HSN.RN.B.4: Simplify radical expressions. Perform operations (add, subtract, multiply, and divide) with radical expressions. Rationalize denominators and/or numerators.
HSA.SSE.A.1: Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity.
HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
HSA.SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
HSA.APR.A.1: Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication.
HSA.APR.B.3: Identify zeros of polynomials (linear, quadratic only) when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.
HSA.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.
HSA.CED.A.3: Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.
HSA.CED.A.4: Rearrange literal equations using the properties of equality.
HSA.REI.A.1: Assuming that equations have a solution, construct a solution and justify the reasoning used.
HSA.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
HSA.REI.B.3: Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters.
HSA.REI.B.4: Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (𝘹 – 𝘱)² = 𝘲 that has the same solutions. Solve quadratic equations (as appropriate to the initial form of the equation) by: inspection of a graph, taking square roots, completing the square, using the quadratic formula, factoring. Recognize complex solutions and write them as 𝘢 ± 𝘣𝘪 for real numbers 𝘢 and 𝘣. (Algebra 2 only)
HSA.REI.C.5: Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.
HSA.REI.C.6: Solve systems of equations algebraically and graphically.
HSA.REI.C.7: Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically.
HSA.REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
HSA.REI.D.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); Find the solutions approximately by using technology to graph the functions, making tables of values, finding successive approximations. Include cases (but not limited to) where f(x) and/or g(x) are linear, polynomial, absolute value, exponential. (Introduction in Algebra 1, Mastery in Algebra 2)
HSA.REI.D.12: Solve linear inequalities and systems of linear inequalities in two variables by graphing.
HSF.IF.A.1: 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. Understand that 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. Understand that the graph of 𝑓 is the graph of the equation 𝑦 = 𝑓(𝑥).
HSF.IF.B.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 relationship.
HSF.IF.B.5: Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes.
HSF.IF.B.6: Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.
HSF.IF.C.7: Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior.
HSF.IF.C.8: Write expressions for functions in different but equivalent forms to reveal key features of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values (vertex), and symmetry of the graph, and interpret these in terms of a context.
HSF.BF.A.1: Write a function that describes a relationship between two quantities. From a context, determine an explicit expression, a recursive process, or steps for calculation.
HSF.BF.B.3: Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of 𝑘 (𝑘, a constant both positive and negative); Find the value of 𝑘 given the graphs of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
HSF.LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. Show that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
HSF.LE.A.2: Construct linear and exponential equations, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
HSF.LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any polynomial function.
HSF.LE.B.5: In terms of a context, interpret the parameters (rates of growth or decay, domain and range restrictions where applicable, etc.) in a function.
HSS.ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).
HSS.ID.A.2: 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.
HSS.ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
HSS.ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
HSS.ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
HSS.ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.
Correlation last revised: 1/22/2020