# New Hampshire State Standards for Mathematics: Grade 10

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NH.M:N&O:10. NECAP - High School - Grade Level Expectation: Number and Operations.

M:N&O:10:1. No standard listed at this level.

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, rational bases with integer exponents, square roots, absolute values, integers, or numbers represented in scientific notation using number lines or equality and inequality symbols. (State)

M:N&O:10:3. No standard listed at this level.

M:N&O:10:4. Accurately solves problems that involve but are not limited to proportional relationships, percents, ratios, and rates. (The problems might be drawn from contexts outside of and within mathematics including those that cut across content strands or disciplines.) (State)

M:N&O:10:5. No standard at this level

M:N&O:10:6. Uses a variety of mental computation strategies to solve problems. Calculates benchmark perfect squares and related square roots. Determines any whole number percentage of a number or any multiples of 100% up to 500%. Determines benchmark fractions of a number.

M:N&O:10:7. Makes appropriate estimates in a given situation by determining the level of accuracy needed and analyzing the accuracy of results. Estimates tips, discounts, and tax and estimates the value of a non-perfect square root or cube root.

M:N&O:10:8. Applies properties of numbers to solve problems, to simplify computations, or to compare and contrast the properties of numbers and number systems.

NH.M:G&M:10. NECAP - High School - Grade Level Expectation: Geometry and Measurement.

M:G&M:10:1. No standard listed at this level.

M:G&M:10:2. Creates formal proofs of propositions (e.g. angles, lines, circles, distance, midpoint and polygons including triangle ratios).

M:G&M:10:3. No standard listed at this level.

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. (State)

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

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. (State)

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. (State)

M:G&M:10:8. No standard listed 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. (State)

M:G&M:10:10. 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, or by solving related problems.

NH.M:F&A:10. NECAP - High School - Grade Level Expectation: Functions and Algebra.

M:F&A:10:1. Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs to solve problems. (State)

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). (State)

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. (State)

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. (State)

NH.M:DSP:10. NECAP - High School - Grade Level Expectation: Data, Statistics, and Probability.

M:DSP:10:1. Interprets a given representation (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). (State)

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. (State)

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. (State)

M:DSP:10:4. Uses counting techniques to solve contextualized problems involving combinations or permutations (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, or others). (State)

M:DSP:10:5. Solves problems involving experimental or theoretical probability. (State)

M:DSP:10:6. 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.