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Browse by Grade & Topic: Complex%20Numbers
Find Gizmos organized by grade level and topic.
See How FREE Gizmos WorkBinomial Probabilities
Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation.
Lesson Info Launch GizmoGeometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the...
Lesson Info Launch GizmoBox-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot...
Lesson Info Launch GizmoAdding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows.
Lesson Info Launch GizmoArithmetic 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 GizmoPolling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate...
Lesson Info Launch GizmoPopulations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample...
Lesson Info Launch GizmoFraction Artist 2 (Area Models of Fractions)
Extend understanding of fractions by making modern paintings in the style of Piet Mondrian. Create and analyze paintings with different-sized sections. Compare the sizes of unit fractions....
Lesson Info Launch GizmoFraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside...
Lesson Info Launch GizmoFido's Flower Bed (Perimeter and Area)
Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of...
Lesson Info Launch GizmoCritter Count (Modeling Multiplication)
Use groups of critters on leaves to model multiplication as repeated addition. Change the expression to change the number of groups or the number of critters per group. Display the...
Lesson Info Launch GizmoSpin the Big Wheel! (Probability)
Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table...
Lesson Info Launch GizmoQuilting Bee (Symmetry)
Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded...
Lesson Info Launch GizmoElevator Operator (Line Graphs)
Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either...
Lesson Info Launch GizmoCity Tour (Coordinates)
FREE with no time limit!
Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For...
Lesson Info Launch GizmoNumber Line Frog Hop (Addition and Subtraction)
Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you...
Lesson Info Launch GizmoAdding Whole Numbers and Decimals (Base-10 Blocks)
FREE with no time limit!
Use base-10 blocks to model two numbers. Then combine the blocks to model the sum. Blocks of equal value can be exchanged from one area of the mat to the other to help understand carrying...
Lesson Info Launch GizmoCannonball Clowns (Number Line Estimation)
Launch clowns from a circus cannon and try to hit the target. Drag digit cards on the control panel to set the launch distance and choose an appropriate unit of distance. After practicing...
Lesson Info Launch GizmoRoad Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each...
Lesson Info Launch GizmoWhole Numbers with Base-10 Blocks
- New!
Use base-10 blocks to model, add, and subtract whole numbers. Learn about place value using flats (hundreds), rods (tens), and cubes (ones). Group or ungroup blocks as needed to add or...
Lesson Info Launch GizmoRadians
- New!
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 GizmoAdding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation.
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 GizmoPolling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help...
Lesson Info Launch GizmoFraction Garden (Comparing Fractions)
Plant flowers in two gardens to help develop fraction sense. The two gardens act as number lines, from 0 to 1. Use the flowers in the gardens to compare fractions and to explore equivalent...
Lesson Info Launch GizmoChocomatic (Multiplication, Arrays, and Area)
FREE with no time limit!
Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all...
Lesson Info Launch GizmoMovie Reviewer (Mean and Median)
Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance...
Lesson Info Launch GizmoReaction Time 1 (Graphs and Statistics)
Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be...
Lesson Info Launch GizmoRock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient...
Lesson Info Launch GizmoFunction Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines....
Lesson Info Launch GizmoLucky Duck (Expected Value)
- New!
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How...
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 GizmoIndependent and Dependent Events
FREE with no time limit!
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings...
Lesson Info Launch GizmoAdding and Subtracting Integers with Chips
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 GizmoGraphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then...
Lesson Info Launch GizmoMeasuring Trees
Measure the height, diameter, and circumference of trees in a forest. Count growth rings to determine the age of each tree. Grow the trees for several years and investigate how growth is...
Lesson Info Launch GizmoNo Alien Left Behind (Division with Remainders)
The alien school children from the planet Zigmo travel to distant planets on a field trip. The goal is to select a bus size so that all buses are full and no aliens are left behind. This...
Lesson Info Launch GizmoToy Factory (Set Models of Fractions)
Create a set of stuffed animals: monkeys, giraffes, and rabbits. Toys can be painted red, green, or blue. Describe the makeup of the set (animals or colors) with fractions. Arrange the toys...
Lesson Info Launch GizmoModeling Decimals (Area and Grid Models)
Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a...
Lesson Info Launch GizmoRounding Whole Numbers (Number Line)
Place points on a number line. Round these values to the nearest ten or hundred. Visualize rounding by showing the number line as a hill or series of hills. These hills cause the points to...
Lesson Info Launch GizmoMascot Election (Pictographs and Bar Graphs)
A brand new school is opening and it is time to elect the school mascot! Students can choose the Eagle, Lion, Bear, or Wolf. Voting results can be displayed in a table, tally chart,...
Lesson Info Launch GizmoBalancing Blocks (Volume)
This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The...
Lesson Info Launch GizmoCorrelation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
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 GizmoComparing and Ordering Decimals
Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line.
Lesson Info Launch GizmoPermutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree...
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 GizmoModeling Fractions (Area Models)
FREE with no time limit!
Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare...
Lesson Info Launch GizmoModeling Whole Numbers and Decimals (Base-10 Blocks)
Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks...
Lesson Info Launch GizmoMultiplying Decimals (Area Model)
Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece...
Lesson Info Launch GizmoSubtracting Whole Numbers and Decimals (Base-10 Blocks)
Use base-10 blocks to model a starting number. Then subtract blocks from this number by dragging them into a subtraction bin. Blocks of equal value can be exchanged from one section of the...
Lesson Info Launch GizmoFactor Trees (Factoring Numbers)
The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes...
Lesson Info Launch GizmoFunction Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines....
Lesson Info Launch GizmoDescribing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't...
Lesson Info Launch GizmoProbability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner,...
Lesson Info Launch GizmoEstimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake.
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 GizmoReaction Time 2 (Graphs and Statistics)
Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be...
Lesson Info Launch GizmoAdding Fractions (Fraction Tiles)
Add fractions with the help of the Fractionator, a fraction-tile-making machine in the Gizmo. Model sums by placing the tiles on side-by-side number lines. Explore the usefulness of common...
Lesson Info Launch GizmoFunction Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines....
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 GizmoIntegers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line.
Lesson Info Launch GizmoTheoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner,...
Lesson Info Launch GizmoEquivalent Fractions (Fraction Tiles)
Explore fractions using the Fractionator, the machine that makes fraction tiles. Compare fractions and find equivalent fractions by arranging the tiles on two horizontal rows. Explore...
Lesson Info Launch GizmoFractions Greater than One (Fraction Tiles)
Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as...
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 GizmoSimplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps.
Lesson Info Launch GizmoHistograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected.
Lesson Info Launch GizmoTreasure Hunter (Decimals on the Number Line)
Drive a desert highway searching for buried treasure. Learn to use the car's tens, ones, tenths, and hundredths gears, along with a GPS system (number line), to find the right place to dig....
Lesson Info Launch GizmoTarget Sum Card Game (Multi-digit Addition)
Play an addition card game! The goal is to create a sum that is as close as possible to the target sum. Students will deepen their understanding of place value as they get better at playing...
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 GizmoMultiplying with Decimals
Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region.
Lesson Info Launch GizmoCargo Captain (Multi-digit Subtraction)
You are the captain of an interplanetary cargo ship, delivering important supplies to the outer planets. The cargo can be stored in barrels, crates, and holds. (There are 10 barrels in a...
Lesson Info Launch GizmoFraction Artist 1 (Area Models of Fractions)
Develop understanding of fractions by making modern paintings. Find different ways to divide a canvas into equal-sized sections. Make paintings to represent simple fractions and to find...
Lesson Info Launch GizmoCircles
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 GizmoOrdering and Approximating Square Roots
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid.
Lesson Info Launch GizmoTrends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line.
Lesson Info Launch GizmoSolving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line.
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 GizmoAnimal Group Behavior
- Stem Case
A farmer in Africa is having problems with elephants eating her corn and cotton crops. As a wildlife biologist, students learn about animal group behavior and relationships of elephants and...
Lesson Info STEM CasesSquare 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.
Lesson Info Launch GizmoSolving 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...
Lesson Info Launch GizmoSums and Differences with Decimals
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 GizmoMean, Median, and Mode
FREE with no time limit!
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable...
Lesson Info Launch GizmoCenter of Mass
Drag blocks onto a two-dimensional surface and observe the effects on the center of mass. Use a grid to calculate the coordinates of the center of mass. Investigate predefined shapes or...
Lesson Info Launch GizmoStem-and-Leaf Plots
Build a data set and compare the line plot of the data set to the stem-and-leaf plot.
Lesson Info Launch GizmoCircumference and Area of Circles
Resize a circle and compare its radius, circumference, and area.
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 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 GizmoChords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center.
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 GizmoModeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps.
Lesson Info Launch GizmoInscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept.
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 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 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 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 GizmoSolving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line.
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 GizmoRational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers.
Lesson Info Launch GizmoDividing Fractions
Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change.
Lesson Info Launch GizmoDividing Mixed Numbers
Choose the correct steps to divide mixed numbers. Use step-by-step feedback to diagnose and correct incorrect steps.
Lesson Info Launch GizmoEstimating Sums and Differences
Estimate the sum or difference of two fractions using area models. Compare estimates to exact sums and differences.
Lesson Info Launch GizmoFinding Factors with Area Models
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 GizmoFractions with Unlike Denominators
Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically.
Lesson Info Launch GizmoMultiplying Mixed Numbers
Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps.
Lesson Info Launch GizmoPercents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms.
Lesson Info Launch GizmoImproper Fractions and Mixed Numbers
Represent a quantity given by a shaded region as an improper fraction and as a mixed number. Experiment with different shaded regions sliced differently.
Lesson Info Launch GizmoOrdering Percents, Fractions, and Decimals Greater Than 1
Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals.
Lesson Info Launch GizmoMultiplying Fractions
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 GizmoAnimal Group Behavior
- Stem Case
A farmer in Africa is having problems with elephants eating her corn and cotton crops. As a wildlife biologist, students learn about animal group behavior and relationships of elephants and...
Lesson Info STEM CasesBeam to Moon (Ratios and Proportions)
FREE with no time limit!
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve...
Lesson Info Launch GizmoPart-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms.
Lesson Info Launch GizmoPercent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the...
Lesson Info Launch GizmoPercents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model.
Lesson Info Launch GizmoProportions and Common Multipliers
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 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 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 GizmoBeam to Moon (Ratios and Proportions) - Metric
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve...
Lesson Info Launch GizmoNumber Systems
Explore number systems and convert numbers from one base to another using counter beads in place-value columns.
Lesson Info Launch GizmoExponents 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.
Lesson Info Launch GizmoDividing Exponential Expressions
FREE with no time limit!
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoMultiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps.
Lesson Info Launch GizmoFinding Patterns
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 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 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 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 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 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 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 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 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 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 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 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 GizmoAddition of Polynomials
Add polynomials using an area model. Use step-by-step feedback to diagnose any mistakes.
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 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 GizmoConcurrent Lines, Medians, and Altitudes
FREE with no time limit!
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and...
Lesson Info Launch GizmoConstructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction.
Lesson Info Launch GizmoConstructing Congruent Segments and Angles
Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction.
Lesson Info Launch GizmoInvestigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
Lesson Info Launch GizmoParallel, Intersecting, and Skew Lines
Explore the properties of intersecting, parallel, and skew lines as well as lines in the plane. Rotate the plane and lines in three-dimensional space to ensure a full understanding of...
Lesson Info Launch GizmoArea 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...
Lesson Info Launch GizmoClassifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals.
Lesson Info Launch GizmoParallelogram Conditions
Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram.
Lesson Info Launch GizmoPolygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate...
Lesson Info Launch GizmoSpecial Parallelograms
Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition?
Lesson Info Launch GizmoArea of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation.
Lesson Info Launch GizmoSegment and Angle Bisectors
Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the...
Lesson Info Launch GizmoCongruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent.
Lesson Info Launch GizmoIsosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles.
Lesson Info Launch GizmoProving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence.
Lesson Info Launch GizmoSimilarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles.
Lesson Info Launch GizmoTriangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the...
Lesson Info Launch GizmoTriangle Inequalities
Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles.
Lesson Info Launch GizmoClassifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle.
Lesson Info Launch GizmoDistance Formula
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 GizmoPythagorean Theorem
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 GizmoPythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem.
Lesson Info Launch GizmoSine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change.
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 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 GizmoPerimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare.
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 GizmoSimilar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related.
Lesson Info Launch Gizmo3D and Orthographic Views
Arrange blocks in a three-dimensional space so that the top view, front view, and side view match the target top view, front view, and side view.
Lesson Info Launch GizmoPyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the...
Lesson Info Launch GizmoPrisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the...
Lesson Info Launch GizmoSurface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid.
Lesson Info Launch GizmoSurface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid.
Lesson Info Launch GizmoPerimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle).
Lesson Info Launch GizmoElapsed Time
Calculate the difference between the times given by two analog clocks. Rotate the hands of the clocks to change the time and see how the calculation changes.
Lesson Info Launch GizmoPoints in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.
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 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 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 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 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 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 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 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 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 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 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 ax2+bx+c
Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes.
Lesson Info Launch GizmoModeling the Factorization of x2+bx+c
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes.
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 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 GizmoBiconditional Statements
Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form.
Lesson Info Launch GizmoConditional Statements
Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form.
Lesson Info Launch GizmoRiemann Sum
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 GizmoAdding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation.
Lesson Info Launch GizmoCity Tour (Coordinates)
FREE with no time limit!
Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For...
Lesson Info Launch GizmoAdding Whole Numbers and Decimals (Base-10 Blocks)
FREE with no time limit!
Use base-10 blocks to model two numbers. Then combine the blocks to model the sum. Blocks of equal value can be exchanged from one area of the mat to the other to help understand carrying...
Lesson Info Launch GizmoChocomatic (Multiplication, Arrays, and Area)
FREE with no time limit!
Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all...
Lesson Info Launch GizmoIndependent and Dependent Events
FREE with no time limit!
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings...
Lesson Info Launch GizmoModeling Fractions (Area Models)
FREE with no time limit!
Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare...
Lesson Info Launch GizmoMean, Median, and Mode
FREE with no time limit!
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable...
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 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 GizmoBeam to Moon (Ratios and Proportions)
FREE with no time limit!
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve...
Lesson Info Launch GizmoDividing Exponential Expressions
FREE with no time limit!
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose 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 GizmoConcurrent Lines, Medians, and Altitudes
FREE with no time limit!
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and...
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 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 GizmoHow Free Gizmos Work
Start teaching with 20-40 Free Gizmos. See the full list.
Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.
All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.
Free Gizmos change each semester. The new collection will be available January 1 and July 1.
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
STEM Cases take between 30-90 minutes for students to complete, depending on the case.
Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
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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