West Virginia

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Skills available for West Virginia high school math standards

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West Virginia College- and Career-Readiness Standards (adopted in 2023): Algebra I West Virginia College- and Career-Readiness Standards (adopted in 2023): Algebra I
West Virginia College- and Career-Readiness Standards (adopted in 2023): Algebra II/Math III West Virginia College- and Career-Readiness Standards (adopted in 2023): Algebra II/Math III
West Virginia College- and Career-Readiness Standards (adopted in 2023): Applied Statistics West Virginia College- and Career-Readiness Standards (adopted in 2023): Applied Statistics
West Virginia College- and Career-Readiness Standards (adopted in 2023): Calculus West Virginia College- and Career-Readiness Standards (adopted in 2023): Calculus
West Virginia College- and Career-Readiness Standards (adopted in 2023): Geometry West Virginia College- and Career-Readiness Standards (adopted in 2023): Geometry
West Virginia College- and Career-Readiness Standards (adopted in 2023): Introduction to Mathematical Applications West Virginia College- and Career-Readiness Standards (adopted in 2023): Introduction to Mathematical Applications
West Virginia College- and Career-Readiness Standards (adopted in 2023): Mathematical Practices West Virginia College- and Career-Readiness Standards (adopted in 2023): Mathematical Practices
West Virginia College- and Career-Readiness Standards (adopted in 2023): Mathematics I West Virginia College- and Career-Readiness Standards (adopted in 2023): Mathematics I
West Virginia College- and Career-Readiness Standards (adopted in 2023): Mathematics II West Virginia College- and Career-Readiness Standards (adopted in 2023): Mathematics II
West Virginia College- and Career-Readiness Standards (adopted in 2023): Quantitative Reasoning West Virginia College- and Career-Readiness Standards (adopted in 2023): Quantitative Reasoning
West Virginia College- and Career-Readiness Standards (adopted in 2023): Statistics West Virginia College- and Career-Readiness Standards (adopted in 2023): Statistics
West Virginia College- and Career-Readiness Standards (adopted in 2023): Transition Mathematics for Seniors West Virginia College- and Career-Readiness Standards (adopted in 2023): Transition Mathematics for Seniors
West Virginia College- and Career-Readiness Standards (adopted in 2023): Trigonometry/Precalculus/Math IV West Virginia College- and Career-Readiness Standards (adopted in 2023): Trigonometry/Precalculus/Math IV
College- and Career-Readiness Standards: Advanced Mathematical Modeling College- and Career-Readiness Standards: Advanced Mathematical Modeling
College- and Career-Readiness Standards: Algebra I College- and Career-Readiness Standards: Algebra I
College- and Career-Readiness Standards: Algebra II College- and Career-Readiness Standards: Algebra II
College- and Career-Readiness Standards: Calculus College- and Career-Readiness Standards: Calculus
College- and Career-Readiness Standards: Geometry College- and Career-Readiness Standards: Geometry
College- and Career-Readiness Standards: Mathematics I College- and Career-Readiness Standards: Mathematics I
College- and Career-Readiness Standards: Mathematics II College- and Career-Readiness Standards: Mathematics II
College- and Career-Readiness Standards: Mathematics III LA College- and Career-Readiness Standards: Mathematics III LA
College- and Career-Readiness Standards: Mathematics III STEM College- and Career-Readiness Standards: Mathematics III STEM
College- and Career-Readiness Standards: Mathematics III Technical Readiness College- and Career-Readiness Standards: Mathematics III Technical Readiness
College- and Career-Readiness Standards: Mathematics IV - Trigonometry/Pre-Calculus College- and Career-Readiness Standards: Mathematics IV - Trigonometry/Pre-Calculus
College- and Career-Readiness Standards: Mathematics IV Technical Readiness College- and Career-Readiness Standards: Mathematics IV Technical Readiness
College- and Career-Readiness Standards: STEM Readiness College- and Career-Readiness Standards: STEM Readiness
College- and Career-Readiness Standards: Transition Mathematics for Seniors College- and Career-Readiness Standards: Transition Mathematics for Seniors
West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics I West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics I
West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics II West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics II
West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics III West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics III
West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics IV West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics IV
West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics STEM Readiness West Virginia Next Generation Content Standards and Objectives (Common Core): High School Mathematics STEM Readiness
West Virginia Next Generation Content Standards and Objectives (Common Core): Transition Mathematics for Seniors West Virginia Next Generation Content Standards and Objectives (Common Core): Transition Mathematics for Seniors

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Statistics and Probability

Summarize, represent, and interpret data on a single count or measurement variable.
- M.A1HS.32 Select applicable representations to display data on the real number line (e.g., dot plots, histograms, and box plots).
- M.A1HS.33 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation only as a tool to describe spread and not to explicitly find standard deviation) of two or more different data sets.
- M.A1HS.34 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  - Box plots (A1-HH.9)
  - Identify an outlier and describe the effect of removing it (A1-II.5)
- Checkpoint opportunity
  - Checkpoint: Line plots, histograms, and box plots (A1-HH.12)
  - Checkpoint: Compare data sets (A1-II.8)
Summarize, represent, and interpret data on two categorical and quantitative variables.
- M.A1HS.35 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
  - M.A1HS.35.a 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.
  - M.A1HS.35.b Informally assess the fit of a function by plotting and analyzing residuals. Focus should be on situations for which linear models are appropriate.
    - Interpret a scatter plot (A1-JJ.1)
  - M.A1HS.35.c Fit a linear function for scatter plots that suggest a linear association.
    - Write equations for lines of best fit (A1-JJ.5)
Interpret linear models.
- M.A1HS.36 Interpret the rate of change and the constant term of a linear model in the context of the data. Use technology to compute and interpret the correlation coefficient of a linear fit.
- M.A1HS.37 Distinguish between correlation and causation.
  - Correlation and causation (A1-JJ.11)
- Checkpoint opportunity
  - Checkpoint: Linear modeling (A1-JJ.12)

Basics of Geometry

Experiment with transformations in the plane.
- M.GHS.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)
- Checkpoint opportunity
  - Checkpoint: Definitions of geometric objects (G-D.9)
Identify and utilize inductive and deductive reasoning.
- M.GHS.2 Construct and justify the validity of a logical argument.
  - M.GHS.2.a Identify the converse, inverse, and contrapositive of a conditional statement.
    - Converses, inverses, and contrapositives (G-A.5)
  - M.GHS.2.b Translate a short, verbal argument into symbolic form.
    - Truth tables (G-A.7)
    - Truth values (G-A.8)
  - M.GHS.2.c Use Venn diagrams to represent set relationships.
    - Use Venn diagrams to solve problems (G)
  - M.GHS.2.d Use inductive and deductive reasoning.
Prove geometric theorems.
- M.GHS.3 Use appropriate methods of proof to 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.
- Checkpoint opportunity
  - Checkpoint: Line and angle theorems (G-D.10)
Use coordinates to prove simple geometric theorems algebraically.
- M.GHS.4 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- Checkpoint opportunity
  - Checkpoint: Partition a line segment (G-B.16)
Make geometric constructions.
- M.GHS.5 Make formal geometric constructions with a variety of tools and methods, such as a compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.:
  - M.GHS.5.a copying a segment;
    - Construct a congruent segment (G-B.8)
  - M.GHS.5.b copying an angle;
    - Construct a congruent angle (G-C.8)
  - M.GHS.5.c bisecting a segment;
  - M.GHS.5.d bisecting an angle;
    - Construct an angle bisector (G-C.7)
  - M.GHS.5.e constructing perpendicular lines, including the perpendicular bisector of a line segment; and
    - Construct the midpoint or perpendicular bisector of a segment (G-B.15)
    - Construct a perpendicular line (G-D.2)
  - M.GHS.5.f constructing a line parallel to a given line through a point not on the line.
    - Construct parallel lines (G-D.6)

Transformations and Congruence

Experiment with transformations in the plane.
- M.GHS.6 Build on prior knowledge from rigid motions to:
  - M.GHS.6.a represent transformations using geometric concepts in the plane.
  - M.GHS.6.b describe transformations as functions that take points in the plane as inputs and give other points as outputs.
  - M.GHS.6.c compare transformations that preserve distance and angle to those that do not.
- M.GHS.7 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-H.15)
- M.GHS.8 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-H.7)
- M.GHS.9 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, for example, graph paper, tracing paper, or geometry software. Describe a sequence of transformations that will carry a given figure onto another.
- Checkpoint opportunity
  - Checkpoint: Congruence transformations (G-H.17)
Understand congruence in terms of rigid motions.
- M.GHS.10 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.
- M.GHS.11 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.
  - Prove triangles are congruent using rigid motions (G-L.1)
- M.GHS.12 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
- M.GHS.13 Use congruence criteria for triangles to solve problems and to prove relationships in geometric figures.
- Checkpoint opportunity
  - Checkpoint: Rigid motion and congruence (G-L.13)
Use coordinates to prove simple geometric theorems algebraically.
- M.GHS.16 Use coordinates to prove simple geometric theorems about right triangles, quadrilaterals, and circles algebraically (e.g., derive the equation of a circle of given center and radius using the Pythagorean Theorem).
  - Classify shapes on the coordinate plane: justify your answer (G-O.13)

West Virginia

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Actions

Expressions and Equations

Interpret the structure of expressions and equations in terms of the context they model.

M.A1HS.1 Interpret linear, exponential, and quadratic expressions that represent a quantity in terms of its context.

M.A1HS.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

M.A1HS.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

M.A1HS.1.c Interpret the parameters in a linear function or exponential function of the form f(x) = a*bx in terms of a context.

M.A1HS.2 Use the structure of quadratic and exponential expressions to identify ways to rewrite them.

Extend the properties of exponents to rational exponents.

M.A1HS.3 Explain the connections between expressions with rational exponents and expressions with radicals using properties of exponents. Extend from application of properties of exponents for expressions with integer exponents.

M.A1HS.4 Rewrite expressions involving radicals, including simplifying, and rational exponents using the properties of exponents.

Checkpoint opportunity

Write expressions in equivalent forms to solve problems.

M.A1HS.5 Choose and produce an equivalent form of linear, exponential, and quadratic expressions to reveal and explain properties of the quantity represented by the expression through connections to a graphical representation of the function.

M.A1HS.5.c Use the properties of exponents to transform expressions in exponential functions. For example, the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Create equations that describe numbers or relationships.

M.A1HS.7 Create equations and inequalities in one variable, representing linear and exponential relationships, and use them to solve problems. In the case of exponential equations, limit to situations with integer inputs.

M.A1HS.8 Create equations in two or more variables, representing linear and exponential relationships between quantities. In the case of exponential equations, limit to situations with integer inputs.

M.A1HS.9 Represent constraints by linear equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

Checkpoint opportunity

Solve equations and inequalities in one variable.

M.A1HS.10 Solve linear equations including equations with coefficients represented by letters, simple exponential equations that rely on application of the laws of exponents, and compound linear inequalities in one variable.

Checkpoint opportunity

Solve systems of equations.

M.A1HS.12 Analyze and solve pairs of simultaneous linear equations.

M.A1HS.12.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

M.A1HS.12.b Solve simple cases by inspection (e.g., 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6).

M.A1HS.12.c Solve real-word and mathematical problems leading to two linear equations in two variables (e.g., given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair).

M.A1HS.13 Understand and demonstrate ways to manipulate a system of two equations in two variables while preserving its solution set.

M.A1HS.14 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Include examples of solution sets with no solutions, an infinite number of solutions, and one solution.

Represent and solve equations and inequalities graphically.

M.A1HS.16 Recognize that the graph of a linear or exponential equation in two variables is the set of all its solutions plotted in the coordinate plane.

M.A1HS.18 Graph the solutions of a linear inequality in two variables as a half-plane and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Checkpoint opportunity

Functions

Understand the concept of a function and use function notation.

M.A1HS.20 Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context.

M.A1HS.21 Recognize arithmetic and geometric 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).

Checkpoint opportunity

Interpret functions that arise in applications in terms of a context.

M.A1HS.22.a Key features of linear and exponential graphs include: intercepts; and intervals where the function is increasing, decreasing, positive, or negative.

Analyze functions using different representations.

M.A1HS.23 Graph linear, exponential, and quadratic functions expressed symbolically and show key features of the graph.

M.A1HS.23.a For linear functions, focus on intercepts.

M.A1HS.23.b For exponential functions, focus on intercepts and end behavior.

M.A1HS.24 Compare properties of two linear, exponential, or quadratic functions each represented in a different way, such as algebraically, graphically, numerically in tables, or from verbal descriptions.

M.A1HS.25 Write a function defined by a linear, exponential, or quadratic expression in different but equivalent forms to reveal and explain different properties of the function.

M.A1HS.25.b Use the properties of exponents to interpret expressions in exponential functions.

Checkpoint opportunity

Build a function that models a relationship between two quantities.

M.A1HS.26 Write linear, exponential, and quadratic functions that describe a relationship between two quantities.

M.A1HS.26.a Determine an explicit expression, a recursive process, or steps for calculation from a context.

M.A1HS.26.b Combine standard function types using arithmetic operations.

M.A1HS.27 Construct linear and exponential functions, including arithmetic and geometric sequences to model situations, given a graph, a description of a relationship or given input-output pairs (include reading these from a table).

Checkpoint opportunity

Build new functions from existing functions.

Construct and compare linear, quadratic, and exponential models and solve problems.

M.A1HS.29 Distinguish between situations that can be modeled with linear functions, with exponential functions, and with quadratic functions.

M.A1HS.29.a Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.

M.A1HS.29.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

M.A1HS.29.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

M.A1HS.29.d Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. Extend the comparison of linear and exponential growth to quadratic growth.

Checkpoint opportunity

Geometry

Use coordinates to prove simple geometric theorems algebraically.

M.A1HS.30 Prove the slope criteria for parallel and perpendicular lines and use the slope criteria 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).

M.A1HS.31 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Checkpoint opportunity

Statistics and Probability

Summarize, represent, and interpret data on a single count or measurement variable.

M.A1HS.32 Select applicable representations to display data on the real number line (e.g., dot plots, histograms, and box plots).

M.A1HS.33 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation only as a tool to describe spread and not to explicitly find standard deviation) of two or more different data sets.

M.A1HS.34 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Checkpoint opportunity

Summarize, represent, and interpret data on two categorical and quantitative variables.

M.A1HS.35 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

M.A1HS.35.a 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.

M.A1HS.35.b Informally assess the fit of a function by plotting and analyzing residuals. Focus should be on situations for which linear models are appropriate.

M.A1HS.1.c Interpret the parameters in a linear function or exponential function of the form f(x) = a*b^x in terms of a context.

M.A1HS.5.c Use the properties of exponents to transform expressions in exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.