# 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 , the irrational number can be estimated to be between 5 and 6 because 30 is between 25 and 36. By considering and , a closer approximation for is 5.5. So, the expression 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.)
Strand: Number Sense and Operations
Date Adopted or Revised: 08/20
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.