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Vermont Math Standards - High School
MathScore aligns to the Vermont Math Standards for High School. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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View the Vermont Math Standards at other levels.
Arithmetic, Number and Operation Concepts
MHS: 1 Accurately solves problems involving conceptual understanding and magnitude of real numbers, or simple vectors. StateMHS: 2 In high school, MHS: 1 and MHS: 2 have been combined and extended in MHS: 1.
NECAP M(N&O)-10-2 Demonstrates understanding of the relative magnitude of real numbers by solving problems involving ordering or comparing rational numbers, common irrational numbers (e.g.,√2, π ), rational bases with integer exponents, square roots, absolute values, integers, or numbers represented in scientific notation using number lines or equality and inequality symbols. (Absolute Value 1 , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Scientific Notation , Estimating Square Roots )
MHS: 3 No MHS: 3 at this grade level
MHS: 4 Accurately solves problems involving proportional reasoning or percents involving the effect of changing the base, rate, or percentage (the three cases of percent), or variations on order of finding percentages (10% off followed by 5% off), and compound interest. State (IMPORTANT: Applies the conventions of order of operations.)
NECAP M(N&O)-10-4 Accurately solves problems involving rational numbers within mathematics, across content strands, disciplines or contexts (with emphasis on, but not limited to, proportions, percents, ratios, and rates). (Unit Cost , Purchases At Stores , Restaurant Bills , Commissions , Proportions 2 , Simple Interest , Compound Interest , Distance, Rate, and Time , Train Problems , Mixture Word Problems , Work Word Problems )
MHS: 5 No MHS: 5 at this grade level
MHS: 6 No MHS: 6 at this grade level
MHS: 7 Estimates and evaluates the reasonableness of numerical computations and solutions, including those carried out with technology.
MHS: 8 Applies properties of numbers (greatest common factor [GCF], least common multiple [LCM], prime factorization, inverses, and identities), or properties of operations to solve problems and to simplify computations. (Prime Factoring , Prime Factoring 2 , Greatest Common Factor , Least Common Multiple , Estimating Square Roots )
Geometry and Measurement Concepts
MHS: 9 Models situations geometrically to solve problems connecting to other areas of mathematics or to other disciplines (i.e., diagrams, coordinate systems, transformations). State
NECAP M(G&M)-10-9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope. In high school, parts of MHS: 9 have been combined and extended in MHS: 11. (Parallel and Perpendicular Lines , Line Segments , Translations and Reflections , Determining Slope , Applied Linear Equations 2 )
MHS: 10 In high school, MHS: 10 has been combined and extended in MHS: 11.
MHS: 11 Uses the attributes, geometric properties, or theorems involving lines, polygons and circles (e.g., parallel, perpendicular, bisectors, diagonals, radii, diameters, central angles, arc length excluding radians), the Pythagorean Theorem, Triangle Inequality Theorem to solve mathematical situations or problems in context. State
NECAP M(G&M)-10-2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem). (Triangle Angles 2 , Identifying Angles , Solving For Angles , Polygon Angles , Angle Measurements , Angle Measurements 2 )
MHS: 12 In high school, parts of MHS: 12 have been combined and extended in MHS: 13.
MHS: 13 Applies concepts of similarity, congruency or right triangle trigonometry to determine length or angle measures and to solve problems involving scale. State
NECAP M(G&M)-10-4 Applies the concepts of congruency by solving problems on or off a coordinate plane involving reflections, translations, or rotations; or solves problems using congruency involving problems within mathematics or across disciplines or contexts. NECAP M(G&M)-10-5 Applies concepts of similarity by solving problems within mathematics or across disciplines or contexts. (Proportions 2 )
MHS: 14 Demonstrates conceptual understanding of perimeter, circumference, or area of two-dimensional figures or composites of two-dimensional figures or surface area or volume of three-dimensional figures or composites of three-dimensional figures in problem-solving situations and uses appropriate units of measure and expresses formulas for the perimeter, and area of two-dimensional figures or composites of two-dimensional figures or surface area or volume of three-dimensional figures or composites of three-dimensional figures. State
NECAP M(G&M)-10-6 Solves problems involving perimeter, circumference, or area of two-dimensional figures (including composite figures) or surface area or volume of three-dimensional figures (including composite figures) within mathematics or across disciplines or contexts. (Triangle Area , Triangle Area 2 , Parallelogram Area , Perimeter , Rectangular Solids , Rectangular Solids 2 , Circle Area , Circle Circumference , Triangular Prisms , Cylinders , Irregular Shape Areas , Perimeter and Area of Composite Figures , Perimeter and Area Word Problems , Trapezoids )
MHS: 15 Measures and uses units of measures appropriately and consistently when solving problems across the content strands. Makes conversions within or across systems and makes decisions concerning an appropriate degree of accuracy in problem situations involving measurement. Uses measurement conversion strategies, such as unit/dimensional analysis or uses quotient measures, such as speed and density, that give per unit amounts, or uses product measures, such as person hours to solve problems.
NECAP M(G&M)-10-7 Uses units of measure appropriately and consistently when solving problems across content strands; makes conversions within or across systems and makes decisions concerning an appropriate degree of accuracy in problem situations involving measurement in other GSEs. (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion , Area and Volume Conversions )
MHS: 16 No MHS: 16 at this grade level
MHS: 17 Constructs1 or accurately represents congruent angles, perpendicular lines, equilateral or isosceles triangles, triangle given the side segments, or inscribe or circumscribe a figure.
MHS: 18 No MHS: 18 at this grade level
Functions and Algebra Concepts
MHS: 19 Solves and models problems by formulating, extending, or generalizing linear and common nonlinear functions/relations.) State
NECAP M(F&A)-10-1 Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs in problem solving situations And makes connections among representations of functions/relations (equations, tables, graphs, symbolic notation, text). (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Nonlinear Functions )
MHS: 20 Demonstrates conceptual understanding of linear relationships and linear and nonlinear functions (including f(x) = ax2, f(x) = ax3, absolute value function, exponential growth) through analysis of intercepts, domain, range and constant and variable rates of change in mathematical and contextual situations. State
NECAP M(F&A)-10-2 Demonstrates conceptual understanding of linear and nonlinear functions and relations (including characteristics of classes of functions) through an analysis of constant, variable, or average rates of change, intercepts, domain, range, maximum and minimum values, increasing and decreasing intervals and rates of change (e.g., the height is increasing at a decreasing rate); describes how change in the value of one variable relates to change in the value of a second variable; or works between and among different representations of functions and relations (e.g., graphs, tables, equations, function notation). (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Nonlinear Functions , Domain and Range )
MHS: 21 Demonstrates conceptual understanding of algebraic expressions by evaluating, simplifying, or writing algebraic expressions; and writes equivalent forms of algebraic expressions or formulas (d = rt→ r = d/t or solves a multivariable equation or formula for one variable in terms of the others). State
MHS: 22 Demonstrates conceptual understanding of equality by solving linear equations, systems of two linear equations, or problems using tables, graphs, algebraic manipulation, or technology. State
NECAP M(F&A).10.4 Demonstrates conceptual understanding of equality by solving problems involving algebraic reasoning about equality; by translating problem situations into equations; by solving linear equations (symbolically and graphically) and expressing the solution set symbolically or graphically, or provides the meaning of the graphical interpretations of solution(s) in problem-solving situations; or by solving problems involving systems of linear equations in a context (using equations or graphs) or using models or situations; Demonstrates conceptual understanding of inequality by solving linear inequalities, comparing values of systems of linear functions, using tables, graphs, algebraic manipulation, or technology. (Single Variable Equations 2 , Single Variable Equations 3 , Number Line Inequalities , Absolute Value Equations , System of Equations Substitution , System of Equations Addition , Age Problems , Mixture Word Problems , Work Word Problems , Integer Word Problems )
Data, Statistics, and Probability Concepts
MHS: 23 Interprets a given representation(s) (box-and-whisker or scatter plots, histograms, frequency charts) to make observations, to answer questions or justify conclusions, to make predictions, or to solve problems. State
NECAP M(DSP)-10-1 Interprets a given representation(s) (e.g., box-and-whisker plots, scatter plots, bar graphs, line graphs, circle graphs, histograms, frequency charts) to make observations, to answer questions, to analyze the data to formulate or justify conclusions, critique conclusions, make predictions, or to solve problems within mathematics or across disciplines or contexts (e.g., media, workplace, social and environmental situations). (IMPORTANT: Analyzes data consistent with concepts and skills in M(DSP)-10-2.) (IMPORTANT: Analyzes data consistent with concepts and skills in MHS: 24.) (Bar Graphs , Line Graphs )
MHS: 24 Analyzes patterns, trends, or distributions in single variable and two variable data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode), dispersion (range or variation), outliers, quartile values, or regression line or correlation (high, low/positive, negative) to analyze situations, or to solve problems; and evaluates the sample from which the statistics were developed (bias, random, or nonrandom). State
NECAP M(DSP)-10-2 Analyzes patterns, trends, or distributions in data in a variety of contexts by determining, using, or analyzing measures of central tendency (mean, median, or mode), dispersion (range or variation), outliers, quartile values, estimated line of best fit, regression line, or correlation (strong positive, strong negative, or no correlation) to solve problems; and solve problems involving conceptual understanding of the sample from which the statistics were developed. (Stem And Leaf Plots )
MHS: 25 Organizes and displays data using scatter plots, histograms, or frequency distributions to answer questions related to the data, to analyze the data to formulate or justify conclusions, make predictions, or to solve problems; or identifies representations or elements of representations that best display a given set of data or situation, consistent with the representations required in MHS: 23. (IMPORTANT: Analyzes data consistent with concepts and skills in MHS: 24.)
NECAP M(DSP)-10-3 Identifies or describes representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M(DSP)-10-1.
MHS: 26 Uses combinations, arrangements or permutations to solve problems or to determine theoretical probability and experimental probability. State
NECAP M(DSP)-10-4 Uses counting techniques to solve problems in context involving combinations or permutations using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, or others).
MHS: 27 For a probability event chooses an appropriate probability model/simulations and uses it to estimate a theoretical probability for a chance event and uses the concept of a probability distribution to determine whether an event is rare or reasonably likely.
MHS: 28 In response to a question, designs investigations, considers how data-collection methods affect the nature of the data set (i.e., sample size, bias, randomization, control group), collects data using observations, surveys and experiments, purposes and justifies conclusions and predictions based on the data. (Requires outside materials )
MHS: 29 Compares and contrasts theoretical and experimental probabilities of events; and determines and/or interprets the expected outcome of an event.
NECAP M(DSP)-10-5 Solves problems involving experimental or theoretical probability. (Probability , Probability 2 , Object Picking Probability )
Mathematical Problem Solving and Reasoning
MHS: 30 Demonstrate understanding of mathematical problem solving and communication by:
• Approach and Reasoning-The strategies and skills used to solve the problem, and the reasoning that supports the approach;
• Execution-The answer and the mathematical work that supports it;
• Observations and Extensions-Demonstration of observation, connections, application, extensions, and generalizations;
• Mathematical Communication-The use of mathematical vocabulary and representation to communicate the solution; and
• Presentation-Effective communication of how the problem was solved, and of the reasoning used. (Unit Cost , Triangle Area 2 , Rectangular Solids 2 , Perimeter and Area Word Problems , Algebraic Terms , Age Problems , Distance, Rate, and Time , Train Problems , Mixture Word Problems , Work Word Problems , Integer Word Problems )
1 Construct-to draw a figure without measuring devices, using only a straight-edge and compass. "Accurately represents" may include, for example, folding paper, using a protractor.
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