Curriculum / Math / 11th Grade / Unit 4: Rational and Radical Functions / Lesson 5
Math
Unit 4
11th Grade
Lesson 5 of 18
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Lesson Notes
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Write radical and rational exponent expressions in equivalent forms.
The core standards covered in this lesson
N.RN.A.2 — Rewrite expressions involving radicals and rational exponents using the properties of exponents.
The foundational standards covered in this lesson
8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3<sup>-5</sup> = 3<sup>-3</sup> = 1/3³ = 1/27.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Students will likely need to review exponent rules in conjunction with rational exponents. They have not worked extensively with this concept since Algebra 1.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
For $${x>0}$$, the expression $${3(\sqrt{x})^5\over(\sqrt[3]{x})^2}$$ can be written in the form $${3x^a}$$, where a is a fraction. What is the value of $$a$$?
Write each expression so that the fraction has a rational expression in the denominator.
a. $${x-9\over{\sqrt{x-9}}}$$
b. $${x-9\over{\sqrt{x}+3}}$$
Algebra II > Module 1 > Topic C > Lesson 28 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Rationalize the denominator.
$${x^2-16\over{\sqrt{x}-2}}$$
Rewrite the following expression with a radical, in simplest form.
$${8x^2\over2x^{-5\over2}}$$
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Multiply and divide rational expressions and simplify using equivalent expressions.
Topic A: Introduction to Rational and Radical Functions and Expressions
Define rational functions. Identify domain restrictions of rational functions.
Standards
A.APR.D.6F.IF.B.5
Identify domain restrictions algebraically for non-invertible functions.
F.BF.B.4F.IF.C.7.B
Graph and transform square root and cubic root functions.
F.BF.B.3F.IF.C.7.B
Write rational functions in equivalent radical form and identify domain restrictions of rational and radical functions.
F.IF.B.5N.RN.A.2
N.RN.A.2
A.APR.D.6A.APR.D.7
Add and subtract rational expressions.
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Topic B: Features of Rational Functions and Graphing Rational Functions
Identify asymptotic discontinuities (also known as infinite discontinuities) and removable discontinuities in a rational function and describe why these discontinuities exist.
A.APR.D.6F.IF.C.7.D
Identify features of rational functions with equal degrees in the numerator and the denominator. Describe how to calculate features of these types of rational functions algebraically.
Identify features of rational functions with a larger degree in the denominator than in the numerator. Describe how to calculate these features algebraically.
Identify features of rational functions with a larger degree in the numerator than in the denominator. Describe how to calculate these features algebraically.
Analyze the graph and equations of rational functions and identify features. Use features of a rational function to identify and construct appropriate equations and graphs.
Describe transformations of rational functions.
F.BF.B.3F.IF.C.7.D
Topic C: Solve Rational and Radical Equations and Model with Rational Functions
Solve simple radical equations.
A.REI.A.2
Solve radical equations and identify extraneous solutions.
Solve rational equations.
A.APR.D.6A.REI.A.2A.REI.D.11
Write and solve rational functions for contextual situations.
A.APR.D.6A.CED.A.2N.Q.A.1
Analyze rational and radical functions in context and write rational functions for percent applications.
A.APR.D.6A.CED.A.2A.REI.A.2
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