# Florida - Mathematics: Algebra I

## End of Course Specifications: Benchmarks | Adopted: 2010

### MA.912.A: : Algebra

MA.912.A.2.3: : Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions.

Introduction to Functions

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

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

Points, Lines, and Equations

Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

MA.912.A.2.4: : Determine the domain and range of a relation.

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

MA.912.A.3.1: : Solve linear equations in one variable that include simplifying algebraic expressions.

Solving Algebraic Equations II

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

MA.912.A.3.2: : Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality.

Equivalent Algebraic Expressions I

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

Equivalent Algebraic Expressions II

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

Square Roots

Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview

MA.912.A.3.3: : Solve literal equations for a specified variable.

Area of Triangles

Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview

Solving Formulas for any Variable

Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps. 5 Minute Preview

MA.912.A.3.4: : Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.

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

Comparing and Ordering Decimals

Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview

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

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

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

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

Solving Linear Inequalities in One Variable

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

Systems of Linear Inequalities (Slope-intercept form)

Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview

MA.912.A.3.5: : Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.

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

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

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

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

Systems of Linear Inequalities (Slope-intercept form)

Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview

MA.912.A.3.7: : Rewrite equations of a line into slope-intercept form and standard form.

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

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

Points, Lines, and Equations

Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

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

Standard Form of a Line

Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

MA.912.A.3.8: : Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form.

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

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

Points, Lines, and Equations

Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Slope

Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview

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

Standard Form of a Line

Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

MA.912.A.3.9: : Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line.

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

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

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

Points, Lines, and Equations

Slope

Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview

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

Standard Form of a Line

MA.912.A.3.10: : Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

MA.912.A.3.11: : Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.

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

MA.912.A.3.12: : Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph.

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

Linear Inequalities in Two Variables

Point-Slope Form of a Line

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

Slope-Intercept Form of a Line

Standard Form of a Line

Systems of Linear Inequalities (Slope-intercept form)

Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response. 5 Minute Preview

MA.912.A.3.13: : Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology.

Solving Linear Systems (Slope-Intercept Form)

Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an *x*, *y*)

MA.912.A.3.14: : Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods.

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

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

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 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

Solving Linear Systems (Slope-Intercept Form)

Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an *x*, *y*)

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

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.3.15: : Solve real-world problems involving systems of linear equations and inequalities in two and three variables.

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

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 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

Solving Linear Systems (Slope-Intercept Form)

Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an *x*, *y*)

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

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.4.1: : Simplify monomials and monomial expressions using the laws of integral exponents.

Dividing Exponential Expressions

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

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

Multiplying Exponential Expressions

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

Simplifying Algebraic Expressions II

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

MA.912.A.4.2: : Add, subtract, and multiply polynomials.

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

Addition of Polynomials

Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview

Modeling the Factorization of *x*^{2}+*bx*+*c*

Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview

MA.912.A.4.3: : Factor polynomial expressions.

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

Modeling the Factorization of *ax*^{2}+*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 *x*^{2}+*bx*+*c*

Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview

MA.912.A.4.4: : Divide polynomials by monomials and polynomials with various techniques, including synthetic division.

Dividing Exponential Expressions

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

Dividing Polynomials Using Synthetic Division

Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview

MA.912.A.5.4: : Solve algebraic proportions.

Direct and Inverse Variation

Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview

MA.912.A.6.1: : Simplify radical expressions.

Operations with Radical Expressions

Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

Simplifying Radical Expressions

Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview

MA.912.A.6.2: : Add, subtract, multiply and divide radical expressions (square roots and higher).

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

MA.912.A.7.1: : Graph quadratic equations with and without graphing technology.

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

Quadratics in Polynomial Form

Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview

Quadratics in Vertex Form

Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview

Roots of a Quadratic

Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview

MA.912.A.7.2: : Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula.

Modeling the Factorization of *x*^{2}+*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

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

Roots of a Quadratic

Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview

MA.912.A.7.8: : Use quadratic equations to solve real-world problems.

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

MA.912.A.10.1: : Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guessing- and-checking, solving a simpler problem, writing an equation, working backwards, and creating a table.

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

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

Using Algebraic Equations

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

MA.912.A.10.3: : Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities rational or radical expressions or logarithmic or exponential functions).

Linear Functions

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

### MA.912.A.2: : Draw and interpret graphs of relations. Understand the notation and concept of a function, find domains and ranges, and link equations to functions.

MA.912.A.2.3: : Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions.

Introduction to Functions

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

Linear Functions

Points, Lines, and Equations

MA.912.A.2.4: : Determine the domain and range of a relation.

Introduction to Functions

### MA.912.A.3: : Solve linear equations and inequalities.

MA.912.A.3.1: : Solve linear equations in one variable that include simplifying algebraic expressions.

Solving Algebraic Equations II

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

MA.912.A.3.2: : Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality.

Equivalent Algebraic Expressions I

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

Equivalent Algebraic Expressions II

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

Square Roots

Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview

MA.912.A.3.3: : Solve literal equations for a specified variable.

Area of Triangles

Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview

Solving Formulas for any Variable

Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps. 5 Minute Preview

MA.912.A.3.4: : Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.

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

Comparing and Ordering Decimals

Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview

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

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

Linear Inequalities in Two Variables

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

Solving Linear Inequalities in One Variable

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

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.3.5: : Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.

Compound Inequalities

Linear Inequalities in Two Variables

Solving Equations by Graphing Each Side

Standard Form of a Line

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.3.7: : Rewrite equations of a line into slope-intercept form and standard form.

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

MA.912.A.3.8: : Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form.

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Points, Lines, and Equations

Slope

Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview

Slope-Intercept Form of a Line

Standard Form of a Line

MA.912.A.3.9: : Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line.

Cat and Mouse (Modeling with Linear Systems)

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope

Slope-Intercept Form of a Line

Standard Form of a Line

MA.912.A.3.10: : Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

MA.912.A.3.11: : Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.

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

MA.912.A.3.12: : Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph.

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

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Quadratic Inequalities

Slope-Intercept Form of a Line

Standard Form of a Line

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.3.13: : Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology.

Solving Linear Systems (Slope-Intercept Form)

*x*, *y*)

MA.912.A.3.14: : Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods.

Cat and Mouse (Modeling with Linear Systems)

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

Solving Equations by Graphing Each Side

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

Solving Linear Systems (Slope-Intercept Form)

*x*, *y*)

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

Systems of Linear Inequalities (Slope-intercept form)

MA.912.A.3.15: : Solve real-world problems involving systems of linear equations and inequalities in two and three variables.

Linear Programming

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

*x*, *y*) point to be a solution of an equation, or of a system of equations.
5 Minute Preview

Solving Linear Systems (Slope-Intercept Form)

*x*, *y*)

Solving Linear Systems (Standard Form)

*x*, *y*) values are solutions of an equation, or of a system of equations.
5 Minute Preview

Systems of Linear Inequalities (Slope-intercept form)

### MA.912.A.4: : Perform operations on polynomials. Find factors of polynomials, learning special techniques for factoring quadratics. Understand the relationships among the solutions of polynomial equations, the zeros of a polynomial function, the x-intercepts of a graph, and the factors of a polynomial.

MA.912.A.4.1: : Simplify monomials and monomial expressions using the laws of integral exponents.

Dividing Exponential Expressions

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

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

Multiplying Exponential Expressions

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

Simplifying Algebraic Expressions II

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

MA.912.A.4.2: : Add, subtract, and multiply polynomials.

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

Addition of Polynomials

Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes. 5 Minute Preview

Modeling the Factorization of *x*^{2}+*bx*+*c*

MA.912.A.4.3: : Factor polynomial expressions.

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

Modeling the Factorization of *ax*^{2}+*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 *x*^{2}+*bx*+*c*

MA.912.A.4.4: : Divide polynomials by monomials and polynomials with various techniques, including synthetic division.

Dividing Exponential Expressions

Dividing Polynomials Using Synthetic Division

Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview

### MA.912.A.5: : Simplify rational expressions and solve rational equations using what they have learned about factoring polynomials.

MA.912.A.5.4: : Solve algebraic proportions.

Direct and Inverse Variation

Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview

### MA.912.A.6: : Simplify and perform operations on radical expressions and equations. Rationalize square root expressions and understand and use the concepts of negative and rational exponents. Add, subtract, multiply, divide, and simplify radical expressions and expressions with rational exponents. Solve radical equations and equations with terms that have rational exponents.

MA.912.A.6.1: : Simplify radical expressions.

Operations with Radical Expressions

Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

Simplifying Radical Expressions

Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps. 5 Minute Preview

MA.912.A.6.2: : Add, subtract, multiply and divide radical expressions (square roots and higher).

Operations with Radical Expressions

### MA.912.A.7: : Draw graphs of quadratic functions. Solve quadratic equations and solve these equations by factoring, completing the square and by using the quadratic formula. Use graphing calculators to find approximate solutions of quadratic equations.

MA.912.A.7.1: : Graph quadratic equations with and without graphing technology.

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

Quadratics in Polynomial Form

Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview

Quadratics in Vertex Form

Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview

Roots of a Quadratic

Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview

MA.912.A.7.2: : Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula.

Modeling the Factorization of *x*^{2}+*bx*+*c*

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

Roots of a Quadratic

MA.912.A.7.8: : Use quadratic equations to solve real-world problems.

Addition and Subtraction of Functions

### MA.912.A.10: : In a general sense, all of mathematics is problem solving. In all of mathematics, use problem-solving skills, choose how to approach a problem, explain the reasoning, and check the results

MA.912.A.10.1: : Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guessing- and-checking, solving a simpler problem, writing an equation, working backwards, and creating a table.

Absolute Value Equations and Inequalities

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

Using Algebraic Equations

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

MA.912.A.10.3: : Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities rational or radical expressions or logarithmic or exponential functions).

Linear Functions

### MA.912.D: : Discrete Mathematics

MA.912.D.7.1: : Perform set operations such as union and intersection, complement, and cross product.

Compound Inequalities

### MA.912.D.7: : Operate with sets and use set theory to solve problems.

MA.912.D.7.1: : Perform set operations such as union and intersection, complement, and cross product.

Compound Inequalities

### MA.912.G.1: : Understand geometric concepts, applications, and their representations with coordinate systems. Find lengths and midpoints of line segments, slopes, parallel and perpendicular lines, and equations of lines. Using a compass and straightedge, patty paper, a drawing program or other techniques, students also construct lines and angles, explaining and justifying the processes used.

MA.912.G.1.4: : Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

Point-Slope Form of a Line

Points, Lines, and Equations

Correlation last revised: 9/16/2020

About STEM Cases

Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.

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STEM Cases take between 30-90 minutes for students to complete, depending on the case.

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Multiple grade-appropriate versions, or levels, exist for each STEM Case.

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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