Year+Outline

= YEAR OUTLINE _ =

__**Unit 1: Reasoning and Proof**__
Objectives Upon completion of these topics students will be able to: __**Lesson 1: Reasoning Strategies**__ • Recognize inductive reasoning in making conjectures. • Recognizing the need for proof & being able to create a simple deductive argument. • Using a counterexample to prove a claim is false. • Write if-then statements and their converse. • Use if-then reasoning in arguments. • Determine angle relationship theorems involving intersecting lines. • Use angle relationship theorems involving two parallel lines cut by a transversal. • Use angle sum theorem & exterior angle theorem for triangles. __**Lesson 3: Algebraic Reasoning & Proof**__ • Use algebraic notation to represent patterns & relationships between variables. • Use algebraic transformations of expressions, equations, and inequalities to establish general propositions about quantitative relationships.
 * __Lesson 2: Geometric Reasoning & Proof__**

__**Unit 2: Inequalities & Linear Programming**__
Objectives Upon completion of these topics students will be able to: • Write inequalities to express questions about functions of one or two variables • Given a graph of one or more functions solve inequalities related to the function(s). • Solve quadratic inequalities by solving algebraically & using graphs. • Use a number line to show the solution set of an inequality. __**Lesson 2: Inequalities with Two Variables**__ • Graph the solution set of a linear inequality in two variables. • Graph the solution set of a system of inequalities in two variables. • Solve linear programming problems involving two independent variables.
 * __Lesson 1: Inequalities in One Variable__**

**__Unit 3: Similarity & Congruence__**
Objectives Upon completion of these topics students will be able to: __**Lesson 1: Reasoning About Similar Triangles**__ • Identify similar polygons & determine the scale factor • Review & extend the law of cosines & sines. • Use SSS, SAS, & AA to prove triangles are similar. • Develop the ability to write synthetic & analytic arguments. __**Lesson 2: Reasoning About Congruent Triangles**__ • Understand that congruence is a special case of similarity. • Use SSS, SAS, AAS, & ASA to prove triangles are congruent. • Know & be able to use both necessary & sufficient conditions for quadrilaterals to be (special) parallelograms. • Know & be able to use the midpoint connector theorem for triangles & quadrilaterals.

__**Unit 6: Circles & Circular Functions**__
Objectives Upon completion of these topics students will be able to: __**Lesson 1: Properties of Circles**__ • Determine & prove a line tangent to a circle is perpendicular to its radius at the point of tangency & that 2 tangents that meet at the same exterior point are congruent • State, prove & apply the relationships among the measures of central angles, their chords, and their arcs. • State, prove & apply the properties relating a radius, a chord, and the midpoint & perpendicular bisector of the chord. • State, prove & apply the inscribed angle theorem & property that angles that intercept the same or congruent arcs are congruent. __**Lesson 2: Circle Supplement Packet**__ • Determine lengths of intersecting chords’ segments. • Determine measures of angles formed by intersecting chords. • Determine measure of arcs intercepted by intersecting chords.

__**Unit 7: Recursion & Iteration**__
Objectives Upon completion of these topics students will be able to: __**Lesson1: Modeling Sequential Change using Recursion & Iteration**__ • Use iteration and recursion to model real-world situations involving sequential change. • Understanding basic concepts of recursive formulas. • Understand how changing parameters effects the long-term behavior of recursive formulas and models. • Using subscript notation and NOW and NEXT to represent formulas. __**Lesson 2: Recursive Views of Functions**__ • Understand arithmetic sequences and their connections to linear functions, using recursive formulas, and applications. • Understand geometric sequences and their connections to exponential functions, using recursive formulas, function formulas, and applications. • Understand and apply arithmetic and geometric series.

__**Unit 8: Inverse Functions**__
Objectives Upon completion of these topics students will be able to: __**Lesson 1: What is an Inverse Function?**__ • Solve problems using direct and inverse variation. • Discover conditions that guarantee existence of an inverse for a given function • Develop and use strategies for recognizing invertible functions from the study of tables of values and graphs. • Develop and use strategies for finding rules of inverses for linear and power models. __**Lesson 2: Common Logarithms & Their Properties**__ • Express a positive number as a power of 10. • Define and evaluate common logarithms. • Use logarithms to solve exponential equations. • Develop and use the basic properties of logarithms. __**Logarithm Supplement Packet**__ • Define and evaluate natural logs. • Using natural logarithms to solve exponential equations. • Solving exponential equations by getting the same base. • Solve word problems involving half-lives, exponential growth & decay, compound interest, etc. (including word problems involving natural logarithms.)

__**Unit 5: Polynomial & Rational Functions**__
Objectives Upon completion of these topics students will be able to: __**Lesson 1: Polynomial Expressions & Functions**__ • Model problem situations with polynomial functions. • Identify patterns relating rules and graphs of polynomial functions. • Add, subtract, multiply, and divide polynomials. • Find zeroes of polynomials and create polynomial functions given the zeroes. __**Lesson 2: Quadratic Polynomials**__ • Express quadratics in vertex form. • Use vertex form of quadratics expressions to solve quadratic equations and locate the vertex. • Completing the square. • Quadratic formula extending into complex numbers. • Create rational functions to model problem situations • Analyze graphs of rational functions and their asymptotes. • Simplify rational expressions. • Add, subtract, multiply & divide rational expressions.
 * __Lesson 3: Rational Expressions & Functions__**

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