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Curriculum Standards:


Analyze functions that include absolute value expressions. - HSM.A1.5.1
Distinguish between relations and functions. - A1.F.1.1
Graph and apply piecewise-defined functions. - HSM.A1.5.2
Identify the dependent and independent variables as well as the domain and range given a function, equation, or graph. Identify restrictions on the domain and range in real-world contexts. - A1.F.1.2
Express linear equations in slope-intercept, point-slope, and standard forms and convert between these forms. Given sufficient information (slope and y-intercept, slope and one-point on the line, two points on the line, x- and y-intercept, or a set of data points), write the equation of a line. - A1.A.4.3
Rewrite expressions involving radicals and rational exponents using the properties of exponents. Instructional Note: Address this standard before discussing exponential functions with continuous domains. - LER.M.A1HS.12
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. - LER.M.A1HS.13
Translate between a graph and a situation described qualitatively. - A1.A.4.4
Calculate and interpret slope and the x- and y-intercepts of a line using a graph, an equation, two points, or a set of data points to solve real-world and mathematical problems. - A1.A.4.1
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. (e.g., We define 5¹/³ to be the cube root of 5 because we want (5¹/³)³ = 5(¹/³)³ to hold, so (5¹/³)³ must equal 5.) Instructional Note: Address this standard before discussing exponential functions with continuous domains. - LER.M.A1HS.11
Graph and apply step functions. - HSM.A1.5.3
Graph and analyze transformations of the absolute value function. - HSM.A1.5.4
Add, subtract, and multiply polynomials. - HSM.A2.3.2
Prove and use polynomial identities. - HSM.A2.3.3
Predict the behavior of polynomial functions. - HSM.A2.3.1
Identify symmetry in and transform polynomial functions. - HSM.A2.3.7
Write linear functions, using function notation, to model real-world and mathematical situations. - A1.F.1.3
Given a graph modeling a real-world situation, read and interpret the linear piecewise function (excluding step functions). - A1.F.1.4
Use inverse functions to solve problems. - HSM.A1.10.7
Add, subtract, and multiply functions. - HSM.A1.10.6
Change functions to compress or stretch their graphs. - HSM.A1.10.5
Graph and analyze transformations of functions. - HSM.A1.10.4
Identify the function family when given an equation or graph. - HSM.A1.10.3
Identify the key features of the cube root function. - HSM.A1.10.2
Describe the key features of the square root function. - HSM.A1.10.1
determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line; - EI.A.6.a
write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line; and - EI.A.6.b
graph linear equations in two variables. - EI.A.6.c
Identify different types of symmetry in two-dimensional figures. - HSM.G.3.5
Use graphs to find approximate solutions to systems of equations. - HSM.A1.4.1
Solve systems of linear equations using the substitution method. - HSM.A1.4.2
Solve systems of linear equations using the elimination method. - HSM.A1.4.3
Graph solutions to linear inequalities in two variables. - HSM.A1.4.4
Graph and solve a system of linear inequalities. - HSM.A1.4.5
Find the zeros of quadratic functions. - HSM.A2.2.3
Solve problems with complex numbers. - HSM.A2.2.4
Identify key features of quadratic functions. - HSM.A2.2.1
Write and graph quadratic functions in standard form. - HSM.A2.2.2
Solve linear-quadratic systems. - HSM.A2.2.7
Solve quadratic equations by completing the square. - HSM.A2.2.5
Solve quadratic equations using the Quadratic Formula. - HSM.A2.2.6
Organize data in two-way frequency tables and use them to make inferences and generalizations. - HSM.A1.11.5
Quantify and analyze the spread of data. - HSM.A1.11.4
Interpret shapes of data displays representing different types of data distributions. - HSM.A1.11.3
Use measures of center and spread to compare data sets. - HSM.A1.11.2
Organize and understand data using dot plots, histograms, and box plots. - HSM.A1.11.1
solve multistep linear inequalities in one variable algebraically and represent the solution graphically; - EI.A.5.a
Combine standard function types using arithmetic operations. Example:: For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. - QFM.M.A1HS.57.b
represent the solution of linear inequalities in two variables graphically; - EI.A.5.b
solve practical problems involving inequalities; and - EI.A.5.c
represent the solution to a system of inequalities graphically. - EI.A.5.d
intercepts; - F.A.7.d
values of a function for elements in its domain; and - F.A.7.e
Use the properties of exponents to transform expressions for exponential functions. Example:: For example the expression 1.15 to the 𝘵 power can be rewritten as ((1.15 to the 1/12 power) to the 12𝘵𝘵 power) is approximately equal to (1.012 to the 12𝘵𝘵𝘵 power) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. - EE.M.A1HS.43.c
connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs. - F.A.7.f
Factor a quadratic trinomial. - HSM.A1.7.5
Factor a quadratic trinomial when a ≠ 1. - HSM.A1.7.6
determining whether a relation is a function; - F.A.7.a
domain and range; - F.A.7.b
Solve systems of linear inequalities with a maximum of two variables; graph and interpret the solutions on a coordinate plane. - A1.A.2.3
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. - EE.M.A1HS.43.b
Factor special trinomials. - HSM.A1.7.7
zeros; - F.A.7.c
Factor a quadratic expression to reveal the zeros of the function it defines. - EE.M.A1HS.43.a
Represent relationships in various contexts with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions. - A1.A.2.1
Combine like terms to simplify polynomials. - HSM.A1.7.1
Multiply two polynomials. - HSM.A1.7.2
Represent relationships in various contexts with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line. - A1.A.2.2
Use patterns to multiply binomials. - HSM.A1.7.3
Factor a polynomial. - HSM.A1.7.4
evaluate algebraic expressions for given replacement values of the variables. - EO.A.1.b
Relate roots and rational exponents and use them to simplify expressions and solve equations. - HSM.A2.5.1
represent verbal quantitative situations algebraically; and - EO.A.1.a
Solve radical equations and inequalities. - HSM.A2.5.4
Perform operations on functions to answer real-world questions. - HSM.A2.5.5
Use properties of exponents and radicals to simplify radical expressions. - HSM.A2.5.2
Graph and transform radical functions. - HSM.A2.5.3
Identify and generate equivalent representations of linear equations, graphs, tables, and real-world situations. - A1.F.3.1
Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of real-world and mathematical problems. - A1.F.3.2
Represent the inverse of a relation using tables, graphs, and equations. - HSM.A2.5.6
Add, subtract, and multiply functions using function notation. - A1.F.3.3
Use perpendicular and angle bisectors to solve problems. - HSM.G.5.1
Informally assess the fit of a function by plotting and analyzing residuals. Instructional Note: Focus should be on situations for which linear models are appropriate. - DS.M.A1HS.37.b
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. - DS.M.A1HS.37.a
Use properties of exponents to solve equations with rational exponents. - HSM.A1.6.1
Distinguish between linear and nonlinear (including exponential) functions arising from real-world and mathematical situations that are represented in tables, graphs, and equations. Understand that linear functions grow by equal intervals and that exponential functions grow by equal factors over equal intervals. - A1.F.2.1
Fit a linear function for scatter plots that suggest a linear association. - DS.M.A1HS.37.c
Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Use the pattern, find the next term. - A1.A.3.5
Simplify polynomial expressions by adding, subtracting, or multiplying. - A1.A.3.2
Interpret the parameters in a linear or exponential function in terms of a context. Instructional Note: Limit exponential functions to those of the form f(x) = bˣ + k. - LER.M.A1HS.32
Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1. - A1.A.3.3
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). Instructional Note: In constructing linear functions, draw on and consolidate previous work in Grade 8 on finding equations for lines and linear functions. - LER.M.A1HS.30
Describe and graph exponential functions. - HSM.A1.6.2
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Instructional Note: Limit to comparisons between exponential and linear models. - LER.M.A1HS.31
Solve equations involving several variables for one variable in terms of the others. - A1.A.3.1
Use exponential functions to model situations and make predictions. - HSM.A1.6.3
Identify and describe geometric sequences. - HSM.A1.6.4
Perform, analyze, and use transformations of exponential functions. - HSM.A1.6.5
adding, subtracting, multiplying, and dividing polynomials; and - EO.A.2.b
Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals. - LER.M.A1HS.29.a
applying the laws of exponents to perform operations on expressions; - EO.A.2.a
factoring completely first- and second-degree binomials and trinomials in one variable. - EO.A.2.c
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Instructional Note: Limit to linear and exponential functions. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions. - LER.M.A1HS.27
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 (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Instructional Note: Focus on vertical translations of graphs of linear and exponential functions. Relate the vertical translation of a linear function to its y-intercept. While applying other transformations to a linear graph is appropriate at this level, it may be difficult for students to identify or distinguish between the effects of the other transformations included in this standard. - LER.M.A1HS.28
Recognize that geometric sequences are exponential using equations, tables, graphs and verbal descriptions. Given the formula f(x) = a(r)x, find the next term and define the meaning of a and r within the context of the problem. - A1.A.3.6
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.) Instructional Note: Focus on linear and exponential functions. Include comparisons of two functions presented algebraically. Example:: For example, compare the growth of two linear functions, or two exponential functions such as y = 3ⁿ and y = 100²ⁿ) - LER.M.A1HS.25
Solve rational equations and identify extraneous solutions. - HSM.A2.4.5
Find the sum or difference of rational expressions. - HSM.A2.4.4
Recognize the graph of the functions f(x) = |x| and f(x) = x and predict the effects of transformations [f (x + c) and f(x) + c, where c is a positive or negative constant] algebraically and graphically using various methods and tools that may include graphing calculators. - A1.F.2.2
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. - LER.M.A1HS.29.b
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. Instructional Note: Focus on linear functions and exponential functions whose domain is a subset of the integers. The Unit on Quadratic Functions and Modeling in this course and the Algebra II course address other types of functions. - LER.M.A1HS.23
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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Instructional Note: Focus on linear and exponential functions. - LER.M.A1HS.21
Relate the domain of a function to its graph and where applicable, to the quantitative relationship it describes. (e.g., If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.) Instructional Note: Focus on linear and exponential functions. - LER.M.A1HS.22
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (e.g., The Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n)+ f(n-1) for n ≥ 1. Instructional Note: Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of function at this stage is not advised. Students should apply these concepts throughout their future mathematics courses. Draw examples from linear functions and exponential functions having integral domains. Draw connection to M.A1HS.27, which requires students to write arithmetic and geometric sequences. Emphasize arithmetic and geometric sequences as examples of linear and exponential functions. - LER.M.A1HS.20
Recognize 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). Instructional Note: Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of function at this stage is not advised. Students should apply these concepts throughout their future mathematics courses. Draw examples from linear functions and exponential functions having integral domains. - LER.M.A1HS.18
Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context. Instructional Note: Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of function at this stage is not advised. Students should apply these concepts throughout their future mathematics courses. Draw examples from linear functions and exponential functions having integral domains. - LER.M.A1HS.19
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. Instructional Note: Focus on cases where f(x) and g(x) are linear or exponential. - LER.M.A1HS.16
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. - LER.M.A1HS.17
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Instructional Note: Build on student experiences graphing and solving systems of linear equations from middle school to focus on justification of the methods used. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution); connect to standards in Geometry which require students to prove the slope criteria for parallel lines. - LER.M.A1HS.14
Recognize 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). Instructional Note: Focus on linear and exponential equations and be able to adapt and apply that learning to other types of equations in future courses. - LER.M.A1HS.15
Write and solve equations with a variable on both sides to solve problems. - HSM.A1.1.3
Rewrite and use literal equations to solve problems. - HSM.A1.1.4
Solve and graph inequalities. - HSM.A1.1.5
Write and solve compound inequalities. - HSM.A1.1.6
Calculate, interpret, and apply expected value. - HSM.G.12.5
Use matrices to represent and solve systems of equations. - HSM.A2.10.5
Reason about operations with real numbers. - HSM.A1.1.1
Create and solve linear equations with one variable. - HSM.A1.1.2
Write equivalent radical expressions. - HSM.A1.9.3
Interpret complicated expressions by viewing one or more of their parts as a single entity. Instructional Note: Exponents are extended from the integer exponents found in the unit on Relationships between Quantities and Reasoning with Equations to rational exponents focusing on those that represent square or cube roots. Example:: For example, interpret P(1 + r)ⁿ as the product of P and a factor not depending on P. - EE.M.A1HS.41.b
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Instructional Note: Compare linear and exponential growth to quadratic growth. - QFM.M.A1HS.60
Interpret parts of an expression, such as terms, factors, and coefficients. - EE.M.A1HS.41.a
Solve quadratic equations by taking square roots. - HSM.A1.9.4
Use completing the square to solve quadratic equations. - HSM.A1.9.5
Use the quadratic formula to solve quadratic equations. - HSM.A1.9.6
Write and solve absolute-value equations and inequalities - HSM.A1.1.7
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. - RQ.M.A1HS.1
Define appropriate quantities for the purpose of descriptive modeling. Instructional Note: Working with quantities and the relationships between them provides grounding for work with expressions, equations, and functions. - RQ.M.A1HS.2
Use tables and graphs to find solutions of quadratic equations. - HSM.A1.9.1
Interpret parts of an expression, such as terms, factors, and coefficients. - RQ.M.A1HS.4.a
Find the solution of a quadratic equation by factoring. - HSM.A1.9.2
Interpret complicated expressions by viewing one or more of their parts as a single entity. (e.g., Interpret P(1 + r)ⁿ as the product of P and a factor not depending on P. - RQ.M.A1HS.4.b
Use relationships among events to find probabilities. - HSM.G.12.1
Represent data with plots on the real number line (dot plots, histograms, and box plots). - DS.M.A1HS.33
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. Instructional Note: Limit to linear and exponential equations, and, in the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs. - RQ.M.A1HS.5
square roots of whole numbers and monomial algebraic expressions; - EO.A.3.a
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: Limit to linear and exponential equations, and, in the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs. - RQ.M.A1HS.6
Combine standard function types using arithmetic operations. (e.g., Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.) - LER.M.A1HS.26.b
numerical expressions containing square or cube roots. - EO.A.3.c
cube roots of integers; and - EO.A.3.b
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. Instructional Note: Students should focus on and master linear equations and be able to extend and apply their reasoning to other types of equations in future courses. Students will solve exponential equations with logarithms in Algebra II. - RQ.M.A1HS.9
Solve a system with linear and quadratic equations. - HSM.A1.9.7
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal and conditional relative frequencies). Recognize possible associations and trends in the data. - DS.M.A1HS.36
The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions. - S.A.9
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) Instructional Note: Limit to linear equations and inequalities. - RQ.M.A1HS.7
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Instructional Note: In grades 6 – 8, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points. - DS.M.A1HS.35
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. Instructional Note: In grades 6 – 8, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points. - DS.M.A1HS.34
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.) Instructional Note: Limit to formulas with a linear focus. - RQ.M.A1HS.8
The student, given a data set or practical situation, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically. - S.A.8
Use the unit circle to evaluate the trigonometric functions of any angle. - HSM.A2.7.3
Compute (using technology) and interpret the correlation coefficient of a linear fit. Instructional Note: Build on students’ work with linear relationships in eighth grade and introduce the correlation coefficient. The focus here is on the computation and interpretation of the correlation coefficient as a measure of how well the data fit the relationship. - DS.M.A1HS.39
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Instructional Note: Build on students’ work with linear relationships in eighth grade and introduce the correlation coefficient. The focus here is on the computation and interpretation of the correlation coefficient as a measure of how well the data fit the relationship. - DS.M.A1HS.38
Create and use graphs of sine and cosine functions. - HSM.A2.7.4
Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. Instructional Note: Focus on linear functions but consider simple situations where the domain of the function must be restricted in order for the inverse to exist, such as f(x) = x², x > 0. Example:: For example, f(x) = 2 x³ or f(x) = (x+1)/(x-1) for x ≠ 1. - QFM.M.A1HS.59
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 (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Instructional Note: Focus on quadratic functions, and consider including absolute value functions. - QFM.M.A1HS.58
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Instructional Note: Highlight issues of domain, range, and usefulness when examining piecewise-defined functions. Extend work with quadratics to include the relationship between coefficients and roots, and that once roots are known, a quadratic equation can be factored. Example:: For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. - QFM.M.A1HS.56
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. Instructional Note: Focus on quadratic functions; compare with linear and exponential functions studied in the Unit on Linear and Exponential Relationships. - QFM.M.A1HS.53
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Instructional Note: Focus on quadratic functions; compare with linear and exponential functions studied in the Unit on Linear and Exponential Relationships. Example:: For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. - QFM.M.A1HS.52
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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Instructional Note: Focus on quadratic functions; compare with linear and exponential functions studied in the Unit on Linear and Exponential Relationships. - QFM.M.A1HS.51
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. Instructional Note: Connect to physical situations (e.g., finding the perimeter of a square of area 2). - QFM.M.A1HS.50
Distinguish between correlation and causation. Instructional Note: The important distinction between a statistical relationship and a cause-and-effect relationship is the focus. - DS.M.A1HS.40
Use the structure of an expression to identify ways to rewrite it. Instructional Note: Focus on quadratic and exponential expressions. Example:: For example, see x⁴ – y⁴ as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²). - EE.M.A1HS.42
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R. Instructional Note: Extend work on linear and exponential equations in the Relationships between Quantities and Reasoning with Equations unit to quadratic equations. Extend this standard to formulas involving squared variables. - EE.M.A1HS.47
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: Extend work on linear and exponential equations in the Relationships between Quantities and Reasoning with Equations unit to quadratic equations. - EE.M.A1HS.46
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. Instructional Note: Extend work on linear and exponential equations in the Relationships between Quantities and Reasoning with Equations unit to quadratic equations. - EE.M.A1HS.45
Recognize 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. Instructional Note: Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of x. - EE.M.A1HS.44
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Instructional Note: Include systems consisting of one linear and one quadratic equation. Include systems that lead to work with fractions. Example:: For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3. Example:: For example, finding the intersections between x² + y² = 1 and y = (x+1)/2 leads to the point (3/5, 4/5) on the unit circle, corresponding to the Pythagorean triple 3² + 4² = 5². - EE.M.A1HS.49
Describe a data set using data displays, describe and compare data sets using summary statistics, including measures of central tendency, location, and spread. Know how to use calculators, spreadsheets, or other appropriate technology to display data and calculate summary statistics. - A1.D.1.1
Collect data and use scatterplots to analyze patterns and describe linear relationships between two variables. Using graphing technology, determine regression lines and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions. - A1.D.1.2
Interpret graphs as being discrete or continuous. - A1.D.1.3
Use quadratic functions to model real-world situations. - HSM.A1.8.4
Determine whether a linear, exponential, or quadratic function best models a data set. - HSM.A1.8.5
Solve absolute value equations and interpret the solutions in the original context. - A1.A.1.2
Analyze and solve real-world and mathematical problems involving systems of linear equations with a maximum of two variables by graphing (may include graphing calculator or other appropriate technology), substitution, and elimination. Interpret the solutions in the original context. - A1.A.1.3
Identify key features of the graph of the quadratic parent function. - HSM.A1.8.1
Graph quadratic functions using the vertex form. - HSM.A1.8.2
Use knowledge of solving equations with rational values to represent and solve mathematical and real-world problems (e.g., angle measures, geometric formulas, science, or statistics) and interpret the solutions in the original context. - A1.A.1.1
Graph quadratic functions using standard form. - HSM.A1.8.3
Graph logarithmic functions and find equations of the inverses of exponential and logarithmic functions. - HSM.A2.6.4
Recognize the key features of exponential functions. - HSM.A2.6.1
Write exponential models in different ways to solve problems. - HSM.A2.6.2
Identify, write, and use geometric sequences and series. - HSM.A2.6.7
Use properties of logarithms to rewrite expressions. - HSM.A2.6.5
Solve exponential and logarithmic equations. - HSM.A2.6.6
Determine whether a function is a relation. - HSM.A1.3.1
Identify, evaluate, and graph linear functions. - HSM.A1.3.2
Use relationships among events to find probabilities. - HSM.A2.12.1
Transform linear equations - HSM.A1.3.3
Identify and describe arithmetic sequences. - HSM.A1.3.4
Use a scatter plot to describe the relationship between two data sets. - HSM.A1.3.5
Find the line of best fit for a data set and evaluate its goodness of fit. - HSM.A1.3.6
Calculate, interpret, and apply expected value. - HSM.A2.12.5
Interpret key features of linear, quadratic, and absolute value functions given an equation or a graph. - HSM.A2.1.1
Interpret arithmetic sequences and series. - HSM.A2.1.4
Graph exponential and logarithmic functions, showing intercepts and end behavior and trigonometric functions, showing period, midline and amplitude. - LER.M.A1HS.24.b
Use graphs and tables to approximate solutions to algebraic equations and inequalities. - HSM.A2.1.5
Graph linear and quadratic functions and show intercepts, maxima, and minima. - LER.M.A1HS.24.a
Apply transformations to graph functions and write equations. - HSM.A2.1.2
Graph and interpret piecewise-defined functions. - HSM.A2.1.3
Understand and apply the geometric properties of a parabola. - HSM.A2.9.1
Use a variety of tools to solve systems of linear equations and inequalities. - HSM.A2.1.6
Solve systems of equations using matrices. - HSM.A2.1.7
Understand and apply the geometric properties of a hyperbola. - HSM.A2.9.4
Write, graph, and apply the equation of a circle. - HSM.A2.9.2
Graph linear and quadratic functions and show intercepts, maxima, and minima. - QFM.M.A1HS.54.a
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - QFM.M.A1HS.54.b
multistep linear equations in one variable algebraically; - EI.A.4.a
quadratic equations in one variable algebraically; - EI.A.4.b
literal equations for a specified variable; - EI.A.4.c
systems of two linear equations in two variables algebraically and graphically; and - EI.A.4.d
practical problems involving equations and systems of equations. - EI.A.4.e
Use the relationships between sides, segments, and angles of triangles to solve problems. - HSM.G.5
Use inductive reasoning to make conjectures about mathematical relationships. - HSM.G.1.4
Use properties of segments and angles to find their measures. - HSM.G.1.1
Write and graph linear equations using point-slope form. - HSM.A1.2.2
Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. - EE.M.A1HS.48.b
Write and graph linear equations using standard form. - HSM.A1.2.3
Write equations of parallel lines and perpendicular lines. - HSM.A1.2.4
Evaluate data distributions. - HSM.A2.11.3
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. Derive the quadratic formula from this form. - EE.M.A1HS.48.a
Write and graph linear equations using slope-intercept form. - HSM.A1.2.1
Verify and use trigonometric identities. - HSM.A2.8.3
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. - QFM.M.A1HS.55.a
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Instructional Note: Extend earlier work with solving linear equations to solving linear inequalities in one variable and to solving literal equations that are linear in the variable being solved for. Include simple exponential equations that rely only on application of the laws of exponents, such as 5ˣ = 125 or 2ˣ = 1 /16. - RQ.M.A1HS.10
Use slope to solve problems about parallel and perpendicular lines. - HSM.G.2.4




List of all Files Validated:


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