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Equivalent Algebraic Expressions I
5 Minute Preview
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
5 Minute Preview
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 GizmoSolving Algebraic Equations I
5 Minute Preview
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
5 Minute Preview
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 GizmoSimplifying Algebraic Expressions I
5 Minute Preview
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
5 Minute Preview
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 GizmoUsing Algebraic Expressions
5 Minute Preview
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
5 Minute Preview
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 GizmoSolving Linear Systems (Slope-Intercept Form)
5 Minute Preview
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)
5 Minute Preview
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 GizmoOperations with Radical Expressions
5 Minute Preview
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
5 Minute Preview
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps.
Lesson Info Launch GizmoDividing Polynomials Using Synthetic Division
5 Minute Preview
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 GizmoReflections
5 Minute Preview
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 GizmoFinding Patterns
5 Minute Preview
Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid.
Lesson Info Launch GizmoExponents and Power Rules
5 Minute Preview
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps.
Lesson Info Launch GizmoFactoring Special Products
5 Minute Preview
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 One-Step Equations
5 Minute Preview
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps.
Lesson Info Launch GizmoCircles
5 Minute Preview
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.
Lesson Info Launch GizmoLinear Inequalities in Two Variables
5 Minute Preview
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 GizmoQuadratic Inequalities
5 Minute Preview
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 GizmoSolving Equations by Graphing Each Side
5 Minute Preview
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 Linear Systems (Matrices and Special Solutions)
5 Minute Preview
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)
5 Minute Preview
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 GizmoTranslations
5 Minute Preview
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
Lesson Info Launch GizmoModeling and Solving Two-Step Equations
- Free!
FREE with no time limit!
5 Minute Preview
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 GizmoRotations, Reflections, and Translations
- Free!
FREE with no time limit!
5 Minute Preview
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
Lesson Info Launch GizmoPermutations and Combinations
5 Minute Preview
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree...
Lesson Info Launch GizmoDividing Exponential Expressions
- Free!
FREE with no time limit!
5 Minute Preview
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoMultiplying Exponential Expressions
5 Minute Preview
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoSolving Equations on the Number Line
5 Minute Preview
Solve an equation involving decimals using dynamic arrows on a number line.
Lesson Info Launch GizmoSlope
5 Minute Preview
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 GizmoSquare Roots
5 Minute Preview
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.
Lesson Info Launch GizmoModeling the Factorization of ax2+bx+c
5 Minute Preview
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 x2+bx+c
5 Minute Preview
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 GizmoQuadratics in Factored Form
5 Minute Preview
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
5 Minute Preview
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 GizmoArithmetic Sequences
5 Minute Preview
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 GizmoGeometric Sequences
5 Minute Preview
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 GizmoAbsolute Value Equations and Inequalities
5 Minute Preview
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 GizmoPolynomials and Linear Factors
5 Minute Preview
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 GizmoQuadratics in Vertex Form
5 Minute Preview
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 GizmoRadical Functions
5 Minute Preview
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 GizmoRational Functions
5 Minute Preview
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 GizmoStandard Form of a Line
5 Minute Preview
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 GizmoDistance Formula
5 Minute Preview
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and...
Lesson Info Launch GizmoLinear Functions
5 Minute Preview
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 GizmoFinding Factors with Area Models
5 Minute Preview
Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree.
Lesson Info Launch GizmoMultiplying Mixed Numbers
5 Minute Preview
Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps.
Lesson Info Launch GizmoOrdering and Approximating Square Roots
5 Minute Preview
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid.
Lesson Info Launch GizmoDistance-Time Graphs
5 Minute Preview
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 GizmoDistance-Time and Velocity-Time Graphs
5 Minute Preview
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 GizmoSolving Formulas for any Variable
5 Minute Preview
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoMultiplying Fractions
5 Minute Preview
Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to...
Lesson Info Launch GizmoDistance-Time Graphs - Metric
5 Minute Preview
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
5 Minute Preview
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 GizmoAbsolute Value with Linear Functions
5 Minute Preview
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 GizmoCompound Inequalities
5 Minute Preview
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 GizmoCat and Mouse (Modeling with Linear Systems)
5 Minute Preview
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 GizmoPoints in the Coordinate Plane
5 Minute Preview
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 GizmoSolving Linear Inequalities in One Variable
5 Minute Preview
Solve one-step inequalities in one variable. Graph the solution on a number line.
Lesson Info Launch GizmoDirect and Inverse Variation
5 Minute Preview
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 GizmoIntroduction to Functions
5 Minute Preview
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 GizmoHyperbolas
5 Minute Preview
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 GizmoLogarithmic Functions
5 Minute Preview
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 GizmoPoints in the Complex Plane
5 Minute Preview
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.
Lesson Info Launch GizmoSimplifying Trigonometric Expressions
5 Minute Preview
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps.
Lesson Info Launch GizmoSine Function
5 Minute Preview
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 GizmoTangent Function
5 Minute Preview
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 GizmoPoint-Slope Form of a Line
5 Minute Preview
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
5 Minute Preview
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 GizmoDilations
5 Minute Preview
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 GizmoProportions and Common Multipliers
5 Minute Preview
Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the...
Lesson Info Launch GizmoCompound Interest
- Free!
FREE with no time limit!
5 Minute Preview
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 GizmoExploring Linear Inequalities in One Variable
5 Minute Preview
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality.
Lesson Info Launch GizmoSolving Two-Step Equations
5 Minute Preview
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoArithmetic and Geometric Sequences
5 Minute Preview
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 GizmoCalorimetry Lab
5 Minute Preview
Investigate how calorimetry can be used to find relative specific heat values when different substances are mixed with water. Modify initial mass and temperature values to see effects on...
Lesson Info Launch GizmoAdding and Subtracting Integers with Chips
5 Minute Preview
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction.
Lesson Info Launch GizmoCat and Mouse (Modeling with Linear Systems) - Metric
5 Minute Preview
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 GizmoAddition and Subtraction of Functions
5 Minute Preview
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
5 Minute Preview
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes.
Lesson Info Launch GizmoExponential Growth and Decay
5 Minute Preview
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 GizmoCosine Function
5 Minute Preview
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 GizmoEllipses
5 Minute Preview
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 GizmoExponential Functions
5 Minute Preview
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!
FREE with no time limit!
5 Minute Preview
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!
FREE with no time limit!
5 Minute Preview
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 GizmoGeneral Form of a Rational Function
5 Minute Preview
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 GizmoParabolas
5 Minute Preview
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 GizmoRiemann Sum
5 Minute Preview
Approximate the area under a curve in an interval using rectangles. Compare the results of left-hand summation to the results of right-hand summation. Vary the interval and the number of...
Lesson Info Launch GizmoRoots of a Quadratic
5 Minute Preview
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 GizmoSum and Difference Identities for Sine and Cosine
5 Minute Preview
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 GizmoTranslating and Scaling Sine and Cosine Functions
5 Minute Preview
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 GizmoAdding Vectors
5 Minute Preview
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation.
Lesson Info Launch GizmoPythagorean Theorem
5 Minute Preview
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle.
Lesson Info Launch GizmoFractions with Unlike Denominators
5 Minute Preview
Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically.
Lesson Info Launch GizmoPythagorean Theorem with a Geoboard
5 Minute Preview
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem.
Lesson Info Launch GizmoPercents, Fractions, and Decimals
5 Minute Preview
Compare a quantity represented by an area with its percent, fraction, and decimal forms.
Lesson Info Launch GizmoSums and Differences with Decimals
5 Minute Preview
Find the sum or difference of two decimal numbers using area models. Find the decimals and their sum or difference on a number line.
Lesson Info Launch GizmoModeling and Solving Two-Step Equations
- Free!
FREE with no time limit!
5 Minute Preview
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 GizmoDividing Exponential Expressions
- Free!
FREE with no time limit!
5 Minute Preview
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoRotations, Reflections, and Translations
- Free!
FREE with no time limit!
5 Minute Preview
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
Lesson Info Launch GizmoIntroduction to Exponential Functions
- Free!
FREE with no time limit!
5 Minute Preview
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!
FREE with no time limit!
5 Minute Preview
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 GizmoCompound Interest
- Free!
FREE with no time limit!
5 Minute Preview
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 GizmoSorry, we could not find any Search Results to show you for STEM Cases!
Equivalent Algebraic Expressions I
5 Minute Preview
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.
Lesson Info Launch GizmoEquivalent Algebraic Expressions II
5 Minute Preview
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.
Lesson Info Launch GizmoSolving Algebraic Equations I
5 Minute Preview
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 inverses to isolate a variable – a foundational skill for solving algebraic equations.
Lesson Info Launch GizmoSolving Algebraic Equations II
5 Minute Preview
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.
Lesson Info Launch GizmoSimplifying Algebraic Expressions I
5 Minute Preview
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 grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form.
Lesson Info Launch GizmoSimplifying Algebraic Expressions II
5 Minute Preview
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!
Lesson Info Launch GizmoUsing Algebraic Expressions
5 Minute Preview
Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression.
Lesson Info Launch GizmoUsing Algebraic Equations
5 Minute Preview
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.
Lesson Info Launch GizmoSolving Linear Systems (Slope-Intercept Form)
5 Minute Preview
Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an
Solving Linear Systems (Standard Form)
5 Minute Preview
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.
Lesson Info Launch GizmoOperations with Radical Expressions
5 Minute Preview
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
5 Minute Preview
Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps.
Lesson Info Launch GizmoDividing Polynomials Using Synthetic Division
5 Minute Preview
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 GizmoReflections
5 Minute Preview
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 GizmoFinding Patterns
5 Minute Preview
Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid.
Lesson Info Launch GizmoExponents and Power Rules
5 Minute Preview
Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps.
Lesson Info Launch GizmoFactoring Special Products
5 Minute Preview
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 One-Step Equations
5 Minute Preview
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps.
Lesson Info Launch GizmoCircles
5 Minute Preview
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.
Lesson Info Launch GizmoLinear Inequalities in Two Variables
5 Minute Preview
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.
Lesson Info Launch GizmoQuadratic Inequalities
5 Minute Preview
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.
Lesson Info Launch GizmoSolving Equations by Graphing Each Side
5 Minute Preview
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 Linear Systems (Matrices and Special Solutions)
5 Minute Preview
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.
Lesson Info Launch GizmoSystems of Linear Inequalities (Slope-intercept form)
5 Minute Preview
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.
Lesson Info Launch GizmoTranslations
5 Minute Preview
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
Lesson Info Launch GizmoModeling and Solving Two-Step Equations
- Free!
FREE with no time limit!
5 Minute Preview
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 GizmoRotations, Reflections, and Translations
- Free!
FREE with no time limit!
5 Minute Preview
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
Lesson Info Launch GizmoPermutations and Combinations
5 Minute Preview
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle.
Lesson Info Launch GizmoDividing Exponential Expressions
- Free!
FREE with no time limit!
5 Minute Preview
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoMultiplying Exponential Expressions
5 Minute Preview
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoSolving Equations on the Number Line
5 Minute Preview
Solve an equation involving decimals using dynamic arrows on a number line.
Lesson Info Launch GizmoSlope
5 Minute Preview
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 GizmoSquare Roots
5 Minute Preview
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.
Lesson Info Launch GizmoModeling the Factorization of ax2+bx+c
5 Minute Preview
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 x2+bx+c
5 Minute Preview
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 GizmoQuadratics in Factored Form
5 Minute Preview
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
5 Minute Preview
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 GizmoArithmetic Sequences
5 Minute Preview
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 GizmoGeometric Sequences
5 Minute Preview
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 GizmoAbsolute Value Equations and Inequalities
5 Minute Preview
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.
Lesson Info Launch GizmoPolynomials and Linear Factors
5 Minute Preview
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 GizmoQuadratics in Vertex Form
5 Minute Preview
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 GizmoRadical Functions
5 Minute Preview
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 GizmoRational Functions
5 Minute Preview
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation.
Lesson Info Launch GizmoStandard Form of a Line
5 Minute Preview
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 GizmoDistance Formula
5 Minute Preview
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation.
Lesson Info Launch GizmoLinear Functions
5 Minute Preview
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 GizmoFinding Factors with Area Models
5 Minute Preview
Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree.
Lesson Info Launch GizmoMultiplying Mixed Numbers
5 Minute Preview
Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps.
Lesson Info Launch GizmoOrdering and Approximating Square Roots
5 Minute Preview
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid.
Lesson Info Launch GizmoDistance-Time Graphs
5 Minute Preview
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 of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs.
Lesson Info Launch GizmoDistance-Time and Velocity-Time Graphs
5 Minute Preview
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 of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.
Lesson Info Launch GizmoSolving Formulas for any Variable
5 Minute Preview
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoMultiplying Fractions
5 Minute Preview
Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product.
Lesson Info Launch GizmoDistance-Time Graphs - Metric
5 Minute Preview
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 speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs.
Lesson Info Launch GizmoDistance-Time and Velocity-Time Graphs - Metric
5 Minute Preview
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 of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.
Lesson Info Launch GizmoAbsolute Value with Linear Functions
5 Minute Preview
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.
Lesson Info Launch GizmoCompound Inequalities
5 Minute Preview
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.
Lesson Info Launch GizmoCat and Mouse (Modeling with Linear Systems)
5 Minute Preview
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.
Lesson Info Launch GizmoPoints in the Coordinate Plane
5 Minute Preview
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 GizmoSolving Linear Inequalities in One Variable
5 Minute Preview
Solve one-step inequalities in one variable. Graph the solution on a number line.
Lesson Info Launch GizmoDirect and Inverse Variation
5 Minute Preview
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.
Lesson Info Launch GizmoIntroduction to Functions
5 Minute Preview
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.
Lesson Info Launch GizmoHyperbolas
5 Minute Preview
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 GizmoLogarithmic Functions
5 Minute Preview
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function.
Lesson Info Launch GizmoPoints in the Complex Plane
5 Minute Preview
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.
Lesson Info Launch GizmoSimplifying Trigonometric Expressions
5 Minute Preview
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps.
Lesson Info Launch GizmoSine Function
5 Minute Preview
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 GizmoTangent Function
5 Minute Preview
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 GizmoPoint-Slope Form of a Line
5 Minute Preview
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
5 Minute Preview
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 GizmoDilations
5 Minute Preview
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
Proportions and Common Multipliers
5 Minute Preview
Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator.
Lesson Info Launch GizmoCompound Interest
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FREE with no time limit!
5 Minute Preview
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 graph, which has a more step-like appearance.
Lesson Info Launch GizmoExploring Linear Inequalities in One Variable
5 Minute Preview
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality.
Lesson Info Launch GizmoSolving Two-Step Equations
5 Minute Preview
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoArithmetic and Geometric Sequences
5 Minute Preview
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.
Lesson Info Launch GizmoCalorimetry Lab
5 Minute Preview
Investigate how calorimetry can be used to find relative specific heat values when different substances are mixed with water. Modify initial mass and temperature values to see effects on the system. One or any combination of the substances can be mixed with water. A dynamic graph (temperature vs. time) shows temperatures of the individual substances after mixing.
Lesson Info Launch GizmoAdding and Subtracting Integers with Chips
5 Minute Preview
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction.
Lesson Info Launch GizmoCat and Mouse (Modeling with Linear Systems) - Metric
5 Minute Preview
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.
Lesson Info Launch GizmoAddition and Subtraction of Functions
5 Minute Preview
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
5 Minute Preview
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes.
Lesson Info Launch GizmoExponential Growth and Decay
5 Minute Preview
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 GizmoCosine Function
5 Minute Preview
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 GizmoEllipses
5 Minute Preview
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 Pythagorean relationship, and discover the string property.
Lesson Info Launch GizmoExponential Functions
5 Minute Preview
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
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FREE with no time limit!
5 Minute Preview
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
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FREE with no time limit!
5 Minute Preview
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior.
Lesson Info Launch GizmoGeneral Form of a Rational Function
5 Minute Preview
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 GizmoParabolas
5 Minute Preview
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 GizmoRiemann Sum
5 Minute Preview
Approximate the area under a curve in an interval using rectangles. Compare the results of left-hand summation to the results of right-hand summation. Vary the interval and the number of rectangles and explore how the graph of the rectangles and curve change in response.
Lesson Info Launch GizmoRoots of a Quadratic
5 Minute Preview
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.
Lesson Info Launch GizmoSum and Difference Identities for Sine and Cosine
5 Minute Preview
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 GizmoTranslating and Scaling Sine and Cosine Functions
5 Minute Preview
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 GizmoAdding Vectors
5 Minute Preview
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation.
Lesson Info Launch GizmoPythagorean Theorem
5 Minute Preview
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle.
Lesson Info Launch GizmoFractions with Unlike Denominators
5 Minute Preview
Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically.
Lesson Info Launch GizmoPythagorean Theorem with a Geoboard
5 Minute Preview
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem.
Lesson Info Launch GizmoPercents, Fractions, and Decimals
5 Minute Preview
Compare a quantity represented by an area with its percent, fraction, and decimal forms.
Lesson Info Launch GizmoSums and Differences with Decimals
5 Minute Preview
Find the sum or difference of two decimal numbers using area models. Find the decimals and their sum or difference on a number line.
Lesson Info Launch GizmoModeling and Solving Two-Step Equations
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FREE with no time limit!
5 Minute Preview
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 GizmoDividing Exponential Expressions
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FREE with no time limit!
5 Minute Preview
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoRotations, Reflections, and Translations
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FREE with no time limit!
5 Minute Preview
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
Lesson Info Launch GizmoIntroduction to Exponential Functions
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FREE with no time limit!
5 Minute Preview
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
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FREE with no time limit!
5 Minute Preview
Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior.
Lesson Info Launch GizmoCompound Interest
- Free!
FREE with no time limit!
5 Minute Preview
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 graph, which has a more step-like appearance.
Lesson Info Launch GizmoFind Your Solution
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