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- HSN-RN.A.1Explain 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 5<sup>1/3</sup> to be the cube root of 5 because we want (5<sup>1/3</sup>)<sup>3</sup> = 5<sup>(1/3)3</sup> to hold, so (5<sup>1/3</sup>)<sup>3</sup> must equal 5.
- HSN-RN.A.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Ordering Exponents

8th Grade Math

Â» Unit:

Law and Order: Special Exponents Unit

Big Idea:Instead of seeing exponents as simply "repeated multiplication," we want students to find elegant and simple ways of comparing exponents.

Dividing Radicals Made Easy Through the History of Rationalizing

Algebra I

Â» Unit:

Radical Expressions, Equations, and Rational Exponents

Big Idea:The main idea of this lesson is that students compare dividing radicals by hand without rationalizing and realize why rationalizing came about and how it works.

Multiplying Radical Expressions

Algebra I

Â» Unit:

Radical Expressions, Equations, and Rational Exponents

Big Idea:The skill building in this lesson allows students to demonstrate the distributive property and multiplying two binomials with radical expressions.

Introduction to Radicals

Algebra I

Â» Unit:

Radical Expressions, Equations, and Rational Exponents

Big Idea:The point of this lesson is for students to understand the difference between exact and approximate solutions.

Simplify and Rewrite Radicals as Rational Exponents and Vice Versa.

Algebra I

Â» Unit:

Radical Expressions, Equations, and Rational Exponents

Big Idea:The Laws of Exponents Still Apply! To Fractional Exponents.

Gallery Walk of Application Problems Involving Radicals

Algebra I

Â» Unit:

Radical Expressions, Equations, and Rational Exponents

Big Idea:To Critique and Share Work, Knowledge, and Friendly Feedback! (MP3)

Stretching Exponential Functions (and your mind)

12th Grade Math

Â» Unit:

Exponential Functions and Equations

Big Idea:Studentsâ algebraic skills are reinforced as they discover that some different transformations are actually equivalent.

Rational Exponents

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:Keep students from being irrational about rational exponents with this lesson.

Introduction to Exponential Functions - Rational Exponents

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:This multi-faceted lesson creatively activates the students' prior knowledge of exponents in a fun and engaging way - it also includes a âfar-outâ example that leaves them with a hunger to learn âexponentiallyâ more!

Add and Subtract Radical Expressions

Algebra I

Â» Unit:

Radical Expressions, Equations, and Rational Exponents

Big Idea:To introduce like terms using Radicals from student's prior knowledge of like terms in Polynomials.

Real Number Exponents

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:It's not enough to be rational, let's get real with exponents.

An "Exponentially" Rewarding Battle!

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:This lesson serves as a âBattleshipâ review of real number exponents (both irrational and rational) as well as solving exponential equations. Students engage in battle while trying to sink a partnerâs fleet of answers!

Calculator Boot-Camp and Solving Exponential Equations

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:This lesson places a high emphasis on teaching the students how to properly use a calculator when solving exponential/logarithmic equations.

Discovering Solutions to Exponential Equations

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:Students will be challenged to make use of structure (and experiences in previous lessons) to solve their first exponential equations!

Productive Struggle - A Pre-Spring Break Challenge of Exponential Functions

Algebra II

Â» Unit:

Exponential and Logarithmic Functions

Big Idea:This lesson (taking place on the day before spring break) is designed to keep the students engaged â rather than mentally hitting the beach early!

HSN-RN.A.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 5^{1/3} to be the cube root of 5 because we want (5^{1/3})^{3} = 5^{(1/3)3} to hold, so (5^{1/3})^{3} must equal 5.

HSN-RN.A.2

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