# Browse by Grade & Topic: Algebra

## Find Gizmos organized by grade level and topic.

See How FREE Gizmos WorkArithmetic 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...

Lesson Info Launch GizmoRadians

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As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the belt’s...

Lesson Info Launch GizmoArithmetic 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.

Lesson Info Launch GizmoSine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle.

Lesson Info Launch GizmoCosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle.

Lesson Info Launch GizmoGeometric 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.

Lesson Info Launch GizmoTangent Function

Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle.

Lesson Info Launch GizmoDrug Dosage

A drug prescription must be carefully planned to maximize benefit while avoiding an overdose. In this Gizmo, you can give a patient one or more pills and monitor the levels of medication in...

Lesson Info Launch GizmoDye Elimination

When a foreign substance such as a drug is ingested, it often remains in the bloodstream for a long time. This Gizmo models the elimination of substances from the bloodstream using water...

Lesson Info Launch GizmoSound Beats and Sine Waves

Listen to and see interference patterns produced by sound waves with similar frequencies. Test your ability to distinguish and match sounds as musicians do when they tune their instruments....

Lesson Info Launch GizmoTranslating and Scaling Sine and Cosine Functions

Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function.

Lesson Info Launch GizmoSimplifying Trigonometric Expressions

Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps.

Lesson Info Launch GizmoSum and Difference Identities for Sine and Cosine

Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps.

Lesson Info Launch GizmoEquivalent 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...

Lesson Info Launch GizmoEquivalent 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...

Lesson Info Launch GizmoSimplifying Algebraic Expressions I

Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro...

Lesson Info Launch GizmoSimplifying 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...

Lesson Info Launch GizmoSolving Algebraic Equations I

Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use...

Lesson Info Launch GizmoSolving 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...

Lesson Info Launch GizmoUsing Algebraic Expressions

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

Lesson Info Launch GizmoUsing 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...

Lesson Info Launch GizmoOrder of Operations

FREE *with no time limit!*

Select and evaluate the operations in an expression following the correct order of operations.

Lesson Info Launch GizmoSolving Equations on the Number Line

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

Lesson Info Launch GizmoModeling One-Step Equations

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

Lesson Info Launch GizmoModeling and Solving Two-Step Equations

FREE *with no time limit!*

Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps.

Lesson Info Launch GizmoSolving 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.

Lesson Info Launch GizmoSolving Two-Step Equations

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

Lesson Info Launch GizmoSolving Formulas for any Variable

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

Lesson Info Launch GizmoSlope

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.

Lesson Info Launch GizmoPoints in the Coordinate Plane

Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response.

Lesson Info Launch GizmoIntroduction 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...

Lesson Info Launch GizmoLeast-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.

Lesson Info Launch GizmoStandard 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.

Lesson Info Launch GizmoPoint-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.

Lesson Info Launch GizmoSlope-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.

Lesson Info Launch GizmoTranslating 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...

Lesson Info Launch GizmoLinear 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.

Lesson Info Launch GizmoDistance-Time Graphs

Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed...

Lesson Info Launch GizmoCompound Interest

FREE *with no time limit!*

Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME...

Lesson Info Launch GizmoPoints, 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.

Lesson Info Launch GizmoDistance-Time and Velocity-Time Graphs

Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity...

Lesson Info Launch GizmoDistance-Time Graphs - Metric

Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the...

Lesson Info Launch GizmoDistance-Time and Velocity-Time Graphs - Metric

Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity...

Lesson Info Launch GizmoCompound 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...

Lesson Info Launch GizmoSolving Linear Inequalities in One Variable

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

Lesson Info Launch GizmoAbsolute 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. ...

Lesson Info Launch GizmoLinear 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...

Lesson Info Launch GizmoExploring 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.

Lesson Info Launch GizmoCat 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...

Lesson Info Launch GizmoSolving Linear Systems (Slope-Intercept Form)

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

Lesson Info Launch GizmoSolving 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...

Lesson Info Launch GizmoLinear 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...

Lesson Info Launch GizmoSolving 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...

Lesson Info Launch GizmoSystems 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...

Lesson Info Launch GizmoCat and Mouse (Modeling with Linear Systems) - Metric

Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the...

Lesson Info Launch GizmoZap It! Game

Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible.

Lesson Info Launch GizmoQuadratics 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.

Lesson Info Launch GizmoQuadratics 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.

Lesson Info Launch GizmoQuadratic 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...

Lesson Info Launch GizmoQuadratics 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.

Lesson Info Launch GizmoRoots 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...

Lesson Info Launch GizmoAbsolute 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...

Lesson Info Launch GizmoOperations with Radical Expressions

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

Lesson Info Launch GizmoSimplifying Radical Expressions

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

Lesson Info Launch GizmoRadical 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.

Lesson Info Launch GizmoLogarithmic 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...

Lesson Info Launch GizmoExponential Growth and Decay

Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph.

Lesson Info Launch GizmoExponential 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.

Lesson Info Launch GizmoIntroduction to Exponential Functions

FREE *with no time limit!*

Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph.

Lesson Info Launch GizmoLogarithmic 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...

Lesson Info Launch GizmoDirect 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...

Lesson Info Launch GizmoGeneral 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.

Lesson Info Launch GizmoRational 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...

Lesson Info Launch GizmoAddition 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.

Lesson Info Launch GizmoAddition of Polynomials

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

Lesson Info Launch GizmoFactoring 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.

Lesson Info Launch GizmoModeling 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.

Lesson Info Launch GizmoModeling 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.

Lesson Info Launch GizmoDividing 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.

Lesson Info Launch GizmoGraphs of Polynomial Functions

FREE *with no time limit!*

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...

Lesson Info Launch GizmoPolynomials 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.

Lesson Info Launch GizmoDilations

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

Lesson Info Launch GizmoReflections

Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated.

Lesson Info Launch GizmoTranslations

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

Lesson Info Launch GizmoRotations, Reflections, and Translations

FREE *with no time limit!*

Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.

Lesson Info Launch GizmoEllipses

Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their...

Lesson Info Launch GizmoHyperbolas

Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response.

Lesson Info Launch GizmoParabolas

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.

Lesson Info Launch GizmoOrder of Operations

FREE *with no time limit!*

Select and evaluate the operations in an expression following the correct order of operations.

Lesson Info Launch GizmoModeling and Solving Two-Step Equations

FREE *with no time limit!*

Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps.

Lesson Info Launch GizmoCompound Interest

FREE *with no time limit!*

Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME...

Lesson Info Launch GizmoIntroduction to Exponential Functions

FREE *with no time limit!*

Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph.

Lesson Info Launch GizmoGraphs of Polynomial Functions

FREE *with no time limit!*

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...

Lesson Info Launch GizmoRotations, Reflections, and Translations

FREE *with no time limit!*

Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.

Lesson Info Launch GizmoHow Free Gizmos Work

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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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