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# Course Syllabus for Algebra I

## Scope And Sequence:

 Fall Semester 1st Quarter Algebraic Thinking UNIT UNDERSTANDING Discovering Algebra An Investigative Approach PV Unit 1 Patterns & Variables “Students recognize similarities and generalize patterns; use patterns to create models and make predictions; describe the nature of patterns and relationships; and construct representations of mathematical relationships.” - 2005-2006 Algebra 1 Curriculum Guide Chapter 1 – Data Exploration ϒ Bar Graphs & Dot Plots ϒ Measures of Center ϒ Histograms ϒ Two-Variable Data DR Unit 2 Data Representations “Students demonstrate the ability to interpret or analyze information from visual representations of numerical information, including line graphs, bar graphs, circle graphs, histograms, … scatter plots, charts, and tables. Students can identify trends or patterns, draw conclusions, select the appropriate graph, determine a suitable scale, or create appropriate displays of given data.” - 2005-2006 Algebra 1 Curriculum Guide Chapter 2 - Proportional Reasoning and Probability ϒ Proportions ϒ Measurement Systems ϒ Percent Rate of Change ϒ Circle and Frequency Graphs PR Unit 3 Proportional Reasoning “Students use tables and graphs – an alternative approach – to work with proportions using visual models. Students are asked to discuss proportional relationships, rather than numerical quantities, to force them to discuss the relative size of these relationships without resorting to a “trick” or rule.” - 2005-2006 Algebra 1 Curriculum Guide Chapter 3 - Variation and Graphs ϒ Rates (of Change) ϒ Direct & Indirect Variation ϒ Scale & Similarity 2nd Quarter Modeling Rates of Change UNIT UNDERSTANDING Discovering Algebra An Investigative Approach LN Unit 4 Linear and Non-Linear Models “The goal of this unit is to expose students to the concept of rate of change in multiple contexts through continued opportunities to analyze relationships. It builds on the work they have already done in studying patterns and variables, developing tools for presenting data, and delving into the concept of proportionality.” - 2005-2006 Algebra 1 Curriculum Guide Chapter 4 – Linear Equations ϒ Order of Operations & Distributive Property ϒ Expressions ϒ Recursive Sequences ϒ Linear Plots ϒ Slope-Intercept Form of a Linear Equation ϒ Solving Equations RL Unit 5 Representing Linear Models “The goal of this unit is to expose students to the concept of rate of change in multiple contexts through continued opportunities to analyze relationships. It builds on the work they have already done in studying patterns and variables, developing tools for presenting data, and delving into the concept of proportionality.” - 2005-2006 Algebra 1 Curriculum Guide Chapter 5 – Fitting a Line to Data ϒ Slope ϒ Point-Slope Form of a Linear Equation ϒ Equivalent Algebraic Equations GL Unit 6 Graphing Linear Models “The Graphing Linear Models unit focuses on linear functions in the coordinate plane. After students’ broad experience with linear relationships, both equations and inequalities, in contextual situations, they are ready to intensify and formulize the study of the graphs of such equations and inequalities. As they search for patterns, students will move from graphing the values generated in the tables to generalizing an infinite linear representation of the relationship.” - 2005-2006 Algebra 1 Curriculum Guide Chapter 6 – Systems of Equations and Inequalities ϒ Solving Systems of Equations o Graphing Method o Substitution Method o Elimination Method ϒ Inequalities o One Variable o Two Variables o Systems of Inequalities Spring Semester 3rd Quarter Processes and Symbols UNIT UNDERSTANDING Discovering Algebra An Investigative Approach EE Unit 7 Evaluating Expressions “This unit focuses on using algebra tiles to model, simplify, and evaluate expressions, and solve equations. Students use the algebra tile models to assist them in translating the visual representation to the symbolic representation of the problem. Students also analyze the soundness of the problem. Students also analyze the soundness of the results of symbol manipulation by evaluating the expression for each procedural step in solving the problem.” - 2005-2006 Algebra 1 Curriculum Guide Chapter 7 – Exponents and Exponential Models ϒ Recursive Routines ϒ Exponential Equation and Rules of Exponents ϒ Scientific Notation ϒ Exponential Growth and Decay SE Unit 8 Solving Equations and Inequalities “The goal for students in this unit is to solve problems involving equations and inequalities. This involves finding solutions for linear equations and linear absolute value equations, solution sets for linear inequalities, and approximate solutions for simple quadratic equations. Additionally, the student should check their work by applying these solutions to the original problem.” - 2005-2006 Algebra 1 Curriculum Guid Chapter 8 – Functions ϒ Function Notation ϒ Interpreting Graphs ϒ Absolute Value Functions ϒ Parabolic Functions SS Unit 9 Systems of Equations and Inequalities “Building on the work of solving equations and inequalities, the section conclude with solving systems of equations and systems of inequalities. A table is used to build the linear inequalities from the written situation. Solving the system step-by-step graphically builds understanding of systems of equations and inequalities. We make the distinction between the solution to a system of linear equations as being an ordered pair, the intersection point, and the solution to a system of linear inequalities as being a set of ordered pairs.” - 2005-2006 Algebra 1 Curriculum Guide TERRA NOVA ASSESSMENTS 4th Quarter Algebraic Structures UNIT UNDERSTANDING Discovering Algebra An Investigative Approach FG Unit 10 Functions and Their Graphs “The goal for students in this unit is to understand the role of functions in describing relationships mathematically in order to predict behavior, to be able to use the language and notation of functions, and to extend the kinds of functions they are able to use graphically in order to model real world situations.” - 2005-2006 Algebra 1 Curriculum Guide Chapter 9 – Transformations ϒ Translating Points and Graphs ϒ Reflecting Points and Graphs ϒ Stretching and Shrinking Graphs Rational Functions EF Unit 11 Exponential Functions “The goal for students in this unit is to be able to model real world situations that have an exponential pattern of change, to represent such situations using tables, graphs, explicit and recursive functions, and to analyze and interpret such functions to answer questions and solve problems.” - 2005-2006 Algebra 1 Curriculum Guide Chapter 10 – Quadratic Models ϒ Solving Quadratic Equations ϒ Finding Roots and Vertex ϒ Vertex Form of the Equation ϒ General Form of the Equation ϒ Factored Form ϒ Completing the Square ϒ Quadratic Formula ϒ Cubic Functions FF Unit 12 Families of Functions “The goal for students in this capstone unit is to summarize and synthesize the learning of the course, by examining the two families of functions studied in depth – linear and exponential – as well as those that have been studied less formally – absolute value, quadratic, and step or piecewise functions – and to analyze and connect these functions to problem situations, the shape of their graphs, patterns in tables, and the form of their equations, as well as the effect of transformations on their graphs or equations.” - 2005-2006 Algebra 1Curriculum Guide Chapter 11 – Introduction to Geometry ϒ Parallel and Perpendicular ϒ Midpoint ϒ Pythagorean Theorem ϒ Radical Expressions ϒ Similar Triangles ϒ Trigonometric Functions