#### EA.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

EA.1.3: Apply algebraic methods to solve problems in real-world contexts.

EA.1.5: Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

#### EA.2: The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.

EA.2.1: Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers).

EA.2.2: Apply the laws of exponents and roots to solve problems.

EA.2.3: Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation.

EA.2.4: Use dimensional analysis to convert units of measure within a system.

EA.2.5: Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions.

EA.2.7: Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.

EA.2.8: Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).

EA.2.9: Carry out a procedure to perform operations with matrices (including addition, subtraction, and scalar multiplication).

#### EA.3: The student will demonstrate through the mathematical processes an understanding of relationships and functions.

EA.3.1: Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph.

EA.3.3: Carry out a procedure to evaluate a function for a given element in the domain.

EA.3.5: Carry out a procedure to graph parent functions (including y = x, y = x², y = the square root of x, y = the absolute value of x, and y = 1/x).

EA.3.6: Classify a variation as either direct or inverse.

EA.3.7: Carry out a procedure to solve literal equations for a specified variable.

EA.3.8: Apply proportional reasoning to solve problems.

#### EA.4: The student will demonstrate through the mathematical processes an understanding of the procedures for writing and solving linear equations and inequalities.

EA.4.1: Carry out a procedure to write an equation of a line with a given slope and a y-intercept.

EA.4.2: Carry out a procedure to write an equation of a line with a given slope passing through a given point.

EA.4.3: Carry out a procedure to write an equation of a line passing through two given points.

EA.4.4: Use a procedure to write an equation of a trend line from a given scatterplot.

EA.4.5: Analyze a scatterplot to make predictions.

EA.4.6: Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard).

EA.4.7: Carry out procedures to solve linear equations for one variable algebraically.

EA.4.8: Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution.

EA.4.9: Carry out a procedure to solve systems of two linear equations graphically.

EA.4.10: Carry out a procedure to solve systems of two linear equations algebraically.

#### EA.5: The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.

EA.5.1: Carry out a procedure to graph a line when given the equation of the line.

EA.5.2: Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b.

EA.5.3: Carry out a procedure to graph the line with a given slope and a y-intercept.

EA.5.4: Carry out a procedure to graph the line with a given slope passing through a given point.

EA.5.6: Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally.

EA.5.7: Apply the concept of slope as a rate of change to solve problems.

EA.5.11: Analyze given information to write a system of linear equations that models a given problem situation.

EA.5.12: Analyze given information to write a linear inequality in one variable that models a given problem situation.

#### EA.6: The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

EA.6.1: Analyze the effects of changing the leading coefficient a on the graph of y = ax².

EA.6.2: Analyze the effects of changing the constant c on the graph of y = x² + c.

EA.6.3: Analyze the graph of a quadratic function to determine its equation.

EA.6.4: Carry out a procedure to solve quadratic equations by factoring.

#### IA.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

IA.1.3: Apply algebraic methods to solve problems in real-world contexts.

IA.1.5: Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

#### IA.2: The student will demonstrate through the mathematical processes an understanding of functions, systems of equations, and systems of linear inequalities.

IA.2.2: Carry out a procedure to solve a system of linear inequalities graphically.

IA.2.3: Analyze a problem situation to determine a system of linear inequalities that models the problem situation.

IA.2.4: Use linear programming to solve contextual problems involving a system of linear inequalities.

IA.2.7: Carry out a procedure to graph translations of parent functions (including y = x, y = x², y = square root of x, y = absolute value of x, and y = 1/x).

IA.2.8: Carry out a procedure to graph transformations of parent functions (including y = x, y = x², and y = absolute value of x).

IA.2.9: Carry out a procedure to graph discontinuous functions (including piecewise and step functions).

IA.2.11: Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function).

#### IA.3: The student will demonstrate through the mathematical processes an understanding of quadratic equations and the complex number system.

IA.3.1: Carry out a procedure to simplify expressions involving powers of i.

IA.3.2: Carry out a procedure to perform operations with complex numbers (including addition, subtraction, multiplication, and division).

IA.3.3: Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula).

IA.3.4: Use the discriminant to determine the number and type of solutions of a quadratic equation.

IA.3.5: Analyze given information (including quadratic models) to solve contextual problems.

IA.3.6: Carry out a procedure to write an equation of a quadratic function when given its roots.

#### IA.4: The student will demonstrate through the mathematical processes an understanding of algebraic expressions and nonlinear functions.

IA.4.1: Carry out a procedure to perform operations (including multiplication, exponentiation, and division) with polynomial expressions.

IA.4.2: Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions.

IA.4.9: Carry out a procedure to solve radical equations algebraically.

IA.4.13: Carry out a procedure to graph logarithmic functions.

IA.4.14: Carry out a procedure to graph exponential functions.

#### IA.5: The student will demonstrate through the mathematical processes an understanding of conic sections.

IA.5.1: Carry out a procedure to graph the circle whose equation is the form x² + y² = r².

IA.5.2: Carry out a procedure to write an equation of a circle centered at the origin when given its radius.

IA.5.3: Carry out a procedure to graph the ellipse whose equation is the form (x²/a²) + (y²/b²) = 1.

IA.5.4: Carry out a procedure to write an equation of an ellipse centered at the origin when given information from among length of major axis, length of minor axis, and vertices.

IA.5.5: Carry out a procedure to graph the hyperbola whose equation is the form (x²/a²) - (y²/b²) = 1.

IA.5.6: Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices.

IA.5.7: Match the equation of a conic section with its graph.

#### IA.6: The student will demonstrate through the mathematical processes an understanding of sequences and series.

IA.6.1: Categorize a sequence as arithmetic, geometric, or neither.

IA.6.2: Carry out a procedure to write a specified term of an arithmetic or geometric sequence when given the nth term of the sequence.

IA.6.3: Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four consecutive terms of the sequence.

IA.6.4: Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four terms of the sequence.

IA.6.7: Carry out a procedure to determine consecutive terms of a sequence that is defined recursively.

IA.6.8: Carry out a procedure to define a sequence recursively when given four or more consecutive terms of the sequence.

IA.6.9: Translate between the explicit form and the recursive form of sequences.

#### G.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

G.1.3: Apply basic rules of logic to determine the validity of the converse, inverse, and contrapositive of a conditional statement.

G.1.10: Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing devices).

#### G.2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

G.2.2: Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems.

G.2.3: Use the congruence of line segments and angles to solve problems.

G.2.5: Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line).

G.2.6: Use scale factors to solve problems involving scale drawings and models.

G.2.7: Use geometric probability to solve problems.

#### G.3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

G.3.1: Carry out a procedure to compute the perimeter of a triangle.

G.3.2: Carry out a procedure to compute the area of a triangle.

G.3.4: Apply properties of isosceles and equilateral triangles to solve problems.

G.3.5: Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems.

G.3.6: Apply the triangle sum theorem to solve problems.

G.3.7: Apply the triangle inequality theorem to solve problems.

G.3.8: Apply congruence and similarity relationships among triangles to solve problems.

G.3.9: Apply theorems to prove that triangles are either similar or congruent.

G.3.10: Use the Pythagorean theorem and its converse to solve problems.

G.3.11: Use the properties of 45-45-90 and 30-60-90 triangles to solve problems.

G.3.12: Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles.

#### G.4: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them.

G.4.1: Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures.

G.4.2: Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures.

G.4.3: Apply procedures to compute measures of interior and exterior angles of polygons.

G.4.4: Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons.

G.4.5: Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems.

G.4.6: Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems.

#### G.5: The student will demonstrate through the mathematical processes an understanding of the properties of circles, the lines that intersect them, and the use of their special segments.

G.5.1: Carry out a procedure to compute the circumference of circles.

G.5.2: Carry out a procedure to compute the area of circles.

G.5.4: Carry out a procedure to compute the length of an arc or the area of a sector of a circle.

G.5.5: Apply the properties of the component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems.

G.5.7: Apply the properties of central angles, inscribed angles, and arcs of circles to solve problems.

#### G.6: The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors.

G.6.1: Use the distance formula to solve problems.

G.6.2: Use the midpoint formula to solve problems.

G.6.3: Apply transformations-translation, reflection, rotation, and dilation-to figures in the coordinate plane by using sketches and coordinates.

G.6.4: Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices.

G.6.5: Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method.

G.6.6: Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement.

G.6.8: Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement.

#### G.7: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects.

G.7.1: Carry out a procedure to compute the surface area of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, and hemispheres).

G.7.2: Carry out a procedure to compute the volume of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, hemispheres, and composite objects).

G.7.4: Apply congruence and similarity relationships among geometric objects to solve problems.

G.7.5: Apply a procedure to draw a top view, front view, and side view of a three-dimensional object.

G.7.6: Apply a procedure to draw an isometric view of a three-dimensional object.

#### PC.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

PC.1.1: Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.

PC.1.5: Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

PC.1.6: Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.

PC.1.7: Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

#### PC.2: The student will demonstrate through the mathematical processes an understanding of the characteristics and behaviors of functions and the effect of operations on functions.

PC.2.1: Carry out a procedure to graph parent functions (including y = x to the nth power, y = log base a of x, y = ln x, y = 1/x, y = e to the x power, y = a to the x power, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC.2.2: Carry out a procedure to graph transformations (including -f(x), a * f(x), f(x) + d, f(x - c), f(-x), f(b * x), |f(x)|, and f(|x|)) of parent functions and combinations of transformations.

PC.2.3: Analyze a graph to describe the transformation (including -f(x), a * f(x), f(x) + d, f(x - c), f(-x), f(b * x), |f(x)|, and f(|x|)) of parent functions.

PC.2.4: Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y = x to the nth power, y = log base a of x, y = ln x, y = 1/x, y = e to the x power, y = a to the x power, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC.2.5: Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = x to the nth power, y = log base a of x, y = ln x, y = 1/x, y = e to the x power, y = a to the x power, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC.2.7: Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function.

PC.2.8: Carry out a procedure to determine whether the inverse of a function exists.

#### PC.3: The student will demonstrate through the mathematical processes an understanding of the behaviors of polynomial and rational functions.

PC.3.1: Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.

PC.3.3: Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.

PC.3.4: Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

PC.3.5: Analyze given information to write a polynomial function that models a given problem situation.

#### PC.4: The student will demonstrate through the mathematical processes an understanding of the behaviors of exponential and logarithmic functions.

PC.4.1: Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior.

PC.4.2: Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior.

PC.4.3: Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

PC.4.4: Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).

PC.4.6: Analyze given information to write an exponential function that models a given problem situation.

PC.4.8: Carry out a procedure to solve exponential equations algebraically.

PC.4.9: Carry out a procedure to solve exponential equations graphically.

#### PC.5: The student will demonstrate through the mathematical processes an understanding of the behaviors of trigonometric functions.

PC.5.1: Understand how angles are measured in either degrees or radians.

PC.5.2: Carry out a procedure to convert between degree and radian measures.

PC.5.4: Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

PC.5.14: Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.

#### PC.6: The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically.

PC.6.1: Carry out a procedure to graph the circle whose equation is the form (x-h)² + (y-k)² = r².

PC.6.2: Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.

PC.6.4: Carry out a procedure to graph the ellipse whose equation is the form (((x-h)²)/a²) + (((y-k)²)/b²) = 1.

PC.6.5: Carry out a procedure to graph the hyperbola whose equation is the form (((x-h)²)/a²) - (((y-k)²)/b²) = 1.

PC.6.6: Carry out a procedure to graph the parabola whose equation is the form y-k = a(x-h)².

#### DA.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

DA.1.1: Execute procedures to conduct simple probability experiments and collect data by using manipulatives (including spinners, dice, cards, and coins).

DA.1.2: Execute procedures to find measures of probability and statistics by using tools such as handheld computing devices, spreadsheets, and statistical software.

DA.1.4: Design and conduct a statistical research project and produce a report that summarizes the findings.

DA.1.5: Apply the principles of probability and statistics to solve problems in real-world contexts.

DA.1.6: Communicate a knowledge of data analysis and probability by using mathematical terminology appropriately.

#### DA.2: The student will demonstrate through the mathematical processes an understanding of the design of a statistical study.

DA.2.1: Classify a data-collection procedure as a survey, an observational study, or a controlled experiment.

DA.2.2: Compare various random sampling techniques (including simple, stratified, cluster, and systematic).

DA.2.3: Analyze a data-collection procedure to classify the technique used as either simple cluster, systematic, or convenience sampling.

DA.2.5: Judge which of two or more possible experimental designs will best answer a given research question.

DA.2.6: Generate a research question and design a statistical study to answer a given research question.

#### DA.3: The student will demonstrate through the mathematical processes an understanding of the methodology for collecting, organizing, displaying, and interpreting data.

DA.3.1: Use manipulatives, random number tables, and technology to collect data and conduct experiments and simulations.

DA.3.2: Organize and interpret data by using pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots.

DA.3.3: Select appropriate graphic display(s) from among pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots when given a data set or problem situation.

DA.3.4: Represent frequency distributions by using displays such as categorical frequency distributions/Pareto charts, histograms, frequency polygons, and cumulative frequency distributions/ogives.

DA.3.6: Classify graphically and analytically the correlation between two variables as either positive, negative, or zero.

DA.3.7: Carry out a procedure to determine an equation of a trend line for a scatterplot exhibiting a linear pattern by using visual approximation.

DA.3.8: Carry out a procedure using technology to determine a line of best fit for a scatterplot exhibiting a linear pattern.

DA.3.9: Explain the meaning of the correlation coefficient r.

#### DA.4: The student will demonstrate through the mathematical processes an understanding of basic statistical methods of analyzing data.

DA.4.4: Use procedures and/or technology to find measures of central tendency (mean, median, and mode) for given data.

DA.4.6: Use procedures and/or technology to find measures of spread (range, variance, standard deviation, and interquartile range) and outliers for given data.

DA.4.7: Use procedures and/or technology to find measures of position (including median, quartiles, percentiles, and standard scores) for given data.

DA.4.10: Use a knowledge of the empirical rule to solve problems involving data that are distributed normally.

#### DA.5: The student will demonstrate through the mathematical processes an understanding of the basic concepts of probability.

DA.5.1: Construct a sample space for an experiment and represent it as a list, chart, picture, or tree diagram.

DA.5.2: Use counting techniques to determine the number of possible outcomes for an event.

DA.5.3: Classify events as either dependent or independent.

DA.5.6: Use the binomial probability distribution to solve problems.

DA.5.7: Carry out a procedure to compute simple probabilities and compound probabilities (including conditional probabilities).

DA.5.8: Use a procedure to find geometric probability in real-world contexts.

DA.5.9: Compare theoretical and experimental probabilities.

DA.5.10: Construct and compare theoretical and experimental probability distributions.

DA.5.12: Understand the law of large numbers.

Correlation last revised: 5/24/2018

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