Manchester Academic Standards for Mathematics 9-12 by Category 5-30-14.docx

Manchester Academic Standards for Mathematics 9-12

(updated 5-30-14)

The Manchester Academic Standards for Mathematics in Grades 9-12 are organized into six categories to align with competencies: Numbers and Operations; Algebraic Expressions; Equations and Inequalities; Functions; Data, Statistics, and Probability; and Geometry. Standards with (+) are designated as mathematics that students should learn in order to take advanced mathematics courses such as calculus or advanced statistics.

Sources from among the following: Common Core State Standards (© Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.); Massachusetts Mathematics Curriculum Framework (November 2000); Pennsylvania Common Core Standards for Mathematics (2013); K-12 Mathematics New Hampshire Curriculum Framework (2006); Content and Performance Standards for Alaska Students (2006); Indiana Academic Standards (2011).

Category: Numbers and Operations | References | |

Competency Numbers and Operations (NO): Students will demonstrate the ability to use properties of the complex number system and to reason quantitatively when analyzing, representing, and solving problems. | NHDOE Mathematics Competencies | |

MAS:M:HS:NO:1 | Use the definition of rational exponents and properties of exponents to rewrite and evaluate expressions involving radicals and rational exponents. | CCSS:N-RN.1 CCSS:N-RN.2 |

MAS:M:HS:NO:2 | Use properties of rational and irrational numbers to perform arithmetic operations on irrational numbers. | CCSS:N-RN.3 |

MAS:M:HS:NO:3 | Choose appropriate units for scales in graphs, data displays, and formulas. | CCSS:N-Q.1,2 |

MAS:M:HS:NO:4 | Interpret the units used in graphs, data displays, and formulas. | CCSS:N-Q.1 |

MAS:M:HS:NO:5 | Choose an appropriate level of accuracy in measurements. | CCSS:N-Q.3 |

MAS:M:HS:NO:6 | Use the definition and apply the properties of complex numbers to perform arithmetic operations; (+) use conjugates to find quotients of complex numbers. | CCSS:N-CN.1,2,3 (cluster) |

MAS:M:HS:NO:7 | (+) Convert between polar and rectangular coordinates, and equations. | CCSS:N-CN.4,5 |

MAS:M:HS:NO:8 | (+) Graph equations in the polar coordinate plane. | CCSS:N-CN.4,5 |

MAS:M:HS:NO:9 | (+) Find products, quotients, powers, and roots of complex numbers in polar form. | CCSS:N-CN.4,5 |

MAS:M:HS:NO:10 | (+) Use and apply the algebraic and geometric properties of vectors to perform operations and solve problems. | CCSS:N-VM:1-5 |

MAS:M:HS:NO:11 | (+) Use matrices to represent and organize data. | CCSS:N-VM:6 |

MAS:M:HS:NO:12 | (+) Use and apply the properties of matrices to perform operations and solve problems. | CCSS:N-VM:6-10 (cluster) |

Category: Algebraic Expressions | References | |

Competency Algebraic Expressions (AE): Students will demonstrate the ability to simplify, evaluate, and solve problems using algebraic expressions. | MSD Mathematics Competencies | |

MAS:M:HS:AE:1 | Interpret the structure of an expression such as terms, factors, and coefficients. | CCSS:A-SSE.1 |

MAS:M:HS:AE:2 | Use properties of algebra to rewrite and factor expressions in order to solve problems | CCSS:A-SSE.2,3 CCSS:A-APR.4 CCSS:A-APR.6 |

MAS:M:HS:AE:3 | Perform arithmetic operations on polynomial expressions. | CCSS:A-APR.1 |

MAS:M:HS:AE:4 | (+) rewrite and factor expressions containing complex numbers | CCSS:N-CN.8 |

MAS:M:HS:AE:5 | (+) Perform arithmetic operations on rational expressions. | CCSS:A-APR.7 |

MAS:M:HS:AE:6 | (+) Write and find the coefficients of specified terms in binomial expansions | CCSS:A-APR.5 |

Category: Equations and Inequalities | References | |

Competency Equations and Inequalities (EQ): Students will demonstrate the ability to solve equations and inequalities, algebraically and graphically; and to create and use algebraic models to solve problems. | MSD Mathematics Competencies | |

MAS:M:HS:EQ:1 | Explain each step in solving an equation citing properties of equality | CCSS:A-REI.1 |

MAS:M:HS:EQ:2 | Solve linear equations and inequalities in one variable | CCSS:A-REI.3 |

MAS:M:HS:EQ:3 | Rearrange formulas and literal equations to solve for a specified variable | CCSS:A-CED.4 |

MAS:M:HS:EQ:4 | Solve quadratic equations, with real or complex solutions, and inequalities in one variable. | CCSS:N-CN:7 CCSS:A-REI.4 |

MAS:M:HS:EQ:5 | Solve equations and inequalities involving absolute value expressions. | CCSS:A-REI.3 CCSS:A-REI.4 |

MAS:M:HS:EQ:6 | Solve systems of equations in two variables, algebraically and graphically; (+) use matrices to solve systems of equations. | CCSS:A-REI.5,6 CCSS:A-REI.8,9 |

MAS:M:HS:EQ:7 | Solve a system consisting of a linear equation and a quadratic equation, algebraically and graphically. | CCSS:A-REI.7 |

MAS:M:HS:EQ:8 | Write and graph an equation in two variables. | CCSS:A-REI.10 |

MAS:M:HS:EQ:9 | Graph a linear inequality in two variables. | CCSS:A-REI.12 |

MAS:M:HS:EQ:10 | Solve rational equations in one variable. | CCSS:A-REI.2 |

MAS:M:HS:EQ:11 | Solve radical equations in one variable. | CCSS:A-REI.2 |

MAS:M:HS:EQ:12 | Model a real-world situation by writing and solving an equation or inequality in one variable | CCSS:A-CED.1 |

MAS:M:HS:EQ:13 | Model a real-world situation by writing and solving an equation or inequality in two or more variables | CCSS:A-CED.2 |

MAS:M:HS:EQ:14 | Model a real-world situation by writing and solving a system of equations or inequalities in two or more variables | CCSS:A-CED.3 |

MAS:M:HS:EQ:15 | Derive the formulas for the sums of arithmetic and geometric series, and use the formulas to solve problems. | CCSS:A-SSE.4 CCSS:A-CED.4 |

Category: Functions | References | |

Competency Functions and Relations (FR): Students will demonstrate the ability to identify, represent, interpret, analyze, and use functions and relations to solve problems. | MSD Mathematics Competencies | |

MAS:M:HS:FR:1 | Identify a function using the definition. | CCSS:F-IF.1 |

MAS:M:HS:FR:2 | Use function notation, evaluate functions, and interpret statements that use function notation in terms of a context. | CCSS:F-IF.2 |

MAS:M:HS:FR:3 | Recognize that sequences are functions. | CCSS:F-IF.3 |

MAS:M:HS:FR:4 | Interpret key features of functions modeled in graphs and tables | CCSS:F-IF.4 |

MAS:M:HS:FR:5 | Sketch graphs of functions, displaying key features, given a description of a relationship. | CCSS:F-IF.4 |

MAS:M:HS:FR:6 | Define the domain and the range of a given function. | CCSS:F-IF.5 |

MAS:M:HS:FR:7 | Calculate and interpret the average rate of change of a function, presented algebraically, graphically, or numerically over a specified interval. | CCSS:F-IF.6 |

MAS:M:HS:FR:8 | Graph linear, quadratic, polynomial, (+) rational, square root, cube root, exponential, logarithmic, piecewise-defined, step, and absolute value functions showing key features of each graph to include intercepts, maxima, minima, zeros, asymptotes, and end behavior. | CCSS:F-IF.7 |

MAS:M:HS:FR:9 | Write a function defined by an expression in equivalent forms to show and explain the relationship between zeros, roots, and factors of polynomials. | CCSS:F-IF.8 CCSS:A-APR.2,3 CCSS:N-CN:9 |

MAS:M:HS:FR:10 | Analyze and compare functions algebraically, graphically, and numerically to find key features | CCSS:F-IF.8,9 |

MAS:M:HS:FR:11 | Write a function rule that describes a relationship between two quantities. | CCSS:F-BF.1 |

MAS:M:HS:FR:12 | Define and use arithmetic and geometric sequences, both recursively and explicitly, to model situations and translate between the two forms. | CCSS:F-BF.2 CCSS:F-IF.3 |

MAS:M:HS:FR:13 | Interpret the effects of transformations on functions. | CCSS:F-BF.3 |

MAS:M:HS:FR:14 | Find and graph the inverse of an invertible function | CCSS:F-BF.4 |

MAS:M:HS:FR:15 | (+) Verify by composition that one function is the inverse of another | CCSS:F-BF.4 |

MAS:M:HS:FR:16 | (+) Create an invertible function from a non-invertible function by restricting the domain | CCSS:F-BF.4 |

MAS:M:HS:FR:17 | (+) Use inverse relationships of exponents and logarithms to solve equations and problems | CCSS:F-BF.5 |

MAS:M:HS:FR:18 | Construct and compare linear, quadratic, and exponential models and solve problems while interpreting the parameters in terms of the context | CCSS:F-LE.1,2,3,4,5 (cluster) |

Competency Trigonometric Functions (TF): Students will demonstrate the ability to identify, represent, interpret, analyze, and use trigonometric functions to solve problems. | MSD Mathematics Competencies | |

MAS:M:HS:TF:1 | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | CCSS:F-TF.1 |

MAS:M:HS:TF:2 | Use the unit circle to evaluate trigonometric functions. | CCSS:F-TF.2 |

MAS:M:HS:TF:3 | Use special triangles to determine the values of sine, cosine, and tangent. | CCSS:F-TF.3 |

MAS:M:HS:TF:4 | Use the unit circle to explain symmetry and periodicity of trigonometric functions. | CCSS:F-TF.4 |

MAS:M:HS:TF:5 | Use trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. | CCSS:F-TF.5 |

MAS:M:HS:TF:6 | (+) Find inverses of trigonometric functions by restricting domains when necessary. | CCSS:F-TF.6 |

MAS:M:HS:TF:7 | (+) Use inverse trigonometric functions to solve equations and problems. | CCSS:F-TF.7 |

MAS:M:HS:TF:8 | Prove the Pythagorean identity and use it to solve problems. | CCSS:F-TF.8 |

MAS:M:HS:TF:9 | (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. | CCSS:F-TF.9 |

Category: Data, Statistics, and Probability | References | |

Competency Data and Statistics (DS): Students will demonstrate the ability to apply statistical methods or reasoning to summarize, represent, interpret, and justify conclusions using categorical and quantitative data. | ||

MAS:M:HS:DS:1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). | CCSS:S-ID.1 |

MAS:M:HS:DS:2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | CCSS:S-ID.2 |

MAS:M:HS:DS:3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | CCSS:S-ID.3 |

MAS:M:HS:DS:4 | Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | CCSS:S-ID.4 |

MAS:M:HS:DS:5 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | CCSS:S-ID.6 |

MAS:M:HS:DS:6 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | CCSS:S-ID.7 |

MAS:M:HS:DS:7 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | CCSS:S-ID.8 |

MAS:M:HS:DS:8 | Distinguish between correlation and causation. | CCSS:S-ID.9 |

MAS:M:HS:DS:9 | Make inferences and justify conclusions from sample surveys, experiments, and observational studies. | CCSS:S-IC.1-6 (cluster) |

Competency Probability (PR): Students will demonstrate the ability to apply the rules of probability to determine the likelihood of a given outcome. | ||

MAS:M:HS:PR:1 | Use independence and conditional probability to interpret data. | CCSS:S-CP:1-5 (cluster) |

MAS:M:HS:PR:2 | Use the rules of probability to compute probabilities of compound events in a uniform probability model. | CCSS:S-CP:6,7 |

MAS:M:HS:PR:3 | (+) Apply the general multiplication rule in a uniform probability model and interpret the answer in terms of the model | CCSS:S-CP:8 |

MAS:M:HS:PR:4 | (+) Use combinations and permutations to compute probabilities and solve problems | CCSS:S-CP:9 |

MAS:M:HS:PR:5 | (+) Calculate expected values and use them to solve problems. | CCSS:S-MD:1-4 (cluster) |

MAS:M:HS:PR:6 | (+) Use probability to evaluate outcomes of decisions. | CCSS:S-MD:5-7 (cluster) |

Category: Geometry | References | |

Competency Congruence (GC): Students will demonstrate the ability to use reasoning to construct and apply viable arguments about congruence. | NHDOE Mathematics Competencies | |

MAS:M:HS:GC:1 | Know precise definitions of angle, polygons, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | CCSS:G-CO:1 |

MAS:M:HS:GC:2 | Use geometric terms, definitions, diagrams, and properties to identify relationships involving congruence between geometric figures. | CCSS:G-CO:6,7,8 |

MAS:M:HS:GC:3 | Prove theorems about line segments, angles, congruent triangles, and parallelograms. | CCSS:G-CO:9,10,11 |

MAS:M:HS:GC:4 | Apply theorems about congruence to prove relationships in geometric figures and solve problems. | CCSS:G-MG:3 CCSS:G.SRT.5 CCSS:G.CO.7,8 |

MAS:M:HS:GC:5 | Use a variety of tools to construct geometric figures while applying the properties of congruence | CCSS:G-CO:12,13 |

Competency Similarity (GS): Students will demonstrate the ability to use reasoning to construct and apply viable arguments about similarity. | NHDOE Mathematics Competencies | |

MAS:M:HS:GS:1 | Use geometric terms, definitions, diagrams, and properties to identify relationships involving similarity between geometric figures. | CCSS:G-SRT:1,2,3 |

MAS:M:HS:GS:2 | Prove theorems about similar triangles. | CCSS:G-SRT:4 |

MAS:M:HS:GS:3 | Apply theorems about similarity to prove relationships in geometric figures and solve problems. | CCSS:G.SRT.5 CCSS:G-MG:3 |

MAS:M:HS:GS:4 | Use the Pythagorean Theorem and apply trigonometric ratios to solve problems involving right triangles. | CCSS:G.SRT:6,7,8 (cluster) |

MAS:M:HS:GS:5 | (+) Apply the formula to find the area of a triangle | CCSS:G.SRT.9 |

MAS:M:HS:GS:6 | (+) Prove and apply the Law of Sines and the Law of Cosines | CCSS:G.SRT.10,11 |

Competency Circles (GCL): Students will demonstrate the ability to reason with and apply theorems about circles. | NHDOE Mathematics Competencies | |

MAS:M:HS:GCL:1 | Use geometric terms, definitions, diagrams and properties to identify relationships involving circles. | CCSS:G-C-2 |

MAS:M:HS:GCL:2 | Prove theorems about circles. | CCSS: G-C-3 |

MAS:M:HS:GCL:2 | Apply theorems about circles to solve problems. | CCSS:G-C:1,2 |

MAS:M:HS:GCL:3 | Use a variety of tools to construct geometric figures while applying the properties of circles | CCSS:GC:3,4 |

Competency Coordinate Geometry (CG): Students will demonstrate the ability to apply algebraic models to express geometric relationships. | NHDOE Mathematics Competencies | |

MAS:M:HS:CG:1 | Use coordinate geometry to calculate distance, midpoint, and slope | CCSS:GPE:4,6,7 |

MAS:M:HS:CG:2 | Apply coordinate geometry to prove and identify geometric relationships algebraically; and solve problems | CCSS:GPE:4,5 |

MAS:M:HS:CG:3 | Use geometric figures and their properties to represent transformations in the plane | CCSS:G-CO:2,3,4,5 |

MAS:M:HS:CG:4 | Translate between the geometric descriptions and the equations for circles and parabolas | CCSS:G-GPE:1,2 (cluster) |

MAS:M:HS:CG:5 | (+)Translate between the geometric descriptions and the equations for ellipses and hyperbolas | CCSS:G-GPE:3 (cluster) |

Competency Measurement (GM): Students will demonstrate the ability to explain, apply, and model geometric measurement formulas. | NHDOE Mathematics Competencies | |

MAS:M:HS:GM:1 | Use geometric terms, definitions, diagrams, and properties to identify two or three-dimensional geometric figures. | CCSS:G-GMD:1 |

MAS:M:HS:GM:2 | Calculate perimeter, circumference, and area of two-dimensional geometric figures to solve problems | CCSS:G-GMD:1 CCSS:G-GC-5 CCSS:G-MG-3 |

MAS:M:HS:GM:3 | Calculate surface area and volume of three-dimensional geometric figures to solve problems | CCSS:G-GMD:3 CCSS:G-MG-3 |

MAS:M:HS:GM:4 | Identify the shapes of two-dimensional cross sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects | CCSS:G-GMD:4 |