MA 11.1.1.c Use drawings, words, and symbols to explain the effects of operations such as multiplication and division on the magnitude of quantities in the real number system, including powers and roots (e.g., if you take the square root of a number, will the result always be smaller than the original number?).
MA 11.1.2 Students will compute with real and complex numbers.
MA 11.1.2.a Compute with subsets of the complex number system, including imaginary, rational, irrational, integers, whole, and natural numbers.
MA 11.1.2.b Simplify expressions with rational exponents.
MA 11.1.2.c Select, apply, and explain the method of computation when problem solving using real numbers (e.g., models, mental computation, paper-pencil, or technology).
MA 11.1.2.d Use estimation methods to check the reasonableness of real number computations and decide if the problem calls for an approximation (including appropriate rounding) or an exact number.
MA 11.2 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
MA 11.2.1 Students will demonstrate, represent, and show relationships with functions.
MA 11.2.1.a Define a function and use function notation.
MA 11.2.1.b Analyze a relation to determine if it is a function given graphs, tables, or algebraic notation.
MA 11.2.1.c Classify a function given graphs, tables, or algebraic notation, as linear, quadratic, or neither.
MA 11.2.1.d Identify domain and range of functions represented in either algebraic or graphical form.
MA 11.2.1.e Analyze and graph linear functions and inequalities (point-slope form, slope-intercept form, standard form, intercepts, rate of change, parallel and perpendicular lines, vertical and horizontal lines, and inequalities).
MA 11.2.1.f Analyze and graph absolute value functions (finding the vertex, symmetry, transformations, determine intercepts, and minimums or maximums using the piecewise definition).
MA 11.2.1.g Analyze and graph quadratic functions (standard form, vertex form, finding zeros, symmetry, transformations, determine intercepts, and minimums or maximums).
MA 11.2.1.h Represent, interpret, and analyze inverses of functions algebraically and graphically.
MA 11.2.2 Students will apply the operational properties when evaluating rational expressions, and solving linear and quadratic equations, and inequalities.
MA 11.2.2.a Convert equivalent rates (e.g., miles per hour to feet per second).
MA 11.2.2.b Identify and explain the properties used in solving equations and inequalities.
MA 11.2.2.c Simplify algebraic expressions involving integer and fractional exponents.
MA 11.2.2.d Perform operations on rational expressions (add, subtract, multiply, divide, and simplify).
MA 11.2.2.e Evaluate expressions at specified values of their variables (polynomial, rational, radical, and absolute value).
MA 11.2.2.f Solve an equation involving several variables for one variable in terms of the others.
MA 11.2.2.g Solve linear and absolute value equations and inequalities.
MA 11.2.2.h Analyze and solve systems of two linear equations and inequalities in two variables algebraically and graphically.
MA 11.2.2.i Perform operations (addition subtraction, multiplication, and division) on polynomials.
MA 11.2.2.j Factor polynomials to include factoring out monomial terms and factoring quadratic expressions.
MA 11.2.2 k. Recognize polynomial multiplication patterns and their related factoring patterns (e.g., (a + b)² = a² + 2ab + b², a² – b² = (a + b) (a - b)).
MA 11.2.2.l Make the connection between the factors of a polynomial and the zeros of a polynomial.
MA 11.2.2.m Combine functions by composition and perform operations (addition, subtraction, multiplication, division) on functions.
MA 11.2.2.n Solve quadratic equations involving real coefficients and real or imaginary roots.
MA 11.2.3 Students will solve real-world problems involving linear equations and inequalities, systems of linear equations, quadratic, exponential, square root, and absolute value functions.
MA 11.2.3.a Analyze, model, and solve real-world problems using various representations (graphs, tables, linear equations and inequalities, systems of linear equations, quadratic, exponential, square root, and absolute value functions).
MA 11.3 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
MA 11.3.1 Students will identify and describe geometric characteristics and create two- and three-dimensional shapes.
MA 11.3.1.a Know and use precise definitions of ray, line segment, angle, perpendicular lines, parallel lines, and congruence based on the undefined terms of geometry: point, line and plane.
MA 11.3.1.b Prove geometric theorems about angles, triangles, congruent triangles, similar triangles, parallel lines with transversals, and quadrilaterals using deductive reasoning.
MA 11.3.1.c Apply geometric properties to solve problems involving similar triangles, congruent triangles, quadrilaterals, and other polygons.
MA 11.3.1.d Identify and apply right triangle relationships including sine, cosine, tangent, special right triangles, and the converse of the Pythagorean Theorem.
MA 11.3.1.e Create geometric models to visualize, describe, and solve problems using similar triangles, right triangles, and trigonometry.
MA 11.3.1.f Know and use precise definitions and terminology of circles, including central angle, inscribed angle, arc, intercepted arc, chord, secant, and tangent.
MA 11.3.1.g Apply the properties of central angles, inscribed angles, angles formed by intersecting chords, and angles formed by secants and/or tangents to find the measures of angles related to the circle.
MA 11.3.1.h Sketch, draw, and construct appropriate representations of geometric objects using a variety of tools and methods which may include ruler/straight edge, protractor, compass, reflective devices, paper folding, or dynamic geometric software.
MA 11.3.2 Students will determine location, orientation, and relationships on the coordinate plane.
MA 11.3.2.a Derive and apply the midpoint formula.
MA 11.3.2.b Use coordinate geometry to analyze linear relationships to determine if lines are parallel or perpendicular.
MA 11.3.2.c Given a line, write the equation of a line that is parallel or perpendicular to it.
MA 11.3.2.d Derive and apply the distance formula.
MA 11.3.2.e Use coordinate geometry to prove triangles are right, acute, obtuse, isosceles, equilateral, or scalene.
MA 11.3.2.f Use coordinate geometry to prove quadrilaterals are trapezoids, isosceles trapezoids, parallelograms, rectangles, rhombi, kites, or squares.
MA 11.3.2.g Perform and describe positions and orientation of shapes under a single translation using algebraic notation on a coordinate plane.
MA 11.3.2.h Perform and describe positions and orientation of shapes under a rotation about the origin in multiples of 90 degrees using algebraic notation on a coordinate plane.
MA 11.3.2.i Perform and describe positions and orientation of shapes under a reflection across a line using algebraic notation on a coordinate plane.
MA 11.3.2.j Perform and describe positions and orientation of shapes under a single dilation on a coordinate plane.
MA 11.3.2.k Derive the equation of a circle given the radius and the center.
MA 11.3.3 Students will perform and compare measurements and apply formulas.
MA 11.3.3.a Convert between various units of length, area, and volume (e.g., such as square feet to square yards).
MA 11.3.3.b Convert between metric and standard units of measurement.
MA 11.3.3.c Apply the effect of a scale factor to determine the length, area, and volume of similar two- and three-dimensional shapes and solids.
MA 11.3.3.d Find arc length and area of sectors of a circle.
MA 11.3.3.e Determine surface area and volume of spheres, cones, pyramids, and prisms using formulas and appropriate units.
MA 11.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
MA 11.4.1 Students will create displays that represent data.
No additional indicator(s) at this level. Mastery is expected at previous grade levels.
MA 11.4.2 Students will analyze data to address the situation.
MA 11.4.2.a Identify and compute measures of central tendency (mean, median, mode) when provided data both with and without technology.
MA 11.4.2.b Explain how transformations of data, including outliers, affect measures of central tendency.
MA 11.4.2.c Compare data sets and formulate conclusions.
MA 11.4.2.d Support conclusions with valid arguments.
MA 11.4.2.e Develop linear equations for linear models to predict unobserved outcomes using the regression line and correlation coefficient with technology.
MA 11.4.2.f Describe the shape, identify any outliers, and determine the spread of a data set.
MA 11.4.2.g Explain the impact of sampling methods, bias, and the phrasing of questions asked during data collection, and the conclusions that can rightfully be made.
MA 11.4.2.h Explain the differences between a randomized experiment and observational studies.
MA 11.4.2.i Using scatter plots, analyze patterns and describe relationships in paired data.
MA 11.4.2.j Recognize when arguments based on data confuse correlation with causation.
MA 11.4.2.k Interpret data represented by the normal distribution, formulate conclusions, and recognize that some data sets are not normally distributed.
MA 11.4.3 Students will interpret and apply concepts of probability.
MA 11.4.3.a Construct sample spaces and probability distributions.
MA 11.4.3.b Use appropriate counting techniques to determine the probability of an event.
MA 11.4.3.c Determine if events are mutually exclusive and calculate their probabilities in either case.
MA 12.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
MA.12.1.1 Students will demonstrate, represent, and show relationships among the complex numbers.
MA 12.1.1.a (AT) Graph complex numbers on the complex plane.
MA 12.1.1.b (AT) Determine the magnitude of complex numbers.
MA 12.1.1.c (AT) Use matrices to represent and manipulate data.
MA 12.1.1.d (AT) Recognize the role that additive and multiplicative identities play in matrix operations.
MA 12.1.1.e (AT) Recognize that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
MA 12.1.1.f (AT) Derive and use the formulas for the general term and summation of finite arithmetic and geometric series.
MA 12.1.2 Students will compute with matrices.
MA 12.1.2.a (AT) Multiply matrices by scalars to produce new matrices.
MA 12.1.2.b (AT) Add, subtract, and multiply matrices of appropriate dimensions.
MA 12.2 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
MA 12.2.1 Students will demonstrate, represent, and show relationships with non-linear and trigonometric functions.
MA 12.2.1.a (AT) Analyze and graph non-linear functions (e.g., quadratic, trigonometric, square root, logarithmic, rational, higher-order polynomials, exponential, absolute value, piecewise, and sinusoidal).
MA 12.2.1.b (AT) Use the unit circle to define the trigonometric functions on all real numbers.
MA 12.2.1.c (AT) Evaluate sine, cosine, and tangent functions at positive and negative multiples of 30, and 45 degrees.
MA 12.2.1.d (AT) Create new functions out of existing functions using addition, subtraction, multiplication, division, translation, dilation, and composition.
MA 12.2.1.e (AT) Use limits to describe the behavior of a function near its asymptotes and removable discontinuities.
MA 12.2.1.f (AT) Understand that the radian measure of an angle is the length of the arc on the unit circle subtended by that angle.
MA 12.2.1.g (AT) Convert between radian and degree measures of an angle.
MA 12.2.2 Students will apply the identities when evaluating and solving trigonometric equations.
MA 12.2.2.a (AT) Use trigonometric identities to solve trigonometric equations.
MA 12.2.2.b (AT) Explain symmetry (odd and even) and periodicity of trigonometric functions.
MA 12.2.2.c (AT) Create an invertible function from a non-invertible function by restricting the domain (e.g.,arcsin, arccos, and arctan).
MA 12.2.2.d (AT) Find the period, amplitude, and midline of a trigonometric function of the form y=A + Bsin (Cx), where A, B, and C are parameters, and identify these properties on a graph of the function.
MA 12.2.3 Students will solve real-world problems involving trigonometric functions.
MA 12.2.3.a (AT) Model periodic events with specified amplitude, frequency, and shifts.
MA 12.2.3.b (AT) Solve real-world problems using trigonometric and inverse trigonometric functions.
MA 12.3 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
MA 12.3.1 Students will identify and describe geometric characteristics and create two- and three-dimensional shapes.
MA 12.3.1.a (AT) Apply the Law of Sines and the Law of Cosines to find unknown measures in triangles.
MA 12.3.1.b (AT) Prove and apply properties of lengths of chords, secant segments, and tangent segments.
MA 12.3.2 Students will determine location, orientation, and relationships on the coordinate plane.
MA 12.3.2.a (AT) Identify features of a function (e.g., local and global maxima and minima, concavity, approximate locations of points of inflection and vertical and horizontal asymptotes) from its graph.
MA 12.3.2.b (AT) Identify symmetry properties of a function (e.g., axis of symmetry of a parabola) and know the connection between its symmetry properties and specific transformations.
MA 12.3.2.c (AT) Recognize that vector quantities have both magnitude and direction and can be represented by directed line segments.
MA 12.3.2.d (AT) Add and subtract vectors graphically and algebraically.
MA 12.3.2.e (AT) Perform scalar multiplication of a vector and show it graphically.
MA 12.3.2.f (AT) Derive the equations of parabolas, ellipses, and hyperbolas from a graph or given parameters.
MA 12.3.2.g (AT) Determine the three-dimensional object created by rotating or revolving a two-dimensional object about an axis.
MA 12.3.2.h (AT) Determine the shape of a two-dimensional cross-section of a three-dimensional object.
MA 12.3.3 Students will perform and compare measurements and apply formulas.
MA 12.3.3.a (AT) Use Cavalieri's Principle to determine the volume of a sphere and other solid figures.
MA 12.3.3.b (AT) Determine the tolerance interval and percent of error in measurement.
MA 12.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.
MA 12.4.1 Representations: Students will create displays that represent data.
No additional indicator(s) at this level. Mastery is expected at previous grade levels.
MA 12.4.2 Analysis & Applications: Students will analyze data to address the situation.
MA 12.4.2.a (AT) Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
MA 12.4.3 Probability: Students will interpret and apply concepts of probability.
MA 12.4.3.a (AT) Calculate the expected value of a random variable and interpret it as the mean of a probability distribution.
MA 12.4.3.b (AT) Determine possible outcomes of a decision by assigning probabilities to outcome values and finding expected values.
MA 12.4.3.c (AT) Evaluate and compare strategies on the basis of expected values.
MA 12.4.3.d (AT) Analyze decisions and strategies using probability concepts (e.g., medical testing and product testing).