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Real Numbers

8th Grade

Alabama Course of Study Standards: 1

Define the real number system as composed of rational and irrational numbers.
  1. Explain that every number has a decimal expansion; for rational numbers, the decimal expansion repeats or terminates.
  2. Convert a decimal expansion that repeats into a rational number.

Arkansas Academic Standards: 8.NS.A.1

Know that numbers that are not rational are called irrational:
  • Understand that every number has a decimal expansion
For example: 2=2.00...
  • Write a fraction a/b as a repeating decimal
  • Write a repeating decimal as a fraction

Arizona - K-12 Academic Standards: 8.NS.A.1

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion. Know that numbers whose decimal expansions do not terminate in zeros or in a repeating sequence of fixed digits are called irrational.

Common Core State Standards: Math.8.NS.1 or 8.NS.A.1

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Georgia Standards of Excellence (GSE): 8.NR.1.1

Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.

North Carolina - Standard Course of Study: 8.NS.1

Understand that every number has a decimal expansion. Building upon the definition of a rational number, know that an irrational number is defined as a non-repeating, non-terminating decimal.

New York State Next Generation Learning Standards: 8.NS.1

Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion eventually repeats. Know that other numbers that are not rational are called irrational.

Alabama Course of Study Standards: 2

Locate rational approximations of irrational numbers on a number line, compare their sizes, and estimate the values of the irrational numbers.

Arkansas Academic Standards: 8.NS.A.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 2)

For example: By truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Arizona - K-12 Academic Standards: 8.NS.A.2

Use rational approximations of irrational numbers to compare the size of irrational numbers. Locate them approximately on a number line diagram, and estimate their values.

Common Core State Standards: Math.8.NS.2 or 8.NS.A.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Georgia Standards of Excellence (GSE): 8.NR.1.2

Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.

North Carolina - Standard Course of Study: 8.NS.2

Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line. Estimate the value of expressions involving:
  • Square roots and cube roots to the tenths.
  • to the hundredths.

New York State Next Generation Learning Standards: 8.NS.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.

Wisconsin Academic Standards: 8.NS.A.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., 2).
For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Pennsylvania Core Standards: CC.2.1.8.E.1

Distinguish between rational and irrational numbers using their properties.

Pennsylvania Core Standards: M08.A-N.1.1.1

Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).

Pennsylvania Core Standards: M08.A-N.1.1.2

Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).

Pennsylvania Core Standards: CC.2.1.8.E.4

Estimate irrational numbers by comparing them to rational numbers.

Pennsylvania Core Standards: M08.A-N.1.1.3

Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144).

Pennsylvania Core Standards: M08.A-N.1.1.4

Use rational approximations of irrational numbers to compare and order irrational numbers.

Pennsylvania Core Standards: M08.A-N.1.1.5

Locate/identify rational and irrational numbers at their approximate locations on a number line

Florida - Benchmarks for Excellent Student Thinking: 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.

Florida - Benchmarks for Excellent Student Thinking: MA.8.NSO.1.2

Plot, order and compare rational and irrational numbers, represented in various forms

Georgia Standards of Excellence (GSE): 8.NR.1.1

Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.

Georgia Standards of Excellence (GSE): 8.NR.1.2

Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.

8th Grade Math - Real Numbers Lesson
 






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