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Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.

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Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.

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Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.

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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.

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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.

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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.

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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.

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Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common.

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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.

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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.

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Measure the height and velocity of two objects connected by a massless rope over a pulley. Observe the forces acting on each mass throughout the simulation. Calculate the acceleration of the objects, and relate these calculations to Newton's Laws of Motion. The mass of each object can be manipulated, as well as the mass and radius of the pulley.

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What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.

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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.

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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.

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

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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.

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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.

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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.

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

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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 asymptote in the graph.

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Investigate how an inclined plane redirects and reduces the force pulling a brick downward, with or without friction. A toy car can apply a variable upward force on the brick, and the mechanical advantage and efficiency of the plane can be determined. A graph of force versus distance illustrates the concept of work.

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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.

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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.

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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.

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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.

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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.

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

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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 denominators in adding. Express sums as improper fractions or mixed numbers.

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Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response.

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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.

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

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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 improper fractions on the top number line, and as mixed numbers on the bottom number line.

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Have you ever used a glove warmer to keep your hands warm? How about an instant cold pack to treat an injury? In the Feel the Heat Gizmo, create your own hot and cold packs using various salts dissolved in water and different bag materials. Learn about exothermic and endothermic processes and how energy is absorbed or released when bonds are broken and new bonds form.

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Use a pulley system to lift a heavy weight to a certain height. Measure the force required to lift the weight using up to three fixed and three movable pulleys. The weight to be lifted and the efficiency of the pulley system can be adjusted, and the height of the weight and the total input distance are reported.

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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.

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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.

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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.

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Use a lever to lift a pig, turkey, or sheep. A strongman provides up to 1000 newtons of effort. The fulcrum, strongman, and animals can be moved to any position to create first-, second-, or third-class levers.

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Lift food using ants with the help of a slanted stick. The steepness of the stick, the number of ants, and the size of the item being lifted can be varied. Observe the effect of friction on sliding objects.

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Use a wheel and axle to move a heavy load. Find out how many athletes it takes to move the load under different conditions. The radii of the wheel and the axle can be adjusted to help study mechanical advantage.

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Observe and measure transverse, longitudinal, and combined waves on a model of a spring moved by a hand. Adjust the amplitude and frequency of the hand, and the tension and density of the spring. The speed and power of the waves is reported, and the wavelength and amplitude can be measured.

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Create molecules using building blocks of carbon, hydrogen, oxygen, nitrogen, and other elements. Connect atoms by bonds, then create double or triple bonds if desired. For each completed molecule, write the chemical formula and, if the molecule is included in the database, observe the 3D structure. Create a variety of challenge molecules including cyclic molecules and isomers.

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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.

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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.

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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.

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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!

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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 simplifying fractions. Add fractions and express sums as improper fractions or mixed numbers.

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One of the simplest machines is a see-saw lever. Place up to eight objects on the lever at different locations and try to balance it. Calculate net torque and moment of inertia based on the positions of the objects and the mass of the bar. The mass of each object can be changed, and the fulcrum position can be shifted as well.

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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 into groups to simplify the fractions.

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Lift a variety of heavy objects (armchair, safe, piano) using pulleys and a rope. Systems of one, two, four, or six pulleys can be used. Up to six people can be used to pull on the rope, which adds force (effort).

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Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.

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Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.

FREE with no time limit!

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Study wave motion, diffraction, interference, and refraction in a simulated ripple tank. A wide variety of scenarios can be chosen, including barriers with one or two gaps, multiple wave sources, reflecting barriers, or submerged rocks. The wavelength and strength of waves can be adjusted, as well as the amount of damping in the tank.

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Explore how a changing magnetic field can induce an electric current. A magnet can be moved up or down at a constant velocity below a loop of wire, or the loop of wire may be dragged in any direction or rotated. The magnetic and electric fields can be displayed, as well as the magnetic flux and the current in the wire.

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

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Shoot a beam of light at a metal plate in a virtual lab and observe the effect on surface electrons. The type of metal as well as the wavelength and amount of light can be adjusted. An electric field can be created to resist the electrons and measure their initial energies.

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Select a sample cell from an animal, plant, or bacterium and view the cell under a microscope. Select each organelle on the image to learn more about its structure and function. Closeup views and animations of certain organelles is provided.

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Label a diagram that illustrates the anatomy of a flower, and understand the function of each structure. Compare the processes of self pollination and cross pollination, and explore how fertilization takes place in a flowering plant.

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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 together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo.

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Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation.

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Everything we know about the world comes through our senses: sight, hearing, touch, taste, and smell. In the Senses Gizmo, explore how stimuli are detected by specialized cells, transmitted through nerves, and processed in the brain.

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Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line.

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Create circuits using batteries, light bulbs, switches, fuses, and a variety of materials. Examine series and parallel circuits, conductors and insulators, and the effects of battery voltage. Thousands of different circuits can be built with this Gizmo.

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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 model. Students can also find the median, mode, and range of the data set.

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In 1915, Alfred Wegener proposed that all of Earth's continents were once joined in an ancient supercontinent he called Pangaea. Wegener's idea of moving continents led to the modern theory of plate tectonics. Create your own version of Pangaea by fitting Earth's landmasses together like puzzle pieces. Use evidence from fossils, rocks, and glaciers to refine your map.

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In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck!

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Build compound circuits with series and parallel elements. Calculate voltages, resistance, and current across each component using Ohm's law and the equivalent resistance equation. Check your answers using a voltmeter, ammeter, and ohmmeter. Learn the function of fuses as a safety device.

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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 dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model.

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The atomic mass for each element listed in the periodic table is actually the weighted average mass of all of the different isotopes of the element. In the Average Atomic Mass Gizmo, use a mass spectrometer to separate an element into its isotopes. Then, calculate the average atomic mass by considering the mass and abundance of each isotope.

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Using an earthquake recording station, learn how to determine the distance between the station and an earthquake based on the time difference between the arrival of the primary and secondary seismic waves. Use this data to find the epicenter in the Earthquakes 2 - Location of Epicenter Gizmo.

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Locate the epicenter of an earthquake by analyzing seismic data from three recording stations. Measure difference in P- and S-wave arrival times, then use data from the Earthquakes 1 - Recording Station Gizmo to find the distance of the epicenter from each station.

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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. Calculate the number of "sound beats" you will hear based on the frequency of each sound. [Note: Headphones are recommended for this Gizmo.]

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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 check your accuracy. The Gizmo can also be used to create a data table based on a given graph.

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Imagine a gigantic pitcher standing on Earth, ready to hurl a huge baseball. What will happen as the ball is thrown harder and harder? Find out with the Gravity Pitch Gizmo. Observe the path of the ball when it is thrown at different velocities. Throw the ball on different planets to see how each planet's gravity affects the ball.

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Control a simulated person running on a treadmill. Your challenge is to use clothing, exercise, and sweat to maintain a constant body temperature as air temperature goes up and down. Sweating (perspiration) can be controlled automatically by the Gizmo or, for a challenge, manually by the user. Don't forget to eat and drink!

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Concussion rates in youth impact sports are high despite the use of helmets. In this STEM case, students act as materials scientists to learn about the physics behind concussions and helmet function. Students will use their understanding of Newton’s First and Second Laws of Motion to investigate helmet padding material to determine which material is best at reducing force during an impact.

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Measure the time required to write a word when the mouse behaves in a normal fashion and when the direction of motion is reversed from left to right, up to down, or both. Run several experiments in each mode to see if your brain and muscles are able to adapt to the new direction of motion. Determine which type of inversion is easiest to adjust to and whether you can train yourself to function normally when the inversion is present.

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In the role of a physician assistant, students help a young man, named Anthony, who has Type II diabetes and high blood pressure. Students must make a diagnosis and then must apply the principles of filtration and homeostasis to help Anthony.

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Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo.

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Digestion is a complex process, involving a wide variety of organs and chemicals that work together to break down food, absorb nutrients, and eliminate wastes. But have you ever wondered what would happen if some of those organs were eliminated, or if the sequence was changed? Can the digestive system be improved? Find out by designing your own digestive system with the Digestive System Gizmo.

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In this follow-up to the Genetic Engineering Gizmo, explore how farmers can maximize yield while limiting ecosystem damage using genetically modified corn. Choose the corn type to plant and the amount of herbicide and insecticide to use, then measure corn yields and monitor wildlife populations and diversity. Observe the long-term effects of pollutants on a nearby stream ecosystem.

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The Coriolis effect causes winds to be deflected as they move across Earth's surface, resulting in circular patterns of winds. This effect is caused by two factors, Earth's rotation and frame of reference. In the Coriolis Effect Gizmo, students will build their understanding of this phenomenon using the analogy of two kids playing catch: first on a train, then on a merry-go-round, and finally on Earth's surface.

FREE with no time limit!

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In 1915, Alfred Wegener proposed that all of Earth's continents were once joined in an ancient supercontinent he called Pangaea. Wegener's idea of moving continents led to the modern theory of plate tectonics. Create your own version of Pangaea by fitting Earth's landmasses together like puzzle pieces. Use evidence from fossils, rocks, and glaciers to refine your map.

FREE with no time limit!

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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.

FREE with no time limit!

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Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response.

FREE with no time limit!

5 Minute Preview

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

FREE with no time limit!

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.

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.

FREE with no time limit!

5 Minute Preview

Study wave motion, diffraction, interference, and refraction in a simulated ripple tank. A wide variety of scenarios can be chosen, including barriers with one or two gaps, multiple wave sources, reflecting barriers, or submerged rocks. The wavelength and strength of waves can be adjusted, as well as the amount of damping in the tank.

Video Preview

Concussion rates in youth impact sports are high despite the use of helmets. In this STEM case, students act as materials scientists to learn about the physics behind concussions and helmet function. Students will use their understanding of Newton’s First and Second Laws of Motion to investigate helmet padding material to determine which material is best at reducing force during an impact.

Video Preview

In the role of a physician assistant, students help a young man, named Anthony, who has Type II diabetes and high blood pressure. Students must make a diagnosis and then must apply the principles of filtration and homeostasis to help Anthony.