SC--College- and Career-Ready Standards

AAPR.1: Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations.

Addition and Subtraction of Functions

Addition of Polynomials

Modeling the Factorization of *x*^{2}+*bx*+*c*

AAPR.2: Know and apply the Division Theorem and the Remainder Theorem for polynomials.

Dividing Polynomials Using Synthetic Division

AAPR.3: Graph polynomials identifying zeros when suitable factorizations are available and indicating end behavior. Write a polynomial function of least degree corresponding to a given graph.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

AAPR.4: Prove polynomial identities and use them to describe numerical relationships.

ACE.1: Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable.

Compound Inequalities

Linear Inequalities in Two Variables

Solving Equations on the Number Line

Solving Two-Step Equations

ACE.2: Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales.

Absolute Value Equations and Inequalities

Circles

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Polynomial Form

Quadratics in Vertex Form

Solving Equations on the Number Line

Standard Form of a Line

Using Algebraic Equations

ACE.3: Use systems of equations and inequalities to represent constraints arising in real-world situations. Solve such systems using graphical and analytical methods, including linear programing. Interpret the solution within the context of the situation.

Cat and Mouse (Modeling with Linear Systems)

Linear Programming

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

ACE.4: Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.

Area of Triangles

Solving Formulas for any Variable

AREI.1: Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

AREI.2: Solve simple rational and radical equations in one variable and understand how extraneous solutions may arise.

AREI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Area of Triangles

Compound Inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations I

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Formulas for any Variable

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

AREI.4: Solve mathematical and real-world problems involving quadratic equations in one variable.

AREI.4.a: Use the method of completing the square to transform any quadratic equation in 𝑥 into an equation of the form (x − h)² = k that has the same solutions. Derive the quadratic formula from this form.

AREI.4.b: Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Points in the Complex Plane

Roots of a Quadratic

AREI.5: Justify that the solution to a system of linear equations is not changed when one of the equations is replaced by a linear combination of the other equation.

Solving Linear Systems (Standard Form)

AREI.6: Solve systems of linear equations algebraically and graphically focusing on pairs of linear equations in two variables.

AREI.6.a: Solve systems of linear equations using the substitution method.

Cat and Mouse (Modeling with Linear Systems)

Solving Equations by Graphing Each Side

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

AREI.6.b: Solve systems of linear equations using linear combination.

Solving Equations by Graphing Each Side

Solving Linear Systems (Standard Form)

AREI.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Understand that such systems may have zero, one, two, or infinitely many solutions.

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

AREI.8: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

AREI.9: Using technology for matrices of dimension 3 × 3 or greater, find the inverse of a matrix if it exists and use it to solve systems of linear equations.

Solving Linear Systems (Matrices and Special Solutions)

AREI.10: Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

Circles

Point-Slope Form of a Line

Standard Form of a Line

AREI.11: Solve an equation of the form f(x) = g(x) graphically by identifying the x - coordinate(s) of the point(s) of intersection of the graphs of y = f(x) and y =g(x).

Absolute Value Equations and Inequalities

Point-Slope Form of a Line

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Standard Form of a Line

AREI.12: Graph the solutions to a linear inequality in two variables.

Linear Inequalities in Two Variables

Systems of Linear Inequalities (Slope-intercept form)

ASE.1: Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions.

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

ASE.2: Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

ASE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

ASE.3.a: Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain the connection between the zeros of the function, its linear factors, the x-intercepts of its graph, and the solutions to the corresponding quadratic equation.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

Zap It! Game

ASE.3.b: Determine the maximum or minimum value of a quadratic function by completing the square.

ASE.3.c: Use the properties of exponents to transform expressions for exponential functions.

Dividing Exponential Expressions

FBF.1: Write a function that describes a relationship between two quantities.

FBF.1.a: Write a function that models a relationship between two quantities using both explicit expressions and a recursive process and by combining standard forms using addition, subtraction, multiplication and division to build new functions.

Addition and Subtraction of Functions

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

FBF.1.b: Combine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations.

Addition and Subtraction of Functions

FBF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

FBF.3: Describe the effect of the transformations kf (x), f(x) + k, f(x + k), and combinations of such transformations on the graph of y = f(x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

FBF.4: Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x) = y and g(y) = x, for all values of x in the domain of f and all values of y in the domain of g, and find inverse functions for one-to-one function or by restricting the domain.

FBF.4.b: If a function has an inverse, find values of the inverse function from a graph or table.

FBF.5: Understand and verify through function composition that exponential and logarithmic functions are inverses of each other and use this relationship to solve problems involving logarithms and exponents.

FIF.1: Extend previous knowledge of a function to apply to general behavior and features of a function.

FIF.1.a: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.

Introduction to Functions

Logarithmic Functions

Radical Functions

FIF.1.b: Represent a function using function notation and explain that f(x) denotes the output of function f that corresponds to the input x.

Introduction to Functions

Linear Functions

Points, Lines, and Equations

FIF.1.c: Understand that the graph of a function labeled as f is the set of all ordered pairs (x,y) that satisfy the equation y = f(x).

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Introduction to Functions

Linear Functions

Logarithmic Functions

Parabolas

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Standard Form of a Line

FIF.3: Define functions recursively and recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Arithmetic Sequences

Geometric Sequences

FIF.4: Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity.

Absolute Value with Linear Functions

Compound Interest

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Introduction to Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

FIF.5: Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.

Introduction to Functions

Logarithmic Functions

Radical Functions

FIF.6: Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context.

Cat and Mouse (Modeling with Linear Systems)

Slope

FIF.7: Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases.

FIF.7.a: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

General Form of a Rational Function

FIF.7.c: Graph exponential and logarithmic functions, showing intercepts and end behavior.

Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

FIF.7.d: Graph trigonometric functions, showing period, midline, and amplitude.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

FIF.8: Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function.

FIF.8.a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

Quadratics in Vertex Form

Roots of a Quadratic

FIF.8.b: Interpret expressions for exponential functions by using the properties of exponents.

Compound Interest

Exponential Functions

FIF.9: Compare properties of two functions given in different representations such as algebraic, graphical, tabular, or verbal.

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Quadratics in Polynomial Form

Quadratics in Vertex Form

FLQE.1: Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by a constant percent rate per unit interval.

FLQE.1.a: Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

Compound Interest

Direct and Inverse Variation

Exponential Functions

Exponential Growth and Decay

Introduction to Exponential Functions

Slope-Intercept Form of a Line

FLQE.1.b: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Compound Interest

Exponential Growth and Decay

FLQE.2: Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables.

Absolute Value with Linear Functions

Arithmetic Sequences

Arithmetic and Geometric Sequences

Compound Interest

Exponential Functions

Geometric Sequences

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

FLQE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or more generally as a polynomial function.

Compound Interest

Introduction to Exponential Functions

FLQE.5: Interpret the parameters in a linear or exponential function in terms of the context.

Arithmetic Sequences

Compound Interest

Exponential Growth and Decay

Introduction to Exponential Functions

FT.1: Understand that the radian measure of an angle is the length of the arc on the unit circle subtended by the angle.

Sine Function

Tangent Function

FT.2: Define sine and cosine as functions of the radian measure of an angle in terms of the x - and y - coordinates of the point on the unit circle corresponding to that angle and explain how these definitions are extensions of the right triangle definitions.

FT.2.a: Define the tangent, cotangent, secant, and cosecant functions as ratios involving sine and cosine.

Simplifying Trigonometric Expressions

Sine, Cosine, and Tangent Ratios

FT.2.b: Write cotangent, secant, and cosecant functions as the reciprocals of tangent, cosine, and sine, respectively.

Simplifying Trigonometric Expressions

Tangent Function

FT.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4, and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π − x, π + x, and 2π − x in terms of their values for x, where x is any real number.

Cosine Function

Sine Function

Sum and Difference Identities for Sine and Cosine

Tangent Function

Translating and Scaling Sine and Cosine Functions

FT.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

FT.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

FT.8: Justify the Pythagorean, even/odd, and cofunction identities for sine and cosine using their unit circle definitions and symmetries of the unit circle and use the Pythagorean identity to find sinA, cosA, or tanA, given sinA, cosA, or tanA, and the quadrant of the angle.

FT.9: Justify the sum and difference formulas for sine, cosine, and tangent and use them to solve problems.

Sum and Difference Identities for Sine and Cosine

GCI.2: Identify and describe relationships among inscribed angles, radii, and chords; among inscribed angles, central angles, and circumscribed angles; and between radii and tangents to circles. Use those relationships to solve mathematical and real-world problems.

Chords and Arcs

Inscribed Angles

GCI.3: Construct the inscribed and circumscribed circles of a triangle using a variety of tools, including a compass, a straightedge, and dynamic geometry software, and prove properties of angles for a quadrilateral inscribed in a circle.

Concurrent Lines, Medians, and Altitudes

Inscribed Angles

GCO.1: Define angle, perpendicular line, parallel line, line segment, ray, circle, and skew in terms of the undefined notions of point, line, and plane. Use geometric figures to represent and describe real-world objects.

Circles

Constructing Parallel and Perpendicular Lines

Inscribed Angles

Parallel, Intersecting, and Skew Lines

GCO.2: Represent translations, reflections, rotations, and dilations of objects in the plane by using paper folding, sketches, coordinates, function notation, and dynamic geometry software, and use various representations to help understand the effects of simple transformations and their compositions.

Absolute Value with Linear Functions

Dilations

Holiday Snowflake Designer

Reflections

Rotations, Reflections, and Translations

Similar Figures

Translations

GCO.3: Describe rotations and reflections that carry a regular polygon onto itself and identify types of symmetry of polygons, including line, point, rotational, and self-congruence, and use symmetry to analyze mathematical situations.

Constructing Congruent Segments and Angles

GCO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Circles

Rotations, Reflections, and Translations

Similar Figures

Translations

GCO.6: Demonstrate that triangles and quadrilaterals are congruent by identifying a combination of translations, rotations, and reflections in various representations that move one figure onto the other.

Reflections

Rotations, Reflections, and Translations

Translations

GCO.7: Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Angle- Angle-Side, and Hypotenuse-Leg congruence conditions.

Congruence in Right Triangles

Proving Triangles Congruent

GCO.8: Prove, and apply in mathematical and real-world contexts, theorems about lines and angles, including the following:

GCO.8.a: vertical angles are congruent;

GCO.8.b: when a transversal crosses parallel lines, alternate interior angles are congruent, alternate exterior angles are congruent, and consecutive interior angles are supplementary;

GCO.8.c: any point on a perpendicular bisector of a line segment is equidistant from the endpoints of the segment;

GCO.9: Prove, and apply in mathematical and real-world contexts, theorems about the relationships within and among triangles, including the following:

GCO.9.a: measures of interior angles of a triangle sum to 180°;

Isosceles and Equilateral Triangles

Polygon Angle Sum

Triangle Angle Sum

GCO.9.b: base angles of isosceles triangles are congruent;

Isosceles and Equilateral Triangles

Triangle Inequalities

GCO.9.d: the medians of a triangle meet at a point.

Concurrent Lines, Medians, and Altitudes

GCO.10: Prove, and apply in mathematical and real-world contexts, theorems about parallelograms, including the following:

GCO.10.a: opposite sides of a parallelogram are congruent;

Classifying Quadrilaterals

Parallelogram Conditions

Special Parallelograms

GCO.10.b: opposite angles of a parallelogram are congruent;

Classifying Quadrilaterals

Parallelogram Conditions

Special Parallelograms

GCO.10.c: diagonals of a parallelogram bisect each other;

Parallelogram Conditions

Special Parallelograms

GCO.10.d: rectangles are parallelograms with congruent diagonals;

GCO.11: Construct geometric figures using a variety of tools, including a compass, a straightedge, dynamic geometry software, and paper folding, and use these constructions to make conjectures about geometric relationships.

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

Segment and Angle Bisectors

GGMD.1: Explain the derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone. Apply these formulas to solve mathematical and real-world problems.

Circumference and Area of Circles

Prisms and Cylinders

Pyramids and Cones

GGMD.2: Explain the derivation of the formulas for the volume of a sphere and other solid figures using Cavalieri’s principle.

Prisms and Cylinders

Pyramids and Cones

GGMD.3: Apply surface area and volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems and justify results. Include problems that involve algebraic expressions, composite figures, geometric probability, and real-world applications.

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

GGPE.1: Understand that the standard equation of a circle is derived from the definition of a circle and the distance formula.

GGPE.2: Use the geometric definition of a parabola to derive its equation given the focus and directrix.

GGPE.3: Use the geometric definition of an ellipse and of a hyperbola to derive the equation of each given the foci and points whose sum or difference of distance from the foci are constant.

GGPE.5: Analyze slopes of lines to determine whether lines are parallel, perpendicular, or neither. Write the equation of a line passing through a given point that is parallel or perpendicular to a given line. Solve geometric and real-world problems involving lines and slope.

Cat and Mouse (Modeling with Linear Systems)

Slope

Slope-Intercept Form of a Line

GGPE.7: Use the distance and midpoint formulas to determine distance and midpoint in a coordinate plane, as well as areas of triangles and rectangles, when given coordinates.

GSRT.1: Understand a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. Verify experimentally the properties of dilations given by a center and a scale factor. Understand the dilation of a line segment is longer or shorter in the ratio given by the scale factor.

GSRT.2: Use the definition of similarity to decide if figures are similar and justify decision. Demonstrate that two figures are similar by identifying a combination of translations, rotations, reflections, and dilations in various representations that move one figure onto the other.

Dilations

Perimeters and Areas of Similar Figures

Similar Figures

Similarity in Right Triangles

GSRT.3: Prove that two triangles are similar using the Angle-Angle criterion and apply the proportionality of corresponding sides to solve problems and justify results.

GSRT.4: Prove, and apply in mathematical and real-world contexts, theorems involving similarity about triangles, including the following:

GSRT.4.a: A line drawn parallel to one side of a triangle divides the other two sides into parts of equal proportion.

GSRT.4.b: If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

GSRT.4.c: The square of the hypotenuse of a right triangle is equal to the sum of squares of the other two sides.

Circles

Cosine Function

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine Function

Surface and Lateral Areas of Pyramids and Cones

Tangent Function

GSRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Congruence in Right Triangles

Constructing Congruent Segments and Angles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures

Similarity in Right Triangles

GSRT.6: Understand how the properties of similar right triangles allow the trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.

Cosine Function

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

GSRT.8: Solve right triangles in applied problems using trigonometric ratios and the Pythagorean Theorem.

Cosine Function

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

NCNS.1: Know there is a complex number i such that i² = −1, and every complex number has the form a + bi with a and b real.

Points in the Complex Plane

Roots of a Quadratic

NCNS.2: Use the relation i²= −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

NCNS.3: Find the conjugate of a complex number in rectangular and polar forms and use conjugates to find moduli and quotients of complex numbers.

Points in the Complex Plane

Roots of a Quadratic

NCNS.4: Graph complex numbers on the complex plane in rectangular and polar form and explain why the rectangular and polar forms of a given complex number represent the same number.

NCNS.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

NCNS.6: Determine the modulus of a complex number by multiplying by its conjugate and determine the distance between two complex numbers by calculating the modulus of their difference.

NCNS.7: Solve quadratic equations in one variable that have complex solutions.

Points in the Complex Plane

Roots of a Quadratic

NVMQ.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.

NVMQ.2: Represent and model with vector quantities. Use the coordinates of an initial point and of a terminal point to find the components of a vector.

NVMQ.3: Represent and model with vector quantities. Solve problems involving velocity and other quantities that can be represented by vectors.

NVMQ.4: Perform operations on vectors.

NVMQ.4.a: Add and subtract vectors using components of the vectors and graphically.

NVMQ.4.b: Given the magnitude and direction of two vectors, determine the magnitude of their sum and of their difference.

NVMQ.7: Perform operations with matrices of appropriate dimensions including addition, subtraction, and scalar multiplication.

NVMQ.11: Apply 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

SPCR.1: Describe events as subsets of a sample space and

SPCR.1.a: Use Venn diagrams to represent intersections, unions, and complements.

SPCR.2: Use the multiplication rule to calculate probabilities for independent and dependent events. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Independent and Dependent Events

SPCR.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

Independent and Dependent Events

SPCR.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

SPCR.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events

SPCR.6: Calculate the conditional probability of an event A given event B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

Independent and Dependent Events

SPCR.7: Apply the Addition Rule and the Multiplication Rule to determine probabilities, including conditional probabilities, and interpret the results in terms of the probability model.

Independent and Dependent Events

SPCR.8: Use permutations and combinations to solve mathematical and real-world problems, including determining probabilities of compound events. Justify the results.

Binomial Probabilities

Permutations and Combinations

SPMJ.1: Understand statistics and sampling distributions as a process for making inferences about population parameters based on a random sample from that population.

Polling: City

Polling: Neighborhood

Populations and Samples

SPMJ.2: Distinguish between experimental and theoretical probabilities. Collect data on a chance event and use the relative frequency to estimate the theoretical probability of that event. Determine whether a given probability model is consistent with experimental results.

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

SPMJ.3: Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods to reduce bias.

Describing Data Using Statistics

Polling: City

Polling: Neighborhood

SPMJ.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

SPMJ.6: Evaluate claims and conclusions in published reports or articles based on data by analyzing study design and the collection, analysis, and display of the data.

Polling: City

Polling: Neighborhood

Populations and Samples

Real-Time Histogram

SPID.1: Select and create an appropriate display, including dot plots, histograms, and box plots, for data that includes only real numbers.

Box-and-Whisker Plots

Correlation

Histograms

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

Stem-and-Leaf Plots

SPID.2: Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets that include all real numbers.

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Polling: City

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

SPID.3: Summarize and represent data from a single data set. Interpret differences in shape, center, and spread in the context of the data set, accounting for possible effects of extreme data points (outliers).

Box-and-Whisker Plots

Describing Data Using Statistics

Least-Squares Best Fit Lines

Mean, Median, and Mode

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Stem-and-Leaf Plots

SPID.4: 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 calculators, spreadsheets, and tables to estimate areas under the normal curve.

Polling: City

Populations and Samples

Real-Time Histogram

SPID.5: Analyze bivariate categorical data using two-way tables and identify possible associations between the two categories using marginal, joint, and conditional frequencies.

SPID.6: Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

SPID.7: Create a linear function to graphically model data from a real-world problem and interpret the meaning of the slope and intercept(s) in the context of the given problem.

Correlation

Solving Using Trend Lines

SPID.8: Using technology, compute and interpret the correlation coefficient of a linear fit.

SPID.9: Differentiate between correlation and causation when describing the relationship between two variables. Identify potential lurking variables which may explain an association between two variables.

SPID.10: Create residual plots and analyze those plots to compare the fit of linear, quadratic, and exponential models to a given data set. Select the appropriate model and use it for interpolation.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Zap It! Game

SPMD.1: Develop the probability distribution for a random variable defined for a sample space in which a theoretical probability can be calculated and graph the distribution.

Binomial Probabilities

Geometric Probability

Probability Simulations

Theoretical and Experimental Probability

SPMD.2: Calculate the expected value of a random variable as the mean of its probability distribution. Find expected values by assigning probabilities to payoff values. Use expected values to evaluate and compare strategies in real-world scenarios.

Binomial Probabilities

Lucky Duck (Expected Value)

SPMD.3: Construct and compare theoretical and experimental probability distributions and use those distributions to find expected values.

Lucky Duck (Expected Value)

Probability Simulations

Theoretical and Experimental Probability

SPMD.4: Use probability to evaluate outcomes of decisions by finding expected values and determine if decisions are fair.

Lucky Duck (Expected Value)

Probability Simulations

Theoretical and Experimental Probability

SPMD.5: Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions.

Lucky Duck (Expected Value)

Probability Simulations

Theoretical and Experimental Probability

SPMD.6: Analyze decisions and strategies using probability concepts.

Estimating Population Size

Probability Simulations

Theoretical and Experimental Probability

LC.2: Understand the definition and graphical interpretation of continuity of a function.

LC.2.b: Classify discontinuities as removable, jump, or infinite. Justify that classification using the definition of continuity.

General Form of a Rational Function

D.1.a: Interpret the value of the derivative of a function as the slope of the corresponding tangent line.

Graphs of Derivative Functions

D.1.c: Approximate the derivative graphically by finding the slope of the tangent line drawn to a curve at a given point and numerically by using the difference quotient.

Graphs of Derivative Functions

D.1.f: Understand the definition of the derivative and use this definition to determine the derivatives of various functions.

Graphs of Derivative Functions

D.2.a: Know and apply the derivatives of constant, power, trigonometric, inverse trigonometric, exponential, and logarithmic functions.

Graphs of Derivative Functions

D.3.c: Explain the relationship between the increasing/decreasing behavior of f and the signs of f′. Use the relationship to generate a graph of f given the graph of f′, and vice versa, and to identify relative and absolute extrema of f.

Graphs of Derivative Functions

D.3.d: Explain the relationships among the concavity of the graph of f, the increasing/decreasing behavior of f′ and the signs of f′′. Use those relationships to generate graphs of f, f′, and f′′ given any one of them and identify the points of inflection of f.

Graphs of Derivative Functions

C.I.1.b: Approximate definite integrals by calculating Riemann sums using left, right, and mid-point evaluations, and using trapezoidal sums.

Correlation last revised: 1/22/2020