The Real Number System
HSN-RN.A.1
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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^{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.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.
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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.
13 Lesson(s)
Exponentials and Logarithms: LOUD and CLEAR!
Algebra II »
Unit: Exponential and Logarithmic Functions
Algebra II »
Unit: Exponential and Logarithmic Functions
Big Idea:
This engaging lesson allows the students to apply logarithms to the real world! After finishing the study, students will think twice before playing their music too loud!
Standards:
Favorites
(4)
Resources
(22)
Reflections
(1)
Simplify and Rewrite Radicals as Rational Exponents and Vice Versa.
Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents
Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents
Big Idea:
The Laws of Exponents Still Apply! To Fractional Exponents.
Standards:
Favorites
(12)
Resources
(12)
Rational Exponents
Algebra II »
Unit: Exponential and Logarithmic Functions
Algebra II »
Unit: Exponential and Logarithmic Functions
Big Idea:
Keep students from being irrational about rational exponents with this lesson.
Standards:
Favorites
(13)
Resources
(28)
Reflections
(1)
Introduction to Exponential Functions - Rational Exponents
Algebra II »
Unit: Exponential and Logarithmic Functions
Algebra II »
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 “far-out” example that leaves them with a hunger to learn “exponentially” more!
Standards:
Favorites
(11)
Resources
(13)
Reflections
(2)
Real Number Exponents
Algebra II »
Unit: Exponential and Logarithmic Functions
Algebra II »
Unit: Exponential and Logarithmic Functions
Big Idea:
It's not enough to be rational, let's get real with exponents.
Standards:
Favorites
(1)
Resources
(23)
An "Exponentially" Rewarding Battle!
Algebra II »
Unit: Exponential and Logarithmic Functions
Algebra II »
Unit: Exponential and Logarithmic Functions
Big Idea:
This lesson serves as a “Battleship” review of real number exponents (both irrational and rational) as well as solving exponential equations. Students engage in battle while trying to sink a partner’s fleet of answers!
Standards:
Favorites
(1)
Resources
(27)
Reflections
(2)
Discovering Solutions to Exponential Equations
Algebra II »
Unit: Exponential and Logarithmic Functions
Algebra II »
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!
Standards:
Favorites
(2)
Resources
(15)
Reflections
(1)
Productive Struggle - A Pre-Spring Break Challenge of Exponential Functions
Algebra II »
Unit: Exponential and Logarithmic Functions
Algebra II »
Unit: Exponential and Logarithmic Functions
Big Idea:
This lesson (taking place on the day before spring break) is designed to keep the students engaged – rather than mentally hitting the beach early!
Standards:
Resources
(11)
Rewriting Radical and Rational Exponents (Plus Exponents Review)
Algebra I »
Unit: Exponential Functions
Algebra I »
Unit: Exponential Functions
Big Idea:
Students review basic rules of exponents and use these rules to rewrite radical and rational exponents!
Standards:
Favorites
(5)
Resources
(22)
Reflections
(1)
Real Number Exponents
Algebra II »
Unit: Exponential and Logarithmic Functions
Algebra II »
Unit: Exponential and Logarithmic Functions
Big Idea:
This building-block lesson includes a touch of technology, collaboration, and critical thinking as the students further familiarize themselves with the rules of exponents – but more importantly, extend these rules to irrational exponents
Standards:
Favorites
(4)
Resources
(17)
Reflections
(1)
Rational Exponents
Algebra II »
Unit: Exponents & Logarithms
Algebra II »
Unit: Exponents & Logarithms
Big Idea:
Mathematics is all about patterns, and exponents reveal some "power"-ful ones!
Standards:
Favorites
(4)
Resources
(17)
Reflections
(2)
Khan Academy and Simplifying Radicals
8th Grade Math »
Unit: Gimme the Base: More with Exponents
8th Grade Math »
Unit: Gimme the Base: More with Exponents
Big Idea:
We can use prime factorization to break down the number inside a radical sign and then use those factors to simplify the expression.
Standards:
Favorites
(2)
Resources
(14)
Reflections
(2)
Properties of Exponents
Algebra II »
Unit: Exponential Functions
Algebra II »
Unit: Exponential Functions
Big Idea:
Fractional exponents can be used in place of radical symbol. This can make working with radicals easier in some cases.
Standards:
Favorites
(3)
Resources
(17)
Reflections
(1)
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