21st Century Mathematics
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.
Using Algebraic Equations
Using Algebraic Expressions
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.
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
M.O.A1.2.3: evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.
Solving Formulas for any 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.
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
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.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Introduction to Functions
Linear Functions
Using Algebraic Equations
Using Tables, Rules and Graphs
M.O.A1.2.6: determine the slope of a line through a variety of strategies (e.g. given an equation or graph).
Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs
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.
Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs
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).
Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
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.
Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
M.O.A1.2.10: simplify and evaluate algebraic expressions
M.O.A1.2.10.a: add and subtract polynomials
Addition of Polynomials - Activity A
M.O.A1.2.10.b: multiply and divide binomials by binomials or monomials
Dividing Polynomials Using Synthetic Division
Polynomials and Linear Factors
M.O.A1.2.12: use area models and graphical representations to develop and explain appropriate methods of factoring.
Addition of Polynomials - Activity A
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
M.O.A1.2.13: simplify radical expressions
M.O.A1.2.13.a: through adding, subtracting, multiplying and dividing
Operations with Radical Expressions
Simplifying Radicals - Activity A
M.O.A1.2.13.b: exact and approximate forms
Simplifying Radicals - Activity A
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.
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Roots of a Quadratic
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.
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
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,
Point-Slope Form of a Line - Activity A
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.
Point-Slope Form of a Line - Activity A
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.
Box-and-Whisker Plots
Histograms
Populations and Samples
Scatter Plots - Activity A
Solving Using Trend Lines
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.
Biconditional Statement
Conditional Statement
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.
Biconditional Statement
Conditional Statement
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.
Biconditional Statement
Conditional Statement
Investigating Angle Theorems - Activity A
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine
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.
Investigating Angle Theorems - Activity A
M.O.G.3.7: make conjectures and justify congruence relationships with an emphasis on triangles and employ these relationships to solve problems.
Congruence in Right Triangles
Proving Triangles Congruent
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).
Perimeters and Areas of Similar Figures
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Similar Figures - Activity A
Similar Polygons
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).
Classifying Triangles
Triangle Angle Sum - Activity A
Triangle Inequalities
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.
Perimeters and Areas of Similar Figures
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
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).
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
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.
Classifying Triangles
Triangle Angle Sum - Activity A
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.
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones
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.
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Slope - Activity B
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.
Concurrent Lines, Medians, and Altitudes
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.
Dilations
Holiday Snowflake Designer
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons
Translations
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.
Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Populations and Samples
Standard Form of a Line
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.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
M.O.A2.2. 4: simplify expressions involving radicals and fractional exponents, convert between the two forms, and solve equations containing radicals and exponents.
Simplifying Radicals - Activity A
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..
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Roots of a Quadratic
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.
Addition and Subtraction of Polynomials
Introduction to Functions
Polynomials and Linear Factors
Using Algebraic Equations
Using Tables, Rules and Graphs
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.
Exponential Functions - Activity A
Functions Involving Square Roots
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Reflections of a Linear Function
Reflections of a Quadratic Function
Roots of a Quadratic
Translating and Scaling Functions
Using Tables, Rules and Graphs
M.O.A2.2.9: solve quadratic inequalities, graph their solution sets, and express solutions using interval notation.
Linear Inequalities in Two Variables - Activity A
Quadratic Inequalities - Activity A
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.
Linear Programming - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A
M.O.A2.2.11: solve practical problems involving direct, inverse and joint variation.
Determining a Spring Constant
Direct Variation
Direct and Inverse 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.
Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
M.O.A2.2.13: solve absolute value inequalities graphically, numerically and algebraically and express the solution set in interval notation.
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
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.
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
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.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
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.
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Slope - Activity B
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.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Polynomials and Linear Factors
Using Tables, Rules and Graphs
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.
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Polynomials and Linear Factors
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.
Polynomials and Linear Factors
Roots of a Quadratic
M.O.A3.2.5: solve equations with extraneous roots; explain why the extraneous roots are excluded from the solution set.
Polynomials and Linear Factors
Roots of a Quadratic
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.
Functions Involving Square Roots
Introduction to 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.
Functions Involving Square Roots
Introduction to Functions
Logarithmic Functions: Translating and Scaling
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.
Polynomials and Linear Factors
Roots of a Quadratic
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.
Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
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.
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
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.
Exponential Functions - Activity A
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
M.O.CM.2.3: solve application problems using linear, quadratic and exponential functions with emphasis on data collection and analysis.
Exponential Functions - Activity A
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
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.
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Perimeters and Areas of Similar Figures
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Similar Figures - Activity A
Similar Polygons
M.O.CM.3.2: compute measures to solve real-world problems, using relationships involving perimeter, area, surface area and volume of geometric figures.
Estimating Population Size
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area
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.
Binomial Probabilities
Permutations
Permutations and Combinations
M.O.CM.5.4: design and conduct probability investigations and then determine, analyze, and communicate the results.
Binomial Probabilities
Geometric Probability - Activity A
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.
Box-and-Whisker Plots
Histograms
Populations and Samples
Stem-and-Leaf Plots
M.O.CM.5.6: relate the measures of central tendency and the measures of dispersion to a normal distribution.
Line Plots
Mean, Median and Mode
M.O.CM.5.7: apply the measures of central tendency and the measures of dispersion to workplace situations.
Describing Data Using Statistics
Line Plots
Mean, Median and Mode
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.
Cosine Function
Sine Function
Tangent Function
Unit Circle
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.
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
M.O.T.3.1.c: compare circular functions and the trigonometric function values to draw inferences about coterminal angles and co-functions.
Cosine Function
Sine Function
Tangent Function
Unit Circle
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.
Cosine Function
Sine Function
Tangent Function
M.O.T.3.3: using various methods, basic identities and graphical representation
M.O.T.3.3.a: verify trigonometric identities
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine
M.O.T.3.3.b: prove the sum and difference to two angles, double-angles, and half-angle identities
Sum and Difference Identities for Sine and Cosine
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.
Cosine Function
Sine Function
Tangent Function
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.
Classifying Triangles
Perimeter, Circumference, and Area - Activity B
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.
Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental 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.
Histograms
Populations and Samples
M.O.PS.5.3: determine possible outcomes using tree diagrams and the counting principles of permutations and combinations.
Binomial Probabilities
Permutations
Permutations and Combinations
M.O.PS.5.4: express the chances of events occurring either in terms of a probability or odds.
Binomial Probabilities
Geometric Probability - Activity A
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.
Describing Data Using Statistics
Line Plots
Mean, Median and Mode
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.
Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
M.O.PS.5.9: analyze the role of sampling, randomness, bias, and sample size in data collection and interpretation.
Polling: Neighborhood
Populations and Samples
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.
Correlation
Solving Using Trend Lines
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.
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
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.
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Introduction to Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
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.
Dividing Exponential Expressions
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.
Using Tables, Rules and Graphs
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.
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Radical Functions
Rational Functions
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.
Circles
Ellipse - Activity A
Hyperbola - Activity A
Correlation last revised: 3/29/2010