Skills available for West Virginia Algebra 1 standards
Standards are in bold, followed by a list of the IXL math skills that are aligned to that standards. Students can practice these skills online at www.ixl.com.
Standards: West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics I
9.M.1HS.RBQ Relationships Between Quantities
9 Reason quantitatively and use units to solve problems.
9.M.1HS.RBQ.1 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.
Scale drawings: word problems (A1-C.7)
Convert rates and measurements: customary units (A1-E.1)
Convert rates and measurements: metric units (A1-E.2)
Unit prices with unit conversions (A1-E.3)
Scale drawings: word problems (G-A.2)
Convert rates and measurements: customary units (G-W.1)
Convert rates and measurements: metric units (G-W.2)
Convert square and cubic units of length (G-W.3)
9.M.1HS.RBQ.2 Define appropriate quantities for the purpose of descriptive modeling.
Interpret bar graphs, line graphs, and histograms (A1-N.1)
Create bar graphs, line graphs, and histograms (A1-N.2)
Interpret stem-and-leaf plots (A1-N.4)
Interpret box-and-whisker plots (A1-N.5)
Interpret a scatter plot (A1-KK.8)
Scatter plots: line of best fit (A1-KK.12)
9.M.1HS.RBQ.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Precision (A1-E.4)
Greatest possible error (A1-E.5)
Precision (G-W.4)
Greatest possible error (G-W.5)
Minimum and maximum area and volume (G-W.6)
Percent error (G-W.7)
Percent error: area and volume (G-W.8)
9 Interpret the structure of expressions
9.M.1HS.RBQ.4 Interpret expressions that represent a quantity in terms of its context.
9.M.1HS.RBQ.4.a Interpret parts of an expression, such as terms, factors, and coefficients.
Polynomial vocabulary (A1-Z.1)
Polynomial vocabulary (A2-K.1)
9.M.1HS.RBQ.4.b Interpret complicated expressions by viewing one or more of their parts as a single entity.
Factor using a quadratic pattern (A2-I.4)
Factor using a quadratic pattern (PC-D.14)
9 Create equations that describe numbers or relationships
9.M.1HS.RBQ.5 Create equations and inequalities in one variable and use them to solve problems.
Write variable equations (A1-I.4)
Model and solve equations using algebra tiles (A1-J.1)
Write and solve equations that represent diagrams (A1-J.2)
Solve linear equations: word problems (A1-J.9)
Write inequalities from graphs (A1-K.2)
Write compound inequalities from graphs (A1-K.13)
Consecutive integer problems (A1-O.3)
Weighted averages: word problems (A1-O.5)
Write variable expressions (G-A.5)
Solve linear equations (G-A.6)
Solve linear inequalities (G-A.7)
Solve linear equations (A2-B.1)
Solve linear equations: word problems (A2-B.2)
Write inequalities from graphs (A2-C.2)
Solve linear inequalities (A2-C.4)
Graph solutions to quadratic inequalities (A2-C.10)
Solve quadratic inequalities (A2-C.11)
Graph solutions to quadratic inequalities (PC-K.1)
Solve quadratic inequalities (PC-K.2)
Graph solutions to higher-degree inequalities (PC-K.3)
Solve higher-degree inequalities (PC-K.4)
9.M.1HS.RBQ.6 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Write direct variation equations (A1-R.4)
Write inverse variation equations (A1-R.7)
Write and solve inverse variation equations (A1-R.8)
Find a missing coordinate using slope (A1-S.4)
Slope-intercept form: graph an equation (A1-S.6)
Slope-intercept form: write an equation from a graph (A1-S.7)
Slope-intercept form: write an equation (A1-S.8)
Slope-intercept form: write an equation from a table (A1-S.9)
Slope-intercept form: write an equation from a word problem (A1-S.10)
Write linear functions to solve word problems (A1-S.12)
Complete a table and graph a linear function (A1-S.13)
Write equations in standard form (A1-S.15)
Standard form: graph an equation (A1-S.17)
Point-slope form: graph an equation (A1-S.20)
Point-slope form: write an equation (A1-S.21)
Graph quadratic functions in vertex form (A1-BB.4)
Match quadratic functions and graphs (A1-BB.12)
Write linear, quadratic, and exponential functions (A1-CC.3)
Graph an absolute value function (A1-DD.2)
Graph a linear equation (G-E.3)
Equations of lines (G-E.4)
Graph a quadratic function (A2-J.3)
Write and solve direct variation equations (A2-Q.1)
Write and solve inverse variation equations (A2-Q.2)
Write joint and combined variation equations I (A2-Q.4)
Write joint and combined variation equations II (A2-Q.6)
Solve variation equations (A2-Q.7)
Graph parabolas (A2-T.9)
Graph circles (A2-U.7)
Graph sine functions (A2-Z.4)
Graph cosine functions (A2-Z.8)
Graph sine and cosine functions (A2-Z.9)
Graph a quadratic function (PC-C.3)
Graph sine functions (PC-N.4)
Graph cosine functions (PC-N.8)
Graph sine and cosine functions (PC-N.9)
Graph parabolas (PC-P.3)
Graph circles (PC-P.6)
9.M.1HS.RBQ.7 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.
Solve a system of equations by graphing: word problems (A1-U.3)
Solve a system of equations using substitution: word problems (A1-U.9)
Solve a system of equations using elimination: word problems (A1-U.11)
Solve a system of equations using augmented matrices: word problems (A1-U.13)
Solve a system of equations using any method: word problems (A1-U.15)
Solve systems of linear equations (G-A.8)
Solve a system of equations by graphing: word problems (A2-E.3)
Solve a system of equations using substitution: word problems (A2-E.7)
Solve a system of equations using elimination: word problems (A2-E.9)
Solve a system of equations using any method: word problems (A2-E.11)
Solve systems of linear inequalities by graphing (A2-F.2)
Solve systems of linear and absolute value inequalities by graphing (A2-F.3)
Find the vertices of a solution set (A2-F.4)
Linear programming (A2-F.5)
Solve a system of equations by graphing (PC-I.1)
Solve a system of equations by graphing: word problems (PC-I.2)
Solve a system of equations using substitution (PC-I.4)
Solve a system of equations using substitution: word problems (PC-I.5)
Solve a system of equations using elimination (PC-I.6)
Solve a system of equations using elimination: word problems (PC-I.7)
Solve systems of linear inequalities by graphing (PC-J.1)
Solve systems of linear and absolute value inequalities by graphing (PC-J.2)
Find the vertices of a solution set (PC-J.3)
Linear programming (PC-J.4)
9.M.1HS.RBQ.8 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Rearrange multi-variable equations (A1-I.8)
Rate of travel: word problems (A1-O.4)
Solve multi-variable equations (A2-B.5)
9.M.1HS.LER Linear and Exponential Relationships
9 Represent and solve equations and inequalities graphically
9.M.1HS.LER.1 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Relations: convert between tables, graphs, mappings, and lists of points (A1-Q.1)
Complete a function table from an equation (A1-Q.10)
Interpret the graph of a function: word problems (A1-Q.11)
Complete a table and graph a linear function (A1-S.13)
9.M.1HS.LER.2 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.
Solve a system of equations by graphing (A1-U.2)
Solve a system of equations by graphing: word problems (A1-U.3)
Find the number of solutions to a system of equations by graphing (A1-U.4)
Solve a system of equations by graphing (PC-I.1)
Solve a system of equations by graphing: word problems (PC-I.2)
9.M.1HS.LER.3 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.
Graph a two-variable linear inequality (A1-T.3)
Graph a two-variable linear inequality (A2-C.8)
Solve systems of linear inequalities by graphing (A2-F.2)
Solve systems of linear inequalities by graphing (PC-J.1)
9 Understand the concept of a function and use function notation
9.M.1HS.LER.4 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Domain and range of relations (A1-Q.2)
Identify independent and dependent variables (A1-Q.3)
Identify functions (A1-Q.4)
Identify functions: vertical line test (A1-Q.5)
Find values using function graphs (A1-Q.6)
Complete a function table from a graph (A1-Q.9)
Domain and range of exponential functions (A1-X.3)
Domain and range of absolute value functions (A1-DD.3)
Domain and range of radical functions (A1-FF.2)
Domain and range (A2-D.1)
Identify functions (A2-D.2)
Find values using function graphs (A2-D.4)
Complete a table for a function graph (A2-D.5)
Domain and range (PC-A.1)
Identify functions (PC-A.2)
Find values using function graphs (PC-A.4)
Complete a table for a function graph (PC-A.5)
Domain and range of exponential and logarithmic functions (PC-F.1)
Domain and range of radical functions (PC-G.1)
9.M.1HS.LER.5 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Find values using function graphs (A1-Q.6)
Evaluate a function (A1-Q.7)
Evaluate a function: plug in an expression (A1-Q.8)
Complete a function table from a graph (A1-Q.9)
Complete a function table from an equation (A1-Q.10)
Evaluate an exponential function (A1-X.1)
Complete a function table: quadratic functions (A1-BB.2)
Complete a function table: absolute value functions (A1-DD.1)
Evaluate a radical function (A1-FF.1)
Evaluate functions (A2-D.3)
Find values using function graphs (A2-D.4)
Complete a table for a function graph (A2-D.5)
Evaluate logarithms (A2-R.4)
Evaluate natural logarithms (A2-R.5)
Evaluate logarithms: mixed review (A2-R.12)
Evaluate exponential functions (A2-S.2)
Evaluate functions (PC-A.3)
Find values using function graphs (PC-A.4)
Complete a table for a function graph (PC-A.5)
9.M.1HS.LER.6 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Identify arithmetic and geometric sequences (A1-P.1)
Arithmetic sequences (A1-P.2)
Geometric sequences (A1-P.3)
Evaluate variable expressions for number sequences (A1-P.4)
Write variable expressions for arithmetic sequences (A1-P.5)
Write variable expressions for geometric sequences (A1-P.6)
Number sequences: mixed review (A1-P.7)
Find terms of an arithmetic sequence (A2-BB.1)
Find terms of a geometric sequence (A2-BB.2)
Evaluate explicit formulas for sequences (A2-BB.3)
Evaluate recursive formulas for sequences (A2-BB.4)
Classify formulas and sequences (A2-BB.5)
Write a formula for an arithmetic sequence (A2-BB.6)
Write a formula for a geometric sequence (A2-BB.7)
Write a formula for a recursive sequence (A2-BB.8)
Sequences: mixed review (A2-BB.9)
Find terms of a sequence (PC-W.1)
Find terms of a recursive sequence (PC-W.2)
Identify a sequence as explicit or recursive (PC-W.3)
Find a recursive formula (PC-W.4)
9 Interpret functions that arise in applications in terms of the context
9.M.1HS.LER.7 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.
Identify proportional relationships (A1-R.1)
Find the constant of variation (A1-R.2)
Graph a proportional relationship (A1-R.3)
Identify direct variation and inverse variation (A1-R.6)
Slope-intercept form: find the slope and y-intercept (A1-S.5)
Standard form: find x- and y-intercepts (A1-S.16)
Slopes of parallel and perpendicular lines (A1-S.23)
Characteristics of quadratic functions (A1-BB.1)
Identify linear, quadratic, and exponential functions from graphs (A1-CC.1)
Identify linear, quadratic, and exponential functions from tables (A1-CC.2)
Graph an absolute value function (A1-DD.2)
Rational functions: asymptotes and excluded values (A1-GG.1)
Slopes of lines (G-E.2)
Characteristics of quadratic functions (A2-J.1)
Graph a quadratic function (A2-J.3)
Match quadratic functions and graphs (A2-J.11)
Match polynomials and graphs (A2-K.14)
Rational functions: asymptotes and excluded values (A2-N.1)
Classify variation (A2-Q.3)
Find the constant of variation (A2-Q.5)
Match exponential functions and graphs (A2-S.3)
Linear functions (PC-A.6)
Find the maximum or minimum value of a quadratic function (PC-C.1)
Characteristics of quadratic functions (PC-C.2)
Match quadratic functions and graphs (PC-C.4)
Match polynomials and graphs (PC-D.11)
Rational functions: asymptotes and excluded values (PC-E.1)
9.M.1HS.LER.8 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Domain and range of absolute value functions (A1-DD.3)
Domain and range of radical functions (A1-FF.2)
Domain and range (A2-D.1)
Domain and range of radical functions (A2-L.12)
Domain and range of exponential and logarithmic functions (A2-S.1)
Domain and range (PC-A.1)
Domain and range of exponential and logarithmic functions (PC-F.1)
Domain and range of radical functions (PC-G.1)
9.M.1HS.LER.9 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.
Find the constant of variation (A1-R.2)
Find the slope of a graph (A1-S.2)
Find the slope from two points (A1-S.3)
Slope-intercept form: find the slope and y-intercept (A1-S.5)
Find the slope of a linear function (A2-D.6)
Linear functions (PC-A.6)
Average rate of change I (C-J.1)
9 Analyze functions using different representations
9.M.1HS.LER.10 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
9.M.1HS.LER.10.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
Slope-intercept form: graph an equation (A1-S.6)
Standard form: graph an equation (A1-S.17)
Point-slope form: graph an equation (A1-S.20)
Characteristics of quadratic functions (A1-BB.1)
Graph quadratic functions in vertex form (A1-BB.4)
Match quadratic functions and graphs (A1-BB.12)
Graph a linear equation (G-E.3)
Graph a linear function (A2-D.7)
Graph a quadratic function (A2-J.3)
Match quadratic functions and graphs (A2-J.11)
Find the maximum or minimum value of a quadratic function (PC-C.1)
Characteristics of quadratic functions (PC-C.2)
Graph a quadratic function (PC-C.3)
Match quadratic functions and graphs (PC-C.4)
9.M.1HS.LER.10.b Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Match exponential functions and graphs (A1-X.2)
Find properties of sine functions (A2-Z.1)
Graph sine functions (A2-Z.4)
Find properties of cosine functions (A2-Z.5)
Graph cosine functions (A2-Z.8)
Graph sine and cosine functions (A2-Z.9)
Find properties of sine functions (PC-N.1)
Graph sine functions (PC-N.4)
Find properties of cosine functions (PC-N.5)
Graph cosine functions (PC-N.8)
Graph sine and cosine functions (PC-N.9)
9.M.1HS.LER.11 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Compare linear functions: graphs, tables, and equations (A1-S.14)
Match quadratic functions and graphs (A2-J.11)
Match polynomials and graphs (A2-K.14)
Match quadratic functions and graphs (PC-C.4)
Match polynomials and graphs (PC-D.11)
9 Build a function that models a relationship between two quantities
9.M.1HS.LER.12 Write a function that describes a relationship between two quantities.
9.M.1HS.LER.12.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
Write variable expressions for arithmetic sequences (A1-P.5)
Write variable expressions for geometric sequences (A1-P.6)
Write inverse variation equations (A1-R.7)
Write and solve inverse variation equations (A1-R.8)
Write linear, quadratic, and exponential functions (A1-CC.3)
Write a formula for an arithmetic sequence (A2-BB.6)
Write a formula for a geometric sequence (A2-BB.7)
Write a formula for a recursive sequence (A2-BB.8)
Find a recursive formula (PC-W.4)
9.M.1HS.LER.12.b Combine standard function types using arithmetic operations.
Add and subtract functions (A2-O.1)
Multiply functions (A2-O.2)
Divide functions (A2-O.3)
Add, subtract, multiply, and divide functions (PC-A.8)
9.M.1HS.LER.13 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Write variable expressions for arithmetic sequences (A1-P.5)
Write variable expressions for geometric sequences (A1-P.6)
Write a formula for an arithmetic sequence (A2-BB.6)
Write a formula for a geometric sequence (A2-BB.7)
Write a formula for a recursive sequence (A2-BB.8)
Find a recursive formula (PC-W.4)
Find recursive and explicit formulas (PC-W.5)
Convert a recursive formula to an explicit formula (PC-W.6)
Convert an explicit formula to a recursive formula (PC-W.7)
Convert between explicit and recursive formulas (PC-W.8)
9 Build new functions from existing functions
9.M.1HS.LER.14 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.
Transformations of linear functions (A1-S.25)
Transformations of quadratic functions (A1-BB.3)
Transformations of absolute value functions (A1-DD.4)
Function transformation rules (A2-P.1)
Translations of functions (A2-P.2)
Reflections of functions (A2-P.3)
Dilations of functions (A2-P.4)
Transformations of functions (A2-P.5)
Describe function transformations (A2-P.6)
Function transformation rules (PC-B.1)
Translations of functions (PC-B.2)
Reflections of functions (PC-B.3)
Dilations of functions (PC-B.4)
Transformations of functions (PC-B.5)
Describe function transformations (PC-B.6)
9 Construct and compare linear, quadratic, and exponential models and solve problems
9.M.1HS.LER.15 Distinguish between situations that can be modeled with linear functions and with exponential functions.
9.M.1HS.LER.15.a prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.
Identify linear, quadratic, and exponential functions from tables (A1-CC.2)
9.M.1HS.LER.15.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Solve linear equations: word problems (A1-J.9)
Linear functions over unit intervals (A1-CC.4)
Solve linear equations: word problems (A2-B.2)
Linear functions over unit intervals (A2-D.9)
Linear functions over unit intervals (PC-A.7)
9.M.1HS.LER.15.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Exponential growth and decay: word problems (A1-X.4)
Identify linear, quadratic, and exponential functions from graphs (A1-CC.1)
Identify linear, quadratic, and exponential functions from tables (A1-CC.2)
Exponential functions over unit intervals (A1-CC.5)
Exponential functions over unit intervals (A2-S.9)
Exponential growth and decay: word problems (A2-S.12)
Exponential functions over unit intervals (PC-F.13)
Exponential growth and decay: word problems (PC-F.16)
9.M.1HS.LER.16 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).
Write variable expressions for arithmetic sequences (A1-P.5)
Write variable expressions for geometric sequences (A1-P.6)
Slope-intercept form: write an equation from a graph (A1-S.7)
Slope-intercept form: write an equation (A1-S.8)
Slope-intercept form: write an equation from a table (A1-S.9)
Slope-intercept form: write an equation from a word problem (A1-S.10)
Point-slope form: write an equation (A1-S.21)
Point-slope form: write an equation from a graph (A1-S.22)
Match exponential functions and graphs (A1-X.2)
Write linear, quadratic, and exponential functions (A1-CC.3)
Equations of lines (G-E.4)
Equations of parallel and perpendicular lines (G-E.6)
Write the equation of a linear function (A2-D.8)
Write a formula for an arithmetic sequence (A2-BB.6)
Write a formula for a geometric sequence (A2-BB.7)
Linear functions (PC-A.6)
9.M.1HS.LER.17 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
9 Interpret expressions for functions in terms of the situation they model
9.M.1HS.LER.18 Interpret the parameters in a linear or exponential function in terms of a context.
Solve linear equations: word problems (A1-J.9)
Exponential growth and decay: word problems (A1-X.4)
Solve linear equations: word problems (A2-B.2)
Exponential growth and decay: word problems (A2-S.12)
Compound interest: word problems (A2-S.13)
Continuously compounded interest: word problems (A2-S.14)
Exponential growth and decay: word problems (PC-F.16)
Compound interest: word problems (PC-F.17)
9.M.1HS.RWE Reasoning with Equations
9 Understand solving equations as a process of reasoning and explain the reasoning
9.M.1HS.RWE.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Properties of equality (A1-H.4)
Weighted averages: word problems (A1-O.5)
9 Solve equations and inequalities in one variable
9.M.1HS.RWE.2 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Model and solve equations using algebra tiles (A1-J.1)
Write and solve equations that represent diagrams (A1-J.2)
Solve one-step linear equations (A1-J.3)
Solve two-step linear equations (A1-J.4)
Solve advanced linear equations (A1-J.5)
Solve equations with variables on both sides (A1-J.6)
Find the number of solutions (A1-J.7)
Solve linear equations: word problems (A1-J.9)
Solve linear equations: mixed review (A1-J.10)
Identify solutions to inequalities (A1-K.3)
Solve one-step linear inequalities: addition and subtraction (A1-K.4)
Solve one-step linear inequalities: multiplication and division (A1-K.5)
Solve one-step linear inequalities (A1-K.6)
Graph solutions to one-step linear inequalities (A1-K.7)
Solve two-step linear inequalities (A1-K.8)
Graph solutions to two-step linear inequalities (A1-K.9)
Solve advanced linear inequalities (A1-K.10)
Graph solutions to advanced linear inequalities (A1-K.11)
Graph compound inequalities (A1-K.12)
Write compound inequalities from graphs (A1-K.13)
Solve compound inequalities (A1-K.14)
Graph solutions to compound inequalities (A1-K.15)
Solve linear equations (G-A.6)
Solve linear inequalities (G-A.7)
Solve linear equations (A2-B.1)
Solve linear equations: word problems (A2-B.2)
Solve linear inequalities (A2-C.4)
Graph solutions to linear inequalities (A2-C.5)
9 Solve systems of equations
9.M.1HS.RWE.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.
Solve a system of equations using elimination (A1-U.10)
Solve a system of equations using elimination: word problems (A1-U.11)
Solve a system of equations using augmented matrices (A1-U.12)
Solve a system of equations using augmented matrices: word problems (A1-U.13)
Solve a system of equations using elimination (A2-E.8)
Solve a system of equations using elimination: word problems (A2-E.9)
Solve a system of equations using elimination (PC-I.6)
Solve a system of equations using elimination: word problems (PC-I.7)
9.M.1HS.RWE.4 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Is (x, y) a solution to the system of equations? (A1-U.1)
Solve a system of equations by graphing (A1-U.2)
Solve a system of equations by graphing: word problems (A1-U.3)
Find the number of solutions to a system of equations by graphing (A1-U.4)
Find the number of solutions to a system of equations (A1-U.5)
Classify a system of equations by graphing (A1-U.6)
Classify a system of equations (A1-U.7)
Solve a system of equations using substitution (A1-U.8)
Solve a system of equations using substitution: word problems (A1-U.9)
Solve a system of equations using elimination (A1-U.10)
Solve a system of equations using elimination: word problems (A1-U.11)
Solve a system of equations using augmented matrices (A1-U.12)
Solve a system of equations using augmented matrices: word problems (A1-U.13)
Solve a system of equations using any method (A1-U.14)
Solve a system of equations using any method: word problems (A1-U.15)
Solve systems of linear equations (G-A.8)
Is (x, y) a solution to the system of equations? (A2-E.1)
Solve a system of equations by graphing (A2-E.2)
Solve a system of equations by graphing: word problems (A2-E.3)
Find the number of solutions to a system of equations (A2-E.4)
Classify a system of equations (A2-E.5)
Solve a system of equations using substitution (A2-E.6)
Solve a system of equations using substitution: word problems (A2-E.7)
Solve a system of equations using elimination (A2-E.8)
Solve a system of equations using elimination: word problems (A2-E.9)
Solve a system of equations using any method (A2-E.10)
Solve a system of equations using any method: word problems (A2-E.11)
Solve a system of equations by graphing (PC-I.1)
Solve a system of equations by graphing: word problems (PC-I.2)
Classify a system of equations (PC-I.3)
Solve a system of equations using substitution (PC-I.4)
Solve a system of equations using substitution: word problems (PC-I.5)
Solve a system of equations using elimination (PC-I.6)
Solve a system of equations using elimination: word problems (PC-I.7)
9.M.1HS.DST Descriptive Statistics
9 Summarize, represent, and interpret data on a single count or measurement variable
9.M.1HS.DST.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
Create bar graphs, line graphs, and histograms (A1-N.2)
9.M.1HS.DST.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.
Mean, median, mode, and range (A1-KK.2)
Quartiles (A1-KK.3)
Mean absolute deviation (A1-KK.6)
Variance and standard deviation (A1-KK.7)
Variance and standard deviation (A2-DD.2)
Variance and standard deviation (PC-Z.2)
9.M.1HS.DST.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Interpret box-and-whisker plots (A1-N.5)
Identify an outlier (A1-KK.4)
Identify an outlier and describe the effect of removing it (A1-KK.5)
Identify an outlier (A2-DD.3)
Identify an outlier and describe the effect of removing it (A2-DD.4)
Identify an outlier (PC-Z.3)
Identify an outlier and describe the effect of removing it (PC-Z.4)
9 Summarize, represent, and interpret data on two categorical and quantitative variables
9.M.1HS.DST.4 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.
9.M.1HS.DST.5 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
Outliers in scatter plots (A1-KK.9)
Outliers in scatter plots (A2-DD.5)
Outliers in scatter plots (PC-Z.5)
9.M.1HS.DST.5.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
Find the equation of a regression line (A1-KK.13)
Find the equation of a regression line (PC-Z.8)
Interpret regression lines (PC-Z.9)
Analyze a regression line of a data set (PC-Z.10)
Analyze a regression line using statistics of a data set (PC-Z.11)
9.M.1HS.DST.5.b Informally assess the fit of a function by plotting and analyzing residuals.
Interpret a scatter plot (A1-KK.8)
9.M.1HS.DST.5.c Fit a linear function for a scatter plot that suggests a linear association.
Scatter plots: line of best fit (A1-KK.12)
Find the equation of a regression line (A1-KK.13)
Find the equation of a regression line (PC-Z.8)
9 Interpret linear models
9.M.1HS.DST.6 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Interpret regression lines (A1-KK.14)
Analyze a regression line of a data set (A1-KK.15)
Interpret regression lines (PC-Z.9)
Analyze a regression line using statistics of a data set (PC-Z.11)
9.M.1HS.DST.7 Compute (using technology) and interpret the correlation coefficient of a linear fit.
Match correlation coefficients to scatter plots (A1-KK.10)
Calculate correlation coefficients (A1-KK.11)
Match correlation coefficients to scatter plots (PC-Z.6)
Calculate correlation coefficients (PC-Z.7)
9.M.1HS.DST.8 Distinguish between correlation and causation.
9.M.1HS.CPC Congruence, Proof, and Constructions
9 Experiment with transformations in the plane
9.M.1HS.CPC.1 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.
Angle vocabulary (G-C.1)
9.M.1HS.CPC.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Classify congruence transformations (G-L.1)
Translations: graph the image (G-L.2)
Translations: find the coordinates (G-L.3)
Translations: write the rule (G-L.4)
Reflections: graph the image (G-L.5)
Reflections: find the coordinates (G-L.6)
Rotations: graph the image (G-L.8)
Rotations: find the coordinates (G-L.9)
Compositions of congruence transformations: graph the image (G-L.10)
Congruence transformations: mixed review (G-L.12)
Dilations: graph the image (G-L.13)
Dilations: find the coordinates (G-L.14)
Dilations: scale factor and classification (G-L.15)
Identify transformation matrices (A2-G.15)
Transformation matrices: write the vertex matrix (A2-G.16)
Transformation matrices: graph the image (A2-G.17)
9.M.1HS.CPC.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Transformations that carry a polygon onto itself (G-L.11)
Draw lines of symmetry (G-O.3)
Count lines of symmetry (G-O.4)
9.M.1HS.CPC.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Rotate polygons about a point (G-L.7)
9.M.1HS.CPC.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Translations: graph the image (G-L.2)
Reflections: graph the image (G-L.5)
Rotations: graph the image (G-L.8)
Compositions of congruence transformations: graph the image (G-L.10)
9 Understand congruence in terms of rigid motions
9.M.1HS.CPC.6 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.
Transformations that carry a polygon onto itself (G-L.11)
9.M.1HS.CPC.7 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.
9.M.1HS.CPC.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
9 Make geometric constructions
9.M.1HS.CPC.9 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Construct the midpoint or perpendicular bisector of a segment (G-B.9)
Construct an angle bisector (G-C.6)
Construct a congruent angle (G-C.7)
Construct a perpendicular line (G-D.2)
Construct parallel lines (G-D.5)
Construct an equilateral triangle or regular hexagon (G-G.5)
Construct a square (G-G.6)
9.M.1HS.CPC.10 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Construct an equilateral triangle inscribed in a circle (G-U.13)
Construct a square inscribed in a circle (G-U.14)
Construct a regular hexagon inscribed in a circle (G-U.15)
9.M.1HS.CAG Connecting Algebra and Geometry through Coordinates
9 Use coordinates to prove simple geometric theorems algebraically
9.M.1HS.CAG.1 Use coordinates to prove simple geometric theorems algebraically.
9.M.1HS.CAG.2 prove the slope criteria for parallel and perpendicular lines; 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).
Slopes of parallel and perpendicular lines (A1-S.23)
Write an equation for a parallel or perpendicular line (A1-S.24)
Slopes of parallel and perpendicular lines (G-E.5)
Equations of parallel and perpendicular lines (G-E.6)
9.M.1HS.CAG.3 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Distance between two points (A1-G.3)
Distance formula (G-B.8)
Area and perimeter in the coordinate plane I (G-S.5)
Area and perimeter in the coordinate plane II (G-S.6)