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Common Core State Standards - Mathematics: High School
- Common Core State Standards Adopted: 2011
This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below to go to the Gizmo Details page.
CCSS.Math.Content.HSN.RN: The Real Number System
CCSS.Math.Content.HSN.RN.A: Extend the properties of exponents to rational exponents.
CCSS.Math.Content.HSN.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
CCSS.Math.Content.HSN.CN: The Complex Number System
CCSS.Math.Content.HSN.CN.A: Perform arithmetic operations with complex numbers.
CCSS.Math.Content.HSN.CN.A.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 - Activity A
CCSS.Math.Content.HSN.CN.A.2: Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Points in the Complex Plane - Activity A
CCSS.Math.Content.HSN.CN.A.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Points in the Complex Plane - Activity A
CCSS.Math.Content.HSN.CN.B: Represent complex numbers and their operations on the complex plane.
CCSS.Math.Content.HSN.CN.B.4: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
Complex Numbers in Polar Form
Points in the Complex Plane - Activity A
CCSS.Math.Content.HSN.CN.B.6: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
Absolute Value of a Complex Number
CCSS.Math.Content.HSN.CN.C: Use complex numbers in polynomial identities and equations.
CCSS.Math.Content.HSN.CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.
CCSS.Math.Content.HSN.VM: Vector and Matrix Quantities
CCSS.Math.Content.HSN.VM.A: Represent and model with vector quantities.
CCSS.Math.Content.HSN.VM.A.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 (e.g., 𝙫, |𝙫|, ||𝙫||, 𝘷).
CCSS.Math.Content.HSN.VM.A.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
CCSS.Math.Content.HSN.VM.A.3: Solve problems involving velocity and other quantities that can be represented by vectors.
CCSS.Math.Content.HSN.VM.B: Perform operations on vectors.
CCSS.Math.Content.HSN.VM.B.4a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
CCSS.Math.Content.HSN.VM.B.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
CCSS.Math.Content.HSN.VM.B.5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as 𝘤(𝘷ₓ, 𝘷 subscript 𝘺) = (𝘤𝘷ₓ, 𝘤𝘷 subscript 𝘺).
CCSS.Math.Content.HSA.SSE: Seeing Structure in Expressions
CCSS.Math.Content.HSA.SSE.A: Interpret the structure of expressions
CCSS.Math.Content.HSA.SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.
Exponential Growth and Decay - Activity A
Simple and Compound Interest
Unit Conversions
CCSS.Math.Content.HSA.SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
Exponential Growth and Decay - Activity A
Simple and Compound Interest
Translating and Scaling Functions
Using Algebraic Expressions
CCSS.Math.Content.HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
Factoring Special Products
Modeling the Factorization of ax^{2}+bx+c
Modeling the Factorization of x^{2}+bx+c
CCSS.Math.Content.HSA.SSE.B: Write expressions in equivalent forms to solve problems
CCSS.Math.Content.HSA.SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.
Factoring Special Products
Modeling the Factorization of ax^{2}+bx+c
Modeling the Factorization of x^{2}+bx+c
CCSS.Math.Content.HSA.SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions.
CCSS.Math.Content.HSA.APR: Arithmetic with Polynomials and Rational Expressions
CCSS.Math.Content.HSA.APR.A: Perform arithmetic operations on polynomials
CCSS.Math.Content.HSA.APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Addition of Polynomials - Activity B
CCSS.Math.Content.HSA.APR.B: Understand the relationship between zeros and factors of polynomials
CCSS.Math.Content.HSA.APR.B.2: Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹).
Dividing Polynomials Using Synthetic Division
Polynomials and Linear Factors
CCSS.Math.Content.HSA.APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Polynomials and Linear Factors
Quadratics in Factored Form
CCSS.Math.Content.HSA.APR.C: Use polynomial identities to solve problems
CCSS.Math.Content.HSA.APR.C.5: Know and apply the Binomial Theorem for the expansion of (𝘹 + 𝘺)ⁿ in powers of 𝘹 and y for a positive integer 𝘯, where 𝘹 and 𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle.
CCSS.Math.Content.HSA.CED: Creating Equations
CCSS.Math.Content.HSA.CED.A: Create equations that describe numbers or relationships
CCSS.Math.Content.HSA.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
Absolute Value Equations and Inequalities
Arithmetic Sequences
Exploring Linear Inequalities in One Variable
Exponential Growth and Decay - Activity A
Geometric Sequences
Modeling and Solving Two-Step Equations
Quadratic Inequalities - Activity A
Simple and Compound Interest
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
CCSS.Math.Content.HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
2D Collisions
Air Track
Golf Range
Points, Lines, and Equations
Simple and Compound Interest
Slope-Intercept Form of a Line - Activity B
CCSS.Math.Content.HSA.CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
Linear Programming - Activity A
Maximize Area
Minimize Perimeter
CCSS.Math.Content.HSA.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Solving Formulas for any Variable
CCSS.Math.Content.HSA.REI: Reasoning with Equations and Inequalities
CCSS.Math.Content.HSA.REI.A: Understand solving equations as a process of reasoning and explain the reasoning
CCSS.Math.Content.HSA.REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Modeling One-Step Equations - Activity B
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
CCSS.Math.Content.HSA.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
CCSS.Math.Content.HSA.REI.B: Solve equations and inequalities in one variable
CCSS.Math.Content.HSA.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Exploring Linear Inequalities in One Variable
Modeling One-Step Equations - Activity B
Modeling and Solving Two-Step Equations
Solving Linear Inequalities in One Variable
CCSS.Math.Content.HSA.REI.B.4b: Solve quadratic equations by inspection (e.g., for 𝘹² = 49), 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 ax^{2}+bx+c
Modeling the Factorization of x^{2}+bx+c
Roots of a Quadratic
CCSS.Math.Content.HSA.REI.C: Solve systems of equations
CCSS.Math.Content.HSA.REI.C.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
CCSS.Math.Content.HSA.REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Cat and Mouse (Modeling with Linear Systems) - Activity B
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
CCSS.Math.Content.HSA.REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
System of Two Quadratic Inequalities
CCSS.Math.Content.HSA.REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.
Solving Linear Systems (Matrices and Special Solutions)
CCSS.Math.Content.HSA.REI.D: Represent and solve equations and inequalities graphically
CCSS.Math.Content.HSA.REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Circles
Ellipses - Activity A
Hyperbolas - Activity A
Parabolas - Activity B
Points, Lines, and Equations
CCSS.Math.Content.HSA.REI.D.11: Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
CCSS.Math.Content.HSA.REI.D.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Linear Inequalities in Two Variables - Activity A
CCSS.Math.Content.HSF.IF: Interpreting Functions
CCSS.Math.Content.HSF.IF.A: Understand the concept of a function and use function notation
CCSS.Math.Content.HSF.IF.A.1: 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. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹).
Introduction to Functions
Points, Lines, and Equations
CCSS.Math.Content.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Absolute Value with Linear Functions - Activity A
Quadratic and Absolute Value Functions
Translating and Scaling Functions
CCSS.Math.Content.HSF.IF.B: Interpret functions that arise in applications in terms of the context
CCSS.Math.Content.HSF.IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
CCSS.Math.Content.HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
General Form of a Rational Function
Introduction to Functions
Radical Functions
Rational Functions
CCSS.Math.Content.HSF.IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
CCSS.Math.Content.HSF.IF.C: Analyze functions using different representations
CCSS.Math.Content.HSF.IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form - Activity A
Slope-Intercept Form of a Line - Activity B
CCSS.Math.Content.HSF.IF.C.7b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Absolute Value of a Quadratic Function
Absolute Value with Linear Functions - Activity A
Quadratic and Absolute Value Functions
Radical Functions
CCSS.Math.Content.HSF.IF.C.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form - Activity A
Roots of a Quadratic
Zap It! Game
CCSS.Math.Content.HSF.IF.C.7d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
General Form of a Rational Function
Rational Functions
CCSS.Math.Content.HSF.IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Cosine Function
Exponential Functions - Activity B
Exponential Growth and Decay - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
CCSS.Math.Content.HSF.IF.C.8a: 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 ax^{2}+bx+c
Modeling the Factorization of x^{2}+bx+c
CCSS.Math.Content.HSF.IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions.
Exponential Growth and Decay - Activity A
Simple and Compound Interest
CCSS.Math.Content.HSF.BF: Building Functions
CCSS.Math.Content.HSF.BF.A: Build a function that models a relationship between two quantities
CCSS.Math.Content.HSF.BF.A.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
Arithmetic Sequences
Geometric Sequences
CCSS.Math.Content.HSF.BF.A.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
Geometric Sequences
CCSS.Math.Content.HSF.BF.B: Build new functions from existing functions
CCSS.Math.Content.HSF.BF.B.3: Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Exponential Functions - Activity B
Logarithmic Functions - Activity A
Reflections of a Linear Function
Reflections of a Quadratic Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
CCSS.Math.Content.HSF.BF.B.4b: Verify by composition that one function is the inverse of another.
Logarithmic Functions - Activity A
CCSS.Math.Content.HSF.BF.B.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse.
Logarithmic Functions - Activity A
CCSS.Math.Content.HSF.BF.B.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Logarithmic Functions - Activity A
CCSS.Math.Content.HSF.LE: Linear, Quadratic, and Exponential Models
CCSS.Math.Content.HSF.LE.A: Construct and compare linear, quadratic, and exponential models and solve problems
CCSS.Math.Content.HSF.LE.A.1a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Linear Functions
Simple and Compound Interest
CCSS.Math.Content.HSF.LE.A.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Arithmetic Sequences
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Simple and Compound Interest
CCSS.Math.Content.HSF.LE.A.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Drug Dosage
Exponential Growth and Decay - Activity A
Half-life
CCSS.Math.Content.HSF.LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Defining a Line with Two Points
Exponential Functions - Activity B
Exponential Growth and Decay - Activity A
Point-Slope Form of a Line - Activity A
Simple and Compound Interest
Slope-Intercept Form of a Line - Activity B
CCSS.Math.Content.HSF.LE.A.4: For exponential models, express as a logarithm the solution to 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.
CCSS.Math.Content.HSF.LE.B: Interpret expressions for functions in terms of the situation they model
CCSS.Math.Content.HSF.LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
Arithmetic Sequences
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Growth and Decay - Activity A
Simple and Compound Interest
CCSS.Math.Content.HSF.TF: Trigonometric Functions
CCSS.Math.Content.HSF.TF.A: Extend the domain of trigonometric functions using the unit circle
CCSS.Math.Content.HSF.TF.A.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
CCSS.Math.Content.HSF.TF.A.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
CCSS.Math.Content.HSF.TF.B: Model periodic phenomena with trigonometric functions
CCSS.Math.Content.HSF.TF.B.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
CCSS.Math.Content.HSF.TF.C: Prove and apply trigonometric identities
CCSS.Math.Content.HSF.TF.C.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine
CCSS.Math.Content.HSG.CO: Congruence
CCSS.Math.Content.HSG.CO.A: Experiment with transformations in the plane
CCSS.Math.Content.HSG.CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Circles
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
CCSS.Math.Content.HSG.CO.A.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Dilations
Reflections
Rotations, Reflections, and Translations
Translations
CCSS.Math.Content.HSG.CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Dilations
Reflections
Rotations, Reflections, and Translations
Translations
CCSS.Math.Content.HSG.CO.A.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Dilations
Reflections
Rotations, Reflections, and Translations
Translations
CCSS.Math.Content.HSG.CO.B: Understand congruence in terms of rigid motions
CCSS.Math.Content.HSG.CO.B.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Proving Triangles Congruent
Reflections
Rotations, Reflections, and Translations
Translations
CCSS.Math.Content.HSG.CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
CCSS.Math.Content.HSG.CO.C: Prove geometric theorems
CCSS.Math.Content.HSG.CO.C.9: Prove theorems about lines and angles.
Investigating Angle Theorems - Activity B
CCSS.Math.Content.HSG.CO.C.10: Prove theorems about triangles.
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity B
Triangle Inequalities
CCSS.Math.Content.HSG.CO.C.11: Prove theorems about parallelograms.
Parallelogram Conditions
Special Parallelograms
CCSS.Math.Content.HSG.CO.D: Make geometric constructions
CCSS.Math.Content.HSG.CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
CCSS.Math.Content.HSG.SRT: Similarity, Right Triangles, and Trigonometry
CCSS.Math.Content.HSG.SRT.A: Understand similarity in terms of similarity transformations
CCSS.Math.Content.HSG.SRT.A.1b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Dilations
Similar Figures - Activity A
CCSS.Math.Content.HSG.SRT.A.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
CCSS.Math.Content.HSG.SRT.B: Prove theorems involving similarity
CCSS.Math.Content.HSG.SRT.B.4: Prove theorems about triangles.
Pythagorean Theorem - Activity B
Similar Figures - Activity A
CCSS.Math.Content.HSG.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Dilations
Perimeters and Areas of Similar Figures
Similarity in Right Triangles
CCSS.Math.Content.HSG.SRT.C: Define trigonometric ratios and solve problems involving right triangles
CCSS.Math.Content.HSG.SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Sine, Cosine, and Tangent Ratios
Tangent Ratio
CCSS.Math.Content.HSG.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Distance Formula - Activity A
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard
Sine, Cosine, and Tangent Ratios
Tangent Ratio
CCSS.Math.Content.HSG.C: Circles
CCSS.Math.Content.HSG.C.A: Understand and apply theorems about circles
CCSS.Math.Content.HSG.C.A.2: Identify and describe relationships among inscribed angles, radii, and chords.
CCSS.Math.Content.HSG.C.B: Find arc lengths and areas of sectors of circles
CCSS.Math.Content.HSG.C.B.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
CCSS.Math.Content.HSG.GPE: Expressing Geometric Properties with Equations
CCSS.Math.Content.HSG.GPE.A: Translate between the geometric description and the equation for a conic section
CCSS.Math.Content.HSG.GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Circles
Distance Formula - Activity A
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard
CCSS.Math.Content.HSG.GPE.A.2: Derive the equation of a parabola given a focus and directrix.
Parabola with Horizontal Directrix
Parabolas - Activity B
CCSS.Math.Content.HSG.GPE.A.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
Ellipses - Activity A
Hyperbolas - Activity A
CCSS.Math.Content.HSG.GPE.B: Use coordinates to prove simple geometric theorems algebraically
CCSS.Math.Content.HSG.GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
CCSS.Math.Content.HSG.GMD: Geometric Measurement and Dimension
CCSS.Math.Content.HSG.GMD.A: Explain volume formulas and use them to solve problems
CCSS.Math.Content.HSG.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
Circumference and Area of Circles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity B
CCSS.Math.Content.HSG.GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity B
CCSS.Math.Content.HSS.ID: Interpreting Categorical and Quantitative Data
CCSS.Math.Content.HSS.ID.A: Summarize, represent, and interpret data on a single count or measurement variable
CCSS.Math.Content.HSS.ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).
Box-and-Whisker Plots
Histograms
Mean, Median, and Mode
CCSS.Math.Content.HSS.ID.A.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Box-and-Whisker Plots
Describing Data Using Statistics
Real-Time Histogram
Sight vs. Sound Reactions
CCSS.Math.Content.HSS.ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Mean, Median, and Mode
Reaction Time 2 (Graphs and Statistics)
CCSS.Math.Content.HSS.ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables
CCSS.Math.Content.HSS.ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
Least-Squares Best Fit Lines
Solving Using Trend Lines
CCSS.Math.Content.HSS.ID.B.6b: Informally assess the fit of a function by plotting and analyzing residuals.
CCSS.Math.Content.HSS.ID.B.6c: Fit a linear function for a scatter plot that suggests a linear association.
CCSS.Math.Content.HSS.ID.C: Interpret linear models
CCSS.Math.Content.HSS.ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Cat and Mouse (Modeling with Linear Systems) - Activity B
CCSS.Math.Content.HSS.ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.
CCSS.Math.Content.HSS.IC: Making Inferences and Justifying Conclusions
CCSS.Math.Content.HSS.IC.B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies
CCSS.Math.Content.HSS.IC.B.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.
Estimating Population Size
Polling: City
Polling: Neighborhood
CCSS.Math.Content.HSS.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Real-Time Histogram
Sight vs. Sound Reactions
CCSS.Math.Content.HSS.CP: Conditional Probability and the Rules of Probability
CCSS.Math.Content.HSS.CP.A: Understand independence and conditional probability and use them to interpret data
CCSS.Math.Content.HSS.CP.A.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability
CCSS.Math.Content.HSS.CP.A.2: 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
CCSS.Math.Content.HSS.CP.A.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
CCSS.Math.Content.HSS.CP.B: Use the rules of probability to compute probabilities of compound events in a uniform probability model
CCSS.Math.Content.HSS.CP.B.9: Use permutations and combinations to compute probabilities of compound events and solve problems.
Binomial Probabilities
Permutations and Combinations
CCSS.Math.Content.HSS.MD: Using Probability to Make Decisions
CCSS.Math.Content.HSS.MD.A: Calculate expected values and use them to solve problems
CCSS.Math.Content.HSS.MD.A.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability
CCSS.Math.Content.HSS.MD.A.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability
Content correlation last revised: 3/17/2015