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N - Real Number System

This text resource illustrates the Standards Map for the Number and Quantity Overview Real Number System domain in the Common Core State Standards.

Standards

  3. Common Core Mathematics: Number and Quantity > RN > C.1

    Extend the properties of exponents to rational exponents.

  4. Common Core Mathematics: Number and Quantity > RN > C.1 > S.1

    Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

    For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Explain (how properties of integer exponents allow a radical to be written as rational exponent)
    2 - I can explain how properties of integer exponents allow a radical to be written as a rational exponent.
    A. Radical numbers can be written as numbers with a rational exponent.
    A.1 What is the meaning of a rational exponent?
  5. Common Core Mathematics: Number and Quantity > RN > C.1 > S.2

    Rewrite expressions involving radicals and rational exponents using the properties of exponents.

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Rewrite (expressions involving radicals using the properties of exponents)
    2 - Rewrite (expressions involving rational exponents using the properties of exponents)
    2 - I can rewrite expressions involving radicals using the properties of exponents.
    2 - I can rewrite expressions involving rational exponents using the properties of exponents.
    A. The properties of exponents can be applied to expressions with radicals and rational exponents.
    A.1 How do I use the properties of exponents with radicals?
  6. Common Core Mathematics: Number and Quantity > RN > C.2

    Use properties of rational and irrational numbers.

  7. Common Core Mathematics: Number and Quantity > RN > C.2 > S.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.

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Explain (sum of 2 rationals is rational)
    2 - Explain (sum of rational and irrational numbers is irrational)
    2 - Explain (product of 2 rationals is rational)
    2 - Explain (product of nonzero and irrational numbers is irrational)
    2 - I can explain that the sum of 2 rationals is rational.
    2 - I can explain that the sum of rational and irrational numbers is irrational.
    2 - I can explain that the product of 2 rationals is rational.
    2 - I can explain that the product of nonzero and irrational numbers is irrational.
    A. Rational and irrational numbers can be added and multiplied.
    A.1 What operations can be performed on irrational numbers?
    A.2 What is an irrational number?

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