LEARN NC

K–12 teaching and learning · from the UNC School of Education

Iterating to find the square root of two

http://illuminations.nctm.org/LessonDetail.aspx?ID=L374

A lesson plan for Grades 9–12 Algebra 1 and Algebra 2

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
9–12
Subjects
mathematics (algebra)
Provider
National Council of Teachers of Mathematics

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In this grades 9-12 lesson, students use a computer software program to assist them in determining the square root of two to a given number of decimal places. From this, they will be able to study the repeating-decimal phenomenon of rational numbers and explore the system property of irrationality of numbers, such as two. Illuminations provides an activity sheet, answers to the problems, and detailed instructions for completing the lesson.

Students will:

  • Investigate how technology makes an old algorithm easy to use.
  • Use different modes to see how effective an iterative algorithm is.

NCTM Standards and Expectations:

  • Generalize patterns using explicitly defined and recursively defined functions.
  • Understand relations and functions and select, convert flexibly among, and use various representations for them.
  • Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions.

North Carolina Curriculum Alignment

Mathematics (2004)

Grades 9–12 — Algebra 1

  • Goal 1: Number and Operations - The learner will perform operations with numbers and expressions to solve problems.
    • Objective 1.02: Use formulas and algebraic expressions, including iterative and recursive forms, to model and solve problems.

Grades 9–12 — Algebra 2

  • Goal 1: Number and Operations - The learner will perform operations with complex numbers, matrices, and polynomials.
    • Objective 1.01: Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems.
    • Objective 1.03: Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems.