Access Point #: MAFS.912.N-RN.2.AP.3c (Archived Access Point)


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Know and justify that when multiplying of a nonzero rational number and an irrational number the result is irrational.

Clarifications:

Essential Understandings

Concrete:

  • Recognize rational numbers (numbers you can write as a fraction).
  • Recognize irrational numbers (approximations like square root of 2, or pi).
  • Identify the patterns in multiplying rational numbers by irrational numbers.
Representation:
  • Understand rational number – any number you can write as a fraction.
  • Understand irrational number – non-repeating, non-terminating decimal number (various square roots, pi).
  • The product of a rational number and an irrational. number is an irrational number.
    begin mathsize 12px style e. g. comma space 8 open parentheses 2 straight pi close parentheses space equals space 16 straight pi end style
  • E.g., finding the circumference of a pizza multiplies a rational and irrational number (pi) – when you use the calculator/extended version of pi.

Number: MAFS.912.N-RN.2.AP.3c Category: Access Points
Date Adopted or Revised: 07/14 Cluster: Use properties of rational and irrational numbers. (Algebra 1 - Additional Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Related Standards

Name Description
MAFS.912.N-RN.2.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.



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