M.O.A1.2: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts.

M.O.A1.2.1: formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems.

M.O.A1.2.2: create and solve multi-step linear equations, absolute value equations, and linear inequalities in one variable, (with and without technology); apply skills toward solving practical problems such as distance, mixtures or motion and judge the reasonableness of solutions.

M.O.A1.2.3: evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.

M.O.A1.2.4: develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents.

M.O.A1.2.5: analyze a given set of data and prove the existence of a pattern numerically, algebraically and graphically, write equations from the patterns and make inferences and predictions based on observing the pattern.

M.O.A1.2.6: determine the slope of a line through a variety of strategies (e.g. given an equation or graph).

M.O.A1.2.7: analyze situations and solve problems by determining the equation of a line given a graph of a line, two points on the line, the slope and a point, or the slope and y intercept.

M.O.A1.2.8: identify a real life situation that involves a constant rate of change; pose a question; make a hypothesis as to the answer; develop, justify, and implement a method to collect, organize, and analyze related data; extend the nature of collected, discrete data to that of a continuous linear function that describes the known data set; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using the predictive and analytic tools of algebra (with and without technology).

M.O.A1.2.9: create and solve systems of linear equations graphically and numerically using the elimination method and the substitution method, given a real-world situation.

M.O.A1.2.10: simplify and evaluate algebraic expressions

M.O.A1.2.10.b: multiply and divide binomials by binomials or monomials

M.O.A1.2.12: use area models and graphical representations to develop and explain appropriate methods of factoring.

M.O.A1.2.13.a: through adding, subtracting, multiplying and dividing

M.O.A1.2.13.b: exact and approximate forms

M.O.A1.2.14: choose the most efficient method to solve quadratic equations by graphing (with and without technology), factoring quadratic formula and draw reasonable conclusions about a situation being modeled.

M.O.A1.2.15: describe real life situations involving exponential growth and decay equations including y=2 to the x power and y=(½) to the x power; compare the equation with attributes of an associated table and graph to demonstrate an understanding of their interrelationship.

M.O.A1.2.17: perform a linear regression (with and without technology),

M.O.A1.2.17.b: identify the equation for the line of regression,

M.O.A1.2.17.c: examine the correlation coefficient to determine how well the line fits the data

M.O.A1.2.17.d: use the equation to predict specific values of a variable.

M.O.A1.2.18: compute and interpret the expected value of random variables in simple cases using simulations and rules of probability (with and without technology).

M.O.A1.2.19: gather data to create histograms, box plots, scatter plots and normal distribution curves and use them to draw and support conclusions about the data.

M.O.A1.2.20: design experiments to model and solve problems using the concepts of sample space and probability distribution.

M.O.G.3: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

M.O.G.3.2: differentiate and apply inductive and deductive reasoning, justify conclusions in real-world settings.

M.O.G.3.3: use the basic concepts of symbolic logic including identifying the converse, inverse, and contrapositive of a conditional statement and test the validity of conclusions with methods that include Venn Diagrams.

M.O.G.3.4: validate conclusions by constructing logical arguments using both formal and informal methods with direct and indirect reasoning.

M.O.G.3.5: construct formal and informal proofs by applying definitions, theorems, and postulates related to such topics as complementary, supplementary, vertical angles, angles formed by perpendicular lines, and justify the steps.

M.O.G.3.6: compare and contrast the relationships between angles formed by two lines cut by a transversal when lines are parallel and when they are not parallel, and use the results to develop concepts that will justify parallelism.

M.O.G.3.7: make conjectures and justify congruence relationships with an emphasis on triangles and employ these relationships to solve problems.

M.O.G.3.8: identify general properties of and compare and contrast the properties of convex and concave quadrilaterals

M.O.G.3.8.a: parallelograms

M.O.G.3.8.b: rectangles

M.O.G.3.9: identify a real life situation that involves similarity in two or three dimensions; pose a question; make a hypothesis as to the answer, develop, justify, and implement a method to collect, organize, and analyze related data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using the predictive and analytic tools of algebra and geometry (with and without technology).

M.O.G.3.10: investigate measures of angles and lengths of segments to determine the existence of a triangle (triangle inequality) and to establish the relationship between the measures of the angles and the length of the sides (with and without technology).

M.O.G.3.11: verify and justify the basis for the trigonometric ratios by applying properties of similar triangles and use the results to find inaccessible heights and distances. Using the ratios of similar triangles to find unknown side lengths and angle measures, construct a physical model that illustrates the use of a scale drawing in a real-world situation.

M.O.G.3.12: apply the Pythagorean Theorem and its converse to solve real-world problems and derive the special right triangle relationships (i.e. 30-60-90, 45-45-90).

M.O.G.3.13: investigate measures of angles formed by chords, tangents, and secants of a circle and draw conclusions for the relationship to its arcs.

M.O.G.3.14: find angle measures of interior and exterior angles; given a polygon, find the length of sides from given data; and use properties of regular polygons to find any unknown measurements of sides or angles.

M.O.G.3.16: derive and justify formulas for area, perimeter, surface area, and volume using nets and apply them to solve real-world problems.

M.O.G.3.17: apply concepts of analytical geometry such as formulas for distance, slope, and midpoint and apply these to finding dimensions of polygons on the coordinate plane.

M.O.G.3.18: construct a triangle?s medians, altitudes, angle and perpendicular bisectors using various methods; and develop logical concepts about their relationships to be used in solving real-world problems.

M.O.G.3.19: create and apply concepts using transformational geometry and laws of symmetry, of a reflection, translation, rotation, glide reflection, dilation of a figure, and develop logical arguments for congruency and similarity.

M.O.A2.2: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts.

M.O.A2.2.1: determine equations of lines including parallel, perpendicular, vertical and horizontal lines, and compare and contrast the properties of these equations.

M.O.A2.2.2: factor higher order polynomials by applying various methods including factoring by grouping and the sum and difference of two cubes; analyze and describe the relationship between the factored form and the graphical representation.

M.O.A2.2. 4: simplify expressions involving radicals and fractional exponents, convert between the two forms, and solve equations containing radicals and exponents.

M.O.A2.2. 5: solve quadratic equations over the set of complex numbers: apply the techniques of factoring, completing the square, and the quadratic formula; use the discriminate to determine the number and nature of the roots; identify the maxima and minima; use words, graphs, tables, and equations to generate and analyze solutions to practical problems..

M.O.A2.2.7: define a function and find its zeros; express the domain and range using interval notation; find the inverse of a function; find the value of a function for a given element in its domain; and perform basic operations on functions including composition of functions.

M.O.A2.2.8: analyze families of functions and their transformations; recognize linear, quadratic, radical, absolute value, step, piece-wise, and exponential functions; analyze connections among words, graphs, tables and equations when solving practical problems with and without technology.

M.O.A2.2.9: solve quadratic inequalities, graph their solution sets, and express solutions using interval notation.

M.O.A2.2.10: solve and graph the solution set of systems of linear inequalities in two variables by finding the maximum or minimum values of a function over the feasible region using linear programming techniques.

M.O.A2.2.11: solve practical problems involving direct, inverse and joint variation.

M.O.A2.2.12: analyze the conic sections; identify and sketch the graphs of a parabola, circle, ellipse, and hyperbola and convert between graphs and equations.

M.O.A2.2.13: solve absolute value inequalities graphically, numerically and algebraically and express the solution set in interval notation.

M.O.A2.2.14: define a logarithmic function, transform between exponential and logarithmic forms, and apply the basic properties of logarithms to simplify or expand an expression.

M.O.A2.2.16: describe and illustrate how patterns and sequences are used to develop recursive and closed form equations; analyze and describe characteristics of each form.

M.O.A3.2.1: use properties of analytic geometry to justify and use the distance and midpoint formulas and negative reciprocal criterion for nonvertical perpendicular lines.

M.O.A3.2.2: factor higher order polynomials by using techniques that can be applied to the factoring of second degree polynomials; relate factored forms of polynomials to graphs, tables, and solutions to problems in context.

M.O.A3.2.3: relate analytical attributes such as characteristics of zeros, x and y intercepts, symmetry, asymptotes, end behavior, maximum and minimum points, and domain and range, to graphical and algebraic representations of polynomials and rational functions.

M.O.A3.2.4: analyze the discriminant to classify the roots of quadratic equations with real coefficients, and relate the existence of x intercepts of the graph to information obtained from the discriminant.

M.O.A3.2.5: solve equations with extraneous roots; explain why the extraneous roots are excluded from the solution set.

M.O.A3.2.6: compare and contrast the use of interval notation, set notation, and number line representations to express the domain and range of functions.

M.O.A3.2.7: compare and contrast the domain and range of a modeling function with the restricted domain and range used in a real world situation; justify the restricted domain and range choice for a problem in context.

M.O.A3.2.8: differentiate between functions and relations; evaluate, add, subtract, multiply, divide, rationalize, simplify, and compose functions (including rational, radical and those with fractional exponents); express domain and range of functions.

M.O.A3.2.18: analyze polynomial equations with real coefficients and complex roots using factoring, the Conjugate Roots Theorem, the quadratic formula, or root restricting theorems; confirm roots using numerical and graphical methods; discuss and justify how the graph of a polynomial function gives information about complex zeros.

M.O.A3.2.20: use common and natural logarithms in the evaluation of logarithmic functions whose base is neither 10 nor e. Incorporate the change of base formula and properties of logarithms to simplify and expand algebraic expressions and to solve logarithmic and exponential equations.

M.O.A3.2.22: build on the skills of solving linear equations in two variables using elimination, substitution, or matrix methods to solve systems with three or more unknowns involving real world applications. Categorize systems of equations as zero, one, or infinitely many solutions, by both geometric and algebraic methods.

M.O.CM.2: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts.

M.O.CM.2.2: interpret graphs of functions including linear, quadratic, and exponential.

M.O.CM.2.3: solve application problems using linear, quadratic and exponential functions with emphasis on data collection and analysis.

M.O.CM.2.5: describe and illustrate how calculating costs, simple and compound interest, finance charge, loan payment and tax functions are used to solve real-world problems.

M.O.CM.3: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

M.O.CM.3.1: apply concepts of geometry including the Pythagorean Theorem, similar triangles, and right triangle trigonometry.

M.O.CM.3.2: compute measures to solve real-world problems, using relationships involving perimeter, area, surface area and volume of geometric figures.

M.O.CM.3.3: analyze the connections of various geometric shapes and patterns to art, architecture, and nature.

M.O.CM.5: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them, select and use appropriate statistical methods to analyze data, develop and evaluate inferences and predictions that are based on models, and apply and demonstrate an understanding of basic concepts of probability.

M.O.CM.5.2: integrate other disciplines into the study of mathematics through simulations, research, and projects.

M.O.CM.5.3: determine possible outcomes using tree diagrams and the counting principles of permutations and combinations, develop conclusions and offer solutions for new situations, using real-world data.

M.O.CM.5.4: design and conduct probability investigations and then determine, analyze, and communicate the results.

M.O.CM.5.5: collect and interpret data using various methods of displaying numerical data, including frequency distributions, graphs, histograms, stem-and-leaf plots, and box-and-whiskers plots, using technology when appropriate.

M.O.CM.5.6: relate the measures of central tendency and the measures of dispersion to a normal distribution.

M.O.CM.5.7: apply the measures of central tendency and the measures of dispersion to workplace situations.

M.O.CM.5.8: use statistical tools for workplace applications such as quality control, marketing and predicting trends.

M.O.T.3: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

M.O.T.3.1: apply the right triangle definition of the six trigonometric functions of an angle to determine the values of the function values of an angle in standard position given a point on the terminal side of the angle.

M.O.T.3.1.a: determine the value of the other trigonometric functions given the value of one of the trigonometric functions and verify these values with technology.

M.O.T.3.1.b: using geometric principles and the Pythagorean Theorem, determine the six function values for the special angles and the quadrantal angles and use them in real-world problems.

M.O.T.3.1.c: compare circular functions and the trigonometric function values to draw inferences about coterminal angles and co-functions.

M.O.T.3.2: convert angle measures from degrees to radians (and vice versa) and apply this concept to

M.O.T.3.2.a: create a data set, analyze, and formulate a hypotheses to test and develop formulas for the arclength, area of a sector, and angular velocity and use the formula for application in the real-world.

M.O.T.3.3: using various methods, basic identities and graphical representation

M.O.T.3.3.a: verify trigonometric identities

M.O.T.3.3.b: prove the sum and difference to two angles, double-angles, and half-angle identities

M.O.T.3.6: identify a real life problem utilizing graphs of trigonometric functions and/or the inverse functions; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project using words, graphs, drawings, models, or tables.

M.O.T.3.8: investigate real-world problems within a project based investigation involving triangles using the trigonometric functions, the law of sines and the law of cosines, justify and present results.

M.O.T.3.9: develop and test a hypothesis to find the area of a triangle given the measures of two sides and the included angle or the measures of three sides (Heron's formula) and use these formulas to find total area of figures constructed of multiple shapes.

M.O.T.3.10: express complex numbers in polar form:

M.O.T.3.10.a: perform operations including adding, subtracting, multiplying, and dividing;

M.O.T.3.11: create graphical and algebraic representations for performing vector operations and analyze these to solve real-world problems such as force analysis and navigation.

M.O.PS.5: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them, select and use appropriate statistical methods to analyze data, develop and evaluate inferences and predictions that are based on models, and apply and demonstrate an understanding of basic concepts of probability.

M.O.PS.5.1: distinguish between experimental and theoretical probability.

M.O.PS.5.2: using a real-world problem solving investigation, create and interpret data using various methods of displaying circle graphs, histograms, and frequency curves, make predictions, include information concerning outliers, present and justify results.

M.O.PS.5.3: determine possible outcomes using tree diagrams and the counting principles of permutations and combinations.

M.O.PS.5.4: express the chances of events occurring either in terms of a probability or odds.

M.O.PS.5.5: use the normal distribution and the binomial distribution including Pascal's triangle, to determine probability of events.

M.O.PS.5.6: analyze measures of central tendency (mean, median, and mode) from data presented in a variety of forms such as charts, tables, and graphs or from data created through experimentation.

M.O.PS.5.7: interpret and calculate measures of dispersions (range and standard deviation) from data presented in a variety of forms such as charts, tables and graphs or from data created through experimentation.

M.O.PS.5.9: analyze the role of sampling, randomness, bias, and sample size in data collection and interpretation.

M.O.PS.5.11: determine the correlation values for given data or for data generated by students and use the results to describe the association of the variables within the given data. Identify whether this association is systematic or predictable.

M.O.PC.2: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations, and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts.

M.O.PC.2.1: investigate and sketch the graphs of polynomials and rational functions by analyzing and using the characteristics of zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes and end behavior, maximum and minimum points, and domain and range.

M.O.PC.2.4: establish and explain the inverse relationship between exponential and logarithmic functions; graph related functions and include their domain and range using interval notation.

M.O.PC.2.5: compare laws of exponents to properties of logarithms; solve equations and practical problems involving exponential and logarithmic expressions, including natural and common logarithms; confirm solutions graphically and numerically.

M.O.PC.2.7: use tables of values, graphs, conjectures, algebraic methods, and numerical substitution to find or estimate the limit of a function, a sequence or a series.

M.O.PC.2.8: analyze and describe the geometry of vectors, perform mathematical operations with vectors and use vectors to solve practical problems.

M.O.PC.2.11: use multiple representations, such as words, graphs, tables, and equations, to solve practical problems involving logarithmic, exponential, polynomial, rational, and radical functions; explain how the representations are related to each other, as well as to the problem.

M.O.PC.3: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

M.O.PC.3.2: analyze and describe properties of conic sections; explain the interrelationship among the properties; solve practical problems involving conic sections.

Correlation last revised: 3/29/2010

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.