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Algebra 1 A common Core Curriculum (2015)
1: Solving Linear Equations
1.1: Solving Simple Equations
![Screenshot of Modeling One-Step Equations](/Assets/img/blank.gif)
Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
1.2: Solving Multi-Step Equations
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
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
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
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
1.3: Solving Equations with Variable on Both Sides
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
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
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
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
1.4: Solving Absolute Value Equations
![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
![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
1.5: Rewriting Equations and Formulas
![Screenshot of Solving Formulas for any Variable](/Assets/img/blank.gif)
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
2: Solving Linear Inequalities
2.1: Writing and Graphing Inequalities
![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
![Screenshot of Linear Inequalities in Two Variables](/Assets/img/blank.gif)
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
![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 Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
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
2.3: Solving Inequalities Using Multiplication or Division
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
2.4: Solving Multi-Step Inequalities
![Screenshot of Compound Inequalities](/Assets/img/blank.gif)
Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
![Screenshot of Linear Inequalities in Two Variables](/Assets/img/blank.gif)
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
2.5: Solving Compound Inequalities
![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
![Screenshot of Compound Inequalities](/Assets/img/blank.gif)
Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
2.6: Solving Absolute Value Inequalities
![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
![Screenshot of Compound Inequalities](/Assets/img/blank.gif)
Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
3: Graphing Linear Functions
3.1: Functions
![Screenshot of Function Machines 2 (Functions, Tables, and Graphs)](/Assets/img/blank.gif)
Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
![Screenshot of Function Machines 3 (Functions and Problem Solving)](/Assets/img/blank.gif)
Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
![Screenshot of Linear Functions](/Assets/img/blank.gif)
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
3.2: Linear Functions
![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 Arithmetic Sequences](/Assets/img/blank.gif)
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
![Screenshot of Function Machines 2 (Functions, Tables, and Graphs)](/Assets/img/blank.gif)
Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
![Screenshot of Function Machines 3 (Functions and Problem Solving)](/Assets/img/blank.gif)
Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
![Screenshot of Linear Functions](/Assets/img/blank.gif)
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
3.4: Graphing Linear Equations in Standard Form
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
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
3.5: Graphing Linear Equations in Slope-Intercept Form
![Screenshot of Linear Inequalities in Two Variables](/Assets/img/blank.gif)
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
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
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
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
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
3.6: Transformations of Graphs of Linear Functions
![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
3.7: Graphing Absolute Value Functions
![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 Translating and Scaling Functions](/Assets/img/blank.gif)
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
4: Writing Linear Functions
4.1: Writing Equations in Slope-Intercept Form
![Screenshot of Linear Inequalities in Two Variables](/Assets/img/blank.gif)
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
4.2: Writing Equations in Point-Slope Form
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
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
4.4: Scatter Plots and Lines of Fit
![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
4.5: Analyzing Lines of Fit
![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
4.6: Arithmetic Sequences
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
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
![Screenshot of Arithmetic and Geometric Sequences](/Assets/img/blank.gif)
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
5: Solving Systems of Linear Equations
5.1: Solving Systems of Linear Equations by Graphing
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
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
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
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
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
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
5.2: Solving Systems of Linear Equations by Substitution
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
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
5.3: Solving Systems of Linear Equations by Elimination
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
5.4: Solving Special Systems of Linear Equations
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
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
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
![Screenshot of Solving Linear Systems (Matrices and Special Solutions)](/Assets/img/blank.gif)
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
![Screenshot of Solving Linear Systems (Slope-Intercept Form)](/Assets/img/blank.gif)
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
5.5: Solving Equations by Graphing
![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
![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 Circles](/Assets/img/blank.gif)
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
![Screenshot of Parabolas](/Assets/img/blank.gif)
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
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
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
![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 Solving Equations on the Number Line](/Assets/img/blank.gif)
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
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
5.6: Graphing Linear Inequalities in Two Variables
![Screenshot of Linear Inequalities in Two Variables](/Assets/img/blank.gif)
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
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
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
5.7: Systems of Linear Inequalities
![Screenshot of Linear Programming](/Assets/img/blank.gif)
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
![Screenshot of Systems of Linear Inequalities (Slope-intercept form)](/Assets/img/blank.gif)
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
6: Exponential Functions and Sequences
6.1: Properties of Exponents
![Screenshot of Dividing Exponential Expressions](/Assets/img/blank.gif)
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
![Screenshot of Exponents and Power Rules](/Assets/img/blank.gif)
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
![Screenshot of Multiplying Exponential Expressions](/Assets/img/blank.gif)
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
6.5: Solving Exponential Equations
![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
6.6: Geometric Sequences
![Screenshot of Arithmetic and Geometric Sequences](/Assets/img/blank.gif)
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
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
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
6.7: Recursively Defined Sequences
![Screenshot of Arithmetic Sequences](/Assets/img/blank.gif)
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
![Screenshot of Geometric Sequences](/Assets/img/blank.gif)
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
7: Polynomial Equations and Factoring
7.1: Adding and Subtracting Polynomials
![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
7.2: Multiplying Polynomials
![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
7.3: Special Products of Polynomials
![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
7.4: Solving Polynomial Equations in Factored Form
![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
7.5: Factoring x² + bx + c
![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
7.6: Factoring ax² + bx + c
![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
7.7: Factoring Special Products
![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
7.8: Factoring Polynomials Completely
![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
8: Graphing Quadratic Functions
8.1: Graphing f(x) = ax²
![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 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 Quadratics in Factored Form](/Assets/img/blank.gif)
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
![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
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
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
8.2: Graphing f(x) = ax² + c
![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 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 Quadratics in Factored Form](/Assets/img/blank.gif)
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
![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
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
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
8.3: Graphing f(x) = ax² + bx + c
![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 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 Quadratics in Factored Form](/Assets/img/blank.gif)
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
![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
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
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
8.5: Using Intercept Form
![Screenshot of Cat and Mouse (Modeling with Linear Systems)](/Assets/img/blank.gif)
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
![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 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 Point-Slope Form of a Line](/Assets/img/blank.gif)
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
![Screenshot of Quadratics in Factored Form](/Assets/img/blank.gif)
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
![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
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
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
8.6: Comparing Linear, Exponential, and Quadratic 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
9: Solving Quadratic Equations
9.1: Properties of Radicals
![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
9.2: Solving Quadratic Equations by Graphing
![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
9.3: Solving Quadratic Equations Using Square Roots
![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
9.4: Solving Quadratic Equations by Completing the Square
![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
9.5: Solving Quadratic Equations Using the Quadratic Formula
![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
10: Radical Functions and Equations
10.2: Graphing Cube Root Functions
![Screenshot of Translating and Scaling Functions](/Assets/img/blank.gif)
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
10.3: Solving Radical Equations
![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
10.4: Inverse of a Function
![Screenshot of Function Machines 3 (Functions and Problem Solving)](/Assets/img/blank.gif)
Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
11: Data Analysis and Displays
11.1: Measures of Center and Variation
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
![Screenshot of Describing Data Using Statistics](/Assets/img/blank.gif)
Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview
![Screenshot of Mean, Median, and Mode](/Assets/img/blank.gif)
Mean, Median, and Mode
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview
11.2: Box-and-Whisker Plots
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
11.3: Shapes of Distributions
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
![Screenshot of Describing Data Using Statistics](/Assets/img/blank.gif)
Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview
![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
11.4: Two-Way Tables
![Screenshot of Histograms](/Assets/img/blank.gif)
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
11.5: Choosing a Data Display
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
![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
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.
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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