Objectives
Students will
- Discover Islamic achievements in mathematics.
- Understand Al-Khwarizmi's six standard forms of equations.
- Be able to solve equations in any of the forms.
Materials
Procedures
- Have students research the Arabic numeral system and create a poster based on their research using print and Web resources. The following Web sites are a good starting point:Have the students create a bulletin board from their posters.
- Have students research Islamic contributions to mathematics using print and Web resources. The following Web sites have useful information:
- When students have completed their research, ask them to summarize their findings in a one-page report.
- Have students choose a partner to share their reports and answer any questions. Then have each student summarize the partner's report for the class, including at least three interesting facts.
- Show students how to solve equations in the squares equal to roots form, ax2 = bx, algebraically and geometrically and provide students time for practice.
- Show students how to solve equations in the squares equal to numbers form, ax2 = c, algebraically and geometrically and provide students time for practice.
- Show students how to solve equations in the roots equal to numbers form, bx = c, algebraically and geometrically and provide students time for practice.
- Show students how to solve equations in the squares and roots equal to numbers form, ax2 + bx = c, algebraically and geometrically and provide students time for practice.
- Show students how to solve equations in the squares and numbers equal to roots form, ax2 + c = bx, algebraically and geometrically and provide students time for practice.
- Show students how to solve equations in the roots and numbers equal to squares form, ax2 = bx + c, algebraically and geometrically and provide students time for practice.
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Evaluation
Use the following three-point rubric to evaluate students' work during this lesson.
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Three points: Students were highly engaged in class discussions; produced complete reports, including all of the requested information; clearly demonstrated the ability to solve equations in any of Al-Khwarizmi's six standard forms.
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Two points: Students participated in class discussions; produced an adequate report, including most of the requested information; satisfactorily demonstrated the ability to solve equations in any of Al-Khwarizmi's six standard forms.
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One point: Students participated minimally in class discussions; created an incomplete report with little or none of the requested information; were not able to solve equations in any of Al-Khwarizmi's six standard forms.
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Vocabulary
algebra
Definition:A generalization of the ideas of arithmetic
Context:Al-Khwarizmi defined the three types of numbers required to perform calculations in algebra: roots, squares, and simple numbers.
completing the square
Definition:Method of solving quadratic equations that turns every quadratic equation into an equivalent equation of the form x2 = c.
Context:Al-Khwarizmi solved quadratic equations by completing the square.
root
Definition:A solution x to an equation
Context:To Al-Khwarizmi, solving an equation meant finding its roots.
simple number
Definition:A number that can be expressed without reference to either a root or a square
Context:One of Al-Khwarizmi's six forms of equations is squares equal to simple numbers, x2 = c, where c is any nonnegative number.
square
Definition:A root multiplied by itself
Context:One of Al-Khwarizmi's six forms of equations is squares equal to roots, ax2 = bx.
quadratic equation
Definition:An equation of the form ax2 + bx + c = 0, where a ¹ 0
Context:2x2 + 3x + 5 = 0 is a quadratic equation
quadratic formula
Definition:If ax2 + bx + c = 0, where a ¹ 0, then
Context:The equation x2 - 4x + 5 = 0 can be solved using the quadratic formula where a = 1, b = -4, and c = 5.
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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://standards.nctm.org/document/chapter3/index.htm
This lesson plan addresses the following national standards:
- Understand patterns, relations, and functions; Represent and analyze mathematical situations and structures using algebraic symbols
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 functions and algebra
- Science: Physical Science: Understands the structure and properties of matter; Understands the sources and properties of energy
- World History: Understands how Islamic civilization contributed to mathematics
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