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Virginia - Mathematics: Algebra 1
Standards of Learning | Adopted: 2023
A.EO: : Expressions and Operations
A.EO.1: : The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.
A.EO.1.a: : Translate between verbal quantitative situations and algebraic expressions, including contextual situations.
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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
A.EO.2: : The student will perform operations on and factor polynomial expressions in one variable.
A.EO.2.a: : Determine sums and differences of polynomial expressions in one variable, using a variety of strategies, including concrete objects and their related pictorial and symbolic models.
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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
A.EO.2.b: : Determine the product of polynomial expressions in one variable, using a variety of strategies, including concrete objects and their related pictorial and symbolic models, the application of the distributive property, and the use of area models. The factors should be limited to five or fewer terms (e.g., (4x + 2)(3x + 5) represents four terms and (x + 1)(2x² + x + 3) represents five terms).
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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
A.EO.2.c: : Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors.
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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

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
A.EO.2.d: : Determine the quotient of polynomials, using a monomial or binomial divisor, or a completely factored divisor.
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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
A.EO.3: : The student will derive and apply the laws of exponents.
A.EO.3.a: : Derive the laws of exponents through explorations of patterns, to include products, quotients, and powers of bases.
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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
A.EO.3.b: : Simplify multivariable expressions and ratios of monomial expressions in which the exponents are integers, using the laws 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
A.EO.4: : The student will simplify and determine equivalent radical expressions involving square roots of whole numbers and cube roots of integers.
A.EO.4.a: : Simplify and determine equivalent radical expressions involving the square root of a whole number in simplest form.
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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
A.EO.4.c: : Add, subtract, and multiply radicals, limited to numeric square and cube root expressions.
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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
A.EI: : Equations and Inequalities
A.EI.1: : The student will represent, solve, explain, and interpret the solution to multistep linear equations and inequalities in one variable and literal equations for a specified variable.
A.EI.1.a: : Write a linear equation or inequality in one variable to represent a contextual situation.
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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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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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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 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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Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
A.EI.1.b: : Solve multistep linear equations in one variable, including those in contextual situations, by applying the properties of real numbers and/or properties of equality.

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
A.EI.1.c: : Solve multistep linear inequalities in one variable algebraically and graph the solution set on a number line, including those in contextual situations, by applying the properties of real numbers and/or properties of inequality.
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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
A.EI.1.d: : Rearrange a formula or literal equation to solve for a specified variable by applying the properties of equality.
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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
A.EI.1.e: : Determine if a linear equation in one variable has one solution, no solution, or an infinite number of solutions.
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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
A.EI.1.f: : Verify possible solution(s) to multistep linear equations and inequalities in one variable algebraically, graphically, and with technology to justify the reasonableness of the answer(s). Explain the solution method and interpret solutions for problems given in context.

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

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

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

Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
A.EI.2: : The student will represent, solve, explain, and interpret the solution to a system of two linear equations, a linear inequality in two variables, or a system of two linear inequalities in two variables.
A.EI.2.a: : Create a system of two linear equations in two variables to represent a contextual situation.
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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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Cat and Mouse (Modeling with Linear Systems) - Metric
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 (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
A.EI.2.b: : Apply the properties of real numbers and/or properties of equality to solve a system of two linear equations in two variables, algebraically and 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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Cat and Mouse (Modeling with Linear Systems) - Metric
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 (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

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
A.EI.2.c: : Determine whether a system of two linear equations has one solution, no solution, or an infinite number of solutions.
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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

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
A.EI.2.d: : Create a linear inequality in two variables to represent a contextual situation.
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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
A.EI.2.e: : Represent the solution of a linear inequality in two variables graphically on a coordinate plane.
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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
A.EI.2.f: : Create a system of two linear inequalities in two variables to represent a contextual situation.
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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
A.EI.2.g: : Represent the solution set of a system of two linear inequalities in two variables, graphically on a coordinate plane.
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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
A.EI.2.h: : Verify possible solution(s) to a system of two linear equations, a linear inequality in two variable, or a system of two linear inequalities algebraically, graphically, and with technology to justify the reasonableness of the answer(s). Explain the solution method and interpret solutions for problems given in context.

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

Cat and Mouse (Modeling with Linear Systems) - Metric
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

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
A.EI.3: : The student will represent, solve, and interpret the solution to a quadratic equation in one variable.
A.EI.3.a: : Solve a quadratic equation in one variable over the set of real numbers with rational or irrational solutions, including those that can be used to solve contextual problems.
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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
A.EI.3.b: : Determine and justify if a quadratic equation in one variable has no real solutions, one real solution, or two real solutions.
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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
A.EI.3.c: : Verify possible solution(s) to a quadratic equation in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in 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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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
A.F: : Functions
A.F.1: : The student will investigate, analyze, and compare linear functions algebraically and graphically, and model linear relationships.
A.F.1.a: : Determine and identify the domain, range, zeros, slope, and intercepts of a linear function, presented algebraically or graphically, including the interpretation of these characteristics in contextual situations.
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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
A.F.1.b: : Investigate and explain how transformations to the parent function y = x affect the rate of change (slope) and the y-intercept of a linear function.
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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
A.F.1.c: : Write equivalent algebraic forms of linear functions, including slope-intercept form, standard form, and point-slope form, and analyze and interpret the information revealed by each form.
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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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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
A.F.1.d: : Write the equation of a linear function to model a linear relationship between two quantities, including those that can represent contextual situations. Writing the equation of a linear function will include the following situations:
A.F.1.d.i: : given the graph of a line;
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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
A.F.1.d.ii: : given two points on the line whose coordinates are integers;
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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
A.F.1.d.iii: : given the slope and a point on the line whose coordinates are integers;
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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
A.F.1.d.iv: : vertical lines as x = a; and
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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
A.F.1.d.v: : horizontal lines as y = c.
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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
A.F.1.f: : Graph a linear function in two variables, with and without the use of technology, including those that can represent contextual situations.
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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
A.F.1.g: : For any value, x, in the domain of f, determine f(x), and determine x given any value f(x) in the range of f, given an algebraic or graphical representation of a linear function.
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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
A.F.1.h: : Compare and contrast the characteristics of linear functions represented algebraically, graphically, in tables, and in contextual situations.
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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
A.F.2: : The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships.
A.F.2.a: : Determine whether a relation, represented by a set of ordered pairs, a table, a mapping, or a graph is a function; for relations that are functions, determine the domain and range.
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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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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
A.F.2.b: : Given an equation or graph, determine key characteristics of a quadratic function including x-intercepts (zeros), y-intercept, vertex (maximum or minimum), and domain and range (including when restricted by context); interpret key characteristics as related to contextual situations, where applicable.
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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
A.F.2.c: : Graph a quadratic function, f(x), in two variables using a variety of strategies, including transformations f(x) + k and kf(x), where k is limited to rational values.
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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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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
A.F.2.d: : Make connections between the algebraic (standard and factored forms) and graphical representation of a quadratic 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
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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
A.F.2.e: : Given an equation or graph of an exponential function in the form y = ab^x (where b is limited to a natural number), interpret key characteristics, including y-intercepts and domain and range; interpret key characteristics as related to contextual situations, where applicable.
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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
A.F.2.f: : Graph an exponential function, f(x), in two variables using a variety of strategies, including transformations f(x) + k and kf(x), where k is limited to rational values.
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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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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
A.F.2.g: : For any value, x, in the domain of f, determine f(x) of a quadratic or exponential function. Determine x given any value f(x) in the range of f of a quadratic function. Explain the meaning of x and f(x) in 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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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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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
A.F.2.h: : Compare and contrast the key characteristics of linear functions (f(x) = x), quadratic functions (f(x) = x²), and exponential functions (f(x) = b^x) using tables and graphs.
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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
A.ST: : Statistics
A.ST.1: : The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear and quadratic functions.
A.ST.1.a: : Formulate investigative questions that require the collection or acquisition of bivariate 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

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
A.ST.1.d: : Given a table of ordered pairs or a scatterplot representing no more than 30 data points, use available technology to determine whether a linear or quadratic function would represent the relationship, and if so, determine the equation of the curve of best fit.

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

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
A.ST.1.e: : Use linear and quadratic regression methods available through technology to write a linear or quadratic function that represents the data where appropriate and describe the strengths and weaknesses of the model.

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

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
A.ST.1.f: : Use a linear model to predict outcomes and evaluate the strength and validity of these predictions, including through the use of technology.

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

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
A.ST.1.g: : Investigate and explain the meaning of the rate of change (slope) and y-intercept (constant term) of a linear model in context.

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

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
A.ST.1.h: : Analyze relationships between two quantitative variables revealed in a scatterplot.

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

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
A.ST.1.i: : Make conclusions based on the analysis of a set of bivariate data and communicate the results.

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

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
Correlation last revised: 4/9/2024
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.
How Free Gizmos Work
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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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All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.
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Free Gizmos change each semester. The new collection will be available January 1 and July 1.
Find Your Solution
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