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Scope and Sequence – Algebra 2A 2013-14 Course Algebra 2A (.5 credits) Instructor(s) Sue Harvey, Paul Huggins, Theresa Kahl, Dave Hauser Text Prentice Hall - - Algebra 2 - - 2004 Prerequisite Grade Course Description Geometry or Informal Geometry 11th and 12th This course emphasizes the study of algebraic forms of linear expressions. It includes solving systems of equations and inequalities. Graphing calculators will be used extensively in this course to help tie in the relationship between these functions and real world situations. This course places emphasis on applications and meets the college minimum requirement for an Algebra II course Units Unit 1 ( 2.5 weeks): Equations and Inequalities Common Core State Standards Covered (Codes only): A.REI.1 A.REI.3 A.CED.1 A.REI.11 Unit 2 ( 2 weeks): Linear Equations and Functions Common Core State Standards Covered (Codes only): A.REI.10 A.REI.12 F.IF.1 F.IF.2 G.GPE.L.5 F.LE.2 Unit 3 ( 2 weeks): Liner Applications Common Core State Standards Covered (Codes only): A.CED.2 S.ID.6 S.ID.7 S.ID.8 S.ID.9 A.CED.3 F.IF.5 Unit 4 ( 2 weeks): Systems of Equations Common Core State Standards Covered (Codes only): A.REI.5 A.REI.6 A.REI.10 A.REI.12 (1 week): Oaks Review and Testing EA Opportunities CRLE Opportunities F.IF.6 F.IF.9 Unit 1: Equations and Inequalities Time Frame 2.5 weeks Summary of Algebraic expressions and models Unit Solving linear equations Solving linear inequalities Applications using distance, rate and time Geometry applications Solving two-sided equations with a graphing calculator CCSS Code A.REI.1 A.REI.3 A.CED.1 A.REI.11 Common Core State Standard Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ Major Assignments/ Learning Activities Work Sample Unit Test Learning Targets I can explain why equivalent expressions are equivalent. I can write the equation or inequality that best models the problem. I can solve an equation or inequality I can interpret the solution in the context of the problem. I can infer that the x-coordinate of the points of intersection for y = f(x) and y = g(x) are also solutions for f(x) = g(x). Essential Questions Academic Vocabulary Performance Tasks or Work Samples Expressions, terms, factors, coefficients, simplify, solve, equations, inequality, rate Distance = rate x time work sample Unit 2: Linear Equations and Functions Time Frame 2 weeks Summary of Functions and their graphs Unit Slope Writing equations of lines Parallel and perpendicular lines Solving two variable inequalities Graphing inequalities CCSS Code A.REI.10 A.REI.12 F.IF.1 F.IF.2 G.GPE.5 F.LE.2 Common Core State Standard Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Major Assignments/ Learning Activities Unit Test Learning Targets I can explain that every point on the graph of an equation represents values x and y that make the equation true. I can graph a linear inequality on a coordinate plane resulting in a boundary line (solid or dashed) and a shaded half-plane. I can define a function as a relation in which each input (domain) has exactly one output (range). I can analyze the input and output values of a function based on a problem situation. I determine if lines are parallel/perpendicular using their slopes. I can write an equation for a line that is parallel/perpendicular to a given line that passes through a given point. I can construct a linear function from an arithmetic sequence, graph, table of values, or a description of relationships. I can identify the variables and quantities represented in a real-world problem I can interpret solutions in the context of the situation modeled and decide if they are reasonable. I can state the appropriate domain of a function that represents a problem situation, defend my choice, and explain why other numbers might be excluded from the domain. I can interpret the meaning of the average rate of change (using units) as it relates to a realworld problem. I can compare properties of two functions when represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions) Essential Questions Academic Vocabulary For 2014-15 Performance Tasks or Work Samples None for this unit. Parallel, Perpendicular, half-plane, boundary line, function, relation, domain, range, Unit 3: Linear Applications Time Frame 2 weeks Summary of Application of Linear situations Unit Scatterplots Linear regression Problem solving, real world situations, using linear regression CCSS Code A.CED.2 S.ID.6 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. S.ID.9 A.CED.3 Distinguish between correlation and causation. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★ F.IF.5 Major Assignments/ Common Core State Standard F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Linear Regression Project Work Sample Learning Activities Unit Test Learning Targets I can graph equations on coordinate axis with appropriate labels and scales. I can identify the dependent and independent variable and describe the relationship. I can construct a scatterplot with appropriate scales I can write the equation of the line of best fit (y = mx + b) using technology or by using two points (by hand) on the best-fit line. I can interpret the meaning of the slope and the y-intercept in terms of the units used in the data. I can use the correlation coefficient to determine if a linear model is a good fit for the data. I can recognize that correlation does not imply causation and that causation is not illustrated on a scatter plot. Essential Questions Academic Vocabulary For 2014-15 Performance Tasks or Work Samples Regression Work Sample Scatterplot, dependent, independent, line of best fit, correlation, causation, Unit 4: Systems of Equations Time Frame 2 Weeks Summary of Solving systems of equations by graphing Unit Solving systems of equations by the substitution method Solving systems of equations by the elimination method Solving systems of inequalities by graphing Writing to justify why solutions work CCSS Code Common Core State Standard A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. A.REI.6 A.REI.10 A.REI.12 Major Assignments/ Learning Activities Work Sample Unit Test Learning Targets I can solve systems of linear equations graphically and algebraically. I can solve a system of two equations in two variables by elimination. I can solve a system of two equations in two variables by substitution. I can demonstrate that replacing one equation with the sum of that equation and a multiple of the other creates a system with the same solutions as the original system. I can explain why some linear systems have no solutions and identify linear systems that have no solutions. I can explain why some linear systems have infinitely many solutions and identify linear systems that have infinitely many solutions. I can define linear inequality, half-plane, and boundary. I can graph a linear inequality on a coordinate plane, resulting in a boundary line (solid or dashed) and shaded half-plane I can explain that the solution set for a system of linear inequalities is the intersection of the shaded regions (half-plains) of both inequalities Essential Questions Academic Vocabulary For 2014-15 Performance Tasks or Work Samples Systems Work Sample Solution, substitution, elimination,