Common Core High School Number and Quantity Teaching and Learning Resources

Mathwords.com: Math Dictionary: Key vocabulary for this domain.  Use with RN-A, RN-B:

Interactive Mathematics: Exponents and Radicals begins with introducing laws of exponents and simplifying expressions with integral exponents, then delves into fractional exponents, simplest radical form, addition and subtraction of radicals, multiplication and division of radicals, and equations with radicals.  Use with RN-A.1 and RN-A.2.

Study.com: Algebra:  Each of the following chapters includes video lessons with sample problems and a short quiz in each video.  Multiple choice chapter exams are included.

• Foundations and Linear Equations: nine video lessons. The first video, What are the Different Types of Numbers?, provides a review of subsets of the real number system. Use with RN-A.1.
• Exponents and Polynomials: 10 video lessons.  The chapter begins with the five main properties of exponents, how to define a zero and negative exponent, simplifying expressions with exponents, rational exponents, and simplifying expressions with rational exponents.  Use with RN-A.1 and RN-A.2.

LearnZillion:

• Lesson set: Relate rational exponents to integer exponents, use radical notation: Five video lessons: Apply exponents to physical models, relate fractional exponents to integer exponents, solve for variables with rational exponents; perform operations and solve equations with rational exponents.  Aligns with RN-A.1.
• Lesson set: Rewrite expressions involving radicals and rational exponents: Five video lessons: Simplify square roots using physical models, simplify radical expressions by factoring, estimate the value of square roots, write equivalent radical and rational exponent expressions, explore volume using radical and rational exponent expressions.  Aligns with RN-A.2.

Purple Math: Fractional (Rational) Exponents: Basic theory

West Texas A & M University: Virtual Math Lab:

• College Algebra: Tutorial 5: Rational Exponents: After completing this tutorial, learners should be able to: 1. Rewrite a rational exponent in radical notation. 2. Simplify an expression that contains a rational exponent. 3. Use rational exponents to simplify a radical expression. Video demonstrations and practice problems are included in above.
• Intermediate Algebra: Tutorial 38: Rational Exponents: After completing this tutorial, learners should be able to: 1. Rewrite a rational exponent in radical notation. 2. Simplify an expression that contains a rational exponent. 3. Use rational exponents to simplify a radical expression. Practice problems are included in above.

Khan Academy: Practice questions with videos.

• Exponents and radicals unit.  Aligns with RN-A.1, RN-A.2.
• Rational Exponents and Radicals: A unit.  Evaluate numerical expressions with fractional and integer bases raised to positive and negative fractional exponents and convert between the equivalent forms.  Aligns with RN-A.1, RN-A.2.
• Unit-fraction exponents: Evaluate unit-fraction exponents and radicals and convert between the two forms.  Aligns with RN-A.1.
• Rational exponent challenge. Aligns with RN-A.2.

MathBitsNotebook: Algebra 1: Exponents includes lessons, then practice problems on integer exponent skills (numeric and algebraic) and rational fraction exponent skills.  Use with RN-A.1 and RN-A.2.

Hot Math: Rational Exponents: Practice problems with rational exponents.  Hints and solution steps provided.

Khan Academy: Practice questions with videos.

• Exponents and radicals unit.  Aligns with RN-A.1, RN-A.2.
• Rational Exponents and Radicals: A unit.  Evaluate numerical expressions with fractional and integer bases raised to positive and negative fractional exponents and convert between the equivalent forms.  Aligns with RN-A.1, RN-A.2.
• Properties of Exponents Intro (Rational Exponents). Evaluate and simplify using properties of exponents.  Aligns with RN-A.1, RN-A.2.
• Simplify square roots with variables.  Aligns with RN-A.2.
• Simplify square-root expressions.  Aligns with RN-A.2.

Math Warehouse: Simplify fraction exponents: Formula and examples of how to simplify fraction exponents, including practice problems for learners.

University of Hawaii: Math 110 College Algebra notes: Chapter P.3: Rational Exponents and Radicals: Within this lesson with worked examples are multiple exercises for learners to complete (paper-pencil needed) on simplifying expressions with rational exponents and radicals.

Zweigmedia.com:  Algebra Review Tutorials and examples using fill-in or multiple choice to test understanding.  Learners can also choose to do game versions of some topics.  Use with RN-A:

• Real numbers and operations
• Exponents and radicals:  Part A on integer exponents; Part B on radicals and rational exponents

Illustrative Mathematics: Number and Quantity:

• Evaluating a special exponential expression: This task alsigns with standard RN-A.1.
• Evaluating exponential expressions: This task alsigns with standard RN-A.1.
• Extending the definitions of exponents, variation 2: This task aligns with standard RN-A.1 and involves investigating bacterial growth.
• Checking the calculation of a decimal exponent: This task aligns with standard RN-A.2.  Students justify that 3^1.4 must be less than 6.  The task is open-ended for strategies to use involving rational exponents.
• Kepler's third law of motion: This task aligns with standard RN-A.2.
• Rational or irrational?: This task aligns with standards RN-A.2, RN-B.

Mathematics Vision Project, Secondary 2 Student Edition:

• Module 3: Quadratic Equations: This module contains 10 classroom tasks.  Real number standards addressed in Module 3 include  RN-A.1, RN-A.2 in tasks 1-4 and RN-B.3 within tasks 9-10.

Khan Academy: Algebra 1: Irrational Numbers includes video proofs on sums and products of rational and irrational numbers that align with RN-B.3.

LearnZillion: Lesson set: Identify rules for adding and multiplying rational and irrational numbers: Four video lessons: Distinguish between rational and irrational numbers, predict the result of adding and subtracting rational and irrational numbers, multiply rational and irrational numbers, rationalize the denominator.  Aligns with RN-B.3.

Mathematics Assessment Project, CLASSROOM CHALLENGES, Formative Assessment Lessons: Task 424: Classifying Rational and Irrational Numbers and Task 434: Evaluating Statements about Rational and Irrational Numbers.  These lessons relate to the standard RN-B.3: Use rational and irrational numbers.

Khan Academy: Practice questions with videos.

• Recognizing rational and irrational expressions: Aligns with RN-B.3.

MathBitsNotebook: Algebra 1: Rationals and Irrationals includes lessons on rationals and irrationals, sum/product of two rationals, two irrationals, rationals and irrationals, then practice problems on rational/irrational values, and a speedometer quiz game on these concepts.  Use with RN-B.3.

Shmoop: MATH.N-RN.3 includes a quiz with sums and products involving radicals and problems illustrating RN-B.3.

JMAP.org: Regents Exam Questions N.RN.B.3: Operations with Radicals 1 (pdf) combines multiple choice and constructed response questions.  Aligns with RN-B.3.

Illustrative Mathematics: Number and Quantity:

• Calculating the square root of 2: This task aligns wih standard RN-B.
• Coordinates of equilateral triangles: This task aligns wih standard RN-B.
• Rational or irrational?: This task aligns with standards RN-A.2, RN-B.
• Operations with Rational and Irrational Numbers: Aligns with RN-B.3.
• Sums of Rational and Irrational Numbers: Aligns with RN-B.3.

Mathematics Assessment Project: Standards: High School: Number and Quantity: Quantities:

• Task 289: The Real Number System
• Task 424: Classifying Rational and Irrational Numbers
• Task 434: Evaluating Statements about Rational and Irrational Numbers

Mathematics Vision Project, Secondary 2 Student Edition:

• Module 3: Quadratic Equations: This module contains 10 classroom tasks.  Real number standards addressed in Module 3 include  RN-A.1, RN-A.2 in tasks 1-4 and RN-B.3 within tasks 9-10.