Author:
Mark Freed
Subject:
Mathematics
Material Type:
Teaching/Learning Strategy
Level:
Middle School
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards

OREGON MATH STANDARDS (2021): [8.NS]

OREGON MATH STANDARDS (2021): [8.NS]

Overview

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards. 

Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

2021 Oregon Math Guidance: 8.NS.A.1

ODE and Oregon Math Project Logo

Cluster: 8.NS.A - Know that there are numbers that are not rational, and approximate them by rational numbers.

STANDARD: 8.NS.A.1

 Standards Statement (2021):

Know that real numbers that are not rational are called irrational.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

7.NS.A.2, 7.NS.A.3

8.NS.A.2, HS.NQ.A.1, HS.NQ.A.2

 N/A

8.NS.A.1

8.NS.A Crosswalk

 Standards Guidance:

Terminology

  • Rational numbers are numbers that can be represented by a ratio  where “a” is an integer, and “b” is a non-zero whole number (e.g. natural number set).  
  • Rational numbers have decimal expansions that terminate in zeros or eventually repeat.
  • Irrational numbers cannot be represented by a ratio  and would include non-terminating, non- repeating decimals.

Teaching Strategies

  • Students should be provided with experiences to use numerical reasoning when describing decimal expansions.
  • Students should be able to classify real numbers as rational or irrational.
  • Students should know that when a square root of a positive integer is not an integer, then it is irrational.
  • Students should use prior knowledge about converting fractions to decimals learned in 6th  and 7th grade to connect changing decimal expansion of a repeating decimal into a fraction and a fraction into a repeating decimal.
  • Emphasis is placed on how all rational numbers can be written as an equivalent decimal. The end behavior of the decimal determines the classification of the number.

Examples

  • Understand that every number has a decimal expansion. 
  • For rational numbers show that the decimal expansion terminates or repeats eventually.
  • Convert a decimal expansion which terminates or repeats eventually into a rational number expressed as a fraction.

 

2021 Oregon Math Guidance: 8.NS.A.2

 ODE and Oregon Math Project Logo

Cluster: 8.NS.A - Know that there are numbers that are not rational, and approximate them by rational numbers.

STANDARD: 8.NS.A.2

 Standards Statement (2021):

Use rational approximations of irrational numbers to compare size and locate on a number line.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

8.NS.A.1

HS.NQ.A.2

8.AEE.A.2

8.NS.A.2

8.NS.A Crosswalk

 Standards Guidance:

Teaching Strategies

  • Students should use visual models and numerical reasoning to approximate irrational numbers.

Boundaries

  • Locate the approximate location of irrational numbers on a number line and estimate the value of expressions.
  • For decimal approximations, the concept for this grade level extends to comparing irrational numbers to at least the hundredths place on a number line.

Examples

  • Compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of square roots. For example,
    • Start with locating the nearest perfect squares and obtain closer and closer successive decimal approximations.
  • Using successive approximations, estimate the decimal expansion of  , such as by showing that  is between 4 and 5, then closer to 4 (between 4.0 and 4.5) on a number line.
  • Estimate the value of .
  • By truncating the decimal expansion of , show that  is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
  • Illustrative Mathematics:
  • Student Achievement Partners: