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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. 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? 1 Hempfield School District Curriculum: Unit Template 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 2 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: 3 Hempfield School District Curriculum: Unit Template 4