Gizmos for Florida - Mathematics: Grades 9-12 (Benchmarks for Excellent Student Thinking Standards adopted 2020)

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

MA.912.NSO: : Number Sense and Operations

MA.912.NSO.1: : Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms.

MA.912.NSO.1.2: : Generate equivalent monomial algebraic expressions using the properties of exponents.

MA.912.NSO.1.3: : Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents. Radicands are limited to monomial algebraic expressions.

MA.912.NSO.1.4: : Apply previous understanding of operations with rational numbers to add, subtract, multiply and divide numerical radicals.

MA.912.NSO.1.5: : Add, subtract, multiply and divide algebraic expressions involving radicals. Radicands are limited to monomial algebraic expressions.

MA.912.NSO.1.6: : Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents.

MA.912.NSO.2: : Represent and perform operations with expressions within the complex number system.

MA.912.NSO.2.1: : Extend previous understanding of the real number system to include the complex number system. Add, subtract, multiply and divide complex numbers.

MA.912.NSO.2.2: : Represent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane.

MA.912.NSO.2.3: : Calculate the distance and midpoint between two numbers on the complex coordinate plane.

MA.912.NSO.2.4: : Solve mathematical and real-world problems involving complex numbers represented algebraically or on the coordinate plane.

MA.912.NSO.2.5: : Represent complex numbers on the complex plane in rectangular and polar forms. Explain why the rectangular and polar forms of a given complex number represent the same number.

MA.912.NSO.2.6: : Rewrite complex numbers to trigonometric form. Multiply complex numbers in trigonometric form.

MA.912.NSO.3: : Represent and perform operations with vectors.

MA.912.NSO.3.1: : Apply appropriate notation and symbols to represent vectors in the plane as directed line segments. Determine the magnitude and direction of a vector in component form.

MA.912.NSO.3.2: : Represent vectors in component form, linear form or trigonometric form. Rewrite vectors from one form to another.

MA.912.NSO.3.3: : Solve mathematical and real-world problems involving velocity and other quantities that can be represented by vectors.

MA.912.NSO.3.4: : Solve mathematical and real-world problems involving vectors in two dimensions using the dot product and vector projections.

MA.912.NSO.3.6: : Add and subtract vectors algebraically or graphically.

MA.912.NSO.3.7: : Given the magnitude and direction of two or more vectors, determine the magnitude and direction of their sum.

MA.912.NSO.3.8: : Multiply a vector by a scalar algebraically or graphically.

MA.912.NSO.3.9: : Compute the magnitude and direction of a vector scalar multiple.

MA.912.NSO.4: : Represent and perform operations with matrices.

MA.912.NSO.4.1: : Given a mathematical or real-world context, represent and manipulate data using matrices.

MA.912.NSO.4.2: : Given a mathematical or real-world context, represent and solve a system of two- or three-variable linear equations using matrices.

MA.912.NSO.4.3: : Solve mathematical and real-world problems involving addition, subtraction and multiplication of matrices.

MA.912.NSO.4.4: : Solve mathematical and real-world problems using the inverse and determinant of matrices.

MA.912.AR: : Algebraic Reasoning

MA.912.AR.1: : Interpret and rewrite algebraic expressions and equations in equivalent forms.

MA.912.AR.1.1: : Identify and interpret parts of an expression that represent a quantity in terms of a mathematical or real-world context, including viewing one or more of its parts as a single entity.

MA.912.AR.1.2: : Rearrange equations or formulas to isolate a quantity of interest.

MA.912.AR.1.3: : Add, subtract and multiply polynomial expressions with rational number coefficients.

MA.912.AR.1.5: : Divide polynomial expressions using long division, synthetic division and algebraic manipulation.

MA.912.AR.1.6: : Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of polynomials.

MA.912.AR.1.7: : Rewrite a polynomial expression as a product of polynomials.

MA.912.AR.2: : Write, solve and graph linear equations, functions and inequalities in one and two variables.

MA.912.AR.2.1: : Given a real-world context, write and solve one-variable multi-step linear equations.

MA.912.AR.2.2: : Write a linear two-variable equation to represent relationships between quantities from a graph, a written description or a table of values within a mathematical or real-world context.

MA.912.AR.2.3: : Write a linear two-variable equation for a line that is parallel or perpendicular to a given line and goes through a given point.

MA.912.AR.2.4: : Given a table, equation or written description of a linear function, graph that function, and determine and interpret its key features.

MA.912.AR.2.5: : Solve and graph mathematical and real-world problems that are modeled with linear functions. Interpret key features and determine domain constraints in terms of the context.

MA.912.AR.2.6: : Given a mathematical or real-world context, write and solve one-variable linear inequalities, including compound inequalities. Represent solutions algebraically or graphically.

MA.912.AR.2.7: : Write two-variable linear inequalities to represent relationships between quantities from a graph or a written description within a mathematical or real-world context.

MA.912.AR.2.8: : Given a mathematical or real-world context, graph the solution set to a two-variable linear inequality.

MA.912.AR.3: : Write, solve and graph quadratic equations, functions and inequalities in one and two variables.

MA.912.AR.3.1: : Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real number system.

MA.912.AR.3.2: : Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.

MA.912.AR.3.3: : Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically or graphically.

MA.912.AR.3.4: : Write a quadratic function to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.

MA.912.AR.3.5: : Given the x-intercepts and another point on the graph of a quadratic function, write the equation for the function.

MA.912.AR.3.6: : Given an expression or equation representing a quadratic function, determine the vertex and zeros and interpret them in terms of a real-world context.

MA.912.AR.3.7: : Given a table, equation or written description of a quadratic function, graph that function, and determine and interpret its key features.

MA.912.AR.3.8: : Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the context.

MA.912.AR.3.9: : Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written description.

MA.912.AR.3.10: : Given a mathematical or real-world context, graph the solution set to a two-variable quadratic inequality.

MA.912.AR.4: : Write, solve and graph absolute value equations, functions and inequalities in one and two variables.

MA.912.AR.4.1: : Given a mathematical or real-world context, write and solve one-variable absolute value equations.

MA.912.AR.4.2: : Given a mathematical or real-world context, write and solve one-variable absolute value inequalities. Represent solutions algebraically or graphically.

MA.912.AR.4.3: : Given a table, equation or written description of an absolute value function, graph that function and determine its key features.

MA.912.AR.4.4: : Solve and graph mathematical and real-world problems that are modeled with absolute value functions. Interpret key features and determine domain constraints in terms of the context.

MA.912.AR.5: : Write, solve and graph exponential and logarithmic equations and functions in one and two variables.

MA.912.AR.5.1: : Solve one-variable exponential equations using the properties of exponents.

MA.912.AR.5.2: : Solve equations involving one-variable logarithms or exponents. Interpret solutions as viable in terms of the context and identify any extraneous solutions.

MA.912.AR.5.3: : Given a mathematical or real-world context, classify an exponential function as representing growth or decay.

MA.912.AR.5.4: : Write an exponential function to represent a relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.

MA.912.AR.5.5: : Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents. Interpret the constant percent rate of change in terms of a real-world context.

MA.912.AR.5.6: : Given a table, equation or written description of an exponential function, graph that function and determine its key features.

MA.912.AR.5.7: : Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine domain constraints in terms of the context.

MA.912.AR.5.8: : Given a table, equation or written description of a logarithmic function, graph that function and determine its key features.

MA.912.AR.5.9: : Solve and graph mathematical and real-world problems that are modeled with logarithmic functions. Interpret key features and determine constraints in terms of the context.

MA.912.AR.6: : Solve and graph polynomial equations and functions in one and two variables.

MA.912.AR.6.1: : Given a mathematical or real-world context, when suitable factorization is possible, solve one-variable polynomial equations of degree 3 or higher over the real and complex number systems.

MA.912.AR.6.2: : Explain and apply the Remainder Theorem.

MA.912.AR.6.3: : Given a table, equation or written description of a polynomial function of degree 3 or higher, graph that function and determine its key features.

MA.912.AR.6.4: : Sketch a rough graph of a polynomial function of degree 3 or higher using zeros, multiplicity and knowledge of end behavior.

MA.912.AR.6.5: : Solve and graph mathematical and real-world problems that are modeled with polynomial functions of degree 3 or higher. Interpret key features in terms of the context.

MA.912.AR.7: : Solve and graph radical equations and functions in one and two variables.

MA.912.AR.7.1: : Solve one-variable radical equations. Interpret solutions as viable in terms of context and identify any extraneous solutions.

MA.912.AR.7.2: : Given a table, equation or written description of a square root or cube root function, graph that function and determine its key features.

MA.912.AR.7.3: : Solve and graph mathematical and real-world problems that are modeled with square root or cube root functions. Interpret key features in context.

MA.912.AR.8: : Solve and graph rational equations and functions in one and two variables.

MA.912.AR.8.1: : Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.

MA.912.AR.8.2: : Given a table, equation or written description of a rational function, graph that function and determine its key features.

MA.912.AR.8.3: : Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features in terms of the context.

MA.912.AR.9: : Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.

MA.912.AR.9.1: : Given a mathematical or real-world context, write and solve a system of two-variable linear equations algebraically or graphically.

MA.912.AR.9.4: : Graph the solution set of a system of two-variable linear inequalities.

MA.912.AR.9.5: : Given a real-world context, represent constraints as systems of linear equations or inequalities. Interpret solutions to problems as viable or nonviable options.

MA.912.AR.9.7: : Solve real-world problems involving linear programming.

MA.912.AR.9.9: : Graph and solve mathematical and real-world problems that are modeled with piecewise functions. Interpret key features and determine constraints in terms of the context.

MA.912.AR.10: : Write and solve sequence and series equations, functions and inequalities in one and two variables.

MA.912.AR.10.1: : Given a mathematical or real-world context, write and solve problems involving arithmetic sequences.

MA.912.AR.10.2: : Given a mathematical or real-world context, write and solve problems involving geometric sequences.

MA.912.AR.10.5: : Given a mathematical or real-world context, write a sequence using function notation, defined explicitly or recursively, to represent relationships between quantities from a written description.

MA.912.AR.10.6: : Given a mathematical or real-world context, find the domain of a given sequence defined recursively or explicitly.

MA.912.F: : Functions

MA.912.F.1: : Understand, compare and analyze properties of functions.

MA.912.F.1.1: : Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.

MA.912.F.1.2: : Given a function represented in function notation, evaluate the function for an input in its domain. For a real-world context, interpret the output.

MA.912.F.1.3: : Calculate and interpret the average rate of change of a real-world situation represented graphically, algebraically or in a table over a specified interval.

MA.912.F.1.4: : Demonstrate understanding of the concept of limit and estimate limits from graphs and tables of values, as related to the concept of the derivative of a function.

MA.912.F.1.5: : Compare key features of linear and nonlinear functions each represented in the same way, such as algebraically, graphically, in tables or written descriptions.

MA.912.F.1.6: : Compare key features of two functions each represented in a different way such as algebraically, graphically, in tables or written descriptions.

MA.912.F.1.7: : Determine whether a linear, quadratic or exponential function best models a given real-world situation.

MA.912.F.1.8: : Determine whether a function is even, odd or neither when represented algebraically, graphically or in a table.

MA.912.F.2: : Identify and describe the effects of transformations on functions. Create new functions given transformations.

MA.912.F.2.1: : Identify the effect on the graph or table of a given function after replacing f(x) by f(x) + k, kf(x) and f(x + k) for specific values of k.

MA.912.F.2.2: : Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.

MA.912.F.2.3: : Given the graph or table of f(x) and the graph or table of f(x) + k, kf(x), f(kx) and f(x + k), state the type of transformation and find the value of the real number k.

MA.912.F.2.4: : Given the graph or table of values of two or more transformations of a function, state the type of transformation and find the values of the real number that defines the transformation.

MA.912.F.2.5: : Given two or more transformations and a function, create the table or graph of the transformed function.

MA.912.F.2.6: : Given a graph or table of values of two or more transformations of a function, write the equation of the transformed function.

MA.912.F.3: : Create new functions from existing functions.

MA.912.F.3.1: : Given a mathematical or real-world context, combine two functions, limited to linear and quadratic, using arithmetic operations. When appropriate, include domain restrictions for the new function.

MA.912.F.3.2: : Given a mathematical or real-world context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations. When appropriate, include domain restrictions for the new function.

MA.912.F.3.3: : Solve mathematical and real-world problems involving functions that have been combined using arithmetic operations.

MA.912.F.3.6: : Determine whether an inverse function exists by analyzing tables, graphs and equations.

MA.912.F.3.7: : Represent the inverse of a function algebraically, graphically or in a table. Use composition of functions to verify that one function is the inverse of the other.

MA.912.F.3.9: : Solve mathematical and real-world problems involving inverse functions.

MA.912.FL: : Financial Literacy

MA.912.FL.1: : Determine simple and compound interest and demonstrate its relationship to functions. Calculate and use net present and net future values.

MA.912.FL.1.1: : Compare simple, compound and continuously compounded interest over time.

MA.912.FL.1.2: : Solve problems involving simple, compound and continuously compounded interest, including determining the present value and future value of money.

MA.912.FL.1.4: : Explain the relationship between compound interest and exponential growth and the relationship between continuously compounded interest and exponential growth.

MA.912.FL.1.6: : Solve problems involving potential profit and actual cost.

MA.912.FL.2: : Describe the advantages and disadvantages of short-term and long-term purchases.

MA.912.FL.2.2: : Calculate the finance charges and total amount due on a bill using various forms of credit.

MA.912.FL.2.7: : Solve problems involving student, personal and car loans, including finding the total amount to be paid, adjustable rates and refinancing options.

MA.912.FL.2.12: : Compare interest rate calculations and annual percentage rate calculations, and distinguish between the two rates.

MA.912.GR: : Geometric Reasoning

MA.912.GR.1: : Prove and apply geometric theorems to solve problems.

MA.912.GR.1.1: : Prove relationships and theorems about lines and angles. Solve mathematical and real-world problems involving postulates, relationships and theorems of lines and angles.

MA.912.GR.1.2: : Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.

MA.912.GR.1.3: : Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.

MA.912.GR.1.4: : Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelograms.

MA.912.GR.1.5: : Prove relationships and theorems about trapezoids. Solve mathematical and real-world problems involving postulates, relationships and theorems of trapezoids.

MA.912.GR.1.6: : Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.

MA.912.GR.2: : Apply properties of transformations to describe congruence or similarity.

MA.912.GR.2.1: : Given a preimage and image, describe the transformation and represent the transformation algebraically using coordinates.

MA.912.GR.2.2: : Identify transformations that do or do not preserve distance.

MA.912.GR.2.3: : Specify a sequence of transformations that will map a given figure onto itself or onto another congruent or similar figure.

MA.912.GR.2.5: : Apply rigid transformations to map one figure onto another to justify that the two figures are congruent.

MA.912.GR.2.6: : Justify the criteria for triangle congruence using the definition of congruence in terms of rigid transformations.

MA.912.GR.2.7: : Apply an appropriate transformation to map one figure onto another to justify that the two figures are similar.

MA.912.GR.2.8: : Justify the criteria for triangle similarity using the definition of similarity in terms of non-rigid transformations.

MA.912.GR.3: : Use coordinate geometry to solve problems or prove relationships.

MA.912.GR.3.1: : Given a mathematical or real-world context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.

MA.912.GR.3.2: : Solve geometric problems involving circles, triangles and quadrilaterals on the coordinate plane.

MA.912.GR.3.3: : Solve mathematical and real-world problems on the coordinate plane that involve finding the coordinates of a point on a line segment including the midpoint.

MA.912.GR.3.4: : Solve mathematical and real-world problems on the coordinate plane involving perimeter or area of polygons.

MA.912.GR.4: : Use geometric measurement and dimensions to solve problems.

MA.912.GR.4.1: : Identify the shapes of two-dimensional cross-sections of three-dimensional figures.

MA.912.GR.4.2: : Identify three-dimensional objects generated by rotations of two-dimensional figures.

MA.912.GR.4.3: : Determine how changes in dimensions affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.

MA.912.GR.4.4: : Solve mathematical and real-world problems involving the area of two-dimensional figures.

MA.912.GR.4.5: : Solve mathematical and real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.

MA.912.GR.4.6: : Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.

MA.912.GR.5: : Make formal geometric constructions with a variety of tools and methods.

MA.912.GR.5.1: : Construct a copy of a segment or an angle.

MA.912.GR.5.2: : Construct the bisector of a segment or an angle, including the perpendicular bisector of a line segment.

MA.912.GR.6: : Use properties and theorems related to circles.

MA.912.GR.6.1: : Solve mathematical and real-world problems involving the length of a secant, tangent, segment or chord in a given circle.

MA.912.GR.6.2: : Solve mathematical and real-world problems involving the measures of arcs and related angles, limited to central, inscribed and intersections of a chord, secants or tangents.

MA.912.GR.6.3: : Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.

MA.912.GR.6.4: : Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.

MA.912.GR.6.5: : Apply transformations to prove that all circles are similar.

MA.912.GR.7: : Apply geometric and algebraic representations of conic sections.

MA.912.GR.7.1: : Identify the conic resulting from the cross-section of cones.

MA.912.GR.7.2: : Given a mathematical or real-world context, derive and create the equation of a circle using key features.

MA.912.GR.7.3: : Graph and solve mathematical and real-world problems that are modeled with an equation of a circle. Determine and interpret key features in terms of the context.

MA.912.GR.7.4: : Given a mathematical or real-world context, derive and create the equation of a parabola using key features.

MA.912.GR.7.5: : Graph and solve mathematical and real-world problems that are modeled with an equation of a parabola. Determine and interpret key features in terms of the context.

MA.912.GR.7.6: : Given a mathematical or real-world context, derive and create the equation of an ellipse using key features.

MA.912.GR.7.7: : Graph and solve mathematical and real-world problems that are modeled with an equation of an ellipse. Determine and interpret key features in terms of the context.

MA.912.GR.7.8: : Given a mathematical or real-world context, derive and create the equation of a hyperbola using key features.

MA.912.GR.7.9: : Graph and solve mathematical and real-world problems that are modeled with an equation of a hyperbola. Determine and interpret key features in terms of the context.

MA.912.T: : Trigonometry

MA.912.T.1: : Define and use trigonometric ratios, identities or functions to solve problems.

MA.912.T.1.1: : Define trigonometric ratios for acute angles in right triangles.

MA.912.T.1.2: : Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.

MA.912.T.1.5: : Prove Pythagorean Identities. Apply Pythagorean Identities to calculate trigonometric ratios and to solve problems.

MA.912.T.1.6: : Prove the Double-Angle, Half-Angle, Angle Sum and Difference formulas for sine, cosine, and tangent. Apply these formulas to solve problems.

MA.912.T.1.7: : Simplify expressions using trigonometric identities.

MA.912.T.1.8: : Solve trigonometric equations within a mathematical or real-world context, applying inverse functions and using technology when appropriate.

MA.912.T.2: : Extend trigonometric functions to the unit circle.

MA.912.T.2.1: : Define the trigonometric functions for any angle using right triangles drawn in the unit circle. Determine the values of sine, cosine and tangent of pi/3, pi/4 and pi/6 and their multiples using special triangles.

MA.912.T.2.2: : Define and determine the sine, cosine, tangent, cosecant, secant and cotangent of angles using the unit circle.

MA.912.T.2.3: : Given angles measured in radians or degrees, calculate the values of the six trigonometric functions.

MA.912.T.3: : Graph and apply trigonometric relations and functions.

MA.912.T.3.1: : Describe and demonstrate the connections between right triangle ratios and trigonometric functions.

MA.912.T.3.2: : On the coordinate plane, express the values of sine, cosine and tangent for pi – x, pi + x and 2pi – x in terms of their values for x, where x is any real number.

MA.912.T.3.3: : Given a mathematical or real-world context, choose sine, cosine or tangent trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift and midline.

MA.912.T.3.4: : Given a table, equation or written description of a trigonometric function, graph that function and determine key features.

MA.912.T.3.5: : Graph and solve mathematical and real-world problems that are modeled with trigonometric functions. Interpret key features and determine domain constraints in terms of the context.

MA.912.T.3.7: : Solve mathematical and real-world problems involving applications of trigonometric functions using graphing technology when appropriate.

MA.912.T.4: : Extend rectangular coordinates and equations to polar and parametric forms.

MA.912.T.4.1: : Define polar coordinates and relate polar coordinates to Cartesian coordinates with and without the use of technology.

MA.912.DP: : Data Analysis and Probability

MA.912.DP.1: : Summarize, represent and interpret categorical and numerical data with one and two variables.

MA.912.DP.1.1: : Given a set of data, select an appropriate method to represent the data, depending on whether it is numerical or categorical data and on whether it is univariate or bivariate.

MA.912.DP.1.2: : Interpret data distributions represented in various ways. State whether the data is numerical or categorical, whether it is univariate or bivariate and interpret the different components and quantities in the display.

MA.912.DP.1.3: : Explain the difference between correlation and causation in the contexts of both numerical and categorical data.

MA.912.DP.1.4: : Estimate a population total, mean or percentage using data from a sample survey; develop a margin of error through the use of simulation.

MA.912.DP.1.5: : Interpret the margin of error of a mean or percentage from a data set. Interpret the confidence level corresponding to the margin of error.

MA.912.DP.2: : Solve problems involving univariate and bivariate numerical data.

MA.912.DP.2.1: : For two or more sets of numerical univariate data, calculate and compare the appropriate measures of center and measures of variability, accounting for possible effects of outliers. Interpret any notable features of the shape of the data distribution.

MA.912.DP.2.2: : 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 technology, empirical rules or tables to estimate areas under the normal curve.

MA.912.DP.2.3: : Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and y-intercept of the model. Use the model to solve real-world problems in terms of the context of the data.

MA.912.DP.2.4: : Given a scatter plot that represents bivariate numerical data, assess the fit of a given linear function by plotting and analyzing residuals.

MA.912.DP.2.5: : Given a scatter plot with a line of fit and residuals, determine the strength and direction of the correlation. Interpret strength and direction within a real-world context.

MA.912.DP.2.6: : Compute the correlation coefficient of a linear model using technology. Interpret the strength and direction of the correlation coefficient.

MA.912.DP.3: : Solve problems involving categorical data.

MA.912.DP.3.5: : Solve real-world problems involving univariate and bivariate categorical data.

MA.912.DP.4: : Use and interpret independence and probability.

MA.912.DP.4.2: : Determine if events A and B are independent by calculating the product of their probabilities.

MA.912.DP.4.3: : Calculate the conditional probability of two events and interpret the result in terms of its context.

MA.912.DP.4.4: : Interpret the independence of two events using conditional probability.

MA.912.DP.4.6: : Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

MA.912.DP.4.8: : Apply the general multiplication rule for probability, taking into consideration whether the events are independent, and interpret the result in terms of the context.

MA.912.DP.4.9: : Given a mathematical or real-world situation, calculate the appropriate permutation or combination.

MA.912.DP.4.10: : Compute probabilities of compound events. Solve mathematical and real-world problems using permutations and combinations.

MA.912.DP.5: : Determine methods of data collection and make inferences from collected data.

MA.912.DP.5.1: : Distinguish between a population parameter and a sample statistic.

MA.912.DP.5.2: : Explain how random sampling produces data that is representative of a population.

MA.912.DP.5.3: : Compare and contrast sampling methods.

MA.912.DP.5.4: : Generate multiple samples or simulated samples of the same size to measure the variation in estimates or predictions.

MA.912.DP.5.6: : Determine the appropriate design, survey, experiment or observational study, based on the purpose. Articulate the types of questions appropriate for each type of design.

MA.912.DP.5.7: : Compare and contrast surveys, experiments and observational studies.

MA.912.DP.5.8: : Explain how randomization relates to sample surveys, experiments and observational studies.

MA.912.DP.5.9: : Draw inferences about two populations using data and statistical analysis from two random samples.

MA.912.DP.5.10: : Compare two treatments from an experiment using data from a randomized experiment.

MA.912.DP.5.11: : Determine whether differences between parameters are significant using simulations.

MA.912.DP.5.12: : Evaluate reports based on data from diverse media, print and digital resources by interpreting graphs and tables; evaluating data-based arguments; determining whether a valid sampling method was used; or interpreting provided statistics.

MA.912.DP.6: : Use probability distributions to solve problems.

MA.912.DP.6.2: : Develop a probability distribution for a discrete random variable using theoretical probabilities. Find the expected value and interpret it as the mean of the discrete distribution.

MA.912.DP.6.3: : Develop a probability distribution for a discrete random variable using empirically assigned probabilities. Find the expected value and interpret it as the mean of the discrete distribution.

MA.912.DP.6.4: : Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Evaluate and compare strategies on the basis of the calculated expected values.

MA.912.DP.6.5: : Apply probabilities to make decisions which are equally likely, such as drawing from lots or using a random number generator.

MA.912.DP.6.6: : Analyze decisions that were made and solve problems using probability concepts and strategies.

MA.912.LT: : Logic and Theory

MA.912.LT.1: : Apply recursive methods to solve problems.

MA.912.LT.1.1: : Apply recursive and iterative thinking to solve problems.

MA.912.LT.1.2: : Solve problems and find explicit formulas for recurrence relations using finite differences.

MA.912.LT.4: : Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.

MA.912.LT.4.3: : Identify and accurately interpret “if…then,” “if and only if,” “all” and “not” statements. Find the converse, inverse and contrapositive of a statement.

MA.912.C: : Calculus

MA.912.C.1: : Determine limits and continuity.

MA.912.C.1.11: : Identify the types of discontinuities for a given function.

MA.912.C.2: : Determine derivatives.

MA.912.C.2.1: : Apply and interpret derivatives geometrically and numerically.

MA.912.C.2.2: : Interpret the derivative as an instantaneous rate of change or as the slope of the tangent line.

MA.912.C.2.10: : Find second derivatives and derivatives of higher order.

MA.912.C.3: : Apply derivatives.

MA.912.C.3.1: : Find the slope of a curve at a point, including points at which there are vertical tangent lines and no tangent lines.

MA.912.C.3.3: : Determine where a function is decreasing and increasing using its derivative.

MA.912.C.3.4: : Find local and absolute maximum and minimum points of a function.

MA.912.C.3.5: : Determine the concavity and points of inflection of a function using its second derivative.

MA.912.C.3.6: : Sketch graphs by using first and second derivatives. Compare the corresponding characteristics of the graphs of f, f prime and f double prime.

MA.912.C.3.8: : Find average and instantaneous rates of change. Explain the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed and acceleration.

MA.912.C.4: : Determine integrals.

MA.912.C.4.1: : Find approximate values of integrals by using rectangle approximations.

MA.912.C.4.2: : Calculate the values of Riemann sums over equal subdivisions using left, right and midpoint evaluation points.

Correlation last revised: 9/16/2020

Florida - Mathematics: Grades 9-12

Benchmarks for Excellent Student Thinking Standards | Adopted: 2020