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  • Alabama Standards
  • Mathematics: Algebra 2 with Trigonometry

Alabama - Mathematics: Algebra 2 with Trigonometry

Course of Study | Adopted: 2016

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

N: : Number and Quantity


N-CN: : The Complex Number System

1.1.1: : Perform arithmetic operations with complex numbers.

N-CN.1: : Students will: Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

Screenshot of Points in the Complex Plane

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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Screenshot of Roots of a Quadratic

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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N-CN.2: : Students will: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Screenshot of Points in the Complex Plane

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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N-CN.3: : Students will: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Screenshot of Points in the Complex Plane

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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Launch Gizmo
Screenshot of Roots of a Quadratic

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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1.1.2: : Use complex numbers in polynomial identities and equations.

N-CN.4: : Students will: Solve quadratic equations with real coefficients that have complex solutions.

Screenshot of Points in the Complex Plane

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


Lesson Info
Launch Gizmo
Screenshot of Roots of a Quadratic

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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N-VM: : Vector and Matrix Quantities

1.2.1: : Perform operations on matrices and use matrices in applications.

N-VM.7: : Students will: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

Screenshot of Dilations

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form. 5 Minute Preview


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Screenshot of Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview


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N-VM.8: : Students will: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

Screenshot of Dilations

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form. 5 Minute Preview


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N-VM.9: : Students will: Add, subtract, and multiply matrices of appropriate dimensions.

Screenshot of Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview


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N-VM.11: : Students will: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

Screenshot of Solving Linear Systems (Matrices and Special Solutions)

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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A: : Algebra


A-SSE: : Seeing Structure in Expressions

2.1.1: : Interpret the structure of expressions.

A-SSE.12: : Students will: Interpret expressions that represent a quantity in terms of its context.

A-SSE.12.a: : Interpret parts of an expression such as terms, factors, and coefficients.

Screenshot of Compound Interest

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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Screenshot of Operations with Radical Expressions

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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Screenshot of Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions I

Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview


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Screenshot of Simplifying Algebraic Expressions II

Simplifying Algebraic Expressions II

Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview


Lesson Info
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Screenshot of Solving Formulas for any Variable

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


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A-SSE.12.b: : Interpret complicated expressions by viewing one or more of their parts as a single entity.

Screenshot of Arithmetic Sequences

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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Screenshot of Arithmetic and Geometric Sequences

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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Screenshot of Compound Interest

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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Screenshot of Exponential Growth and Decay

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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Screenshot of Geometric Sequences

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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Screenshot of Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions I

Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Simplifying Algebraic Expressions II

Simplifying Algebraic Expressions II

Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Translating and Scaling Functions

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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Screenshot of Using Algebraic Expressions

Using Algebraic Expressions

Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview


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A-SSE.13: : Students will: Use the structure of an expression to identify ways to rewrite it.

Screenshot of Dividing Exponential Expressions

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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Screenshot of Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions I

Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview


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Screenshot of Equivalent Algebraic Expressions II

Equivalent Algebraic Expressions II

Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview


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Screenshot of Exponents and Power Rules

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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Screenshot of Factoring Special Products

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


Lesson Info
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Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>

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


Lesson Info
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Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>

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


Lesson Info
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Screenshot of Multiplying Exponential Expressions

Multiplying Exponential Expressions

Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview


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Screenshot of Quadratics in Factored Form

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


Lesson Info
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Screenshot of Quadratics in Polynomial Form

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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Screenshot of Quadratics in Vertex Form

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


Lesson Info
Launch Gizmo
Screenshot of Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions I

Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Simplifying Algebraic Expressions II

Simplifying Algebraic Expressions II

Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Simplifying Trigonometric Expressions

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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Screenshot of Solving Algebraic Equations II

Solving Algebraic Equations II

Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview


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Screenshot of Using Algebraic Expressions

Using Algebraic Expressions

Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview


Lesson Info
Launch Gizmo

A-APR: : Arithmetic with Polynomials and Rational Expressions

2.3.1: : Perform arithmetic operations on polynomials.

A-APR.15: : Students will: Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Screenshot of Addition and Subtraction of Functions

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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Screenshot of Addition of Polynomials

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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Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>

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


Lesson Info
Launch Gizmo
Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>

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


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2.3.2: : Understand the relationship between zeros and factors of polynomials.

A-APR.16: : Students will: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

Screenshot of Dividing Polynomials Using Synthetic Division

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


Lesson Info
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Screenshot of Polynomials and Linear Factors

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


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A-APR.17: : Students will: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Screenshot of Graphs of Polynomial Functions

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


Lesson Info
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Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>

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


Lesson Info
Launch Gizmo
Screenshot of Polynomials and Linear Factors

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


Lesson Info
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Screenshot of Quadratics in Factored Form

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


Lesson Info
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Screenshot of Quadratics in Vertex Form

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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2.3.3: : Use polynomial identities to solve problems.

A-APR.18: : Students will: Prove polynomial identities and use them to describe numerical relationships.

Screenshot of Factoring Special Products

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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2.3.4: : Rewrite rational expressions.

A-APR.19: : Students will: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or for the more complicated examples, a computer algebra system.

Screenshot of Dividing Polynomials Using Synthetic Division

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


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A-CED: : Creating Equations

2.4.1: : Create equations that describe numbers or relationships.

A-CED.20: : Students will: Create equations and inequalities in one variable and use them to solve problems.

Screenshot of Absolute Value Equations and Inequalities

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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Screenshot of Arithmetic Sequences

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


Lesson Info
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Screenshot of Compound Interest

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


Lesson Info
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Screenshot of Exploring Linear Inequalities in One Variable

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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Screenshot of Geometric Sequences

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


Lesson Info
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Screenshot of Linear Inequalities in Two Variables

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


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Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview


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Screenshot of Modeling and Solving Two-Step Equations

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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Screenshot of Quadratic Inequalities

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


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Screenshot of Roots of a Quadratic

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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Screenshot of Solving Equations by Graphing Each Side

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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Screenshot of Solving Equations on the Number Line

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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Screenshot of Solving Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview


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Screenshot of Solving Linear Systems (Slope-Intercept Form)

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 (x, y) point to be a solution of one equation, or of a system of two equations. 5 Minute Preview


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Screenshot of Solving Two-Step Equations

Solving Two-Step Equations

Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview


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Screenshot of Using Algebraic Equations

Using Algebraic Equations

Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview


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A-CED.21: : Students will: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Screenshot of Absolute Value Equations and Inequalities

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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Screenshot of Circles

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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Screenshot of Compound Interest

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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Screenshot of Exponential Functions

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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Screenshot of Exponential Growth and Decay

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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Screenshot of Linear Functions

Linear Functions

Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview


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Screenshot of Point-Slope Form of a Line

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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Screenshot of Points, Lines, and Equations

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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Screenshot of Quadratics in Polynomial Form

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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Screenshot of Quadratics in Vertex Form

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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Screenshot of Slope-Intercept Form of a Line

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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Screenshot of Solving Equations by Graphing Each Side

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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Screenshot of Solving Equations on the Number Line

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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Screenshot of Solving Linear Systems (Matrices and Special Solutions)

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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Screenshot of Solving Linear Systems (Slope-Intercept Form)

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 (x, y) point to be a solution of one equation, or of a system of two equations. 5 Minute Preview


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Screenshot of Solving Linear Systems (Standard Form)

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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Screenshot of Standard Form of a Line

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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Screenshot of Using Algebraic Equations

Using Algebraic Equations

Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview


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A-CED.22: : Students will: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

Screenshot of Linear Inequalities in Two Variables

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


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Screenshot of Linear Programming

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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Screenshot of Solving Linear Systems (Standard Form)

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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Screenshot of Systems of Linear Inequalities (Slope-intercept form)

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


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A-CED.23: : Students will: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Screenshot of Area of Triangles

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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Screenshot of Solving Formulas for any Variable

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


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A-REI: : Reasoning with Equations and Inequalities

2.5.1: : Understand solving equations as a process of reasoning, and explain the reasoning.

A-REI.24: : Students will: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Screenshot of Radical Functions

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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2.5.2: : Solve equations and inequalities in one variable.

A-REI.25: : Students will: Recognize when the quadratic formula gives complex solutions, and write them as a ± bi for real numbers a and b.

Screenshot of Factoring Special Products

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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Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>

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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Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>

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


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Screenshot of Points in the Complex Plane

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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Screenshot of Roots of a Quadratic

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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2.5.3: : Solve systems of equations.

A-REI.26: : Students will: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

Screenshot of Solving Linear Systems (Matrices and Special Solutions)

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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2.5.4: : Represent and solve equations and inequalities graphically.

A-REI.27: : Students will: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Screenshot of Cat and Mouse (Modeling with Linear Systems)

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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Screenshot of Point-Slope Form of a Line

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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Screenshot of Solving Equations by Graphing Each Side

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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Screenshot of Solving Linear Systems (Matrices and Special Solutions)

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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Screenshot of Solving Linear Systems (Slope-Intercept Form)

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 (x, y) point to be a solution of one equation, or of a system of two equations. 5 Minute Preview


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Screenshot of Standard Form of a Line

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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A-CS: : Conic Sections

2.6.1: : Understand the graphs and equations of conic sections.

A-CS.28: : Students will: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.

A-CS.28.a: : Formulate equations of conic sections from their determining characteristics.

Screenshot of Addition and Subtraction of Functions

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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Screenshot of Circles

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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Screenshot of Ellipses

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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Screenshot of Hyperbolas

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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Screenshot of Parabolas

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


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F: : Functions


F-IF: : Interpreting Functions

3.1.1: : Interpret functions that arise in applications in terms of the context.

F-IF.29: : Students will: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Screenshot of General Form of a Rational Function

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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Screenshot of Introduction to Functions

Introduction to Functions

Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview


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Screenshot of Logarithmic Functions

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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Screenshot of Logarithmic Functions: Translating and Scaling

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


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Screenshot of Radical Functions

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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Screenshot of Rational Functions

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


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3.1.2: : Analyze functions using different representations.

F-IF.30: : Students will: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.30.a: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Screenshot of Absolute Value Equations and Inequalities

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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Screenshot of Absolute Value with Linear Functions

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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Screenshot of Radical Functions

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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Screenshot of Translating and Scaling Functions

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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F-IF.30.b: : Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Screenshot of Graphs of Polynomial Functions

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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Screenshot of Polynomials and Linear Factors

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


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Screenshot of Quadratics in Factored Form

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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Screenshot of Quadratics in Vertex Form

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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Screenshot of Roots of a Quadratic

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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Screenshot of Zap It! Game

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


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F-IF.30.c: : Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Screenshot of Cosine Function

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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Screenshot of Exponential Functions

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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Screenshot of Exponential Growth and Decay

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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Screenshot of Introduction to Exponential Functions

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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Screenshot of Logarithmic Functions

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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Screenshot of Logarithmic Functions: Translating and Scaling

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


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Screenshot of Sine Function

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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Screenshot of Tangent Function

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


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Screenshot of Translating and Scaling Functions

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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Screenshot of Translating and Scaling Sine and Cosine Functions

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


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F-IF.31: : Students will: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F-IF.31.a: : Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Screenshot of Factoring Special Products

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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Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>

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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Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>

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


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Screenshot of Quadratics in Factored Form

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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Screenshot of Quadratics in Vertex Form

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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Screenshot of Roots of a Quadratic

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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F-IF.31.b: : Use the properties of exponents to interpret expressions for exponential functions.

Screenshot of Compound Interest

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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Screenshot of Exponential Functions

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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Screenshot of Exponential Growth and Decay

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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F-IF.32: : Students will: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Screenshot of Direct and Inverse Variation

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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Screenshot of General Form of a Rational Function

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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Screenshot of Graphs of Polynomial Functions

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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Screenshot of Linear Functions

Linear Functions

Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview


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Screenshot of Logarithmic Functions

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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Screenshot of Quadratics in Polynomial Form

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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Screenshot of Quadratics in Vertex Form

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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F-BF: : Building Functions

3.2.1: : Build a function that models a relationship between two quantities.

F-BF.33: : Students will: Write a function that describes a relationship between two quantities.

F-BF.33.a: : Combine standard function types using arithmetic operations.

Screenshot of Addition and Subtraction of Functions

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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3.2.2: : Build new functions from existing functions.

F-BF.34: : Students will: Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Screenshot of Absolute Value with Linear Functions

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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Screenshot of Exponential Functions

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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Screenshot of Introduction to Exponential Functions

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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Screenshot of Logarithmic Functions

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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Screenshot of Logarithmic Functions: Translating and Scaling

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


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Screenshot of Quadratics in Polynomial Form

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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Screenshot of Quadratics in Vertex Form

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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Screenshot of Radical Functions

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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Screenshot of Rational Functions

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


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Screenshot of Translating and Scaling Functions

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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Screenshot of Translating and Scaling Sine and Cosine Functions

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


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Screenshot of Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview


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Screenshot of Zap It! Game

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


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F-BF.35: : Students will: Find inverse functions.

F-BF.35.a: : Solve an equation of the form f(x) = c for a simple function f that has an inverse, and write an expression for the inverse.

Screenshot of Logarithmic Functions

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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Screenshot of Radical Functions

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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F-LE: : Linear, Quadratic, and Exponential Models

3.3.1: : Construct and compare linear, quadratic, and exponential models and solve problems.

F-LE.36: : Students will: For exponential models, express as a logarithm the solution to (ab) to the (ct) power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Screenshot of Compound Interest

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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Screenshot of Logarithmic Functions

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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F-TF: : Trigonometric Functions

3.4.1: : Extend the domain of trigonometric functions using the unit circle.

F-TF.37: : Students will: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Screenshot of Radians

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


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Screenshot of Sine Function

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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Screenshot of Tangent Function

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


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F-TF.38: : Students will: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Screenshot of Cosine Function

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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Screenshot of Sine Function

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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Screenshot of Tangent Function

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


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F-TF.39: : Students will: Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.

Screenshot of Cosine Function

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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Screenshot of Sine Function

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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Screenshot of Sine, Cosine, and Tangent Ratios

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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Screenshot of Tangent Function

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


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3.4.3: : Model periodic phenomena with trigonometric functions.

F-TF.40: : Students will: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Screenshot of Sound Beats and Sine Waves

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


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Screenshot of Translating and Scaling Functions

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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Screenshot of Translating and Scaling Sine and Cosine Functions

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


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S: : Statistics and Probability


S-MD: : Using Probability to Make Decisions

4.1.1: : Use probability to evaluate outcomes of decisions.

S-MD.41: : Students will: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Screenshot of Lucky Duck (Expected Value)

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


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Screenshot of Probability Simulations

Probability Simulations

Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview


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Screenshot of Theoretical and Experimental Probability

Theoretical and Experimental Probability

Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview


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S-MD.42: : Students will: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Screenshot of Estimating Population Size

Estimating Population Size

Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview


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Screenshot of Lucky Duck (Expected Value)

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


Lesson Info
Launch Gizmo
Screenshot of Probability Simulations

Probability Simulations

Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Theoretical and Experimental Probability

Theoretical and Experimental Probability

Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview


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S-CP: : Conditional Probability and the Rules of Probability

4.4.1: : Understand independence and conditional probability and use them to interpret data.

S-CP.43: : Students will: Describe events as subsets of a sample space (the set of outcomes), using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

Screenshot of Independent and Dependent Events

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


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Screenshot of 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


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Screenshot of Probability Simulations

Probability Simulations

Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Theoretical and Experimental Probability

Theoretical and Experimental Probability

Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview


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S-CP.44: : Students will: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

Screenshot of Independent and Dependent Events

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


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S-CP.45: : Students will: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

Screenshot of Histograms

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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S-CP.46: : Students will: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Screenshot of Independent and Dependent Events

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


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4.4.2: : Use the rules of probability to compute probabilities of compound events in a uniform probability model.

S-CP.47: : Students will: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

Screenshot of Independent and Dependent Events

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


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S-CP.49: : Students will: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

Screenshot of Independent and Dependent Events

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


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S-CP.50: : Students will: Use permutations and combinations to compute probabilities of compound events and solve problems.

Screenshot of Binomial Probabilities

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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Screenshot of 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


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Correlation last revised: 9/16/2020

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