ALEX Classroom Resource

  

Approximating Square Roots of Nonperfect Squares

  Classroom Resource Information  

Title:

 Approximating Square Roots of Nonperfect Squares

URL:

 https://aptv.pbslearningmedia.org/resource/mgbh.math.ns.approxsqroot/approximating-square-roots-of-nonperfect-squares/

Content Source:

 PBS
Type: Audio/Video

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.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
10. Define the real number system as composed of rational and irrational numbers.

a. Explain that every number has a decimal expansion; for rational numbers, the decimal expansion repeats in a pattern or terminates.

b. Convert a decimal expansion that repeats in a pattern into a rational number. [Grade 8, 1]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Provide an example of both rational and irrational numbers in ratio form as well as the decimal expansion taken from the quotient of that ratio.
  • Convert a repeating decimal into a rational number.
Teacher Vocabulary:
  • Real Number System
  • Ratio
  • Rational Number
  • Irrational Number
Knowledge:
Students know:
  • 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.
  • Every real number has a decimal expansion that repeats, terminates, or is both non-repeating and non-terminating.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
15. Use square root and cube root symbols to represent solutions to equations.

a. Evaluate square roots of perfect squares (less than or equal to 225) and cube roots of perfect cubes (less than or equal to 1000).

b. Explain that the square root of a non-perfect square is irrational. [Grade 8, 4]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Evaluate expressions involving squared and cubed numbers.
  • Solve equations with radicals with a square or cube root solution.
Teacher Vocabulary:
  • Radical
  • Square Root
  • Cube Root
Knowledge:
Students know:
  • That the square root of a non-perfect square is an irrational number.
  • Equations can potentially have two solutions.
  • 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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 8
1. Define the real number system as composed of rational and irrational numbers.

a. Explain that every number has a decimal expansion; for rational numbers, the decimal expansion repeats or terminates.

b. Convert a decimal expansion that repeats into a rational number.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Provide an example of both rational and irrational numbers in ratio form as well as the decimal expansion taken from the quotient of that ratio.
  • Convert a repeating decimal into a rational number.
Teacher 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.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.8.1.1: Define expanding decimals, terminating decimals, rational number, and irrational number.
    M.8.1.2: Identify and give examples of rational numbers.
    M.8.1.3: Demonstrate how to convert fractions to decimals.
    M.8.1.4: Recall steps for division of fractions.

    Prior Knowledge Skills:
    • Define rational number.
    • Plot pairs of integers and/or rational numbers on a coordinate plane.
    • Arrange integers and /or rational numbers on a horizontal or vertical number line.
    • Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
    • Identify a rational number as a point on the number line.
    • Recognize place value of whole numbers and decimals.
    • Give examples of rational numbers.
    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.8.1 Add and subtract fractions with like denominators (e.g. halves, thirds, fourths, tenths).
    M.AAS.8.1a Add and subtract decimals to the hundredths place.
    M.AAS.8.1b Convert a fraction with a denominator of 100 to a decimal.
    Mathematics
    MA2019 (2019)
    Grade: 8
    4. Use square root and cube root symbols to represent solutions to equations.

    a. Evaluate square roots of perfect squares (less than or equal to 225) and cube roots of perfect cubes (less than or equal to 1000).

    b. Explain that the square root of a non-perfect square is irrational.
    Unpacked Content
    Evidence Of Student Attainment:
    Students:
    • Evaluate expressions involving squared and cubed numbers.
    • Solve equations with radicals with a square or cube root solution.
    Teacher Vocabulary:
    • Radical
    • Square Root
    • Cube Root
    Knowledge:
    Students know:
    • that the square root of a non-perfect square is an irrational number.
    • Equations can potentially have two solutions.
    • 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.
    Diverse Learning Needs:
    Essential Skills:
    Learning Objectives:
    M.8.4.1: Define square root, cube root, inverse, perfect square, perfect cube, and irrational number.
    M.8.4.2: Recognize the inverse operation of squaring a number is square root and the inverse of cubing a number is cube root.
    M.8.4.3: Restate exponential numbers as repeated multiplication.
    M.8.4.4: Calculate the multiplication of single or multi-digit whole numbers.
    M.8.4.5: Recognize rational and irrational numbers.

    Prior Knowledge Skills:
    • Restate exponential numbers as repeated multiplication.
    • Define rational number.
    Alabama Alternate Achievement Standards
    AAS Standard:
    M.AAS.8.4 Calculate the square of numbers 1 through 10.
    Tags: approximation, fractional approximation, nonperfect squares, square roots
    License Type: Public Domain
    For full descriptions of license types and a guide to usage, visit :
    https://creativecommons.org/licenses
    AccessibilityVideo resources: includes closed captioning or subtitles
    Comments

    This resource includes teaching tips.

      This resource provided by:  
    Author: Kristy Lacks
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