Standards of Learning: Mathematics

Policy Number:

SOL-MAT-001

Version:

1.0

Effective Date:

October 1, 2025

Review Date:

October 1, 2026

Last Updated:

October 17, 2025

Functional Area Manager:

Director of Academic Operations

Consolidated Standards of Learning

Grades 5–8

LHA.MAT.B.001: Classify types of numbers and represent them on a number line, distinguishing between rational and irrational numbers.
LHA.MAT.B.002: Compare and order positive and negative numbers in real-world contexts.
LHA.MAT.B.003: Calculate the absolute value of numbers and interpret its meaning as distance from zero.
LHA.MAT.B.004: Identify factors of numbers and determine the greatest common factor (GCF) for simplifying fractions or solving problems.
LHA.MAT.B.005: Find multiples of numbers and compute the least common multiple (LCM) for applications like adding fractions.
LHA.MAT.B.006: Identify types of fractions (proper, improper, mixed) and perform addition and subtraction with fractions.
LHA.MAT.B.007: Multiply and divide fractions, applying these operations to solve real-world problems.
LHA.MAT.B.008: Add and subtract decimals accurately in various contexts, such as financial calculations.
LHA.MAT.B.009: Multiply decimals and apply the operation to problems like area calculations.
LHA.MAT.B.010: Divide decimals and use the results to solve problems involving rates or ratios.
LHA.MAT.B.011: Add positive and negative numbers, modeling with number lines or real-world scenarios.
LHA.MAT.B.012: Subtract positive and negative numbers, interpreting results in context.
LHA.MAT.B.013: Multiply and divide positive and negative numbers, applying rules of signs.
LHA.MAT.B.014: Solve and graph inequalities on a number line, explaining their solutions.
LHA.MAT.B.015: Represent ratios in multiple forms (e.g., a:b, a/b) and apply them to compare quantities.
LHA.MAT.B.016: Calculate unit rates and unit prices to compare quantities or make purchasing decisions.
LHA.MAT.B.017: Solve proportions to find unknown values in real-world applications.
LHA.MAT.B.018: Convert measurements between units using ratios and proportions.
LHA.MAT.B.019: Calculate percentages and apply them to problems like discounts or taxes.
LHA.MAT.B.020: Solve percent word problems, such as finding part, whole, or percent.
LHA.MAT.B.021: Compute taxes, fees, and surcharges in financial scenarios.
LHA.MAT.B.022: Determine discounts and markups in retail or business contexts.
LHA.MAT.B.023: Calculate gratuity and commission based on given percentages.
LHA.MAT.B.024: Compute simple interest using the formula I = PRT.
LHA.MAT.B.025: Determine percent rate of change in real-world situations, such as price increases.
LHA.MAT.B.026: Create and interpret tables to represent ratio relationships.
LHA.MAT.B.027: Write and simplify algebraic expressions to model situations.
LHA.MAT.B.028: Apply properties (commutative, associative, distributive) to simplify expressions.
LHA.MAT.B.029: Combine like terms in algebraic expressions to simplify them.
LHA.MAT.B.030: Evaluate expressions with exponents, including negative and zero exponents.
LHA.MAT.B.031: Apply the order of operations to evaluate numerical and algebraic expressions.
LHA.MAT.B.032: Convert numbers to and from scientific notation for large or small quantities.
LHA.MAT.B.033: Calculate square and cube roots of perfect squares and cubes.
LHA.MAT.B.034: Compare irrational numbers by approximating their values.
LHA.MAT.B.035: Solve linear equations in one variable using inverse operations.
LHA.MAT.B.036: Solve for a specific variable in a formula or equation.
LHA.MAT.B.037: Solve multistep equations involving multiple operations.
LHA.MAT.B.038: Solve and graph multistep inequalities on a number line.
LHA.MAT.B.039: Write and solve equations and inequalities to model word problems.
LHA.MAT.B.040: Identify basic geometric shapes and their properties.
LHA.MAT.B.041: Measure and classify angles (acute, obtuse, right, straight).
LHA.MAT.B.042: Calculate the area of quadrilaterals using appropriate formulas.
LHA.MAT.B.043: Calculate the area of triangles and apply to real-world problems.
LHA.MAT.B.044: Apply the Pythagorean theorem to find missing side lengths in right triangles.
LHA.MAT.B.045: Calculate the circumference and area of circles using formulas.
LHA.MAT.B.046: Identify and classify three-dimensional figures (e.g., prisms, pyramids).
LHA.MAT.B.047: Calculate the volume of three-dimensional figures using formulas.
LHA.MAT.B.048: Compute the surface area of prisms, cylinders, and other solids.
LHA.MAT.B.049: Identify angles formed by transversals and their relationships (e.g., corresponding, alternate interior).
LHA.MAT.B.050: Create and interpret scale drawings and similar figures.
LHA.MAT.B.051: Calculate measures of central tendency (mean, median, mode) and variation (range).
LHA.MAT.B.052: Create and interpret data displays, such as histograms or box plots.
LHA.MAT.B.053: Calculate basic probabilities for simple events.
LHA.MAT.B.054: Plot points and interpret coordinates on the coordinate plane.
LHA.MAT.B.055: Identify relations, lines, and functions from graphs or tables.
LHA.MAT.B.056: Calculate the slope of a line from two points or a graph.
LHA.MAT.B.057: Graph linear equations and interpret their meaning.
LHA.MAT.B.058: Solve systems of linear equations using substitution or elimination.
LHA.MAT.B.059: Identify and graph nonlinear functions, such as quadratics.
LHA.MAT.B.060: Plot and classify polygons on the coordinate plane.
LHA.MAT.B.061: Perform transformations (reflections, translations, rotations) on figures.
LHA.MAT.B.062: Analyze proportional relationships and represent them graphically.

Grades 9–12

Geometry

LHA.MAT.GEO.001: Identify and describe points, lines, and planes in geometric contexts.
LHA.MAT.GEO.002: Measure and classify angles (e.g., acute, obtuse, right, straight).
LHA.MAT.GEO.003: Identify and apply properties of angle pairs (e.g., complementary, supplementary, vertical).
LHA.MAT.GEO.004: Perform basic geometric constructions using a compass and straightedge.
LHA.MAT.GEO.005: Apply logic and reasoning to analyze geometric relationships.
LHA.MAT.GEO.006: Construct geometric proofs to establish relationships between figures.
LHA.MAT.GEO.007: Identify properties of parallel lines cut by a transversal.
LHA.MAT.GEO.008: Prove special angle pairs (e.g., alternate interior, corresponding) using parallel lines.
LHA.MAT.GEO.009: Prove lines are parallel using angle relationships.
LHA.MAT.GEO.010: Classify triangles by sides and angles and analyze their properties.
LHA.MAT.GEO.011: Calculate interior and exterior angles of triangles.
LHA.MAT.GEO.012: Prove triangle congruence using SSS and SAS criteria.
LHA.MAT.GEO.013: Prove triangle congruence using ASA and AAS criteria.
LHA.MAT.GEO.014: Analyze properties of triangle bisectors and their applications.
LHA.MAT.GEO.015: Apply triangle inequalities to determine valid triangle configurations.
LHA.MAT.GEO.016: Identify and prove properties of parallelograms.
LHA.MAT.GEO.017: Classify and prove properties of rhombuses, rectangles, and squares.
LHA.MAT.GEO.018: Analyze properties of trapezoids and kites in geometric proofs.
LHA.MAT.GEO.019: Calculate angle measures in polygons using formulas.
LHA.MAT.GEO.020: Perform reflections of geometric figures across lines.
LHA.MAT.GEO.021: Perform translations of geometric figures in the coordinate plane.
LHA.MAT.GEO.022: Perform rotations of geometric figures about a point.
LHA.MAT.GEO.023: Apply compositions of transformations to geometric figures.
LHA.MAT.GEO.024: Prove congruence of figures using transformations.
LHA.MAT.GEO.025: Apply ratios and proportions to solve geometric problems.
LHA.MAT.GEO.026: Perform dilations and analyze their effects on figures.
LHA.MAT.GEO.027: Prove similarity of figures using AA, SSS, or SAS criteria.
LHA.MAT.GEO.028: Solve problems using proportions in similar triangles.
LHA.MAT.GEO.029: Calculate slope and write linear equations for geometric applications.
LHA.MAT.GEO.030: Apply the Pythagorean theorem to solve problems in coordinate geometry.
LHA.MAT.GEO.031: Calculate midpoint and distance between points in the coordinate plane.
LHA.MAT.GEO.032: Prove triangle properties using coordinate geometry.
LHA.MAT.GEO.033: Prove quadrilateral properties using coordinate geometry.
LHA.MAT.GEO.034: Apply trigonometric ratios (sine, cosine, tangent) to solve triangle problems.
LHA.MAT.GEO.035: Use the Law of Sines and Law of Cosines to solve triangle problems.
LHA.MAT.GEO.036: Identify and describe fundamental properties of circles.
LHA.MAT.GEO.037: Calculate measures of central angles and arcs in circles.
LHA.MAT.GEO.038: Convert between degrees and radians for angle measures.
LHA.MAT.GEO.039: Analyze relationships between arcs and chords in circles.
LHA.MAT.GEO.040: Calculate measures of inscribed angles in circles.
LHA.MAT.GEO.041: Apply properties of tangents to solve circle problems.
LHA.MAT.GEO.042: Analyze properties of secants in circles.
LHA.MAT.GEO.043: Write and apply equations of circles in the coordinate plane.
LHA.MAT.GEO.044: Calculate areas of parallelograms and triangles.
LHA.MAT.GEO.045: Compute areas of polygons like pentagons or hexagons.
LHA.MAT.GEO.046: Calculate areas of circles and sectors.
LHA.MAT.GEO.047: Determine areas of composite figures by decomposition.
LHA.MAT.GEO.048: Calculate surface areas of prisms and cylinders.
LHA.MAT.GEO.049: Compute surface areas of pyramids and cones.
LHA.MAT.GEO.050: Calculate volumes of prisms and cylinders.
LHA.MAT.GEO.051: Compute volumes of pyramids and cones.
LHA.MAT.GEO.052: Calculate surface area and volume of spheres.
LHA.MAT.GEO.053: Determine volumes of composite figures.
LHA.MAT.GEO.054: Analyze properties of solids of revolution.

Algebra I

LHA.MAT.ALG.001: Classify types of numbers (e.g., integers, rational, irrational) and their properties.
LHA.MAT.ALG.002: Apply algebraic properties (e.g., commutative, associative, distributive) to simplify expressions.
LHA.MAT.ALG.003: Evaluate expressions using the order of operations.
LHA.MAT.ALG.004: Add positive and negative whole numbers in algebraic contexts.
LHA.MAT.ALG.005: Subtract positive and negative whole numbers in algebraic contexts.
LHA.MAT.ALG.006: Multiply and divide positive and negative whole numbers.
LHA.MAT.ALG.007: Multiply and divide positive and negative fractions.
LHA.MAT.ALG.008: Add and subtract positive and negative fractions.
LHA.MAT.ALG.009: Add and subtract decimals in algebraic problems.
LHA.MAT.ALG.010: Multiply and divide decimals in algebraic contexts.
LHA.MAT.ALG.011: Represent and solve problems using ratios.
LHA.MAT.ALG.012: Calculate unit rates for real-world applications.
LHA.MAT.ALG.013: Solve proportions to find unknown values.
LHA.MAT.ALG.014: Calculate percentages and apply to real-world problems.
LHA.MAT.ALG.015: Solve percent applications, such as discounts or taxes.
LHA.MAT.ALG.016: Compute simple interest using the formula I = PRT.
LHA.MAT.ALG.017: Calculate percent rate of change in various contexts.
LHA.MAT.ALG.018: Create and interpret tables to represent ratio relationships.
LHA.MAT.ALG.019: Evaluate expressions with exponents, including negative and zero exponents.
LHA.MAT.ALG.020: Convert numbers to and from scientific notation.
LHA.MAT.ALG.021: Write and simplify algebraic expressions.
LHA.MAT.ALG.022: Evaluate algebraic expressions for given values.
LHA.MAT.ALG.023: Combine like terms to simplify algebraic expressions.
LHA.MAT.ALG.024: Solve one-variable linear equations using inverse operations.
LHA.MAT.ALG.025: Solve one-variable inequalities and graph solutions.
LHA.MAT.ALG.026: Solve compound inequalities and graph their solutions.
LHA.MAT.ALG.027: Rewrite formulas to solve for a specific variable.
LHA.MAT.ALG.028: Solve systems of linear equations using substitution.
LHA.MAT.ALG.029: Solve systems of linear equations using elimination.
LHA.MAT.ALG.030: Identify and graph points and lines in the coordinate plane.
LHA.MAT.ALG.031: Graph a line from a table of values.
LHA.MAT.ALG.032: Calculate the slope of a line from points or equations.
LHA.MAT.ALG.033: Write and graph equations in slope-intercept form.
LHA.MAT.ALG.034: Solve systems of linear equations by graphing.
LHA.MAT.ALG.035: Graph linear inequalities in two variables.
LHA.MAT.ALG.036: Solve systems of linear inequalities by graphing.
LHA.MAT.ALG.037: Calculate measures of central tendency and variation for data sets.
LHA.MAT.ALG.038: Create and interpret data displays, such as histograms or box plots.
LHA.MAT.ALG.039: Calculate probabilities for simple and compound events.
LHA.MAT.ALG.040: Compute permutations and combinations for counting problems.
LHA.MAT.ALG.041: Identify relations and functions from graphs or equations.
LHA.MAT.ALG.042: Use function notation to evaluate and interpret functions.
LHA.MAT.ALG.043: Apply functions to model real-world scenarios.
LHA.MAT.ALG.044: Add and subtract polynomials.
LHA.MAT.ALG.045: Multiply and divide exponents with the same base.
LHA.MAT.ALG.046: Multiply and divide monomials.
LHA.MAT.ALG.047: Multiply and divide polynomials.
LHA.MAT.ALG.048: Factor polynomials using the greatest common factor.
LHA.MAT.ALG.049: Factor polynomials using grouping techniques.
LHA.MAT.ALG.050: Factor trinomials when the leading coefficient is 1.
LHA.MAT.ALG.051: Factor trinomials when the leading coefficient is not 1.
LHA.MAT.ALG.052: Factor polynomials using special formulas (e.g., difference of squares).
LHA.MAT.ALG.053: Calculate square roots and cube roots of numbers.
LHA.MAT.ALG.054: Simplify radical expressions.
LHA.MAT.ALG.055: Add and subtract radical expressions.
LHA.MAT.ALG.056: Multiply and divide radical expressions.
LHA.MAT.ALG.057: Solve quadratic equations by factoring.
LHA.MAT.ALG.058: Solve quadratic equations by taking square roots.
LHA.MAT.ALG.059: Solve quadratic equations by completing the square.
LHA.MAT.ALG.060: Solve quadratic equations using the quadratic formula.
LHA.MAT.ALG.061: Use the discriminant to determine the number of solutions to a quadratic equation.
LHA.MAT.ALG.062: Graph quadratic functions and identify key features (vertex, axis of symmetry).
LHA.MAT.ALG.063: Solve quadratic equations by graphing.

Algebra II

LHA.MAT.AL2.001 Solve linear equations and inequalities using algebraic techniques, including multi-step processes and checking solutions.
LHA.MAT.AL2.002 Graph linear equations and inequalities on the coordinate plane, identifying slopes, intercepts, and solution sets.
LHA.MAT.AL2.003 Solve absolute value equations and inequalities algebraically, interpreting solutions in context.
LHA.MAT.AL2.004 Graph absolute value equations and inequalities, analyzing shifts and reflections on the coordinate plane.
LHA.MAT.AL2.005 Solve systems of linear equations using substitution, elimination, and graphical methods, verifying solutions.
LHA.MAT.AL2.006 Apply properties of exponents and roots to simplify expressions and solve equations.
LHA.MAT.AL2.007 Perform operations with complex numbers, including addition, subtraction, multiplication, and division, and represent them in the complex plane.
LHA.MAT.AL2.008 Analyze relations and functions, distinguishing between the two and determining domain and range.
LHA.MAT.AL2.009 Construct and interpret graphs of linear functions, identifying key features such as slope and intercepts.
LHA.MAT.AL2.010 Graph absolute value functions, describing transformations such as translations and dilations.
LHA.MAT.AL2.011 Apply transformations (e.g., translations, reflections, stretches) to parent functions and analyze their effects on graphs.
LHA.MAT.AL2.012 Perform operations on functions, including addition, subtraction, multiplication, division, and composition, and interpret results.
LHA.MAT.AL2.013 Determine the inverse of a function, verifying the relationship algebraically and graphically.
LHA.MAT.AL2.014 Solve quadratic equations using factoring, completing the square, quadratic formula, and graphing, selecting appropriate methods.
LHA.MAT.AL2.015 Graph quadratic functions, identifying vertices, axes of symmetry, and intercepts, and interpret their significance.
LHA.MAT.AL2.016 Solve nonlinear systems of equations, including combinations of linear and quadratic equations, using algebraic and graphical methods.
LHA.MAT.AL2.017 Perform operations on polynomials, including addition, subtraction, multiplication, and exponentiation, and simplify results.
LHA.MAT.AL2.018 Factor polynomials using techniques such as GCF, difference of squares, and grouping, and apply factoring to solve equations.
LHA.MAT.AL2.019 Divide polynomials using long division and synthetic division, interpreting quotients and remainders.
LHA.MAT.AL2.020 Graph polynomial functions, identifying zeros, end behavior, and turning points.
LHA.MAT.AL2.021 Apply the Rational Zero Theorem to identify possible rational zeros of polynomial functions and verify solutions.
LHA.MAT.AL2.022 Simplify rational expressions by factoring and canceling common factors, ensuring proper domain restrictions.
LHA.MAT.AL2.023 Perform operations on rational expressions, including addition, subtraction, multiplication, and division, and simplify results.
LHA.MAT.AL2.024 Graph rational functions, identifying asymptotes, intercepts, and behavior near undefined points.
LHA.MAT.AL2.025 Simplify radical expressions and perform operations such as addition, subtraction, multiplication, and division with radicals.
LHA.MAT.AL2.026 Solve radical equations algebraically, checking for extraneous solutions, and interpret results in context.
LHA.MAT.AL2.027 Graph radical functions, analyzing domain, range, and transformations from parent functions.
LHA.MAT.AL2.028 Apply properties of rational exponents to simplify expressions and solve equations.
LHA.MAT.AL2.029 Graph exponential functions, identifying growth, decay, and transformations, and interpret their behavior.
LHA.MAT.AL2.030 Graph logarithmic functions, identifying key features such as intercepts, asymptotes, and transformations.
LHA.MAT.AL2.031 Solve exponential and logarithmic equations using properties of logarithms and exponents, verifying solutions.
LHA.MAT.AL2.032 Measure angles in degrees and radians, converting between units and applying to real-world contexts.
LHA.MAT.AL2.033 Evaluate trigonometric functions using the unit circle and apply them to solve problems.
LHA.MAT.AL2.034 Solve problems involving right triangle trigonometry, including applications of sine, cosine, and tangent.
LHA.MAT.AL2.035 Graph trigonometric functions, identifying amplitude, period, phase shift, and vertical shift.
LHA.MAT.AL2.036 Evaluate inverse trigonometric functions and apply them to solve equations and analyze relationships.
LHA.MAT.AL2.037 Verify and apply trigonometric identities to simplify expressions and solve equations.
LHA.MAT.AL2.038 Solve trigonometric equations, finding all solutions within a specified interval and checking for extraneous solutions.

Appendix A: References

Needham, C., & Ku, K. (with Drury, K.). (2020). Everything you need to ace geometry in one big fat notebook: The complete high school study guide. Workman Publishing.

Publishing, W., Quest, E. of B., & Peterson, A. (2016). Everything you need to ace math in one big fat notebook: The complete middle school study guide. Workman Publishing Company, Incorporated.

Vigneri, R., Kim, K., & Warner, S. (2025). Everything you need to ace algebra 2 in one big fat notebook: The complete high school study guide. Workman Publishing Co.

Wang, J., & Ku, K. (2021). Everything you need to ace pre-algebra & algebra 1 in one big fat notebook: The complete high school study guide. Workman Publishing Co.

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