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 fractions visually, on a number line, or numerically using the least common denominator.

Modeling Fractions (Area Models)

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 fractions visually, on a number line, or numerically using the least common denominator.

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 critters either on leaves or as a rectangular array.

Critter 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 critters either on leaves or as a rectangular array.

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.

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

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.

Function 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. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.

Launch a charged particle into a chamber. Charged particles can be added into the chamber to influence the path of the moving particle. The launch speed can be changed as well. Try to match a given path by manipulating the fixed particles in the chamber.

Charge Launcher

Launch a charged particle into a chamber. Charged particles can be added into the chamber to influence the path of the moving particle. The launch speed can be changed as well. Try to match a given path by manipulating the fixed particles in the chamber.

Develop an understanding of ocean tides by comparing the depth of water near a dock to the positions of the Moon, Sun, and Earth. Determine the influence of the Moon and Sun on tides, and compare spring tides to neap tides.

Ocean Tides

Develop an understanding of ocean tides by comparing the depth of water near a dock to the positions of the Moon, Sun, and Earth. Determine the influence of the Moon and Sun on tides, and compare spring tides to neap tides.

Heat or cool a container of water and observe the phase changes that take place. Use a magnifying glass to observe water molecules as a solid, liquid, or gas. Compare the volumes of the three phases of water.

Phases of Water

Heat or cool a container of water and observe the phase changes that take place. Use a magnifying glass to observe water molecules as a solid, liquid, or gas. Compare the volumes of the three phases of water.

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 affected by precipitation.

Measuring 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 affected by precipitation.

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 percent of darts that strike it

Geometric 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 percent of darts that strike it

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.

Rational 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.

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 baseline for percent calculations.

Percent 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 baseline for percent calculations.

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.

Points, Lines, and Equations

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

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 how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling.

Polling: 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 how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling.

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.

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

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.

Equivalent Algebraic Expressions I

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

Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user.

Sight vs. Sound Reactions

Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user.

Attempt to balance specific types of chemical reactions: combination, decomposition, single replacement, and double replacement. While balancing the reactions, the number of atoms on each side is presented as visual, histogram, and numerical data.

Balancing Chemical Equations

Attempt to balance specific types of chemical reactions: combination, decomposition, single replacement, and double replacement. While balancing the reactions, the number of atoms on each side is presented as visual, histogram, and numerical data.

Observe daily weather conditions in a coastal region. Measure temperatures and wind speeds at any location and use this data to map convection currents that form during the day and night. Explain the origin of land breezes and sea breezes.

Coastal Winds and Clouds

Observe daily weather conditions in a coastal region. Measure temperatures and wind speeds at any location and use this data to map convection currents that form during the day and night. Explain the origin of land breezes and sea breezes.

Breed "pure" mice with known genotypes that exhibit specific fur colors, and learn how traits are passed on via dominant and recessive genes. Mice can be stored in cages for future breeding, and the statistics of fur color are reported every time a pair of mice breed. Punnett squares can be used to predict results.

Mouse Genetics (One Trait)

Breed "pure" mice with known genotypes that exhibit specific fur colors, and learn how traits are passed on via dominant and recessive genes. Mice can be stored in cages for future breeding, and the statistics of fur color are reported every time a pair of mice breed. Punnett squares can be used to predict results.

Observe the partial shadows cast by a rectangular block lit by multiple light sources. The number of light sources ranges from one to five, and individual lights can be turned on or off. The light spacing, block width, and distance from the lights to the block can be varied. Light intensity can be observed on a detector.

Penumbra Effect

Observe the partial shadows cast by a rectangular block lit by multiple light sources. The number of light sources ranges from one to five, and individual lights can be turned on or off. The light spacing, block width, and distance from the lights to the block can be varied. Light intensity can be observed on a detector.

Observe daily weather conditions in a coastal region. Measure temperatures and wind speeds at any location and use this data to map convection currents that form during the day and night. Explain the origin of land breezes and sea breezes.

Coastal Winds and Clouds

Observe daily weather conditions in a coastal region. Measure temperatures and wind speeds at any location and use this data to map convection currents that form during the day and night. Explain the origin of land breezes and sea breezes.

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.

Waves

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.

Design your own trebuchet to fling a projectile at a castle wall. All of the dimensions of the trebuchet can be adjusted, as well as the masses of the counterweight and payload. Select a target on the Launch tab, or just see how far your projectile will go.

Trebuchet

Design your own trebuchet to fling a projectile at a castle wall. All of the dimensions of the trebuchet can be adjusted, as well as the masses of the counterweight and payload. Select a target on the Launch tab, or just see how far your projectile will go.

Follow the path of a carbon atom through the atmosphere, biosphere, hydrosphere, and geosphere. Manipulate a simplified model to see how human activities and other factors affect the amount of atmospheric carbon today and in the future.

Carbon Cycle

Follow the path of a carbon atom through the atmosphere, biosphere, hydrosphere, and geosphere. Manipulate a simplified model to see how human activities and other factors affect the amount of atmospheric carbon today and in the future.

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.

Exponential 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.

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.

Cat and Mouse (Modeling with Linear Systems)

Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines.

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.

Sine 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.

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 reshaped.

Concurrent Lines, Medians, and Altitudes

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 reshaped.

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.

Cat and Mouse (Modeling with Linear Systems)

Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines.

Build electrical circuits using batteries, light bulbs, resistors, fuses, wires, and a switch. An ammeter, a voltmeter and an ohmmeter are available for measuring current, voltage and resistance throughout the circuit. The voltage of the battery and the precision of the meters can be adjusted. Multiple circuits can be built for comparison.

Circuits

Build electrical circuits using batteries, light bulbs, resistors, fuses, wires, and a switch. An ammeter, a voltmeter and an ohmmeter are available for measuring current, voltage and resistance throughout the circuit. The voltage of the battery and the precision of the meters can be adjusted. Multiple circuits can be built for comparison.

Observe evolution in a fictional population of bugs. Set the background to any color, and see natural selection taking place. Inheritance of color occurs according to Mendel's laws and probability. Mutations occur at random, and probability of capture by predators is determined by the insect's camouflage.

Evolution: Mutation and Selection

Observe evolution in a fictional population of bugs. Set the background to any color, and see natural selection taking place. Inheritance of color occurs according to Mendel's laws and probability. Mutations occur at random, and probability of capture by predators is determined by the insect's camouflage.

Learn Kepler's three laws of planetary motion by examining the orbit of a planet around a star. The initial position, velocity, and mass of the planet can be varied as well as the mass of the star. The foci and centers of orbits can be displayed and compared to the location of the star. The area swept out by the planet in a given time period can be measured, and data on orbital radii and periods can be plotted in several ways.

Orbital Motion - Kepler's Laws

Learn Kepler's three laws of planetary motion by examining the orbit of a planet around a star. The initial position, velocity, and mass of the planet can be varied as well as the mass of the star. The foci and centers of orbits can be displayed and compared to the location of the star. The area swept out by the planet in a given time period can be measured, and data on orbital radii and periods can be plotted in several ways.

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.

Inclined Plane - Simple Machine

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.

Measure the quantity of a known solution needed to neutralize an acid or base of unknown concentration. Use this information to calculate the unknown concentration. A variety of indicators can be used to show the pH of the solution.

Titration

Measure the quantity of a known solution needed to neutralize an acid or base of unknown concentration. Use this information to calculate the unknown concentration. A variety of indicators can be used to show the pH of the solution.

Explore the abiotic factors that affect Caribbean coral reefs. Many factors can be manipulated in this simplified reef model, including ocean temperature and pH, storm severity, and input of excess sediments and nutrients from logging, sewage, and agriculture. Click "Advance year" to see how the reef responds to these changes.

Coral Reefs 1 - Abiotic Factors

Explore the abiotic factors that affect Caribbean coral reefs. Many factors can be manipulated in this simplified reef model, including ocean temperature and pH, storm severity, and input of excess sediments and nutrients from logging, sewage, and agriculture. Click "Advance year" to see how the reef responds to these changes.