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Concepts In Number TheoryConcepts-In-Number-Theory

  • Subject: Numbers and Operations
  • |
  • Grade(s): 9-12
  • |
  • Duration: Three class periods

Lesson Plan Sections

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.

Materials


  • Discovering Math: Concepts in Number Theory video
  • Computer with Internet access
  • Print resources about the history of Maya mathematics

Procedures

  1. 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: Have the students create a bulletin board from their time lines.
  2. Have students research the Maya calendar using print and Web resources. The following Web sites are a good starting point:
  3. Have students summarize their research in a one-page report
  4. 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.
  5. 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.
  6. 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.
  7. Show students examples of subtracting Maya numbers and provide students time for practice.
  8. 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.
  9. Show students examples of dividing Maya numbers and allow them time for practice.

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Evaluation


Use the following three-point rubric to evaluate 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.

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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

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.

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).

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.

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.

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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://www.nctm.org/standards/content.aspx?id=16909
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, visithttp://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

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