Approximating Square Roots of Nonperfect Squares

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

7, 8

Overview

Visualize a strategy for approximating the square roots of nonperfect squares through modeling. This video focuses on a ratio, the number of extra tiles over the number of tiles for the next square that will give you a fractional approximation of the square root of a number. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers. This resource is part of the Math at the Core: Middle School collection.

Mathematics (2019) Grade(s): 8

MA19.8.1

Define the real number system as composed of rational and irrational numbers.

UP:MA19.8.1

Vocabulary

  • Real Number System
  • Ratio
  • Rational Number
  • Irrational Number

Knowledge

Students:know that any ratio a/b, where b is not equal to zero, has a quotient attained by dividing a by b.
  • know that the real number system contains natural numbers, whole numbers, integers, rational, and irrational numbers.
  • know that every real number has a decimal expansion that is repeating, terminating, or is non-repeating and non-terminating.

    • Skills

    Students are able to:
    • define the real number system by giving its components.
    • Explain the difference between rational and irrational numbers. specifically how their decimal expansions differ.
    • Convert a ratio into its decimal expansion and take a decimal expansion back to ratio form.

    Understanding

    Students understand that:
    • all real numbers are either rational or irrational and
    • Every real number has a decimal expansion that repeats, terminates, or is both non-repeating and non-terminating.
    Mathematics (2019) Grade(s): 8

    MA19.8.4

    Use square root and cube root symbols to represent solutions to equations.

    UP:MA19.8.4

    Vocabulary

    • Radical
    • Square Root
    • Cube Root

    Knowledge

    Students know:
    • that the square root of a non-perfectsquare is an irrational number.
    • Equations can potentially have twosolutions.
    • how to identify a perfect square/cube.

    Skills

    Students are able to:
    • define a perfect square/cube.
    • Evaluate radical expressions representing square and cube roots.
    • Solve equations with a squared or cubed variable.

    Understanding

    Students understand that:
    • there is an inverse relationship between squares and cubes and their roots.

    CR Resource Type

    Audio/Video

    Resource Provider

    PBS

    License Type

    PD
    https://aptv.pbslearningmedia.org/resource/mgbh.math.ns.approxsqroot/approximat…

    Comments or Notes

    This resource includes teaching tips.

    Approved Date

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