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- Mathematics: Grades: 9-12
Florida - Mathematics: Grades 9-12
Benchmarks for Excellent Student Thinking Standards | Adopted: 2020
MA.912.NSO: : Number Sense and Operations
MA.912.NSO.1: : Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms.
MA.912.NSO.1.2: : Generate equivalent monomial algebraic expressions using the properties of exponents.
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Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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Exponents and Power Rules
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview
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Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
MA.912.NSO.1.3: : Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents. Radicands are limited to monomial algebraic expressions.
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Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
MA.912.NSO.1.4: : Apply previous understanding of operations with rational numbers to add, subtract, multiply and divide numerical radicals.
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Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
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Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
MA.912.NSO.1.5: : Add, subtract, multiply and divide algebraic expressions involving radicals. Radicands are limited to monomial algebraic expressions.
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Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
MA.912.NSO.1.6: : Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents.
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Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
MA.912.NSO.2: : Represent and perform operations with expressions within the complex number system.
MA.912.NSO.2.1: : Extend previous understanding of the real number system to include the complex number system. Add, subtract, multiply and divide complex numbers.
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Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
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Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
MA.912.NSO.2.2: : Represent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane.
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Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
MA.912.NSO.2.3: : Calculate the distance and midpoint between two numbers on the complex coordinate plane.
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Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
MA.912.NSO.2.4: : Solve mathematical and real-world problems involving complex numbers represented algebraically or on the coordinate plane.
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Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
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Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
MA.912.NSO.2.5: : Represent complex numbers on the complex plane in rectangular and polar forms. Explain why the rectangular and polar forms of a given complex number represent the same number.
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Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
MA.912.NSO.2.6: : Rewrite complex numbers to trigonometric form. Multiply complex numbers in trigonometric form.
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Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
MA.912.NSO.3: : Represent and perform operations with vectors.
MA.912.NSO.3.1: : Apply appropriate notation and symbols to represent vectors in the plane as directed line segments. Determine the magnitude and direction of a vector in component form.
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Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
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Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
MA.912.NSO.3.2: : Represent vectors in component form, linear form or trigonometric form. Rewrite vectors from one form to another.
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Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
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Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
MA.912.NSO.3.3: : Solve mathematical and real-world problems involving velocity and other quantities that can be represented by vectors.
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Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
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Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
MA.912.NSO.3.4: : Solve mathematical and real-world problems involving vectors in two dimensions using the dot product and vector projections.
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Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
MA.912.NSO.3.6: : Add and subtract vectors algebraically or graphically.
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Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
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Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
MA.912.NSO.3.7: : Given the magnitude and direction of two or more vectors, determine the magnitude and direction of their sum.
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Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
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Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
MA.912.NSO.3.8: : Multiply a vector by a scalar algebraically or graphically.
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Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
MA.912.NSO.3.9: : Compute the magnitude and direction of a vector scalar multiple.
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Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
MA.912.NSO.4: : Represent and perform operations with matrices.
MA.912.NSO.4.1: : Given a mathematical or real-world context, represent and manipulate data using matrices.
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
MA.912.NSO.4.2: : Given a mathematical or real-world context, represent and solve a system of two- or three-variable linear equations using matrices.
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
MA.912.NSO.4.3: : Solve mathematical and real-world problems involving addition, subtraction and multiplication of matrices.
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
MA.912.NSO.4.4: : Solve mathematical and real-world problems using the inverse and determinant of matrices.
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
MA.912.AR: : Algebraic Reasoning
MA.912.AR.1: : Interpret and rewrite algebraic expressions and equations in equivalent forms.
MA.912.AR.1.1: : Identify and interpret parts of an expression that represent a quantity in terms of a mathematical or real-world context, including viewing one or more of its parts as a single entity.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
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Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
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Binomial Probabilities
Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation. 5 Minute Preview
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
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Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
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Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
MA.912.AR.1.2: : Rearrange equations or formulas to isolate a quantity of interest.
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Solving Formulas for any Variable
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps. 5 Minute Preview
MA.912.AR.1.3: : Add, subtract and multiply polynomial expressions with rational number coefficients.
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Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
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Addition of Polynomials
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
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Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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Modeling the Factorization of ax2+bx+c
Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
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Modeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
MA.912.AR.1.5: : Divide polynomial expressions using long division, synthetic division and algebraic manipulation.
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Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview
MA.912.AR.1.6: : Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of polynomials.
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Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
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Addition of Polynomials
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
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Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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Modeling the Factorization of ax2+bx+c
Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
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Modeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
MA.912.AR.1.7: : Rewrite a polynomial expression as a product of polynomials.
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Factoring Special Products
Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps. 5 Minute Preview
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Modeling the Factorization of ax2+bx+c
Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
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Modeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
MA.912.AR.2: : Write, solve and graph linear equations, functions and inequalities in one and two variables.
MA.912.AR.2.1: : Given a real-world context, write and solve one-variable multi-step linear equations.
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Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
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Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
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Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
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Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
MA.912.AR.2.2: : Write a linear two-variable equation to represent relationships between quantities from a graph, a written description or a table of values within a mathematical or real-world context.
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
MA.912.AR.2.3: : Write a linear two-variable equation for a line that is parallel or perpendicular to a given line and goes through a given point.
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
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Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
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Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
MA.912.AR.2.4: : Given a table, equation or written description of a linear function, graph that function, and determine and interpret its key features.
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
MA.912.AR.2.5: : Solve and graph mathematical and real-world problems that are modeled with linear functions. Interpret key features and determine domain constraints in terms of the context.
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
MA.912.AR.2.6: : Given a mathematical or real-world context, write and solve one-variable linear inequalities, including compound inequalities. Represent solutions algebraically or graphically.
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Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
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Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
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Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
MA.912.AR.2.7: : Write two-variable linear inequalities to represent relationships between quantities from a graph or a written description within a mathematical or real-world context.
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Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
MA.912.AR.2.8: : Given a mathematical or real-world context, graph the solution set to a two-variable linear inequality.
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Linear Inequalities in Two Variables
Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response. 5 Minute Preview
MA.912.AR.3: : Write, solve and graph quadratic equations, functions and inequalities in one and two variables.
MA.912.AR.3.1: : Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real number system.
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Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
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Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
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Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
MA.912.AR.3.2: : Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.
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Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
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Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
MA.912.AR.3.3: : Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically or graphically.
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Quadratic Inequalities
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview
MA.912.AR.3.4: : Write a quadratic function to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
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Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
MA.912.AR.3.5: : Given the x-intercepts and another point on the graph of a quadratic function, write the equation for the function.
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Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
MA.912.AR.3.6: : Given an expression or equation representing a quadratic function, determine the vertex and zeros and interpret them in terms of a real-world context.
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Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
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Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
MA.912.AR.3.7: : Given a table, equation or written description of a quadratic function, graph that function, and determine and interpret its key features.
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Quadratics in Factored Form
Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
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Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview
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Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
MA.912.AR.3.8: : Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the context.
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
MA.912.AR.3.9: : Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written description.
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Quadratic Inequalities
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview
MA.912.AR.3.10: : Given a mathematical or real-world context, graph the solution set to a two-variable quadratic inequality.
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Quadratic Inequalities
Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response. 5 Minute Preview
MA.912.AR.4: : Write, solve and graph absolute value equations, functions and inequalities in one and two variables.
MA.912.AR.4.1: : Given a mathematical or real-world context, write and solve one-variable absolute value equations.
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Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
MA.912.AR.4.2: : Given a mathematical or real-world context, write and solve one-variable absolute value inequalities. Represent solutions algebraically or graphically.
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Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
MA.912.AR.4.3: : Given a table, equation or written description of an absolute value function, graph that function and determine its key features.
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Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
MA.912.AR.4.4: : Solve and graph mathematical and real-world problems that are modeled with absolute value functions. Interpret key features and determine domain constraints in terms of the context.
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Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
MA.912.AR.5: : Write, solve and graph exponential and logarithmic equations and functions in one and two variables.
MA.912.AR.5.1: : Solve one-variable exponential equations using the properties of exponents.
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Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
MA.912.AR.5.2: : Solve equations involving one-variable logarithms or exponents. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
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Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
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Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph. 5 Minute Preview
MA.912.AR.5.3: : Given a mathematical or real-world context, classify an exponential function as representing growth or decay.
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Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
MA.912.AR.5.4: : Write an exponential function to represent a relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
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Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
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Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
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Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
MA.912.AR.5.5: : Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents. Interpret the constant percent rate of change in terms of a real-world context.
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Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
MA.912.AR.5.6: : Given a table, equation or written description of an exponential function, graph that function and determine its key features.
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Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
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Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
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Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
MA.912.AR.5.7: : Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine domain constraints in terms of the context.
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Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
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Exponential Growth and Decay
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview
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Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
MA.912.AR.5.8: : Given a table, equation or written description of a logarithmic function, graph that function and determine its key features.
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Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
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Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph. 5 Minute Preview
MA.912.AR.5.9: : Solve and graph mathematical and real-world problems that are modeled with logarithmic functions. Interpret key features and determine constraints in terms of the context.
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Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
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Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph. 5 Minute Preview
MA.912.AR.6: : Solve and graph polynomial equations and functions in one and two variables.
MA.912.AR.6.1: : Given a mathematical or real-world context, when suitable factorization is possible, solve one-variable polynomial equations of degree 3 or higher over the real and complex number systems.
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Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
MA.912.AR.6.2: : Explain and apply the Remainder Theorem.
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Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview
MA.912.AR.6.3: : Given a table, equation or written description of a polynomial function of degree 3 or higher, graph that function and determine its key features.
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Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
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Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
MA.912.AR.6.4: : Sketch a rough graph of a polynomial function of degree 3 or higher using zeros, multiplicity and knowledge of end behavior.
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Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
MA.912.AR.6.5: : Solve and graph mathematical and real-world problems that are modeled with polynomial functions of degree 3 or higher. Interpret key features in terms of the context.
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Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
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Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview
MA.912.AR.7: : Solve and graph radical equations and functions in one and two variables.
MA.912.AR.7.1: : Solve one-variable radical equations. Interpret solutions as viable in terms of context and identify any extraneous solutions.
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
MA.912.AR.7.2: : Given a table, equation or written description of a square root or cube root function, graph that function and determine its key features.
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
MA.912.AR.7.3: : Solve and graph mathematical and real-world problems that are modeled with square root or cube root functions. Interpret key features in context.
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
MA.912.AR.8: : Solve and graph rational equations and functions in one and two variables.
MA.912.AR.8.1: : Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
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Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
MA.912.AR.8.2: : Given a table, equation or written description of a rational function, graph that function and determine its key features.
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General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
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Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
MA.912.AR.8.3: : Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features in terms of the context.
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General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
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Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
MA.912.AR.9: : Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.
MA.912.AR.9.1: : Given a mathematical or real-world context, write and solve a system of two-variable linear equations algebraically or graphically.
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Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
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Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
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Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
MA.912.AR.9.4: : Graph the solution set of a system of two-variable linear inequalities.
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Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
MA.912.AR.9.5: : Given a real-world context, represent constraints as systems of linear equations or inequalities. Interpret solutions to problems as viable or nonviable options.
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Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
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Linear Programming
Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview
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Solving Linear Systems (Matrices and Special Solutions)
Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations. 5 Minute Preview
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Solving Linear Systems (Slope-Intercept Form)
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
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Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
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Systems of Linear Inequalities (Slope-intercept form)
Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview
MA.912.AR.9.7: : Solve real-world problems involving linear programming.
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Linear Programming
Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview
MA.912.AR.9.9: : Graph and solve mathematical and real-world problems that are modeled with piecewise functions. Interpret key features and determine constraints in terms of the context.
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Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
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Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
MA.912.AR.10: : Write and solve sequence and series equations, functions and inequalities in one and two variables.
MA.912.AR.10.1: : Given a mathematical or real-world context, write and solve problems involving arithmetic sequences.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
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Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
MA.912.AR.10.2: : Given a mathematical or real-world context, write and solve problems involving geometric sequences.
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Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
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Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
MA.912.AR.10.5: : Given a mathematical or real-world context, write a sequence using function notation, defined explicitly or recursively, to represent relationships between quantities from a written description.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
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Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
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Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
MA.912.AR.10.6: : Given a mathematical or real-world context, find the domain of a given sequence defined recursively or explicitly.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
MA.912.F: : Functions
MA.912.F.1: : Understand, compare and analyze properties of functions.
MA.912.F.1.1: : Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
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Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
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Introduction to Exponential Functions
Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
MA.912.F.1.2: : Given a function represented in function notation, evaluate the function for an input in its domain. For a real-world context, interpret the output.
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
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Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
MA.912.F.1.3: : Calculate and interpret the average rate of change of a real-world situation represented graphically, algebraically or in a table over a specified interval.
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Cat and Mouse (Modeling with Linear Systems)
Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines. 5 Minute Preview
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Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
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Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
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Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
MA.912.F.1.4: : Demonstrate understanding of the concept of limit and estimate limits from graphs and tables of values, as related to the concept of the derivative of a function.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.F.1.5: : Compare key features of linear and nonlinear functions each represented in the same way, such as algebraically, graphically, in tables or written descriptions.
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Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
MA.912.F.1.6: : Compare key features of two functions each represented in a different way such as algebraically, graphically, in tables or written descriptions.
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Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
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Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
MA.912.F.1.7: : Determine whether a linear, quadratic or exponential function best models a given real-world situation.

Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
MA.912.F.1.8: : Determine whether a function is even, odd or neither when represented algebraically, graphically or in a table.
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Graphs of Polynomial Functions
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview
MA.912.F.2: : Identify and describe the effects of transformations on functions. Create new functions given transformations.
MA.912.F.2.1: : Identify the effect on the graph or table of a given function after replacing f(x) by f(x) + k, kf(x) and f(x + k) for specific values of k.
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
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Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
MA.912.F.2.2: : Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
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Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
MA.912.F.2.3: : Given the graph or table of f(x) and the graph or table of f(x) + k, kf(x), f(kx) and f(x + k), state the type of transformation and find the value of the real number k.
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
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Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
MA.912.F.2.4: : Given the graph or table of values of two or more transformations of a function, state the type of transformation and find the values of the real number that defines the transformation.
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
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Zap It! Game
Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview
MA.912.F.2.5: : Given two or more transformations and a function, create the table or graph of the transformed function.
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Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview

Quadratics in Vertex Form
Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview
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Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
MA.912.F.2.6: : Given a graph or table of values of two or more transformations of a function, write the equation of the transformed function.
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Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview
MA.912.F.3: : Create new functions from existing functions.
MA.912.F.3.1: : Given a mathematical or real-world context, combine two functions, limited to linear and quadratic, using arithmetic operations. When appropriate, include domain restrictions for the new function.
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Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
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Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
MA.912.F.3.2: : Given a mathematical or real-world context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations. When appropriate, include domain restrictions for the new function.
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Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
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Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
MA.912.F.3.3: : Solve mathematical and real-world problems involving functions that have been combined using arithmetic operations.
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Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview
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Solving Linear Systems (Standard Form)
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations. 5 Minute Preview
MA.912.F.3.6: : Determine whether an inverse function exists by analyzing tables, graphs and equations.
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Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
MA.912.F.3.7: : Represent the inverse of a function algebraically, graphically or in a table. Use composition of functions to verify that one function is the inverse of the other.
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Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
MA.912.F.3.9: : Solve mathematical and real-world problems involving inverse functions.
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Logarithmic Functions
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function. 5 Minute Preview
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Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
MA.912.FL: : Financial Literacy
MA.912.FL.1: : Determine simple and compound interest and demonstrate its relationship to functions. Calculate and use net present and net future values.
MA.912.FL.1.1: : Compare simple, compound and continuously compounded interest over time.
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
MA.912.FL.1.2: : Solve problems involving simple, compound and continuously compounded interest, including determining the present value and future value of money.
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
MA.912.FL.1.4: : Explain the relationship between compound interest and exponential growth and the relationship between continuously compounded interest and exponential growth.
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
MA.912.FL.1.6: : Solve problems involving potential profit and actual cost.
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Linear Programming
Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response. 5 Minute Preview
MA.912.FL.2: : Describe the advantages and disadvantages of short-term and long-term purchases.
MA.912.FL.2.2: : Calculate the finance charges and total amount due on a bill using various forms of credit.
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
MA.912.FL.2.7: : Solve problems involving student, personal and car loans, including finding the total amount to be paid, adjustable rates and refinancing options.
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
MA.912.FL.2.12: : Compare interest rate calculations and annual percentage rate calculations, and distinguish between the two rates.
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Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
MA.912.GR: : Geometric Reasoning
MA.912.GR.1: : Prove and apply geometric theorems to solve problems.
MA.912.GR.1.1: : Prove relationships and theorems about lines and angles. Solve mathematical and real-world problems involving postulates, relationships and theorems of lines and angles.
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Concurrent Lines, Medians, and Altitudes
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped. 5 Minute Preview
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Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
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Parallel, Intersecting, and Skew Lines
Explore the properties of intersecting, parallel, and skew lines as well as lines in the plane. Rotate the plane and lines in three-dimensional space to ensure a full understanding of these objects. 5 Minute Preview
MA.912.GR.1.2: : Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.
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Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
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Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
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Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
MA.912.GR.1.3: : Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.
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Concurrent Lines, Medians, and Altitudes
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped. 5 Minute Preview
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Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview
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Segment and Angle Bisectors
Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true. 5 Minute Preview
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Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
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Triangle Inequalities
Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles. 5 Minute Preview
MA.912.GR.1.4: : Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelograms.
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Parallelogram Conditions
Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram. 5 Minute Preview
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Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview
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Special Parallelograms
Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition? 5 Minute Preview
MA.912.GR.1.5: : Prove relationships and theorems about trapezoids. Solve mathematical and real-world problems involving postulates, relationships and theorems of trapezoids.
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Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
MA.912.GR.1.6: : Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.
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Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
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Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
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Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
MA.912.GR.2: : Apply properties of transformations to describe congruence or similarity.
MA.912.GR.2.1: : Given a preimage and image, describe the transformation and represent the transformation algebraically using coordinates.
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
MA.912.GR.2.2: : Identify transformations that do or do not preserve distance.
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
MA.912.GR.2.3: : Specify a sequence of transformations that will map a given figure onto itself or onto another congruent or similar figure.
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
MA.912.GR.2.5: : Apply rigid transformations to map one figure onto another to justify that the two figures are congruent.
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Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
MA.912.GR.2.6: : Justify the criteria for triangle congruence using the definition of congruence in terms of rigid transformations.
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Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
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Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
MA.912.GR.2.7: : Apply an appropriate transformation to map one figure onto another to justify that the two figures are similar.
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
MA.912.GR.2.8: : Justify the criteria for triangle similarity using the definition of similarity in terms of non-rigid transformations.
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
MA.912.GR.3: : Use coordinate geometry to solve problems or prove relationships.
MA.912.GR.3.1: : Given a mathematical or real-world context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.
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Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
MA.912.GR.3.2: : Solve geometric problems involving circles, triangles and quadrilaterals on the coordinate plane.
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Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
MA.912.GR.3.3: : Solve mathematical and real-world problems on the coordinate plane that involve finding the coordinates of a point on a line segment including the midpoint.
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Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
MA.912.GR.3.4: : Solve mathematical and real-world problems on the coordinate plane involving perimeter or area of polygons.
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Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
MA.912.GR.4: : Use geometric measurement and dimensions to solve problems.
MA.912.GR.4.1: : Identify the shapes of two-dimensional cross-sections of three-dimensional figures.
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Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
MA.912.GR.4.2: : Identify three-dimensional objects generated by rotations of two-dimensional figures.
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Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
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Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
MA.912.GR.4.3: : Determine how changes in dimensions affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.
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Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
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Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
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Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
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Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
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Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
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Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
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Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
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Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
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Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
MA.912.GR.4.4: : Solve mathematical and real-world problems involving the area of two-dimensional figures.
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Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
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Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
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Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
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Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
MA.912.GR.4.5: : Solve mathematical and real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
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Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
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Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
MA.912.GR.4.6: : Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
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Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
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Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
MA.912.GR.5: : Make formal geometric constructions with a variety of tools and methods.
MA.912.GR.5.1: : Construct a copy of a segment or an angle.
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Constructing Congruent Segments and Angles
Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
MA.912.GR.5.2: : Construct the bisector of a segment or an angle, including the perpendicular bisector of a line segment.
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Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
MA.912.GR.6: : Use properties and theorems related to circles.
MA.912.GR.6.1: : Solve mathematical and real-world problems involving the length of a secant, tangent, segment or chord in a given circle.
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Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
MA.912.GR.6.2: : Solve mathematical and real-world problems involving the measures of arcs and related angles, limited to central, inscribed and intersections of a chord, secants or tangents.
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Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
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Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
MA.912.GR.6.3: : Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.
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Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
MA.912.GR.6.4: : Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.
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Radians
As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the belt’s wheel. How do you set these to get the distance right? See how this relates to arc length, and discover how radians help make this task easier. 5 Minute Preview
MA.912.GR.6.5: : Apply transformations to prove that all circles are similar.
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Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
MA.912.GR.7: : Apply geometric and algebraic representations of conic sections.
MA.912.GR.7.1: : Identify the conic resulting from the cross-section of cones.
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Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
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Ellipses
Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property. 5 Minute Preview
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Hyperbolas
Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response. 5 Minute Preview
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Parabolas
Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview
MA.912.GR.7.2: : Given a mathematical or real-world context, derive and create the equation of a circle using key features.
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Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
MA.912.GR.7.3: : Graph and solve mathematical and real-world problems that are modeled with an equation of a circle. Determine and interpret key features in terms of the context.
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Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
MA.912.GR.7.4: : Given a mathematical or real-world context, derive and create the equation of a parabola using key features.
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Parabolas
Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview
MA.912.GR.7.5: : Graph and solve mathematical and real-world problems that are modeled with an equation of a parabola. Determine and interpret key features in terms of the context.
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Parabolas
Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview
MA.912.GR.7.6: : Given a mathematical or real-world context, derive and create the equation of an ellipse using key features.
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Ellipses
Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property. 5 Minute Preview
MA.912.GR.7.7: : Graph and solve mathematical and real-world problems that are modeled with an equation of an ellipse. Determine and interpret key features in terms of the context.
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Ellipses
Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property. 5 Minute Preview
MA.912.GR.7.8: : Given a mathematical or real-world context, derive and create the equation of a hyperbola using key features.
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Hyperbolas
Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response. 5 Minute Preview
MA.912.GR.7.9: : Graph and solve mathematical and real-world problems that are modeled with an equation of a hyperbola. Determine and interpret key features in terms of the context.
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Hyperbolas
Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response. 5 Minute Preview
MA.912.T: : Trigonometry
MA.912.T.1: : Define and use trigonometric ratios, identities or functions to solve problems.
MA.912.T.1.1: : Define trigonometric ratios for acute angles in right triangles.
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Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
MA.912.T.1.2: : Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.
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Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
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Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
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Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
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Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
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Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
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Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
MA.912.T.1.5: : Prove Pythagorean Identities. Apply Pythagorean Identities to calculate trigonometric ratios and to solve problems.
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Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
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Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
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Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
MA.912.T.1.6: : Prove the Double-Angle, Half-Angle, Angle Sum and Difference formulas for sine, cosine, and tangent. Apply these formulas to solve problems.
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Sum and Difference Identities for Sine and Cosine
Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
MA.912.T.1.7: : Simplify expressions using trigonometric identities.
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Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
MA.912.T.1.8: : Solve trigonometric equations within a mathematical or real-world context, applying inverse functions and using technology when appropriate.
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Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
MA.912.T.2: : Extend trigonometric functions to the unit circle.
MA.912.T.2.1: : Define the trigonometric functions for any angle using right triangles drawn in the unit circle. Determine the values of sine, cosine and tangent of pi/3, pi/4 and pi/6 and their multiples using special triangles.

Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
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Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
MA.912.T.2.2: : Define and determine the sine, cosine, tangent, cosecant, secant and cotangent of angles using the unit circle.

Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
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Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
MA.912.T.2.3: : Given angles measured in radians or degrees, calculate the values of the six trigonometric functions.

Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
MA.912.T.3: : Graph and apply trigonometric relations and functions.
MA.912.T.3.1: : Describe and demonstrate the connections between right triangle ratios and trigonometric functions.

Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
MA.912.T.3.2: : On the coordinate plane, express the values of sine, cosine and tangent for pi – x, pi + x and 2pi – x in terms of their values for x, where x is any real number.

Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
MA.912.T.3.3: : Given a mathematical or real-world context, choose sine, cosine or tangent trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift and midline.
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Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sound Beats and Sine Waves
Listen to and see interference patterns produced by sound waves with similar frequencies. Test your ability to distinguish and match sounds as musicians do when they tune their instruments. Calculate the number of "sound beats" you will hear based on the frequency of each sound. [Note: Headphones are recommended for this Gizmo.] 5 Minute Preview

Translating and Scaling Sine and Cosine Functions
Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview
MA.912.T.3.4: : Given a table, equation or written description of a trigonometric function, graph that function and determine key features.

Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

Translating and Scaling Sine and Cosine Functions
Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview
MA.912.T.3.5: : Graph and solve mathematical and real-world problems that are modeled with trigonometric functions. Interpret key features and determine domain constraints in terms of the context.

Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sound Beats and Sine Waves
Listen to and see interference patterns produced by sound waves with similar frequencies. Test your ability to distinguish and match sounds as musicians do when they tune their instruments. Calculate the number of "sound beats" you will hear based on the frequency of each sound. [Note: Headphones are recommended for this Gizmo.] 5 Minute Preview

Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

Translating and Scaling Sine and Cosine Functions
Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview
MA.912.T.3.7: : Solve mathematical and real-world problems involving applications of trigonometric functions using graphing technology when appropriate.

Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sound Beats and Sine Waves
Listen to and see interference patterns produced by sound waves with similar frequencies. Test your ability to distinguish and match sounds as musicians do when they tune their instruments. Calculate the number of "sound beats" you will hear based on the frequency of each sound. [Note: Headphones are recommended for this Gizmo.] 5 Minute Preview

Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

Translating and Scaling Sine and Cosine Functions
Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview
MA.912.T.4: : Extend rectangular coordinates and equations to polar and parametric forms.
MA.912.T.4.1: : Define polar coordinates and relate polar coordinates to Cartesian coordinates with and without the use of technology.

Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
MA.912.DP: : Data Analysis and Probability
MA.912.DP.1: : Summarize, represent and interpret categorical and numerical data with one and two variables.
MA.912.DP.1.1: : Given a set of data, select an appropriate method to represent the data, depending on whether it is numerical or categorical data and on whether it is univariate or bivariate.

Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
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Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview

Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
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Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
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Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Stem-and-Leaf Plots
Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
MA.912.DP.1.2: : Interpret data distributions represented in various ways. State whether the data is numerical or categorical, whether it is univariate or bivariate and interpret the different components and quantities in the display.

Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview

Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

Stem-and-Leaf Plots
Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
MA.912.DP.1.3: : Explain the difference between correlation and causation in the contexts of both numerical and categorical data.

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
MA.912.DP.1.4: : Estimate a population total, mean or percentage using data from a sample survey; develop a margin of error through the use of simulation.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.1.5: : Interpret the margin of error of a mean or percentage from a data set. Interpret the confidence level corresponding to the margin of error.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
MA.912.DP.2: : Solve problems involving univariate and bivariate numerical data.
MA.912.DP.2.1: : For two or more sets of numerical univariate data, calculate and compare the appropriate measures of center and measures of variability, accounting for possible effects of outliers. Interpret any notable features of the shape of the data distribution.

Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.2.2: : Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use technology, empirical rules or tables to estimate areas under the normal curve.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.2.3: : Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and y-intercept of the model. Use the model to solve real-world problems in terms of the context of the data.

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
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Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
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Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
MA.912.DP.2.4: : Given a scatter plot that represents bivariate numerical data, assess the fit of a given linear function by plotting and analyzing residuals.

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
MA.912.DP.2.5: : Given a scatter plot with a line of fit and residuals, determine the strength and direction of the correlation. Interpret strength and direction within a real-world context.

Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
MA.912.DP.2.6: : Compute the correlation coefficient of a linear model using technology. Interpret the strength and direction of the correlation coefficient.

Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
MA.912.DP.3: : Solve problems involving categorical data.
MA.912.DP.3.5: : Solve real-world problems involving univariate and bivariate categorical data.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
MA.912.DP.4: : Use and interpret independence and probability.
MA.912.DP.4.2: : Determine if events A and B are independent by calculating the product of their probabilities.
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Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
MA.912.DP.4.3: : Calculate the conditional probability of two events and interpret the result in terms of its context.

Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
MA.912.DP.4.4: : Interpret the independence of two events using conditional probability.

Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
MA.912.DP.4.6: : Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
MA.912.DP.4.8: : Apply the general multiplication rule for probability, taking into consideration whether the events are independent, and interpret the result in terms of the context.

Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
MA.912.DP.4.9: : Given a mathematical or real-world situation, calculate the appropriate permutation or combination.
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Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
MA.912.DP.4.10: : Compute probabilities of compound events. Solve mathematical and real-world problems using permutations and combinations.

Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview
MA.912.DP.5: : Determine methods of data collection and make inferences from collected data.
MA.912.DP.5.1: : Distinguish between a population parameter and a sample statistic.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.5.2: : Explain how random sampling produces data that is representative of a population.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.5.3: : Compare and contrast sampling methods.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
MA.912.DP.5.4: : Generate multiple samples or simulated samples of the same size to measure the variation in estimates or predictions.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.5.6: : Determine the appropriate design, survey, experiment or observational study, based on the purpose. Articulate the types of questions appropriate for each type of design.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.5.7: : Compare and contrast surveys, experiments and observational studies.

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.5.8: : Explain how randomization relates to sample surveys, experiments and observational studies.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.5.9: : Draw inferences about two populations using data and statistical analysis from two random samples.

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.5.10: : Compare two treatments from an experiment using data from a randomized experiment.

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.5.11: : Determine whether differences between parameters are significant using simulations.

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
MA.912.DP.5.12: : Evaluate reports based on data from diverse media, print and digital resources by interpreting graphs and tables; evaluating data-based arguments; determining whether a valid sampling method was used; or interpreting provided statistics.

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
MA.912.DP.6: : Use probability distributions to solve problems.
MA.912.DP.6.2: : Develop a probability distribution for a discrete random variable using theoretical probabilities. Find the expected value and interpret it as the mean of the discrete distribution.

Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
MA.912.DP.6.3: : Develop a probability distribution for a discrete random variable using empirically assigned probabilities. Find the expected value and interpret it as the mean of the discrete distribution.

Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
MA.912.DP.6.4: : Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Evaluate and compare strategies on the basis of the calculated expected values.

Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
MA.912.DP.6.5: : Apply probabilities to make decisions which are equally likely, such as drawing from lots or using a random number generator.

Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
MA.912.DP.6.6: : Analyze decisions that were made and solve problems using probability concepts and strategies.

Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview
MA.912.LT: : Logic and Theory
MA.912.LT.1: : Apply recursive methods to solve problems.
MA.912.LT.1.1: : Apply recursive and iterative thinking to solve problems.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
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Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
MA.912.LT.1.2: : Solve problems and find explicit formulas for recurrence relations using finite differences.
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Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
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Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
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Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
MA.912.LT.4: : Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.
MA.912.LT.4.3: : Identify and accurately interpret “if…then,” “if and only if,” “all” and “not” statements. Find the converse, inverse and contrapositive of a statement.
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Biconditional Statements
Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
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Conditional Statements
Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
MA.912.C: : Calculus
MA.912.C.1: : Determine limits and continuity.
MA.912.C.1.11: : Identify the types of discontinuities for a given function.
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General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
MA.912.C.2: : Determine derivatives.
MA.912.C.2.1: : Apply and interpret derivatives geometrically and numerically.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.C.2.2: : Interpret the derivative as an instantaneous rate of change or as the slope of the tangent line.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.C.2.10: : Find second derivatives and derivatives of higher order.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.C.3: : Apply derivatives.
MA.912.C.3.1: : Find the slope of a curve at a point, including points at which there are vertical tangent lines and no tangent lines.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.C.3.3: : Determine where a function is decreasing and increasing using its derivative.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.C.3.4: : Find local and absolute maximum and minimum points of a function.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.C.3.5: : Determine the concavity and points of inflection of a function using its second derivative.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.C.3.6: : Sketch graphs by using first and second derivatives. Compare the corresponding characteristics of the graphs of f, f prime and f double prime.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.C.3.8: : Find average and instantaneous rates of change. Explain the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed and acceleration.
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Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine. 5 Minute Preview
MA.912.C.4: : Determine integrals.
MA.912.C.4.1: : Find approximate values of integrals by using rectangle approximations.
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Riemann Sum
Approximate the area under a curve in an interval using rectangles. Compare the results of left-hand summation to the results of right-hand summation. Vary the interval and the number of rectangles and explore how the graph of the rectangles and curve change in response. 5 Minute Preview
MA.912.C.4.2: : Calculate the values of Riemann sums over equal subdivisions using left, right and midpoint evaluation points.
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Riemann Sum
Approximate the area under a curve in an interval using rectangles. Compare the results of left-hand summation to the results of right-hand summation. Vary the interval and the number of rectangles and explore how the graph of the rectangles and curve change in response. 5 Minute Preview
Correlation last revised: 9/16/2020
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
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Multiple grade-appropriate versions, or levels, exist for each STEM Case.
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Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
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Start teaching with 20-40 Free Gizmos. See the full list.
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Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.
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Free Gizmos change each semester. The new collection will be available January 1 and July 1.
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