Catlin Gabel

Algebra 1

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Units

Unit	Essential Questions	Content	Skills and Processes	Assessment	Resources
Interpreting Graphs	·What information can be gleaned from a graph?	Intercepts Intersections Rate of Change Slope Domain and Range Independent and Dependent Variables	Compare and contrast different graphs Understand both real-life data graphs and abstract data graphs Identify domain, range, maxima, minima, intercepts, intersections, rates of change, independent and dependent variables Create scenarios that could describe a different graph	Participation Homework Activities Quizzes *Tests	Textbook: Algebra I, Holt Calculator: TI-84 Plus Geometer's Sketchpad
Generalizing Patterns - Pre Algebra Review	·What information do numbers give us? ·How can you manipulate numbers? ·What types of generalizations can be made given different patterns?	Pre-algebra review Variables Exponents Basic operations Radicals Prime factorization Order on a number line Terminology: integers, rationals, even, odd, prime, squares, cubes, powers, etc. Very large and very small numbers Rounding Exact vs. approximate Order of operations Equations and inequalities Translating verbal phrases Problem solving Real number operations (fractions etc) Graphs of patterns Tables of patterns Equations of patterns Function Notation	Evaluate expressions using grouping symbols Evaluate algebraic expressions with variables Evaluate algebraic expressions with exponents Demonstrate an understanding of the importance of priority of operations Combine like terms Solve equations with inequalities Translate verbal phrases into algebraic expressions Create a problem solving plan Solve problems with all operations with integers Represent a given pattern through tables, graphs, or equations *Use and demonstrate understanding of function notation	Participation Homework Activities Quizzes *Tests	Textbook: Algebra I, Holt Calculator: TI-84 Plus
Linear Functions	·How can we make sense of linear relationships?	Solving Linear Equations Graphing Linear Functions *Writing Linear Equations	Solve any linear equation Solve for a variable in terms of other variables (literal equations) Graph a linear function by using tables, intercepts, or slope-intercept form Find the slope of a line Solve equations using graphs Write linear equations in 3 different forms: slope-intercept, point-slope, and standard Move from any form of a linear equation to a different form Create a method for finding the best fit line for a given data set *Make predictions based on linear models created to represent data	Participation Homework Activities Quizzes *Tests	Textbook: Algebra I, Holt Calculator: TI-84 Plus Geometer's Sketchpad
Linear Inequalities	·How can we model behavior that uses phrases surrounding linear relationship like at most or less than?	Solving Linear Inequalities Graphing Linear Inequalities in one and two variables Compound Inequalities Absolute Value Equations and Inequalities	Solve linear inequalities and compound inequalities using algebra Solve linear inequalities and compound inequalities using calculators Graph linear inequalities and compound inequalities on a number line Graph linear inequalities and compound inequalities of two variables on a coordinate plane Write linear inequalities and compound inequalities given a graph Solve absolute value equations and inequalities using algebra *Solve absolute value equations and inequalities using calculators	Participation Homework Activities Quizzes *Tests	Textbook: Algebra I, Holt Calculator: TI-84 Plus
Systems of Equations and Inequalities	·How do we represent relationships that have multiple requirements?	Solving Systems of Equations by: graphing, substitution, or linear combinations Number of solutions to systems *Graphing solutions to systems of inequalities	Solve a system of equations using graphs Solve a system of equations using substitution Solve a system of equations using linear combinations Identify the number of solutions to a system *Graph the solutions to a system of inequalities	Participation Homework Activities Quizzes *Tests	Textbook: Algebra I, Holt Calculator: TI-84 Plus
Exponential Functions	·How do we model and understand exponential growth and decay?	Properties of positive, negative and zero exponents Scientific Notation Exponential Growth Model Exponential Decay Model	Simplify rational expressions that involve integer exponents Multiply and Divide monomial expressions *Demonstrate the understanding and use of exponential growth and decay models in real life scenarios	Participation Homework Activities Quizzes *Tests	Textbook: Algebra I Holt Calculator: TI-84 Plus Geometer's Sketchpad
Polynomials - Specifically Quadratics	·How do we model and understand vertical motion?	Quadratic functions - solving, graphing, writing Square roots Quadratic formula Discriminant Factoring Vertical motion model *Quadratic Inequalities	Simplify radicals Classify polynomials Add and subtract polynomials Multiply polynomials Understand and use standard and vertex form of a quadratic equation Graph Quadratics through: finding vertex, intercepts, other points Write the axis of symmetry Find x-intercepts using the zero-product property and factoring Find x-intercepts using the quadratic formula Use the discriminant to determine the number of solutions of an equation or the number of intercepts of a graph Use the vertical motion model Graph quadratic inequalities	Participation Homework Activities Quizzes *Tests	Textbook: Algebra I, Holt Calculator: TI-84 Plus Geometer's Sketchpad
Radicals	·How can we work with and model square root functions?	Graphing Square Roots Operations with Radical Expressions Solving Radical Equations Completing the Square Pythagorean Thm and Converse Distance and Midpoint Formula *Trigonometric Ratios	Evaluate and create a graph of a square-root function Add, subtract, multiply and divide radical expressions Solve a radical equation Solve a quadratic equation by completing the square Use the Pythagorean Theorem and its converse Find the distance between two points in a coordinate plane Find the midpoint between two points in a coordinate plane Use the sine, cosine and tangent of an angle	Participation Homework Activities Quizzes *Tests	Textbook: Algebra I, Holt Calculator: TI-84 Plus Geometer's Sketchpad
Rational Equations and Functions	·How can we work with and model rational functions?	Ratio Proportions Percents Direct Variation Inverse Variation Operating with Rational Expressions *Graphing Rational Functions	Solve proportions Use equations to solve percent problems Use direct and inverse variation Simplify rational expressions Multiply and divide rational expressions Add and subtract rational expressions Divide polynomials using long division Solve rational equations	Participation Homework Activities Quizzes *Tests	Textbook: Algebra I, Holt Calculator: TI-84Plus