UNIT 1 - Introduction to Functions and Equations
- A.CED.1- Creating Equations. 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.
- A.CED.4- Creating Equations. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
- A.REI.3- Reasoning with Equations and Inequalities. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
- A.SSE1.a- Seeing Structure in Expressions. Interpret parts of an expression, such as terms, factors, and coefficients.
- F-IF.1-6- Interpreting Functions. 1) Understanding domain and range. 2)Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 3)Recognize that sequences are functions. 4)functions modeling a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. 5)Relate the domain of a function to its graph. 6)Calculate and interpret the average rate of change of a function
UNIT 2 - Linear Functions
- A.CED.2- Creating Equations. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- F.BF.1-2- Building Functions. 1)Compose functions. 2)Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
- F.IF.7,9- Interpreting Functions. 7)Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. 9)Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- F.LE.1,5- Linear, Quadratic, and Exponential Models. 1)Distinguish between situations that can be modeled with linear functions and with exponential functions. 5)Interpret the parameters in a linear or exponential function in terms of a context.
- A.REI.10,11- Reasoning with Equations and Inequalities. 10)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). 11)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).
- S.ID.6-9- Interpreting Categorical and Quantitative Data. 6)Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 7)Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 8)Compute (using technology) and interpret the correlation coefficient of a linear fit. 9) Distinguish between correlation and causation.
UNIT 3 - Geometry and Systems
- G.GPE.4-6- Expressing Geometric Properties with Equations. 4)Use coordinates to prove simple geometric theorems algebraically. 5)Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. 6)Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- A.CED.2-3- Creating Equations. 2) Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 3)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.
- A.REI.5-6,10,12- Reasoning with Equations and Inequalities. 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. 6)Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 10)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). 12)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.
UNIT 4 - Exponential Functions
- A.REI.11- Reasoning with Equations and Inequalities. 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).
- F.BF.1,2- Building Functions. 1)Compose functions. 2)Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
- F.IF2-9- Interpreting Functions. 2)Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 9)Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- F.LE-1,3,5-Linear, Quadratic, and Exponential Models. 1)Distinguish between situations that can be modeled with linear functions and with exponential functions. 3)Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 5)Interpret the parameters in a linear or exponential function in terms of a context.
- N.RN.2- The Real Number System. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
- S.ID.6c- Interpreting Categorical and Quantitative Data. Fit a linear function for a scatter plot that suggests a linear association.
UNIT 5 - Quadratic Functions
- A.CED.2- Creating Equations. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- A.REI.1,4,11- Reasoning with Equations and Inequalities. 1)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. 4)Solve quadratic equations in one variable. 11)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).
- A.APR.1,3- Arithmetic with Polynomials and Rational Expressions. 1)Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 3)Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
- F.IF.2,4-9- Interpreting Functions. 2)Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 4)For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship9)Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- A.REI.4- Reasoning with Equations and Inequalities. Solve quadratic equations in one variable.
- A.SSE.3- Seeing Structure in Expressions.Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- F.BF.1- Building Functions. Compose functions.
- N.RN.1-3- The Real Number System. 1)Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. 2)Rewrite expressions involving radicals and rational exponents using the properties of exponents. 3)Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
UNIT 6 - Statistics
- S.ID.1- Interpreting Categorical and Quantitative Data. Represent data with plots on the real number line (dot plots, histograms, and box plots).
- S.ID.2- Interpreting Categorical and Quantitative Data.Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
- S.ID.3- Interpreting Categorical and Quantitative Data. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).