New Hampshire Math Standards

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New Hampshire Math Standards - High School

MathScore aligns to the New Hampshire 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 New Hampshire Math Standards at other levels.

Number and Operations

M:N&O:HS:1 Demonstrates conceptual understanding of rational numbers by knowing why a real number is rational if and only if the number's decimal expansion eventually repeats or terminates.

M:N&O:HS:2 Demonstrates understanding of the relative magnitude of real numbers by solving problems that involve ordering or comparing elements of any subset of the real numbers. (Estimating Square Roots )

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 )

M:N&O:HS:3 No standard at this level

M:N&O:HS:4 Accurately solves problems.
    • Interprets and computes with rational exponents and their relation to radicals, by hand in simple cases (e.g.,4^3/2), and using a calculator when appropriate. (Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Roots Of Exponential Expressions )
    • Interprets and computes in scientific notation with and without a calculator. (Scientific Notation 2 , Scientific Notation )
    • Solves compound interest problems using A=P(1 + r/n)^nt, where n is finite. (Compound Interest )

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 )

M:N&O:HS:5 No standard at this level

M:N&O:HS:6 Uses a variety of mental computation strategies to solve problems (e.g., using compatible numbers, applying properties of operations, using mental imagery, using patterns) and to determine the reasonableness of answers. (IMPORTANT: The intent of this GSE is to embed mental arithmetic throughout the instructional program, not to teach it as a separate unit.) (Percentages , Percent of Quantity , Estimating Square Roots , Perfect Squares )

M:N&O:HS:7 Makes estimates in a given situation (e.g., tips, discounts, tax, the value of a non-perfect square root or cube root) by identifying when estimation is appropriate, selecting the appropriate method of estimation; determining the level of accuracy needed given the situation; analyzing the effect of the estimation method on the accuracy of results; evaluating the reasonableness of solutions appropriate to GSEs across content strands. (IMPORTANT: The intent of this GSE is to embed estimation throughout the instructional program, not to teach it as a separate unit.) (Estimating Square Roots )

M:N&O:HS:8 Applies properties of numbers and field properties (including determining whether a given subset of numbers is closed under a given arithmetic operation) to solve problems or to simplify computations; and compares and contrasts the properties of numbers and number systems; adds and multiplies numerical matrices with attention to the arithmetic properties of these operations.

Geometry and Measurement

M:G&M:HS:1 No standard at this level

M:G&M:HS:2 Creates formal proofs of propositions (e.g., angles, lines, circles, distance, midpoint and polygons including triangle congruence and similarity). (IMPORTANT: It is the intent that students are creating formal proofs as articulated in the process standards, independent of the topic being studied. Furthermore, students should not be limited to any particular method of proof, but rather use a variety of strategies and those that work best for them. Some topics may be treated more formally than others.)

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 , Triangle Angles 2 , Identifying Angles , Irregular Shape Areas , Solving For Angles , Polygon Angles , Angle Measurements , Angle Measurements 2 )
M:G&M:HS.3 No standard at this level

M:G&M:HS:4 Applies the concepts of congruency by using matrices to represent reflections, translations, and rotations.

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.

M:G&M:HS:5 Applies concepts of similarity to define the trigonometric functions as ratios of sides of right triangles; uses the ratios of the sides of special right triangles (30-60-90 and 45-45-90) to determine the sine, cosine and tangent of 30, 45, and 60; and solves related problems.

M:G&M:10:5 Applies concepts of similarity by solving problems within mathematics or across disciplines or contexts. (Proportions 2 )

M:G&M:HS:6 Applies trigonometric formulas (e.g., Law of Sines, Law of Cosines, A=½absinC) to find angles, lengths and areas of polygons.

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 , Trapezoids )

M:G&M:HS:7 Applies informal concepts of successive approximation, upper and lower bounds, and limits in measurement situations (e.g., use successive approximation to find the area of a pond); and uses measurement conversion strategies (e.g., unit/dimensional analysis). (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion , Area and Volume Conversions )

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 )

M:G&M:HS:8 No standard at this level

M:G&M:10:9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope. (Parallel and Perpendicular Lines , Determining Slope , Applied Linear Equations 2 )

M:G&M:HS:10 Demonstrates conceptual understanding of spatial reasoning and visualization by sketching or using dynamic geometric software to generate three-dimensional objects from two-dimensional perspectives, or to generate two-dimensional perspectives from three-dimensional objects, and by solving related problems; perform and justify constructions with a compass and straightedge or dynamic geometric software.

Functions and Algebra

M:F&A:HS:1 Identifies arithmetic and geometric sequences and finds the nth term; then uses the generalization to find a specific term.

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. (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Nonlinear Functions )

M:F&A:HS:2 Demonstrates conceptual understanding of linear and nonlinear functions and relations.
    • Analyzes characteristics of classes of functions (polynomial, rational, and exponential) to include domain, range, intercepts, increasing and decreasing intervals and rates of change. (Domain and Range )
    • Understands one-to-one (injective) functions and that a function that is one-to-one has a converse that is also a function; and finds inverses algebraically and graphically.
    • Graphs polynomial, rational and exponential functions, including vertical and horizontal shifts, stretches, and compressions as well as reflections across vertical and horizontal axes. (Nonlinear Functions )
    • Applies knowledge of functions to interpret and understand situations, design mathematical models, and solve problems in mathematics as well as in the natural and social sciences. (Distance, Rate, and Time )

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 )

M:F&A:HS:3 Demonstrates conceptual understanding of algebraic expressions.
    • Manipulates, evaluates, and simplifies algebraic and numerical expressions. (Absolute Value 2 , Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , Binomial Fraction Simplification , Variable Substitution 2 , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions , Roots Of Exponential Expressions , Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
    • Adds, subtracts, multiplies and divides polynomials and rational expressions. (Foil Method , Trinomial Factoring , Binomial Fraction Simplification , Polynomial Fraction Simplification , Simplifying Algebraic Expressions )
    • Factors quadratic and higher degree polynomials. (Trinomial Factoring )
    • Understands properties of logarithms and converts between logarithmic and exponential forms.
    • Manipulates, evaluates, and simplifies expressions involving rational exponents and radicals and converts between expressions with rational exponents and expressions with radicals. (Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Roots Of Exponential Expressions , Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
    • Understands the effect of simplifying rational expressions on the domain of the related functions (e.g., x²s/x = x for x ≠ 0).

M:F&A:10:3 Demonstrates conceptual understanding of algebraic expressions by solving problems involving algebraic expressions, by simplifying expressions (e.g., simplifying polynomial or rational expressions, or expressions involving integer exponents, square roots, or absolute values), by evaluating expressions, or by translating problem situations into algebraic expressions. (Absolute Value 2 , Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , Foil Method , Trinomial Factoring , Binomial Fraction Simplification , Polynomial Fraction Simplification , Variable Substitution 2 , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions , Roots Of Exponential Expressions , Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )

M:F&A:HS:4 Demonstrates conceptual understanding of equality.
    • Factors, completes the square, uses the quadratic formula, and graphs quadratic functions to solve quadratic equations. (Trinomial Factoring , Quadratic Zero Equations , Quadratic Formula , Quadratic X-Intercepts )
    • Solves equations involving polynomial, rational, and radical expressions. Graphs and interprets the solutions. (Linear Equations , Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , Number Line Inequalities , Quadratic X-Intercepts , Quadratic Zero Equations , Quadratic Formula )
    • Understands extraneous solutions.
    • Finds approximate solutions to equations by graphing each side as a function using technology. Understands that any equation in x can be interpreted as the equation f(x) = g(x) and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).
    • Solves 2×2 and 3×3 systems of linear equations and graphically interprets the solutions. (System of Equations Substitution , System of Equations Addition , Age Problems )
    • Solves systems of linear and quadratic inequalities.
    • Solves systems of equations involving nonlinear expressions and graphically interprets the solutions.
    • Translates problem situations into inequalities; and solves linear and non-linear inequalities (symbolically and graphically). (Single Variable Inequalities , Algebraic Sentences 2 )

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 representations. (Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , 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

M:DSP:HS:1 Interprets a given representation(s) (e.g., regression function including linear, quadratic, and exponential) to analyze the data to make inferences and to formulate, justify, and critique conclusions. (IMPORTANT: Analyze data consistent with concepts and skills in M:DSP:HS:2).
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.) (Bar Graphs , Line Graphs )

M:DSP:HS:2 Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of dispersion (standard deviation, variance, and percentiles).

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 )

M:DSP:HS:3 Organizes and displays one- and two-variable data using a variety of representations (e.g., box-and-whisker plots, scatter plots, bar graphs, line graphs, circle graphs, histograms, frequency charts, linear, quadratic, and exponential regression functions) to analyze the data to formulate or justify conclusions, make predictions, or to solve problems with or without using technology.

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.

M:DSP:HS:4 Uses counting techniques to solve problems in context involving combination or permutations using a variety of strategies (e.g., nCr, nPr, or n!); and finds unions, intersections, and complements of sets. (Intersection and Union )

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).

M:DSP:HS:5 For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the theoretical probability of an event and tests the prediction through experiments and simulations; compares and contrasts theoretical and experimental probabilities; finds the odds of an event and understands the relationship between probability and odds. (Probability )

M:DSP:10:5 Solves problems involving experimental or theoretical probability. (Probability , Probability 2 , Object Picking Probability )

M:DSP:HS:6 In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, research, experimentation) and sampling techniques (e.g., random sample, stratified random sample) to collect the data necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the questions or hypotheses being tested while considering the limitations of the data that could effect interpretations; and when appropriate makes predications, asks new questions, or makes connections to real-world situations. (IMPORTANT: Analyzes data consistent with concepts and skills in M:DSP:10:2.) (Requires outside materials )

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