Download Algebra CP Unit 11 - Hempfield School District

Hempfield School District Curriculum: Unit Template
Course Title: Algebra I (A/B) CP
Unit Title: Radical Expressions and Equations
Names of Teachers who Developed Unit: Beth Barilla, Kendra Crosby, and Ryan Martin
Dates Developed: November 5, 2010
Approximate Dates when Taught During School Year:
Approximate Number of Periods:
Summary: This chapter focuses on the various algebraic and geometric applications that involve
using, simplifying, and combining radical expressions. The chapter begins with the various properties
that are used to simplify radical expressions. These are then applied to problems using the
Pythagorean Theorem, as well as the Distance and Midpoint Formulas, and solving special triangles.
Then students solve radical equations, and graph square root functions such as y  x , including
translating the graphs. Then the solving of right triangles is generalized into the definitions of three
trigonometric functions, and applying them to solve triangles, including problems with angles of
elevation and depression.
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Print Materials Needed:
Resources: Prentice Hall Algebra I 2007
Internet Resource Links: phschool.com
Stage 1: Desired Results
Essential Questions (Include PA Standards, Anchors & Eligible Content)
Big Ideas:
 A single quantity may be represented by many different expressions. The facts about a quantity
may be expressed by many different equations (or inequalities).
 A function is a relationship between variables in which each value of the input variable is
associated with a unique value of the output variable. Functions van be represented in a variety
of ways, such as graphs, tables equations, or words. Each representation is particularly useful
in certain situations. Some important families of functions are developed through
transformations of the simplest form of the function.
 Solving an equation is the process of rewriting the equation to make what is says about its
variable(s) as simple as possible. Properties of numbers and equality can be used to transform
an equation (or inequality) into equivalent, simpler equations (or inequalities) in order to find
solutions. Useful information about equations and inequalities (including solutions) can be
found by analyzing graphs or tables. The numbers and types of solutions vary predictably,
based on the type of equation.
Essential Questions:
 How are radical expressions represented?
 What are the characteristics of square root functions?
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Hempfield School District Curriculum: Unit Template
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How can you solve a radical equation?
Assessment Anchors:

Eligible Content:

Know
Vocabulary:
Angle of Depression
Angle of Elevation
Conjugates
Cosine
Extraneous Solution
Like Radicals
Radical Equation
Radical Expression
Rationalize
Sine
Square Root Function
Standard Deviation
Tangent
Trigonometric Ratios
Unlike Radicals
Facts:
Understand
Do
Students will understand: The Students will be Able to:
Radical expressions can be Simplify Radical Expressions Involving
simplified using the
Products
multiplication property of
Simplify Radical Expressions Involving
square roots.
Quotients
Simplify Radical Sums and Differences
Radical expressions can be Simplify Radical Products and Quotients
simplified using the
Solve Radical Equations
division property of square Solve Radical Equations with Extraneous
roots.
Solutions
Graph Square Root Functions
Rationalizing the
Translate Graphs of Square Root
denominator of a radical
Functions
expression removes the
Find Trigonometric Ratios
radical from the
Solve Problems Using Trigonometric
denominator of the
Ratios
expression.
The properties of real
numbers can be used to
perform operations with
radical expressions.
The denominators of some
radical expressions can be
rationalized by multiplying
by conjugates.
Some radical equations can
be solved by squaring both
sides and testing the
solutions.
When extraneous solutions
are tested, they do not
solve the original equation.
Stage 2: Assessment Evidence
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Hempfield School District Curriculum: Unit Template
Assessments/Performance Tasks
Rubric Titles
Benchmark(s) for Course: Unit’s key Assessments
Self-Assessments
Other Evidence, Summarized
Stage 3: Learning Activities
Differentiation:
Readiness

.
Profile: Learning Styles /
Multiple Intelligences

Interest

Accommodations for ELLs:
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Hempfield School District Curriculum: Unit Template
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