MA.8.NSO.1.1

Extend previous understanding of rational numbers to define irrational numbers within the real number system. Locate an approximate value of a numerical expression involving irrational numbers on a number line.

Examples

Within the expression begin mathsize 12px style 1 plus square root of 30 end style, the irrational number begin mathsize 12px style square root of 30 end style can be estimated to be between 5 and 6 because 30 is between 25 and 36. By considering begin mathsize 12px style open parentheses 5.4 close parentheses squared end style and begin mathsize 12px style open parentheses 5.5 close parentheses squared end style, a closer approximation for begin mathsize 12px style square root of 30 end style is 5.5. So, the expression begin mathsize 12px style 1 plus square root of 30 end style is equivalent to about 6.5.

Clarifications

Clarification 1: Instruction includes the use of number line and rational number approximations, and recognizing pi (π) as an irrational number.

Clarification 2: Within this benchmark, the expectation is to approximate numerical expressions involving one arithmetic operation and estimating square roots or pi (π).

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 8
Strand: Number Sense and Operations
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.8.NSO.1.AP.1: Locate approximations of irrational numbers on a number line.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Sum of Rational Numbers:

Students are asked to define a rational number and then explain why the sum of two rational numbers is rational.

Type: Formative Assessment

Sum of Rational and Irrational Numbers:

Students are asked to describe the difference between rational and irrational numbers and then explain why the sum of a rational and an irrational number is irrational.

Type: Formative Assessment

Product of Non-Zero Rational and Irrational Numbers:

Students are asked to describe the difference between rational and irrational numbers, and then explain why the product of a non-zero rational and an irrational number is irrational.

Type: Formative Assessment

The Root of the Problem:

Students are asked to evaluate perfect square roots and perfect cube roots.

Type: Formative Assessment

Rational Numbers:

Students are asked to identify rational numbers from a list of real numbers, explain how to identify rational numbers, and to identify the number system that contains numbers that are not rational.

Type: Formative Assessment

Decimal to Fraction Conversion:

Students are given several terminating and repeating decimals and asked to convert them to fractions.

Type: Formative Assessment

MFAS Formative Assessments

Decimal to Fraction Conversion:

Students are given several terminating and repeating decimals and asked to convert them to fractions.

Product of Non-Zero Rational and Irrational Numbers:

Students are asked to describe the difference between rational and irrational numbers, and then explain why the product of a non-zero rational and an irrational number is irrational.

Rational Numbers:

Students are asked to identify rational numbers from a list of real numbers, explain how to identify rational numbers, and to identify the number system that contains numbers that are not rational.

Sum of Rational and Irrational Numbers:

Students are asked to describe the difference between rational and irrational numbers and then explain why the sum of a rational and an irrational number is irrational.

Sum of Rational Numbers:

Students are asked to define a rational number and then explain why the sum of two rational numbers is rational.

The Root of the Problem:

Students are asked to evaluate perfect square roots and perfect cube roots.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.