Organization: Pearson Education
Product Name: Envision Integrated Mathematics I
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Curriculum Standards:

Analyze functions that include absolute value expressions. - HSM.A1.5.1
Graph and apply piecewise-defined functions. - HSM.A1.5.2
Prove the slope criteria for parallel and perpendicular lines and uses 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.) Instructional Note: Relate work on parallel lines to work in High School Algebra I involving systems of equations having no solution or infinitely many solutions. - CAG.M.GHS.30
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
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
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
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. - MAFS.K12.MP.3.1.a
Add, subtract, and multiply polynomials. - HSM.A2.3.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. - MAFS.912.F-BF.1.2
Prove and use polynomial identities. - HSM.A2.3.3
vertical and horizontal asymptotes; - F.AII.7.i
end behavior; - F.AII.7.h
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
intercepts; - F.AII.7.e
zeros; - F.AII.7.d
connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs; - F.AII.7.g
Find the point on a directed line segment between two given points that partitions the segment in a given ratio. - CAG.M.GHS.31
domain, range, and continuity; - F.AII.7.a
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. This standard provides practice with the distance formula and its connection with the Pythagorean theorem. - CAG.M.GHS.32
extrema; - F.AII.7.c
intervals in which a function is increasing or decreasing; - F.AII.7.b
Use graphs to find approximate solutions to systems of equations. - HSM.A1.4.1
(HONORS ONLY) Solve an equation of the form ??(????) = ?????? for a simple function ???????? that has an inverse and write an expression for the inverse. Example: For example, ??????????(????????????) =2 ??????????????³ or ????????????????(??????????????????) = (????????????????????+1)/(??????????????????????–1) for ???????????????????????? ? 1. - MAFS.912.F-BF.2.4.a
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
Describe the effect of the transformations ??????????????????????????????????????????????????????(??????????????????????????????), ????????????????????????????????(??????????????????????????????????)+????????????????????????????????????, ??????????????????????????????????????(????????????????????????????????????????+??????????????????????????????????????????), and combinations of such transformations on the graph of ????????????????????????????????????????????=??????????????????????????????????????????????(????????????????????????????????????????????????) for any real number ??????????????????????????????????????????????????. Find the value of ???????????????????????????????????????????????????? given the graphs and write the equation of a transformed parent function given its graph. (Limit to linear; quadratic; exponential with integer exponents; vertical shift and vertical stretch.) - A1.FBF.3
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: For example, if the function ??????????????????????????????????????????????????????(????????????????????????????????????????????????????????) gives the number of person-hours it takes to assemble ?????????????????????????????????????????????????????????? engines in a factory, then the positive integers would be an appropriate domain for the function. - MAFS.912.F-IF.2.5
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. - MAFS.912.F-IF.2.6
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
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. - MAFS.912.F-IF.2.4
Write and graph quadratic functions in standard form. - HSM.A2.2.2
Solve linear-quadratic systems. - HSM.A2.2.7
Solve quadratic equations using the Quadratic Formula. - HSM.A2.2.6
Graph exponential and logarithmic functions. Identify asymptotes and x- and y-intercepts using various methods and tools that may include graphing calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically. - A2.F.1.4
Recognize the graphs of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [f(x + c), f(x) + c, f(cx), and cf(x), where c is a positive or negative real-valued constant] algebraically and graphically, using various methods and tools that may include graphing calculators or other appropriate technology. - A2.F.1.2
Graph piecewise functions with no more than three branches (including linear, quadratic, or exponential branches) and analyze the function by identifying the domain, range, intercepts, and intervals for which it is increasing, decreasing, and constant. - A2.F.1.8
solve multistep linear inequalities in one variable algebraically and represent the solution graphically; - EI.A.5.a
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
Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable. (Limit to linear; quadratic; exponential with integer exponents.) - A1.ACE.1
Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.) - A1.ACE.2
Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines. - A1.ACE.4
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. - MAFS.912.G-SRT.2.5
Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations. (Limit to linear; quadratic.) - A1.AAPR.1
intercepts; - F.A.7.d
values of a function for elements in its domain; and - F.A.7.e
connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs. - F.A.7.f
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
Factor special trinomials. - HSM.A1.7.7
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
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
Multiply two polynomials. - HSM.A1.7.2
Use patterns to multiply binomials. - HSM.A1.7.3
Factor a polynomial. - HSM.A1.7.4
Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function. - 9.2.1.6
evaluate algebraic expressions for given replacement values of the variables. - EO.A.1.b
Understand the concept of an asymptote and identify asymptotes for exponential functions and reciprocals of linear functions, using symbolic and graphical methods. - 9.2.1.7
Make qualitative statements about the rate of change of a function, based on its graph or table of values - 9.2.1.8
Determine how translations affect the symbolic and graphical forms of a function. Know how to use graphing technology to examine translations - 9.2.1.9
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 ???????????????????????????????????????????????????????????? is a function and ?????????????????????????????????????????????????????????????? is an element of its domain, then ????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????) denotes the output of ???????????????????????????????????????????????????????????????????? corresponding to the input ??????????????????????????????????????????????????????????????????????. The graph of ???????????????????????????????????????????????????????????????????????? is the graph of the equation ?????????????????????????????????????????????????????????????????????????? = ????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????). - MAFS.912.F-IF.1.1
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. - MAFS.912.F-IF.1.2
Relate roots and rational exponents and use them to simplify expressions and solve equations. - HSM.A2.5.1
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: For example, the Fibonacci sequence is defined recursively by ????????????????????????????????????????????????????????????????????????????????(0) = ??????????????????????????????????????????????????????????????????????????????????(1) = 1, ????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????+1) = ????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????) + ????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????-1) for ???????????????????????????????????????????????????????????????????????????????????????????????? greater than or equal to 1. - MAFS.912.F-IF.1.3
represent verbal quantitative situations algebraically; and - EO.A.1.a
Perform operations on functions to answer real-world questions. - HSM.A2.5.5
Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data. - A1.SPID.6
Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain - 9.2.1.1
Create a linear function to graphically model data from a real-world problem and interpret the meaning of the slope and intercept(s) in the context of the given problem. - A1.SPID.7
Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables. (Limit to linear; exponential.) - A1.FLQE.2
Find the domain of a function defined symbolically, graphically or in a real-world context. - 9.2.1.3
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or more generally as a polynomial function. - A1.FLQE.3
Obtain information and draw conclusions from graphs of functions and other relations. - 9.2.1.4
Interpret the parameters in a linear or exponential function in terms of the context. (Limit to linear.) - A1.FLQE.5
Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f (x) = ax2 + bx + c, in the form - 9.2.1.5
Using technology, compute and interpret the correlation coefficient of a linear fit. - A1.SPID.8
The student will solve problems involving equations of circles. - PC.G.12
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. - MAFS.912.G-SRT.3.8
Use properties of exponents to solve equations with rational exponents. - HSM.A1.6.1
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Instructional Note: Extend to simple rational and radical equations. - PRR.M.A2HS.16
Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Use the pattern, find the next term. - A1.A.3.5
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) = b? + k. - LER.M.A1HS.32
Simplify polynomial expressions by adding, subtracting, or multiplying. - A1.A.3.2
Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1. - A1.A.3.3
Describe and graph exponential functions. - HSM.A1.6.2
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
Use exponential functions to model situations and make predictions. - HSM.A1.6.3
Solve equations involving several variables for one variable in terms of the others. - A1.A.3.1
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
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
applying the laws of exponents to perform operations on expressions; - EO.A.2.a
Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original. - A1.AREI.1
add, subtract, multiply, divide, and simplify rational algebraic expressions; - EO.AII.1.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
add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents; and - EO.AII.1.b
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
Solve rational equations and identify extraneous solutions. - HSM.A2.4.5
Find the sum or difference of rational expressions. - HSM.A2.4.4
Solve systems of linear equations using the substitution method. - A1.AREI.6
Justify that the solution to a system of linear equations is not changed when one of the equations is replaced by a linear combination of the other equation. - A1.AREI.5
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. - A1.AREI.3
identifying the converse, inverse, and contrapositive of a conditional statement; - RLT.G.1.a
determining the validity of a logical argument. - RLT.G.1.c
translating a short verbal argument into symbolic form; and - RLT.G.1.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
Analyze slopes of lines to determine whether lines are parallel, perpendicular, or neither. Write the equation of a line passing through a given point that is parallel or perpendicular to a given line. Solve geometric and real-world problems involving lines and slope. - G.GGPE.5
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
Given two points, find the point on the line segment between the two points that divides the segment into a given ratio. - G.GGPE.6
Use the distance and midpoint formulas to determine distance and midpoint in a coordinate plane, as well as areas of triangles and rectangles, when given coordinates. - G.GGPE.7
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
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
use knowledge of transformations to convert between equations and the corresponding graphs of functions. - F.AII.6.b
recognize the general shape of function families; and - F.AII.6.a
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
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. - MAFS.912.G-CO.1.1
Solve and graph inequalities. - HSM.A1.1.5
Write and solve compound inequalities. - HSM.A1.1.6
Reason about operations with real numbers. - HSM.A1.1.1
Create and solve linear equations with one variable. - HSM.A1.1.2
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. Example: For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. - MAFS.912.A-CED.1.3
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - MAFS.912.A-CED.1.2
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: For example, rearrange Ohm’s law ?????????????????????????????????????????????????????????????????????????????????????????????????? = ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? to highlight resistance ????????????????????????????????????????????????????????????????????????????????????????????????????????. - MAFS.912.A-CED.1.4
Write and solve absolute-value equations and inequalities - HSM.A1.1.7
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. - MAFS.912.A-CED.1.1
Interpret parts of an expression, such as terms, factors, and coefficients. - RQ.M.A1HS.4.a
Use relationships among events to find probabilities. - HSM.G.12.1
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
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
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
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
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
Solve one-variable rational equations and check for extraneous solutions. - A2.A.1.3
Represent real-world or mathematical problems using exponential equations, such as compound interest, depreciation, and population growth, and solve these equations graphically (including graphing calculator or other appropriate technology) or algebraically. - A2.A.1.2
Fit a linear function for a scatter plot that suggests a linear association. - MAFS.912.S-ID.2.6.c
Informally assess the fit of a function by plotting and analyzing residuals. - MAFS.912.S-ID.2.6.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, quadratic, and exponential models. - MAFS.912.S-ID.2.6.a
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
Use dilation and rigid motion to establish triangle similarity theorems. - HSM.G.7.3
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
Find the lengths of segments using proportional relationships in triangles resulting from parallel lines. - HSM.G.7.5
Use similarity and the geometric mean to solve problems involving right triangles. - HSM.G.7.4
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
Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions. - MAFS.912.G-CO.2.8
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
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. - MAFS.912.G-CO.2.7
Solve real-world and mathematical problems that can be modeled using arithmetic or finite geometric sequences or series given the nth terms and sum formulas. Graphing calculators or other appropriate technology may be used. - A2.A.1.7
Represent real-world or mathematical problems using systems of linear equations with a maximum of three variables and solve using various methods that may include substitution, elimination, and graphing (may include graphing calculators or other appropriate technology). - A2.A.1.8
Solve systems of equations containing one linear equation and one quadratic equation using tools that may include graphing calculators or other appropriate technology. - A2.A.1.9
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
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
Rewrite expressions involving radicals and rational exponents using the properties of exponents. - A2.A.2.4
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. - MAFS.912.A-APR.1.1
Use trigonometry to solve problems. - HSM.G.8.5
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Instructional Note: Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two-column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. - CPC.M.GHS.9
Interpret the parameters in a linear or exponential function in terms of the context. (Limit to linear.) - HSF-LE.B.5
Use trigonometric ratios to find lengths and angle measures of right triangles. - HSM.G.8.2
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Instructional Note: Rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems. - CPC.M.GHS.7
Prove the Pythagorean Theorem using similarity and establish the relationships in special right triangles. - HSM.G.8.1
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Instructional Note: Rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems. - CPC.M.GHS.8
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Instructional Note: Rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems. - CPC.M.GHS.6
Determine whether a function is a relation. - HSM.A1.3.1
Identify, evaluate, and graph linear functions. - HSM.A1.3.2
Transform linear equations - HSM.A1.3.3
Identify and describe arithmetic sequences. - HSM.A1.3.4
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: For example, the Fibonacci sequence is defined recursively by ??(0) = ??(1) = 1, ??(??+1) = ??(??) + ??(??-1) for ?? greater than or equal to 1. - HSF-IF.A.3
Interpret the parameters in a linear or exponential function in terms of a context. - MAFS.912.F-LE.2.5
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. - CPC.M.GHS.1
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 quadratic and exponential functions. - S.AII.9
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
Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions. - A1.ASE.2
Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to linear; quadratic; exponential.) - A1.ASE.1
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 and interpret piecewise-defined functions. - HSM.A2.1.3
Use a variety of tools to solve systems of linear equations and inequalities. - HSM.A2.1.6
Understand that two events ?????????????????????????????????????????????????????????????????????????????????????????????????????????? and ???????????????????????????????????????????????????????????????????????????????????????????????????????????? are independent if the probability of ?????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ???????????????????????????????????????????????????????????????????????????????????????????????????????????????? occurring together is the product of their probabilities, and use this characterization to determine if they are independent. - CCSS.Math.Content.HSS-CP.A.2
Solve systems of equations using matrices. - HSM.A2.1.7
The student will verify and use properties of quadrilaterals to solve problems, including practical problems. - PC.G.9
Interpret the parameters in a linear or exponential function in terms of the context. - A2.FLQE.5
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. - MAFS.912.A-REI.2.3
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. - A2.FBF.2
Use the coordinate plane to analyze geometric figures. - HSM.G.9.1
Use the equations and graphs of circles to solve problems. - HSM.G.9.3
Prove geometric theorems using algebra and the coordinate plane. - HSM.G.9.2
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). - MAFS.912.F-LE.1.2
Write and graph linear equations using point-slope form. - HSM.A1.2.2
Write and graph linear equations using standard form. - HSM.A1.2.3
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. - MAFS.912.F-LE.1.3
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 equations of parallel lines and perpendicular lines. - HSM.A1.2.4
Write and graph linear equations using slope-intercept form. - HSM.A1.2.1
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. Example: For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. - MAFS.912.N-RN.1.1
Rewrite expressions involving radicals and rational exponents using the properties of exponents. - MAFS.912.N-RN.1.2
Identify the effect on the graph of replacing ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) by ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) + ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????, ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????), ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????), and ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? + ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) for specific values of ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? (both positive and negative); find the value of ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 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. - MAFS.912.F-BF.2.3
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Understand that such systems may have zero, one, two, or infinitely many solutions. (Limit to linear equations and quadratic functions.) - A2.AREI.7
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. - CCSS.Math.Content.HSG-CO.C.10
Solve simple rational and radical equations in one variable and understand how extraneous solutions may arise. - A2.AREI.2
properties of special right triangles; and - T.G.8.b
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. - MAFS.912.A-REI.3.5
Define angle, perpendicular line, parallel line, line segment, ray, circle, and skew in terms of the undefined notions of point, line, and plane. Use geometric figures to represent and describe real-world objects. - G.GCO.1
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: For example, find the points of intersection between the line ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? = –3???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and the circle ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² + ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² = 3. - MAFS.912.A-REI.3.7
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. - MAFS.912.A-REI.3.6
Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, and Hypotenuse-Leg congruence c - G.GCO.7
Demonstrate that triangles and quadrilaterals are congruent by identifying a combination of translations, rotations, and reflections in various representations that move one figure onto the other. - G.GCO.6
Prove, and apply in mathematical and real-world contexts, theorems about the relationships within and among triangles, including the following: a) measures of interior angles of a triangle sum to 180°; b) base angles of isosceles triangles are congruent; c) the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; d) the medians of a triangle meet at a point. - G.GCO.9
Prove, and apply in mathematical and real-world contexts, theorems about lines and angles, including the following: a vertical angles are congruent; b) when a transversal crosses parallel lines, alternate interior angles are congruent, alternate exterior angles are congruent, and consecutive interior angles are supplementary; c) any point on a perpendicular bisector of a line segment is equidistant from the endpoints of the segment; d) perpendicular lines form four right angles. - G.GCO.8
Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. - MAFS.912.G-CO.3.10
Distinguish between relations and functions. - A1.F.1.1
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
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. - MAFS.912.N-RN.2.3
Distinguish between correlation and causation. - MAFS.912.S-ID.3.9
Compute (using technology) and interpret the correlation coefficient of a linear fit. - MAFS.912.S-ID.3.8
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. - MAFS.912.S-ID.3.7
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude, and using phase shift. - MAFS.912.F-IF.3.7.e
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. - MAFS.912.F-IF.3.7.c
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. - CCSS.Math.Content.HSG-CO.B.6
(HONORS ONLY) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. - MAFS.912.F-IF.3.7.d
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. - CCSS.Math.Content.HSG-CO.B.7
Graph linear and quadratic functions and show intercepts, maxima, and minima. - MAFS.912.F-IF.3.7.a
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. - CCSS.Math.Content.HSG-CO.B.8
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - MAFS.912.F-IF.3.7.b
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. - MAFS.912.G-CO.4.12
Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. - A2.ACE.2
Write linear functions, using function notation, to model real-world and mathematical situations. - A1.F.1.3
Use systems of equations and inequalities to represent constraints arising in real-world situations. Solve such systems using graphical and analytical methods, including linear programing. Interpret the solution within the context of the situation. (Limit to linear programming.) - A2.ACE.3
Interpret parts of an expression, such as terms, factors, and coefficients. - MAFS.912.A-SSE.1.1.a
Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable. - A2.ACE.1
Use inverse functions to solve problems. - HSM.A1.10.7
Add, subtract, and multiply functions. - HSM.A1.10.6
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
Draw and describe the rotation of a figure about a point of rotation for a given angle of rotation. - HSM.G.3.3
Describe the concepts of intersections, unions and complements using Venn diagrams. Understand the relationships between these concepts and the words AND, OR, NOT, as used in computerized searches and spreadsheets. - 9.4.3.6
Describe the properties of a figure before and after translation. - HSM.G.3.2
Identify different types of symmetry in two-dimensional figures. - HSM.G.3.5
Identify different rigid motions used to transform two-dimensional shapes. - HSM.G.3.4
Use the relationship between conditional probabilities and relative frequencies in contingency tables. - 9.4.3.9
Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes. - 9.4.3.2
Draw and describe the reflection of a figure across a line of reflection. - HSM.G.3.1
Apply probability concepts such as intersections, unions and complements of events, and conditional probability and independence, to calculate probabilities and solve problems. - 9.4.3.5
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² + 9???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? – ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. - MAFS.K12.MP.7.1.a
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - CCSS.Math.Content.HSA-CED.A.2
Solve quadratic equations by inspection, 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 ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????+?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? for real numbers ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. (Limit to non-complex roots.) - A1.AREI.4b
Use the method of completing the square to transform any quadratic equation in ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? into an equation of the form (??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????-h)2=???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? that has the same solutions. Derive the quadratic formula from this form. - A1.AREI.4a
Apply the properties of angles, including corresponding, exterior, interior, vertical, complementary, and supplementary angles to solve real-world and mathematical problems using algebraic reasoning and proofs. - G.2D.1.2
Apply theorems involving the interior and exterior angle sums of polygons and use them to solve real-world and mathematical problems using algebraic reasoning and proofs. - G.2D.1.3
Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments. - G.2D.1.5
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). - MAFS.912.G-GPE.2.5
Find the point on a directed line segment between two given points that partitions the segment in a given ratio. - MAFS.912.G-GPE.2.6
Apply the properties of congruent or similar polygons to solve real-world and mathematical problems using algebraic and logical reasoning. - G.2D.1.7
Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS and HL) and triangle similarity (AA, SSS, SAS). - G.2D.1.8
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. - MAFS.912.G-GPE.2.7
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. - MF.M.A2HS.30.b
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - MF.M.A2HS.30.a
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
Apply the properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve real-world and mathematical problems and determine if two lines are parallel, using algebraic reasoning and proofs. - G.2D.1.1
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
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. - MAFS.912.A-REI.1.2
Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid. - 9.3.4.6
Organize and understand data using dot plots, histograms, and box plots. - HSM.A1.11.1
Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure. - 9.3.4.7
Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments. - 9.3.4.4
Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios. - 9.3.4.2
Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts. - 9.3.4.3
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
Use triangle congruence to solve problems with overlapping triangles. - HSM.G.4.6
Identify congruent right triangles. - HSM.G.4.5
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. - MAFS.912.A-REI.1.1
Apply theorems about isosceles and equilateral triangles to solve problems. - HSM.G.4.2
Use a composition of rigid motions to show that two objects are congruent. - HSM.G.4.1
Determine congruent triangles by comparing two angles and one side. - HSM.G.4.4
Use SAS and SSS to determine whether triangles are congruent. - HSM.G.4.3
Use relationships between circles, angles, and arcs. - HSM.G.10.4
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. - SPT.M.GHS.21
Understand the use of undefined terms, definitions, postulates, and theorems in logical arguments/proofs. - G.RL.1.1
Solve quadratic equations by inspection (e.g., for ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² = 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 ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? ± ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? for real numbers ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. - MAFS.912.A-REI.2.4.b
Analyze and draw conclusions based on a set of conditions using inductive and deductive reasoning. Recognize the logical relationships between a conditional statement and its inverse, converse, and contrapositive. - G.RL.1.2
Find arc length and sector area of a circle and use them to solve problems. - HSM.G.10.1
Relate the length of a chord to the central angle it subtends and the arc it intercepts. - HSM.G.10.3
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
Add, subtract, and multiply functions using function notation. - A1.F.3.3
ordering the angles by degree measure, given side lengths; - T.G.5.b
determining whether a triangle exists; and - T.G.5.c
determining the range in which the length of the third side must lie. - T.G.5.d
ordering the sides by length, given angle measures; - T.G.5.a
Compare a pair of sides of two triangles when the remaining pairs of sides are congruent. - HSM.G.5.5
Use theorems to compare the sides and angles of a triangle. - HSM.G.5.4
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). - MAFS.912.S-ID.1.3
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. - MAFS.912.S-ID.1.2
Represent data with plots on the real number line (dot plots, histograms, and box plots). - MAFS.912.S-ID.1.1
Use perpendicular and angle bisectors to solve problems. - HSM.G.5.1
Graph the solutions to a linear inequality in two variables. - A1.AREI.12
Find the points of concurrency for the medians of a triangle and the altitudes of a triangle. - HSM.G.5.3
Use triangle bisectors to solve problems. - HSM.G.5.2
Solve an equation of the form ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)=??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) graphically by identifying the ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????-coordinate(s) of the point(s) of intersection of the graphs of ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????=??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) and ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????=????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????). (Limit to linear; quadratic; exponential.) - A1.AREI.11
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 geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. - MAFS.912.G-CO.2.6
Create equations and inequalities in one variable and use them to solve problems. Instructional Note: Include equations arising from linear and quadratic functions, and simple rational and exponential functions. - MF.M.A2HS.23
Fit a linear function for scatter plots that suggest a linear association. - DS.M.A1HS.37.c
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: While functions will often be linear, exponential, or quadratic the types of problems should draw from more complex situations than those addressed in Algebra I. (e.g., Finding the equation of a line through a given point perpendicular to another line allows one to find the distance from a point to a line). - MF.M.A2HS.24
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. - MAFS.912.S-ID.2.5
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
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. - CCSS.Math.Content.HSS-ID.A.2
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. - SPT.M.GHS.18
Use the structure of an expression to identify ways to rewrite it. Example: For example, see ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????4 – ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????4 as (????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²)² – (??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²)², thus recognizing it as a difference of squares that can be factored as (????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² – ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²)(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² + ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²). - MAFS.912.A-SSE.1.2
Use the properties of rhombuses, rectangles, and squares to solve problems. - HSM.G.6.5
Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. - MAFS.912.G-CO.3.9
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: Emphasize the selection of a model function based on behavior of data and context. - MF.M.A2HS.27
Use triangle congruence to understand kites and trapezoids. - HSM.G.6.2
Find the sums of the measures of the exterior angles and interior angles of polygons. - HSM.G.6.1
Apply the distance formula and the Pythagorean Theorem and its converse to solve real-world and mathematical problems, as approximate and exact values, using algebraic and logical reasoning (include Pythagorean Triples). - G.RT.1.1
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.) Note: Emphasize the selection of a model function based on behavior of data and context. - MF.M.A2HS.28
The student, given information in the form of a figure or statement, will prove two triangles are congruent. - T.G.6
Write equivalent radical expressions. - HSM.A1.9.3
Solve quadratic equations by taking square roots. - HSM.A1.9.4
Interpret parts of an expression, such as terms, factors, and coefficients. - EE.M.A1HS.41.a
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
Use the quadratic formula to solve quadratic equations. - HSM.A1.9.6
Find the solution of a quadratic equation by factoring. - HSM.A1.9.2
Represent data with plots on the real number line (dot plots, histograms, and box plots). - DS.M.A1HS.33
square roots of whole numbers and monomial algebraic expressions; - EO.A.3.a
Add, subtract, multiply, divide and simplify algebraic fractions. - 9.2.3.4
Check whether a given complex number is a solution of a quadratic equation by substituting it for the variable and evaluating the expression, using arithmetic with complex numbers. - 9.2.3.5
numerical expressions containing square or cube roots. - EO.A.3.c
Apply the properties of positive and negative rational exponents to generate equivalent algebraic expressions, including those involving nth roots. - 9.2.3.6
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
cube roots of integers; and - EO.A.3.b
Justify steps in generating equivalent expressions by identifying the properties used. Use substitution to check the equality of expressions for some particular values of the variables; recognize that checking with substitution does not guarantee equality of expressions for all values of the variables. - 9.2.3.7
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
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
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
Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified points in their domains. - 9.2.3.1
Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. - 9.2.3.3
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
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
solve problems, including practical problems, involving angles formed when parallel lines are intersected by a transversal. - RLT.G.2.b
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
prove two or more lines are parallel; and - RLT.G.2.a
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
Rewrite expressions involving simple radicals and rational exponents in different forms. - A1.NRNS.1
Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation. - A1.FIF.2
Extend previous knowledge of a function to apply to general behavior and features of a function. - A1.FIF.1
Use the definition of the meaning of rational exponents to translate between rational exponent and radical forms. - A1.NRNS.2
Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. (Limit to linear; quadratic; exponential.) - A1.FIF.4
Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context. (Limit to linear; quadratic; exponential.) - A1.FIF.6
Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (Limit to linear; quadratic; exponential.) - A1.FIF.5
Explain why the sum or product of 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. - A1.NRNS.3
quadratic equations over the set of complex numbers; - EI.AII.3.b
Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. (Limit to linear; quadratic; exponential only in the form ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????=??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????+??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????.) - A1.FIF.7
equations containing rational algebraic expressions; and - EI.AII.3.c
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
Construct geometric figures using a variety of tools, including a compass, a straightedge, dynamic geometry software, and paper folding, and use these constructions to make conjectures about geometric relationships. - G.GCO.11
Identify key features of the graph of the quadratic parent function. - HSM.A1.8.1
Solve right triangles in applied problems using trigonometric ratios and the Pythagorean Theorem. - G.GSRT.8
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. - G.GSRT.5
Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts. - 9.2.2.5
The student will solve systems of linear-quadratic and quadratic-quadratic equations, algebraically and graphically. - EI.AII.4
Sketch the graphs of common non-linear functions such as f (x) = vx, f(x) = |x|, f(x) = 1/x, f(x) = x3 and translations of these functions, such as f(x) = vx-2+4. Know how to use graphing technology to graph these functions. - 9.2.2.6
Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. - A2.FIF.5
Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. - A2.FIF.4
Understand that two