayatimeline.html
Have the students create a bulletin board from their time lines.
Have students research the Maya calendar using print and Web resources. The following Web sites are a good starting point:
Maya calendar
http://en.wikipedia.org/wiki/Maya_calendar
The Classic Maya Calendar and Day Numbering System
http://www.eecis.udel.edu/~mills/maya.html
Maya Calendar - Yucatan's Maya World Studies Center
http://www.mayacalendar.com/
Maya Calendar
http://www.michielb.nl/maya/calendar.html
Civilization.ca - Mystery of the Maya - civilization timeline
http://www.civilization.ca/civil/maya/mmc09eng.html
Mayan World
http://www.mayan-world.com/time.htm
The Maya Civilization, The Time-Line
http://www.mexconnect.com/
mex_/travel/ldumois/maya/ldmayatimeline.html
Have the students create a bulletin board from their time lines.
Have students research the Maya calendar using print and Web resources. The following Web sites are a good starting point:
Maya calendar
http://en.wikipedia.org/wiki/Maya_calendar
The Classic Maya Calendar and Day Numbering System
http://www.eecis.udel.edu/~mills/maya.html
Maya Calendar - Yucatan's Maya World Studies Center
http://www.mayacalendar.com/
Maya Calendar
http://www.michielb.nl/maya/calendar.html
Have students summarize their research in a one-page
report
Group students in pairs to share their reports and answer any questions. Then have each student present the main points of their partner's report to the class, including at least two interesting facts.
Review the decimal number system, place value, and expanded notation. Show students how to convert base 20 numbers with decimal digits to base 10 numbers. Have students convert several base 20 numbers to base 10 numbers on their own.
To familiarize the students with Maya numbers, have the students write the Maya numbers from 1 to 26. Show students examples of converting Maya numbers to decimal numbers and converting decimal numbers to Maya numbers.
Remind students of the three rules of addition shown in the video: a dot equals one, five dots equals one bar, and four bars equals one dot in the next place
Show students examples of adding Maya numbers and allow them time for practice.
Show students examples of subtracting Maya numbers and provide students time for practice.
Review the properties of multiplication as they apply to Maya numbers; that is, the identity property, the zero property, and the commutative, associative, and distributive properties. Show students examples of multiplying Maya numbers and allow them time for practice.
Show students examples of dividing Maya numbers and allow them time for practice.
Group students in pairs to share their reports and answer any questions. Then have each student present the main points of their partner's report to the class, including at least two interesting facts.
Review the decimal number system, place value, and expanded notation. Show students how to convert base 20 numbers with decimal digits to base 10 numbers. Have students convert several base 20 numbers to base 10 numbers on their own.
To familiarize the students with Maya numbers, have the students write the Maya numbers from 1 to 26. Show students examples of converting Maya numbers to decimal numbers and converting decimal numbers to Maya numbers.
Remind students of the three rules of addition shown in the video: a dot equals one, five dots equals one bar, and four bars equals one dot in the next place
Show students examples of adding Maya numbers and allow them time for practice.
Show students examples of subtracting Maya numbers and provide students time for practice.
Review the properties of multiplication as they apply to Maya numbers; that is, the identity property, the zero property, and the commutative, associative, and distributive properties. Show students examples of multiplying Maya numbers and allow them time for practice.
Show students examples of dividing Maya numbers and allow them time for practice.
uation
Use the following three-point rubric to uate students'
work during this lesson.
Three points: Students were highly engaged in class discussions; produced complete reports, including all of the requested information; clearly demonstrated the ability to convert between Maya and decimal numbers, and showed a complete understanding of Maya arithmetic.
Two points: Students participated in class discussions; produced an adequate report, including most of the requested information; satisfactorily demonstrated the ability to convert between Maya and decimal numbers, and showed a satisfactory understanding of Maya arithmetic.
One point: Students participated minimally in class discussions; created an incomplete report with little or none of the requested information; were not able to convert between Maya and decimal numbers or adequately perform Maya arithmetic.
Three points: Students were highly engaged in class discussions; produced complete reports, including all of the requested information; clearly demonstrated the ability to convert between Maya and decimal numbers, and showed a complete understanding of Maya arithmetic.
Two points: Students participated in class discussions; produced an adequate report, including most of the requested information; satisfactorily demonstrated the ability to convert between Maya and decimal numbers, and showed a satisfactory understanding of Maya arithmetic.
One point: Students participated minimally in class discussions; created an incomplete report with little or none of the requested information; were not able to convert between Maya and decimal numbers or adequately perform Maya arithmetic.
Vocabulary
decimal number system
Definition: A positional system of numeration that uses decimal digits and a base of 10
Context: The decimal number system is the most common numeral system used around the world.
expanded notation
Definition: A numeral expressed as a sum of the products of each digit and its place value
Context: Expanded notation is used when converting between the Maya number system and
Definition: A positional system of numeration that uses decimal digits and a base of 10
Context: The decimal number system is the most common numeral system used around the world.
expanded notation
Definition: A numeral expressed as a sum of the products of each digit and its place value
Context: Expanded notation is used when converting between the Maya number system and
glyph
Definition: A symbolic figure or a character usually incised or carved in relief
Context: The Maya used glyphs to represent days and months in their calendar.
Definition: A symbolic figure or a character usually incised or carved in relief
Context: The Maya used glyphs to represent days and months in their calendar.
place value
Definition: The value of a digit as determined by its position in a number
Context: In the Maya number , the top dot is in the 202 (four hundreds) place, the shell is in the 201 (twenties) place, and the bottom dot is in the 200 (ones).
Definition: The value of a digit as determined by its position in a number
Context: In the Maya number , the top dot is in the 202 (four hundreds) place, the shell is in the 201 (twenties) place, and the bottom dot is in the 200 (ones).
Maya number system
Definition: A positional system of numeration that uses a base of 20 and three symbols: zero(a shell-shaped glyph), one (a dot), and five (a bar)
Context: Advanced features of the Maya number system are the zero, represented by a shell, and the place value system.
Definition: A positional system of numeration that uses a base of 20 and three symbols: zero(a shell-shaped glyph), one (a dot), and five (a bar)
Context: Advanced features of the Maya number system are the zero, represented by a shell, and the place value system.
vigesimal number system
Definition: Any positional system of numeration that uses a base of 20
Context: The Maya number system is a vigesimal number system.
Definition: Any positional system of numeration that uses a base of 20
Context: The Maya number system is a vigesimal number system.
Academic Standards
National Council of Teachers of Mathematics (NCTM)
The National Council of Teachers of Mathematics provides guidelines for teaching mathematics in grades K-12 to promote mathematical literacy. To view the standards, visit this Web site: http://standards.nctm.org/document/chapter3/index.htm
This lesson plan addresses the following national standards:
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
The National Council of Teachers of Mathematics provides guidelines for teaching mathematics in grades K-12 to promote mathematical literacy. To view the standards, visit this Web site: http://standards.nctm.org/document/chapter3/index.htm
This lesson plan addresses the following national standards:
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Mid-continent Research for Education and Learning
(McREL)
McREL's Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education addresses 14 content areas. To view the standards and benchmarks, visit http://www.mcrel.org/compendium/browse.asp.
This lesson plan addresses the following national standards:
Mathematics: Understands and applies basic and advanced properties of the concepts of numbers; Understands and applies basic and advanced properties of functions and algebra; Understands the general nature and uses of mathematics
Science: Physical Science: Understands the structure and properties of matter; Understands the sources and properties of energy
World History: Understands Maya achievements in mathematics
Historical Understanding: Understands the historical perspective
McREL's Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education addresses 14 content areas. To view the standards and benchmarks, visit http://www.mcrel.org/compendium/browse.asp.
This lesson plan addresses the following national standards:
Mathematics: Understands and applies basic and advanced properties of the concepts of numbers; Understands and applies basic and advanced properties of functions and algebra; Understands the general nature and uses of mathematics
Science: Physical Science: Understands the structure and properties of matter; Understands the sources and properties of energy
World History: Understands Maya achievements in mathematics
Historical Understanding: Understands the historical perspective
Appendix
A member of a Mesoamerican Indian people inhabiting southeast Mexico, Guatemala, and Belize, whose civilization reached its height around a.d. 300-900. The Maya are noted
for their architecture and city planning, their mathematics and
calendar, and their hieroglyphic writing system.
A member of a Mesoamerican Indian people inhabiting southeast Mexico, Guatemala, and Belize, whose civilization reached its height around a.d.
美国小学数学课教案
[汉译 孤云独闲 2007-09-24]
《数学探索课：数论的有关概念》
一、教学目标
1、了解玛雅人在数学方面的成就；
2、了解玛雅日历；
3、学习如何将玛雅数字与十进制数字互相转换；
4、学习基本的玛雅算法：加、减、乘、除。
2、了解玛雅日历；
3、学习如何将玛雅数字与十进制数字互相转换；
4、学习基本的玛雅算法：加、减、乘、除。
二、教学资料
1、有关玛雅数制的录像；
2、计算机并联网；
3、有关玛雅人数学历史的文字资料。
2、计算机并联网；
3、有关玛雅人数学历史的文字资料。
三、教学过程
1、让学生利用书籍或网络查找玛雅文化资料，写出玛雅文化发展的时间表。
推荐网址：[译者省略]
(1)神秘的玛雅人-文明时间表
(2)玛雅人的世界
(3)玛雅文明，时间表
2、让学生创建一个电子公告板。
3、让学生利用书籍或网络查找玛雅日历。
推荐网址：[译者省略]
(1)玛雅日历
(2)传统玛雅日历和天数计数方法；
(3)玛雅日历 - 尤卡坦玛雅研究中心
(4)玛雅日历
4、让学生小结查找结果，写成一页纸的报告。
5、学生分组交流报告并回答他人的提问。然后，每个学生将本组报告的主要观点向全班汇报，其中要包括至少两项令人感兴趣的实例。
6、复习十进制、数位和数位相加记数法。向学生演示如何将以20为基数的小数转化为以10为基数的整数。学生自己练习如何转化。
7、使学生熟悉玛雅数字，让学生写出玛雅数字1-26。
8、向学生演示玛雅数字与十进制数学互相转化的例题。
9、提醒学生注意录像中演示的三条加法法则：1个“点”代表“1”，5个“点”代表1个“节(竖线)”，4个“节”代表下一个数位的1个“点”。
10、向学生演示玛雅数字加法的例题，给学生时间去练习。
11、向学生演示玛雅数字减法的例题，给学生时间去练习。
12、复习乘法的性质并应用到玛雅算法，即：恒等性、为零性以及数的交换、合并、分配。演示玛雅乘法的例题，给学生时间去练习。
13、演示玛雅除法的例题，给学生时间去练习。
推荐网址：[译者省略]
(1)神秘的玛雅人-文明时间表
(2)玛雅人的世界
(3)玛雅文明，时间表
2、让学生创建一个电子公告板。
3、让学生利用书籍或网络查找玛雅日历。
推荐网址：[译者省略]
(1)玛雅日历
(2)传统玛雅日历和天数计数方法；
(3)玛雅日历 - 尤卡坦玛雅研究中心
(4)玛雅日历
4、让学生小结查找结果，写成一页纸的报告。
5、学生分组交流报告并回答他人的提问。然后，每个学生将本组报告的主要观点向全班汇报，其中要包括至少两项令人感兴趣的实例。
6、复习十进制、数位和数位相加记数法。向学生演示如何将以20为基数的小数转化为以10为基数的整数。学生自己练习如何转化。
7、使学生熟悉玛雅数字，让学生写出玛雅数字1-26。
8、向学生演示玛雅数字与十进制数学互相转化的例题。
9、提醒学生注意录像中演示的三条加法法则：1个“点”代表“1”，5个“点”代表1个“节(竖线)”，4个“节”代表下一个数位的1个“点”。
10、向学生演示玛雅数字加法的例题，给学生时间去练习。
11、向学生演示玛雅数字减法的例题，给学生时间去练习。
12、复习乘法的性质并应用到玛雅算法，即：恒等性、为零性以及数的交换、合并、分配。演示玛雅乘法的例题，给学生时间去练习。
13、演示玛雅除法的例题，给学生时间去练习。
四、教学评价
使用下列三个等级评价学生在这一课中的表现：
1、学生积极开展课堂讨论，会写出完整的报告(包含有所需要的信息)，明显地表现出玛雅数字与十进制数字的互相转化的能力，完整地理解玛雅算法。
2、学生参加课堂讨论，写出合适的报告(包含大部分所需要的信息)；比较满意地表现出玛雅数字与十进制数字的互相转化的能力，对玛雅算法有良好的理解。
3、学生参加了最低限度的课堂讨论，所写报告不完整(只包含很少或没有包含所需要的信息)，不能进行玛雅数字与十进制数字的互相转化或正确地进行玛雅算法。
1、学生积极开展课堂讨论，会写出完整的报告(包含有所需要的信息)，明显地表现出玛雅数字与十进制数字的互相转化的能力，完整地理解玛雅算法。
2、学生参加课堂讨论，写出合适的报告(包含大部分所需要的信息)；比较满意地表现出玛雅数字与十进制数字的互相转化的能力，对玛雅算法有良好的理解。
3、学生参加了最低限度的课堂讨论，所写报告不完整(只包含很少或没有包含所需要的信息)，不能进行玛雅数字与十进制数字的互相转化或正确地进行玛雅算法。
[附录1]本课所用术语
1、十进制(decimal number system)
2、数位计值法 (expanded notation)
定义：一种以数字和数位乘积之和的数字表示法。
例如：
4567可以表示为：4000+500+60+7
5.4 可以表示为：5 x 10o + 4 x 0.1 [译者注：10的零次幂]
释义：数位计值法用于玛雅数制与玛雅象形文字。
3、象形文字(glyph)
定义：一种雕刻出的符号或图形文字系统。
释义：玛雅人用象形文字在日历中表示天数和月份。
4、数位值 [译者省略]
5、玛雅数制
定义：一种以20为基数和三个符号构成的数位计值系统。三个符号是：“0”(贝壳形状的图形)，“1”(一个“点”)，“5”(一条竖线)。
释义：玛雅数制先进的部分是它使用了“0”和数位计值概念。
6、以20为基数的计数方法(见上)
2、数位计值法 (expanded notation)
定义：一种以数字和数位乘积之和的数字表示法。
例如：
4567可以表示为：4000+500+60+7
5.4 可以表示为：5 x 10o + 4 x 0.1 [译者注：10的零次幂]
释义：数位计值法用于玛雅数制与玛雅象形文字。
3、象形文字(glyph)
定义：一种雕刻出的符号或图形文字系统。
释义：玛雅人用象形文字在日历中表示天数和月份。
4、数位值 [译者省略]
5、玛雅数制
定义：一种以20为基数和三个符号构成的数位计值系统。三个符号是：“0”(贝壳形状的图形)，“1”(一个“点”)，“5”(一条竖线)。
释义：玛雅数制先进的部分是它使用了“0”和数位计值概念。
6、以20为基数的计数方法(见上)
[附录2]本教案所参照的标准
1、“美国数学教师委员会”制定的标准 [译者省略]
2、“中欧教学研究”制定的《K-12教育原则和标准纲要》。
本教案遵循了以下标准：
(1)数学：理解和运用数的基本性质和高级特性；理解和运用函数和代数的基本性质和高级特性；理解数学的基本性质和运用。
(2)科学：物理：理解事物的结构和性质；理解能量的来源和性质。
(3)世界历史：理解玛雅人在数学方面的成就。
(4)历史概要：理解用历史的方法看问题。
2、“中欧教学研究”制定的《K-12教育原则和标准纲要》。
本教案遵循了以下标准：
(1)数学：理解和运用数的基本性质和高级特性；理解和运用函数和代数的基本性质和高级特性；理解数学的基本性质和运用。
(2)科学：物理：理解事物的结构和性质；理解能量的来源和性质。
(3)世界历史：理解玛雅人在数学方面的成就。
(4)历史概要：理解用历史的方法看问题。
[附录3][译者添加]
马雅人：中美洲印第安人，居住在墨西哥的东南部、危地马拉和伯利兹，其文明在大约公元
300年-900年发展到最高点。马雅人以其建筑、城市规划、数学、历法和象形文字著称。
玛雅数学符号图示：
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