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Virginia - Mathematics: Algebra 2
Standards of Learning | Adopted: 2023
A2.EO: : Expressions and Operations
A2.EO.2: : The student will perform operations on and simplify radical expressions.
A2.EO.2.a: : Simplify and determine equivalent radical expressions that include numeric and algebraic radicands.
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
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
![Screenshot of Simplifying Radical Expressions](/Assets/img/blank.gif)
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
A2.EO.2.b: : Add, subtract, multiply, and divide radical expressions that include numeric and algebraic radicands, simplifying the result. Simplification may include rationalizing the denominator.
![Screenshot of Operations with Radical Expressions](/Assets/img/blank.gif)
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
![Screenshot of Simplifying Radical Expressions](/Assets/img/blank.gif)
Simplifying Radical Expressions
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview
A2.EO.3: : The student will perform operations on polynomial expressions and factor polynomial expressions in one and two variables.
A2.EO.3.a: : Determine sums, differences, and products of polynomials in one and two variables.
![Screenshot of Addition and Subtraction of Functions](/Assets/img/blank.gif)
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
![Screenshot of Addition of Polynomials](/Assets/img/blank.gif)
Addition of Polynomials
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview
![Screenshot of Factoring Special Products](/Assets/img/blank.gif)
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
![Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
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
![Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
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
A2.EO.3.b: : Factor polynomials completely in one and two variables with no more than four terms over the set of integers.
![Screenshot of Factoring Special Products](/Assets/img/blank.gif)
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
![Screenshot of Modeling the Factorization of <em>ax</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
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
![Screenshot of Modeling the Factorization of <em>x</em><sup>2</sup>+<em>bx</em>+<em>c</em>](/Assets/img/blank.gif)
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
A2.EO.3.c: : Determine the quotient of polynomials in one and two variables, using monomial, binomial, and factorable trinomial divisors.
![Screenshot of Dividing Polynomials Using Synthetic Division](/Assets/img/blank.gif)
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
A2.EO.3.d: : Represent and demonstrate equality of polynomial expressions written in different forms and verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials.
![Screenshot of Factoring Special Products](/Assets/img/blank.gif)
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
A2.EO.4: : The student will perform operations on complex numbers.
A2.EO.4.a: : Explain the meaning of i.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
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
A2.EO.4.b: : Identify equivalent radical expressions containing negative rational numbers and expressions in a + bi form.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
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
A2.EO.4.c: : Apply properties to add, subtract, and multiply complex numbers.
![Screenshot of Points in the Complex Plane](/Assets/img/blank.gif)
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
A2.EI: : Equations and Inequalities
A2.EI.1: : The student will represent, solve, and interpret the solution to absolute value equations and inequalities in one variable.
A2.EI.1.b: : Solve an absolute value equation in one variable algebraically and verify the solution graphically.
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
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
A2.EI.1.c: : Create an absolute value inequality in one variable to model a contextual situation.
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
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
A2.EI.1.d: : Solve an absolute value inequality in one variable and represent the solution set using set notation, interval notation, and using a number line.
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
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
A2.EI.1.e: : Verify possible solution(s) to absolute value equations and inequalities 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.
![Screenshot of Absolute Value Equations and Inequalities](/Assets/img/blank.gif)
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
A2.EI.2: : The student will represent, solve, and interpret the solution to quadratic equations in one variable over the set of complex numbers and solve quadratic inequalities in one variable.
A2.EI.2.a: : Create a quadratic equation or inequality in one variable to model a contextual situation.
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
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
A2.EI.2.b: : Solve a quadratic equation in one variable over the set of complex numbers algebraically.
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
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
A2.EI.2.c: : Determine the solution to a quadratic inequality in one variable over the set of real numbers algebraically.
![Screenshot of Quadratic Inequalities](/Assets/img/blank.gif)
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
A2.EI.2.d: : Verify possible solution(s) to quadratic equations or inequalities 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.
![Screenshot of Quadratic Inequalities](/Assets/img/blank.gif)
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
![Screenshot of Quadratics in Polynomial Form](/Assets/img/blank.gif)
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
![Screenshot of Roots of a Quadratic](/Assets/img/blank.gif)
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
A2.EI.5: : The student will represent, solve, and interpret the solution to an equation containing a radical expression.
A2.EI.5.a: : Solve an equation containing no more than one radical expression algebraically and graphically.
![Screenshot of Radical Functions](/Assets/img/blank.gif)
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
A2.EI.5.b: : Verify possible solution(s) to radical equations algebraically, graphically, and with technology, to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.
![Screenshot of Radical Functions](/Assets/img/blank.gif)
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
A2.EI.6: : The student will represent, solve, and interpret the solution to a polynomial equation.
A2.EI.6.a: : Determine a factored form of a polynomial equation, of degree three or higher, given its zeros or the x-intercepts of the graph of its related function.
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
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
A2.EI.6.b: : Determine the number and type of solutions (real or imaginary) of a polynomial equation of degree three or higher.
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
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
A2.F: : Functions
A2.F.1: : The student will investigate, analyze, and compare square root, cube root, rational, exponential, and logarithmic function families, algebraically and graphically, using transformations.
A2.F.1.a: : Distinguish between the graphs of parent functions for square root, cube root, rational, exponential, and logarithmic function families.
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
A2.F.1.b: : Write the equation of a square root, cube root, rational, exponential, and logarithmic function, given a graph, using transformations of the parent function, including f(x) + k; f(kx); f(x + k); and kf(x), where k is limited to rational values. Transformations of exponential and logarithmic functions, given a graph, should be limited to a single transformation.
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
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
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions: Translating and Scaling](/Assets/img/blank.gif)
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
![Screenshot of Radical Functions](/Assets/img/blank.gif)
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
![Screenshot of Rational Functions](/Assets/img/blank.gif)
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
A2.F.1.c: : Graph a square root, cube root, rational, exponential, and logarithmic function, given the equation, using transformations of the parent function including f(x) + k; f(kx); f(x + k); and kf(x), where k is limited to rational values. Use technology to verify transformations of the functions.
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
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
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions: Translating and Scaling](/Assets/img/blank.gif)
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
![Screenshot of Radical Functions](/Assets/img/blank.gif)
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
![Screenshot of Rational Functions](/Assets/img/blank.gif)
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
A2.F.1.d: : Determine when two variables are directly proportional, inversely proportional, or neither, given a table of values. Write an equation and create a graph to represent a direct or inverse variation, including situations in context.
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
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
A2.F.1.e: : Compare and contrast the graphs, tables, and equations of square root, cube root, rational, exponential, and logarithmic functions.
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
A2.F.2: : The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically.
A2.F.2.a: : Determine and identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, including graphs with discontinuities.
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
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
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
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
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
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
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions: Translating and Scaling](/Assets/img/blank.gif)
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
![Screenshot of Polynomials and Linear Factors](/Assets/img/blank.gif)
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
![Screenshot of Radical Functions](/Assets/img/blank.gif)
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
![Screenshot of Rational Functions](/Assets/img/blank.gif)
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
A2.F.2.b: : Compare and contrast the characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions.
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
A2.F.2.c: : Determine the intervals on which the graph of a function is increasing, decreasing, or constant.
![Screenshot of Radical Functions](/Assets/img/blank.gif)
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
A2.F.2.d: : Determine the location and value of absolute (global) maxima and absolute (global) minima of a function.
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
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
A2.F.2.e: : Determine the location and value of relative (local) maxima or relative (local) minima of a function.
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
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
A2.F.2.f: : For any value, x, in the domain of f, determine f(x) using a graph or equation. Explain the meaning of x and f(x) in context, where applicable.
![Screenshot of Absolute Value with Linear Functions](/Assets/img/blank.gif)
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
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
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
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions: Translating and Scaling](/Assets/img/blank.gif)
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
![Screenshot of Radical Functions](/Assets/img/blank.gif)
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
![Screenshot of Rational Functions](/Assets/img/blank.gif)
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
A2.F.2.g: : Describe the end behavior of a function.
![Screenshot of Graphs of Polynomial Functions](/Assets/img/blank.gif)
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
A2.F.2.h: : Determine the equations of any vertical and horizontal asymptotes of a function using a graph or equation (rational, exponential, and logarithmic).
![Screenshot of Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of General Form of a Rational Function](/Assets/img/blank.gif)
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
![Screenshot of Introduction to Exponential Functions](/Assets/img/blank.gif)
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
![Screenshot of Logarithmic Functions: Translating and Scaling](/Assets/img/blank.gif)
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
![Screenshot of Rational Functions](/Assets/img/blank.gif)
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
A2.F.2.i: : Determine the inverse of a function algebraically and graphically, given the equation of a linear or quadratic function (linear, quadratic, and square root). Justify and explain why two functions are inverses of each other.
![Screenshot of Logarithmic Functions](/Assets/img/blank.gif)
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
![Screenshot of Radical Functions](/Assets/img/blank.gif)
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
A2.ST: : Statistics
A2.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 univariate quantitative data represented by a smooth curve, including a normal curve.
A2.ST.1.d: : Identify the properties of a normal distribution.
![Screenshot of Populations and Samples](/Assets/img/blank.gif)
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
A2.ST.1.e: : Describe and interpret a data distribution represented by a smooth curve by analyzing measures of center, measures of spread, and shape of the curve.
![Screenshot of Populations and Samples](/Assets/img/blank.gif)
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
A2.ST.1.j: : Compare multiple data distributions using measures of center, measures of spread, and shape of the distributions.
![Screenshot of Populations and Samples](/Assets/img/blank.gif)
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
A2.ST.2: : 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, quadratic, exponential, or a combination of these functions.
A2.ST.2.a: : Formulate investigative questions that require the collection or acquisition of bivariate data and investigate questions using a data cycle.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
A2.ST.2.b: : Collect or acquire bivariate data through research, or using surveys, observations, scientific experiments, polls, or questionnaires.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
A2.ST.2.c: : Represent bivariate data with a scatterplot using technology.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
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
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
A2.ST.2.e: : Determine the equation(s) of the function(s) that best models the relationship between two variables using technology. Curves of best fit may include a combination of linear, quadratic, or exponential (piecewise-defined) functions.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
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
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
A2.ST.2.f: : Use the correlation coefficient to designate the goodness of fit of a linear function using technology.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
A2.ST.2.g: : Make predictions, decisions, and critical judgments using data, scatterplots, or the equation(s) of the mathematical model.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
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
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
A2.ST.3: : The student will compute and distinguish between permutations and combinations.
A2.ST.3.a: : Compare and contrast permutations and combinations to count the number of ways that events can occur.
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
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
A2.ST.3.b: : Calculate the number of permutations of n objects taken r at a time.
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
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
A2.ST.3.c: : Calculate the number of combinations of n objects taken r at a time.
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
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
A2.ST.3.d: : Use permutations and combinations as counting techniques to solve contextual problems.
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
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
A2.ST.3.e: : Calculate and verify permutations and combinations using technology.
![Screenshot of Permutations and Combinations](/Assets/img/blank.gif)
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
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.
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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.
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