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 x2+bx+c
AAPR.2: Know and apply the Division Theorem and the Remainder Theorem for polynomials.
Dividing Polynomials Using Synthetic Division
Polynomials and Linear Factors
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.
Graphs of Polynomial Functions
Modeling the Factorization of x2+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game
AAPR.4: Prove polynomial identities and use them to describe numerical relationships.
AAPR.5: Apply the Binomial Theorem to expand powers of binomials, including those with one and with two variables. Use the Binomial Theorem to factor squares, cubes, and fourth powers of binomials.
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.
Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Inequalities
Compound Interest
Exploring Linear Inequalities in One Variable
Geometric Sequences
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic 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
Compound Interest
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
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 Inequalities in Two Variables
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 Formulas for any Variable
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.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+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 Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
AREI.6: Solve systems of linear equations algebraically and graphically focusing on pairs of linear equations in two variables.
Cat and Mouse (Modeling with Linear Systems)
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.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 (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
AREI.6.b: Solve systems of linear equations using linear combination.
Cat and Mouse (Modeling with Linear Systems)
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.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.
Absolute Value Equations and Inequalities
Circles
Ellipses
Hyperbolas
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
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
Cat and Mouse (Modeling with Linear Systems)
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
Linear Programming
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
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Translating and Scaling Functions
Using Algebraic Expressions
ASE.2: Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+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.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+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
Exponents and Power Rules
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
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Vertex Form
Radical 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.a: Use composition to verify one function is an inverse of another.
FBF.4.b: If a function has an inverse, find values of the inverse function from a graph or table.
Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions
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.
Absolute Value with Linear Functions
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
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.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.
Absolute Value with Linear Functions
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
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.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
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
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.2: Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation.
Absolute Value with Linear Functions
Translating and Scaling Functions
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
Function Machines 3 (Functions and Problem Solving)
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.
General Form of a Rational Function
Introduction to Functions
Logarithmic Functions
Radical Functions
Rational 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
Rational Functions
FIF.7.b: Graph radical functions over their domain show end behavior.
FIF.7.c: Graph exponential and logarithmic functions, showing intercepts and end behavior.
Cosine Function
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions
FIF.7.d: Graph trigonometric functions, showing period, midline, and amplitude.
Cosine Function
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
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.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+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
Linear 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
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
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.4: Express a logarithm as the solution to the exponential equation, ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
Compound Interest
Logarithmic 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.
Cosine Function
Simplifying Trigonometric Expressions
Sine Function
Sine, Cosine, and Tangent Ratios
FT.9: Justify the sum and difference formulas for sine, cosine, and tangent and use them to solve problems.
Simplifying Trigonometric Expressions
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
Circumference and Area of Circles
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
GCI.5: Derive the formulas for the length of an arc and the area of a sector in a circle and apply these formulas to solve mathematical and real-world problems.
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 Congruent Segments and Angles
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
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
GCO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Circles
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
GCO.5: Predict and describe the results of transformations on a given figure using geometric terminology from the definitions of the transformations, and describe a sequence of transformations that maps a figure onto its image.
Absolute Value with Linear Functions
Circles
Dilations
Holiday Snowflake Designer
Proving Triangles Congruent
Reflections
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;
Investigating Angle Theorems
Triangle Angle Sum
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;
Investigating Angle Theorems
Triangle Angle Sum
GCO.8.c: any point on a perpendicular bisector of a line segment is equidistant from the endpoints of the segment;
Investigating Angle Theorems
Segment and Angle Bisectors
GCO.8.d: perpendicular lines form four right angles.
GCO.9: Prove, and apply in mathematical and real-world contexts, theorems about the relationships within and among triangles, including the following:
Isosceles and Equilateral Triangles
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities
GCO.9.a: measures of interior angles of a triangle sum to 180°;
Isosceles and Equilateral Triangles
Polygon Angle Sum
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities
GCO.9.b: base angles of isosceles triangles are congruent;
Isosceles and Equilateral Triangles
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities
GCO.9.c: the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length;
Isosceles and Equilateral Triangles
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities
GCO.9.d: the medians of a triangle meet at a point.
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities
GCO.10: Prove, and apply in mathematical and real-world contexts, theorems about parallelograms, including the following:
Parallelogram Conditions
Special Parallelograms
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;
Parallelogram Conditions
Special Parallelograms
GCO.10.e: a parallelogram is a rhombus if and only if the diagonals are perpendicular.
Parallelogram Conditions
Special Parallelograms
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.
Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
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:
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures
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.
Chords and Arcs
Congruence in Right Triangles
Constructing Congruent Segments and Angles
Dilations
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
NRNS.2: Use the definition of the meaning of rational exponents to translate between rational exponent and radical forms.
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.5: Multiply a vector by a scalar, representing the multiplication graphically and computing the magnitude of the scalar multiple.
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
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability
SPCR.1.a: Use Venn diagrams to represent intersections, unions, and complements.
SPCR.1.b: Relate intersections, unions, and complements to the words and, or, and not.
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability
SPCR.1.c: Represent sample spaces for compound events using Venn diagrams.
Independent and Dependent Events
Permutations and Combinations
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.
Polling: City
Polling: Neighborhood
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)
Reaction Time 2 (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
Independent and Dependent Events
Lucky Duck (Expected Value)
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)
Polling: City
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: 9/16/2020