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Rational Number ConceptsRational-Number-Concepts

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

Lesson Plan Sections

Objectives


Students will
  • Understand Egyptian achievements in mathematics.
  • Understand how Egyptians used hieroglyphics to write numerals.
  • Multiply and divide numbers using the Egyptian doubling and addition method.
  • Write fractions as Egyptian fractions.

Materials


Procedures

  1. Have students research Egyptian hieroglyphics using print and Web resources. The following Web sites are a good starting point: Have each student use an online translator to create a poster written in hieroglyphics with an English translation on the opposite side. Divide students into groups of four. Have the students in each group translate each other's posters.
  2. Have students research the pyramids of Egypt using print and Web resources. The following web sites are a good starting point:
  3. When students have completed their research, ask them to summarize their findings in a one-page report.
  4. Have each student choose a partner. Ask students to share their reports with their partners and answer any questions. Then have students summarize their partner's report for the class, including at least three interesting facts.
  5. Have the students write Egyptian hieroglyphic symbols for the numbers 1; 10; 100; 1,000; 10,000; 100,000; and 1,000,000. Ask students how the Egyptians would write the number 356. (Use three-100 symbols, five-10 symbols, and six-1 symbols). Ask students why a symbol for zero was not necessary. (Each symbols represents a powers of 10. A number like 104 would be written with one-100 symbol, no 10 symbol, and four 1-symbols.)
  6. Show students examples of multiplying two whole numbers using the doubling and addition method. Allow students time to practice.
  7. Show students examples of dividing two whole numbers without no remainder using the doubling and addition method. Allow students time to practice.
  8. Show students examples of rewriting fractions as unit fractions. Allow students time to practice.
  9. Show students examples of multiplying a whole number and a mixed number using the doubling and addition method. Allow students time to 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 multiply two whole numbers, multiply a whole number and a mixed number, and divide two whole numbers with no remainder using the doubling and addition method; and clearly demonstrated the ability to write fractions as unit fractions.
  • Two points:  Students participated in class discussions; produced an adequate report including most of the requested information; satisfactorily demonstrated the ability to multiply two whole numbers, multiply a whole number and a mixed number, and divide two whole numbers with no remainder using the doubling and addition method; and clearly demonstrated the ability to write fractions as unit fractions.
  • One point:  Students participated minimally in class discussions; created an incomplete report with little or none of the requested information; were not able to multiply two whole numbers, multiply a whole number and a mixed number, or divide two whole numbers with no remainder using the doubling and addition method; or did not clearly demonstrate the ability to write fractions as unit fractions.

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Vocabulary


Egyptian fraction
Definition: A fraction expressed as a sum of unit fractions, where all of the unit fractions in the sum are different
Context: Expressed as an Egyptian fraction,

greedy method
Definition: An algorithm that generates an Egyptian fraction from a given fraction by finding largest denominators first
Context: The first step in the greedy method for converting to an Egyptian fraction is to divide 23 by 11. Then round the answer up to the next whole number and find the reciprocal of the rounded number. . rounds up to 3. is the largest unit fraction in .

hieroglyphics
Definition: The picture script of the ancient Egyptians
Context: The study of ancient Egyptian history was made easier by translating the hieroglyphic symbols found on the walls of temples and tombs.

multiplicand
Definition: A number that is to be multiplied by another number
Context: In the multiplication 6 ' 7, 7 is the multiplicand.

multiplier
Definition: A number by which another number is to be multiplied
Context: In the multiplication 6 ' 7, 6 is the multiplier.

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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; Understand meanings of operations and how they relate to one another; Compute fluently and make reasonable estimates

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; Uses basic and advanced procedures while performing the processes of computation
  • Science: Physical Science: Understands the structure and properties of matter; Understands the sources and properties of energy
  • World History: Understands the major characteristics of civilization and the development of civilizations in Mesopotamia, Egypt, and the Indus Valley

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