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# Standard #: MA.8.NSO.1.1

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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
Status: State Board Approved

#### Related Courses

 Course Number1111 Course Title222 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

 Access Point Number Access Point Title MA.8.NSO.1.AP.1 Locate approximations of irrational numbers on a number line.

#### Formative Assessments

 Name Description Sum of Rational Numbers Students are asked to define a rational number and then explain why the sum of two rational numbers is 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. 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. The Root of the Problem Students are asked to evaluate perfect square roots and perfect cube roots. 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. Decimal to Fraction Conversion Students are given several terminating and repeating decimals and asked to convert them to fractions.
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