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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12.M.TMS.GPE Geometry - Expressing Geometric Properties with Equations

12. Use coordinates to prove simple geometric theorems algebraically
- 12.M.TMS.GPE.1 Use coordinates to prove simple geometric theorems algebraically.
  - Classify shapes on the coordinate plane: justify your answer (G-O.13)
- 12.M.TMS.GPE.2 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

12.M.TMS.MG Geometry - Modeling with Geometry

12. Apply geometric concepts in modeling situations
- 12.M.TMS.MG.1 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

12.M.TMS.SPI Statistics and Probability - Interpreting Categorical & Quantitative Data

12. Summarize, represent, and interpret data on two categorical and quantitative variables
- 12.M.TMS.SPI.1 represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Interpret linear models
  - Interpret a scatter plot (A1-JJ.1)
  - Write equations for lines of best fit (A1-JJ.5)
- 12.M.TMS.SPI.2 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

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12.M.TMS.RN Number and Quantity - The Real Number System

12. Extend the properties of exponents to rational exponents.

12.M.TMS.RN.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.

12.M.TMS.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

12. Work with radicals and integer exponents.

12.M.TMS.RN.3 know and apply the properties of integer exponents to generate equivalent numerical expressions.

12.M.TMS.CNS Number and Quantity - The Complex Number System

12. Perform arithmetic operations with complex numbers.

12.M.TMS.CNS.1 Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

12.M.TMS.CNS.2 Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

12.M.TMS.CNS.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

12. Use complex numbers in polynomial identities and equations.

12.M.TMS.CNS.4 Solve quadratic equations with real coefficients that have complex solutions.

12.M.TMS.SSE Algebra - Seeing Structure in Expressions

12. Interpret the structure of expressions

12.M.TMS.SSE.1 Use the structure of an expression to identify ways to rewrite it.

12. Write expressions in equivalent forms to solve problems

12.M.TMS.SSE.2 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

12.M.TMS.SSE.2.a Factor a quadratic expression to reveal the zeros of the function it defines.

12.M.TMS.SSE.2.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

12.M.TMS.APR Algebra - Arithmetic with Polynomials & Rational Expressions

12. Perform arithmetic operations on polynomials

12.M.TMS.APR.1 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.

12. Understand the relationship between zeros and factors of polynomials

12.M.TMS.APR.2 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

12. Rewrite rational expressions

12.M.TMS.APR.4 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

12.M.TMS.ACE Algebra - Creating Equations

12. Create equations that describe numbers or relationships

12.M.TMS.ACE.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.

12.M.TMS.ACE.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

12.M.TMS.ACE.3 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.

12.M.TMS.REI Algebra - Reasoning with Equations & Inequalities

12. Understand solving equations as a process of reasoning and explain the reasoning

12.M.TMS.REI.1 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

12. Solve equations and inequalities in one variable

12.M.TMS.REI.2 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

12. Solve systems of equations

12.M.TMS.REI.4 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

12. Represent and solve equations and inequalities graphically

12.M.TMS.IF Functions - Interpreting Functions

12. Understand the concept of a function and use function notation

12.M.TMS.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

12. Interpret functions that arise in applications in terms of the context

12.M.TMS.IF.3 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.

12. Analyze functions using different representations

12.M.TMS.IF.4 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

12.M.TMS.IF.4.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

12.M.TMS.IF.4.b Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

12.M.TMS.IF.5 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

12.M.TMS.IF.5.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

12.M.TMS.BF Functions - Building Functions

12. Build a function that models a relationship between two quantities

12.M.TMS.BF.1 Write a function that describes a relationship between two quantities.

12.M.TMS.BF.1.a Combine standard function types using arithmetic operations.

12.M.TMS.BF.1.b Compose functions.

12. Build new functions from existing functions

12.M.TMS.BF.2 Find inverse functions.

12.M.TMS.BF.2.a 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.

12.M.TMS.BF.2.b Verify by composition that one function is the inverse of another.

12.M.TMS.BF.2.c Read values of an inverse function from a graph or a table, given that the function has an inverse.

12.M.TMS.BF.2.d Produce an invertible function from a non-invertible function by restricting the domain.

12. Trigonometric Functions

12.M.TMS.BF.3 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

12.M.TMS.CST Geometry - Congruence, Similarity, Right Triangles, & Trigonometry

12. Prove geometric theorems

12.M.TMS.CST.1 Prove theorems about lines and angles.

12.M.TMS.CST.2 Prove theorems about triangles.

12.M.TMS.CST.3 Prove theorems about parallelograms.

12.M.TMS.CST.4 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

12. Prove theorems involving similarity

12.M.TMS.CST.5 Prove theorems about triangles.

12.M.TMS.CST.6 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

12. Define trigonometric ratios and solve problems involving right triangles

12.M.TMS.CST.7 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

12.M.TMS.CST.8 Explain and use the relationship between the sine and cosine of complementary angles.

12.M.TMS.CST.9 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.