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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Geometry/Trigonometry

Visualize relationships between two-dimensional and three-dimensional objects and apply geometric concepts in modeling situations.
- M.IMA.23 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects (e.g., three-view drawings and blueprints).
  - Cross sections of three-dimensional figures (8)
  - Solids of revolution (G-T.5)
- M.IMA.24 Use two- and three-dimensional shapes and circles, their measures, and their properties to describe objects.
  - M.IMA.24.a Apply concepts of density based on area and volume in modeling situations.
    - Find the density (8)
  - M.IMA.24.b Apply geometric methods to solve design problems to satisfy given constraints (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with topographic grid systems based on ratios).
Use geometric theorems and formulas to solve problems.
- M.IMA.25 Explore theorems about triangles to solve real-world application problems.
- M.IMA.26 Understand and apply the Pythagorean Theorem for solving real-world problems (e.g., checking accuracy on gate construction, conduit bending, roof pitch).
- M.IMA.27 Solve application problems by calculating area and surface area for two-dimensional objects (e.g., calculate the cost of installing flooring in a building and painting the interior and exterior of a building based on square footage).
- M.IMA.28 Solve application problems by calculating volume for three-dimensional objects using formulas for cylinders, pyramids, prisms, cones, and spheres (e.g., compute amount of cement needed for a sidewalk, amount of water in a fire hose, amount of air in ductwork).
- M.IMA.29 Solve application problems by calculating circumference, area, radius, diameter, area of sector, arc length of a circle with appropriate unit labels (e.g., develop a circular watering system).
- Checkpoint opportunity

Modeling

Concrete geometric representation (physical modeling).
- M.IMA.30 Create and use two- and three-dimensional representations of authentic situations using paper techniques or dynamic geometric environments for computer-aided design and other applications.
- M.IMA.31 Gather data, conduct investigations, and apply mathematical concepts and models to solve problems (e.g., designing and building a house or a car).
Summarize, represent, and interpret data on two quantitative variables.
- M.IMA.32 Collect numerical bivariate data; represent data on two quantitative variables on a scatter plot; determine whether or not a relationship exists; if so, describe how the variables are related and select a function to model the data, justify the selection and use the model to make predictions (e.g., cost of the materials for a construction project, cost of the labor for a project, cost and value of a vehicle based on depreciation).
- M.IMA.33 For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Interpret the rate of change and the constant term of a linear model in the context of the data.
- M.IMA.34 Identify positive and negative correlations (e.g., vehicle depreciation). Use technology to compute and interpret the correlation coefficient of a linear fit.
  - Identify trends with scatter plots (8-II.5)
  - Find correlation coefficients (8)
- Checkpoint opportunity

Statistics and Probability: Interpreting Categorical & Quantitative Data

Summarize, represent, and interpret data on a single count or measurement variable.
- M.IMA.35 Select applicable representations to display data on the real number line (e.g., dot plots, histograms, and box plots).
- M.IMA.36 Analyze and interpret tables, charts, and graphs (e.g., interpret a body mass index (BMI) chart).
- M.IMA.37 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.IMA.38 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
- M.IMA.39 Distinguish between correlation and causation.
  - Correlation and causation (A1-JJ.11)

Finance Mathematics

Understanding financial models.
- M.IMA.40 Determine, represent, and analyze mathematical models for loan amortization and the effects of different payments and/or finance terms (e.g., business loans, auto, mortgage, and/or credit card).
- M.IMA.41 Determine, represent, and analyze mathematical models for investments involving simple and compound interest with and without additional deposits (e.g., savings accounts, bonds, and/or certificates of deposit).
  - Simple interest (8-I.10)
  - Compound interest (8-I.11)
Personal use of finance.
- M.IMA.42 Research, develop, and analyze personal budgets based on given parameters (e.g., fixed and discretionary expenses, insurance, gross vs. net pay, types of income, wage, salary, commission, career choice, geographic region, retirement, and/or investment planning).
- M.IMA.43 Research and analyze taxes including payroll, sales, personal property, real estate, and income tax returns.

West Virginia

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Number and Quantity

Mathematics as a language.

M.IMA.1 Demonstrate reasoning skills in developing, explaining, and justifying sound mathematical arguments and analyze the soundness of mathematical arguments of others.

M.IMA.2 Communicate with and about mathematics orally and in writing as part of independent and collaborative work, including making accurate and clear presentations of solutions to problems.

M.IMA.3 Use units to understand problems and to guide the solutions of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Mathematics and Measurement.

M.IMA.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

M.IMA.7 Distinguish between proportional and non-proportional situations, apply proportional reasoning when appropriate, solve for an unknown quantity in proportional situations; apply scale factors to perform indirect measurements using maps, blueprints, concentrations, dosages, and densities.

Checkpoint opportunity

The Real Number System.

Checkpoint opportunity

Algebra - Seeing Structure in Expressions

Understand the connections between proportional relationships, lines, and linear equations.

M.IMA.11 Solve application problems using direct and inverse variation equations (e.g., determine the mechanical advantage of gears, Ohm's Law).

Create equations that describe numbers or relationships.

M.IMA.13 Analyze real-world problem situations and use variables to construct and solve equations and inequalities in one variable, representing linear, exponential, and simple rational functions (e.g., using spreadsheet functions, determine sale price of items).

M.IMA.14 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales (e.g., profit vs. number of units, cost vs. number of units, resistance vs. current).

M.IMA.15 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations (e.g., rearrange Ohm's law V = RI to highlight resistance R).

Checkpoint opportunity

Solve systems of equations.

M.IMA.16 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables (e.g., childcare facility – sq. footage to number of children; solving electrical current in a circuit with multiple paths, break-even point).

Checkpoint opportunity

Functions - Interpreting Functions

Understand the concept of a function and use function notation.

Checkpoint opportunity

Analyze functions using different representations.

M.IMA.18 Interpret the parameters in a linear function in terms of a context.

M.IMA.19 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

M.IMA.20 Describe qualitatively the functional relationship between two quantities by analyzing a graph.

Checkpoint opportunity

Build a function that models a relationship between two quantities.

M.IMA.21 Represent application problems as linear equations. Write a function that describes a relationship between two quantities (e.g., level of education versus pay; rate of speed versus fuel consumption; caloric intake versus expenditure).

M.IMA.22 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.

Geometry/Trigonometry

Visualize relationships between two-dimensional and three-dimensional objects and apply geometric concepts in modeling situations.

M.IMA.23 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects (e.g., three-view drawings and blueprints).

M.IMA.24 Use two- and three-dimensional shapes and circles, their measures, and their properties to describe objects.

M.IMA.24.a Apply concepts of density based on area and volume in modeling situations.

M.IMA.24.b Apply geometric methods to solve design problems to satisfy given constraints (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with topographic grid systems based on ratios).

Use geometric theorems and formulas to solve problems.

M.IMA.25 Explore theorems about triangles to solve real-world application problems.

M.IMA.26 Understand and apply the Pythagorean Theorem for solving real-world problems (e.g., checking accuracy on gate construction, conduit bending, roof pitch).

M.IMA.27 Solve application problems by calculating area and surface area for two-dimensional objects (e.g., calculate the cost of installing flooring in a building and painting the interior and exterior of a building based on square footage).

M.IMA.28 Solve application problems by calculating volume for three-dimensional objects using formulas for cylinders, pyramids, prisms, cones, and spheres (e.g., compute amount of cement needed for a sidewalk, amount of water in a fire hose, amount of air in ductwork).

M.IMA.29 Solve application problems by calculating circumference, area, radius, diameter, area of sector, arc length of a circle with appropriate unit labels (e.g., develop a circular watering system).

Checkpoint opportunity

Modeling

Concrete geometric representation (physical modeling).

M.IMA.30 Create and use two- and three-dimensional representations of authentic situations using paper techniques or dynamic geometric environments for computer-aided design and other applications.

M.IMA.31 Gather data, conduct investigations, and apply mathematical concepts and models to solve problems (e.g., designing and building a house or a car).

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

M.IMA.33 For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Interpret the rate of change and the constant term of a linear model in the context of the data.

M.IMA.34 Identify positive and negative correlations (e.g., vehicle depreciation). Use technology to compute and interpret the correlation coefficient of a linear fit.

Checkpoint opportunity

Statistics and Probability: Interpreting Categorical & Quantitative Data

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

M.IMA.35 Select applicable representations to display data on the real number line (e.g., dot plots, histograms, and box plots).

M.IMA.36 Analyze and interpret tables, charts, and graphs (e.g., interpret a body mass index (BMI) chart).

M.IMA.37 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.IMA.38 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

M.IMA.39 Distinguish between correlation and causation.

Finance Mathematics

Understanding financial models.

M.IMA.40 Determine, represent, and analyze mathematical models for loan amortization and the effects of different payments and/or finance terms (e.g., business loans, auto, mortgage, and/or credit card).

M.IMA.41 Determine, represent, and analyze mathematical models for investments involving simple and compound interest with and without additional deposits (e.g., savings accounts, bonds, and/or certificates of deposit).

Personal use of finance.

M.IMA.42 Research, develop, and analyze personal budgets based on given parameters (e.g., fixed and discretionary expenses, insurance, gross vs. net pay, types of income, wage, salary, commission, career choice, geographic region, retirement, and/or investment planning).

M.IMA.43 Research and analyze taxes including payroll, sales, personal property, real estate, and income tax returns.