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New Hampshire Math Standards - 8th Grade
MathScore aligns to the New Hampshire Math Standards for 8th Grade. 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:8:1 Demonstrates conceptual understanding of rational numbers with respect to absolute values, perfect square and cube roots, and percents as a way of describing change (percent increase and decrease) using explanations, models, or other representations. (Percentage Change , Absolute Value 1 , Absolute Value 2 , Perfect Squares )M:N&O:8:2 Demonstrates understanding of the relative magnitude of numbers by ordering or comparing rational numbers, common irrational numbers (e.g.,√2,π ), numbers with whole number or fractional bases and whole number exponents, square roots, absolute values, integers, or numbers represented in scientific notation using number lines or equality and inequality (Absolute Value 1 , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Scientific Notation , Estimating Square Roots )
M:N&O:8:3 No standard at this grade
M:N&O:8:4 Accurately solves problems involving proportional reasoning (percent increase or decrease, interest rates, markups, or rates); multiplication or division of integers; and squares, cubes, and taking square or cube roots. (IMPORTANT: Applies the conventions of order of operations.) (Order Of Operations , Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Integer Multiplication , Integer Division , Simple Interest , Perfect Squares )
M:N&O:8:5 No standard at this grade
M:N&O:8:6 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; and mentally calculates benchmark perfect squares and related square roots (e.g., 12, 22, … , 122, 152, 202, 252, 1002, 10002); determines the part of a number using benchmark percents and related fractions (1%, 10%, 25%, 33 1/3%, 50%, 66 2/3%, 75%, and 100%) (e.g., 25% of 16; of 330). (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:8:7 Makes estimates in a given situation (including tips, discounts, tax, and the value of a non-perfect square root as between two whole numbers) 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; and evaluating the reasonableness of solutions appropriate to grade level GLEs across content strands. (IMPORTANT: The intent of this GLE is to embed estimation throughout the instructional program, not to teach it as a separate unit.) (Estimated Multiply Divide Word Problems , Estimating Square Roots )
M:N&O:8:8 Applies properties of numbers (odd, even, positive, negative, remainders, divisibility, and prime factorization) and field properties (commutative, associative, identity [including the multiplicative property of one, e.g., 20 × 23 = 20+3 = 23, so 20 = 1], distributive, inverses) to solve problems and to simplify computations, and demonstrates conceptual understanding of field properties as they apply to subsets of real numbers when addition and multiplication are not defined in the traditional ways (e.g., If aΔb = a + b - 1, is Δ a commutative operation?) (Odd or Even Theory , Prime Factoring , Prime Factoring 2 , Divisibility Rules )
Geometry and Measurement
M:G&M:8:1 No standard at this grade
M:G&M:8:2 Applies the Pythagorean Theorem to find a missing side of a right triangle, or in problem solving situations. (Pythagorean Theorem )
M:G&M:8:3 No standard at this grade
M:G&M:8:4 No standard at this grade
M:G&M:8:5 Applies concepts of similarity to determine the impact of scaling on the volume or surface area of three-dimensional figures when linear dimensions are multiplied by a constant factor; to determine the length of sides of similar triangles, or to solve problems involving growth and rate. (Area and Volume Conversions , Area And Volume Proportions , Proportions 2 , Train Problems )
M:G&M:8:6 Demonstrates conceptual understanding of surface area or volume by solving problems involving surface area and volume of rectangular prisms, triangular prisms, cylinders, pyramids, or cones. Expresses all measures using appropriate units. (Rectangular Solids , Rectangular Solids 2 , Triangular Prisms , Cylinders )
M:G&M:8:7 No standard at this grade
M:G&M:8:8 No standard at this grade
M:G&M:8:9 No standard at this grade
M:G&M:8:10 No standard at this grade
Functions and Algebra
M:F&A:8:1 Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables, sequences, graphs, or in problem situations; and generalizes a linear relationship (non-recursive explicit equation); generalizes a linear relationship to find a specific case; generalizes a nonlinear relationship using words or symbols; or generalizes a common nonlinear relationship to find a specific case. (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Nonlinear Functions )
M:F&A:8:2 Demonstrates conceptual understanding of linear relationships (y = kx; y = mx + b) as a constant rate of change by solving problems involving the relationship between slope and rate of change; informally and formally determining slopes and intercepts represented in graphs, tables, or problem situations; or describing the meaning of slope and intercept in context; and distinguishes between linear relationships (constant rates of change) and nonlinear relationships (varying rates of change) represented in tables, graphs, equations, or problem situations; or describes how change in the value of one variable relates to change in the value of a second variable in problem situations with constant and varying rates of change. (Single Variable Equations , Determining Slope )
M:F&A:8:3 Demonstrates conceptual understanding of algebraic expressions by evaluating and simplifying algebraic expressions (including those with square roots, whole number exponents, or rational numbers); or by evaluating an expression within an equation (e.g., determine the value of y when x = 4 given 7√x + 2x). (Linear Equations , Variable Substitution , Absolute Value 2 , Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , 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:8:4 Demonstrates conceptual understanding of equality by showing equivalence between two expressions (expressions consistent with the parameters of the left- and right-hand sides of the equations being solved at this grade level) using models or different representations of the expressions, solving formulas for a variable requiring one transformation (e.g., d = rt; d/r = t); by solving multi-step linear equations with integer coefficients; by showing that two expressions are or are not equivalent by applying commutative, associative, or distributive properties, order of operations, or substitution; and by informally solving problems involving systems of linear equations in a context. (Triangle Area 2 , Rectangular Solids 2 , 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 , Distance, Rate, and Time , Two Variable Equations )
Data, Statistics, and Probability
M:DSP:8:1 Interprets a given representation (line graphs, scatter plots, histograms, or box-and-whisker plots) to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. (IMPORTANT: Analyzes data consistent with concepts and skills in M:DSP:8:2.) (Line Graphs )M:DSP:8:2 Analyzes patterns, trends, or distributions in 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 estimated line of best fit to analyze situations, or to solve problems; and evaluates the sample from which the statistics were developed (bias, random, or non-random). (Mean, Median, Mode , Stem And Leaf Plots )
M:DSP:8:3 Organizes and displays data using scatter plots to answer questions related to the data, to analyze the data to formulate or justify conclusions, to 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 M:DSP:8:1. (IMPORTANT: Analyzes data consistent with concepts and skills in M:DSP:8:2.)
M:DSP:8:4 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:8:5 For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of an event in a problem-solving situation; and predicts the theoretical probability of an event and tests the prediction through experiments and simulations; and compares and contrasts theoretical and experimental probabilities. (Probability , Probability 2 )
M:DSP:8:6 In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, experimentation) to collect the data (numerical or categorical) necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the question or hypothesis being tested while considering the limitations that could affect interpretations; and when appropriate makes predictions; and asks new questions and makes connections to real world situations. (IMPORTANT: Analyzes data consistent with concepts and skills in M:DSP:8:2.) (Requires outside materials )
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