2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 2
5 days
Module 11: Radical Expressions and Equations
Learning Goal
The student is expected to rewrite radical
expressions using rational exponents, rewrite
radical expressions using the properties of
exponents, solve simple radical equations, and
check for extraneous solutions.
Essential Questions
1.
2.
3.
How are rational exponents related to radicals and
roots?
How can you simplify expressions containing rational
exponents or radicals involving nth roots?
How can you solve equations involving square roots and
cube roots?
Approximate Time:
Unit Overview
This unit focuses on finding inverses of quadratic and cubic
functions, using transformations to graph square root and cubic
functions, using rational exponents and the properties of
exponents to rewrite radical expressions, and solving simple
radical equations.
Vertical Progression
Standards in this unit were introduced in Algebra 1 with a focus on creating equations and inequalities in one variable, explaining each step in solving a simple equation, writing
expressions involving radicals and rational exponents using the properties of exponents.
MAFS.912.A-APR.2.3, MAFS.912.A-REI.4.11: Find zeros of quadratic and cubic polynomials and explain why the x coordinates of the points where the graphs of f(x) and g(x) intersect
are the solutions of the equations f(x) = g(x).
Module Focus Standards
Module Topics
Essential Vocabulary
Algebra 2 Item Specs (FSA Reference Sheets located at end of Specs)
High School Flip Book
 extraneous solution
 index
 radical expression
 rational exponent
MAFS.912.A-CED.1.1: (DOK 2) Create equations and inequalities in one variable and Radical Expressions and Rational Exponents
use them to solve problems. Include equations arising from linear and quadratic
(N-RN.1.1)
functions, and simple rational, absolute, and exponential functions.
Core Resource:
 Solve linear and exponential equations in one variable.
 Lesson 11.1 (HMH Book)
 Solve inequalities in one variable.
Additional Resource:
 Solve all available types of equations and inequalities, including root equations
 Converting from Radical to Exponential
and inequalities, in one variable.
Expression – Khan Academy
 Describe the relationships between the quantities in the problem (for example,
how the quantities are changing or growing with respect to each other); express Formative Assessments:
 Lesson Performance Task (HMH pg. 490)
these relationships using mathematical operations to create an appropriate
equation or inequality to solve.
Simplifying Radical Expressions (N-RN.1.2, F Use all available types of functions to create such equations, including root
IF.3.7b)
functions, but constrain to simple cases.
Core Resource:
 Create equations and inequalities in one variable to model real-world situations.  Lesson 11.2 (HMH Book)
 Create equations (linear and exponential) and inequalities in one variable and
Additional Resource:
use them to solve problems.
 Simplifying Rational Exponent Expressions –
MAFS.912.A-REI.1.1: (DOK 3) Explain each step in solving a simple equation as
Khan Academy
following from the equality of numbers asserted at the previous step, starting from
Higher Order Question Stems
 How do you know your answer is correct/
reasonable?
 How are you showing the meaning of the
quantities?
 What patterns do you find in…?
 What are some other problems similar to this
one?
 What would happen if…?
Writing Connections
 Write a precise explanation of your reasoning.
 Justify the approach you took when solving
the problem.
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 2
Module 11: Radical Expressions and Equations
the assumption that the original equation has a solution. Construct a viable
argument to justify a solution method.
 Know that solving an equation means that the equation remains balanced
during each step.
 Recall the properties of equality.
 Explain why, when solving equations, it is assumed that the original equation is
equal.
 Determine if an equation has a solution.
 Choose an appropriate method for solving the equation.
 Justify solution(s) to equations by explaining each step in solving a simple
equation using the properties of equality, beginning with the assumption that
the original equation is equal.
 Construct a mathematically viable argument justifying a given, or selfgenerated, solution method.
MAFS.912.A-REI.1.2: (DOK 3) Solve simple rational and radical equations in one
variable, and give examples showing how extraneous solutions may arise.
 Determine the domain of a rational function.
 Determine the domain of a radical function.
 Solve radical equations in one variable.
 Solve rational equations in one variable.
 Give examples showing how extraneous solutions may arise when solving
rational and radical equations.
MAFS.912.F-IF.3.7b: (DOK 2) Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using technology for more
complicated cases.
b. Graph square root, cube root, and piecewise-defined functions, including step
functions and absolute value functions.
 Graph square root, cube root, and piecewise-defined functions, including step
functions and absolute value functions, by hand in simple cases or using
technology for more complicated cases, and show/label key features of the
graph.
 Determine the difference between simple and complicated linear, quadratic,
square root, cube root, and piecewise-defined functions including step functions
and absolute value functions and know when the use of technology is
appropriate.
Approximate Time:
5 days
 Simplifying Radical Expressions – Khan
Academy
 Write to explain the short cut and justify why
it works.
Formative Assessments:
 Lesson Performance Task (HMH pg. 502)
Link to Webb’s DOK Guide
Solving Radical Equations (A-REI.1.2, ACED.1.1, A-REI.1.1)
Core Resource:
 Lesson 11.3 (HMH Book)
Additional Resource:
 Solving Square Root Equations – Khan
Academy
Formative Assessments:
 Lesson Performance Task (HMH pg. 514)
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 2
Module 11: Radical Expressions and Equations
 Analyze the difference between simple and complicated linear, quadratic,
square root, cube root, piecewise-defined, exponential, logarithmic, and
trigonometric functions, including step and absolute value functions.
 Select the appropriate type of function, taking into consideration the key
features, domain, and range, to model a real-world situation.
MAFS.912.N-RN.1.1: (DOK 2) 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.
 Define radical notation as a convention used to represent rational exponents.
 Explain the properties of operations of rational exponents as an extension of the
properties of integer exponents.
 Explain how radical notation, rational exponents, and properties of integer
exponents relate to one another.
MAFS.912.N-RN.1.2: (DOK 1) Rewrite expressions involving radicals and rational
exponents using the properties of exponents.
 Using the properties of exponents, rewrite a radical expression as an expression
with a rational exponent.
 Using the properties of exponents, rewrite an expression with a rational
exponent as a radical expression.
Mathematical Practice Standards
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.6.1: Attend to precision.
MAFS.K12.MP.7.1: Look for and make use of structure.
MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning.
Approximate Time:
5 days