The Real Number System
HSN-RN.A.2
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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.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
30 Lesson(s)
Ordering Exponents
8th Grade Math »
Unit: Law and Order: Special Exponents Unit
8th Grade Math »
Unit: Law and Order: Special Exponents Unit
Dividing Radicals Made Easy Through the History of Rationalizing
Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents
Algebra I »
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.
Standards:
Favorites
(7)
Resources
(12)
Multiplying Radical Expressions
Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents
Algebra I »
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.
Standards:
Favorites
(2)
Resources
(13)
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
(13)
Resources
(12)
Introduction to Radicals
Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents
Algebra I »
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.
Standards:
Favorites
(12)
Resources
(12)
Stretching Exponential Functions (and your mind)
12th Grade Math »
Unit: Exponential Functions and Equations
12th Grade Math »
Unit: Exponential Functions and Equations
Big Idea:
Students’ algebraic skills are reinforced as they discover that some different transformations are actually equivalent.
Standards:
Favorites
(2)
Resources
(19)
Gallery Walk of Application Problems Involving Radicals
Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents
Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents
Big Idea:
To Critique and Share Work, Knowledge, and Friendly Feedback! (MP3)
Standards:
Favorites
(7)
Resources
(18)
Reflections
(2)
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)
Add and Subtract Radical Expressions
Algebra I »
Unit: Radical Expressions, Equations, and Rational Exponents
Algebra I »
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.
Standards:
Favorites
(4)
Resources
(10)
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)
Calculator Boot-Camp and Solving Exponential Equations
Algebra II »
Unit: Exponential and Logarithmic Functions
Algebra II »
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.
Standards:
Resources
(19)
Reflections
(1)
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)
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