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 have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar.
Chocomatic (Multiplication, Arrays, and Area)
Compare average temperatures, precipitation, humidity, and wind speed for a variety of locations across the globe. Explore the influence of latitude, proximity to oceans, elevation, and other factors on climate. Observe how animals and plants are adapted to climate and their environment. This lesson uses U.S. customary units.
Comparing Climates (Customary)
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.
Explore the motion of particles as they bounce around from one side of a room to the other through an adjustable gap or partition. The mass of the particles can be adjusted, as well as the temperature of the room and the initial number of particles. In a real-world context, this can be used to learn about how odors travel, fluids move through gaps, the thermodynamics of gases, and statistical probability.
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.
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 the body through time. Based on the reaction of the patient, determine the ideal levels of medication. Create a dosage schedule so these levels are maintained through time. Four types of pills, each with a different release pattern and target organ, are available for use.
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 and dye. Add dye to a container of water, and then add beakers of pure water while removing beakers of dyed water. The amount of dye remaining is recorded after each cycle. The volumes of all containers can be adjusted, as well as the amount of dye used. This provides a good example of exponential decay.
A falling cylinder is attached to a rotating propeller that stirs and heats the water in a beaker. The mass and height of the cylinder, as well as the quantity and initial temperature of water can be adjusted. The temperature of the water is measured as energy is converted from one form to another.
Energy Conversion in a System
Observe and manipulate the populations of four creatures (trees, deer, bears, and mushrooms) in a forest. Investigate the feeding relationships (food web) in the forest. Determine which creatures are producers, consumers, and decomposers. Pictographs and line graphs show changes in populations over time.
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 fractions that are equivalent to one-half.
Fraction Artist 1 (Area Models of Fractions)
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 the area models to shade them. Compare the numbers visually or on a number line.
Fraction, Decimal, Percent (Area and Grid Models)
Try to get a hole in one by adjusting the velocity and launch angle of a golf ball. Explore the physics of projectile motion in a frictional or ideal setting. Horizontal and vertical velocity vectors can be displayed, as well as the path of the ball. The height of the golfer and the force of gravity are also adjustable.
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.
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 with replacement of the marbles to study independent events, or without replacement to explore dependent events.
Independent and Dependent Events
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear.
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 height.
Mean, Median, and Mode
Explore how sex cells are produced by the process of meiosis. Compare meiosis in male and female germ cells, and use crossovers to increase the number of possible gamete genotypes. Using meiosis and crossovers, create "designer" fruit fly offspring with desired trait combinations.
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps.
Modeling and Solving Two-Step Equations
Explore examples of nuclear fusion and fission reactions. Follow the steps of the proton-proton chain, CNO cycle, and fission of uranium-235. Write balanced nuclear equations for each step, and compare the energy produced in each process.
Find the effect of length, mass, and angle on the period of a pendulum. The pendulum is attached to a clock that can be adjusted to tell time accurately. The clock can be located on Earth or Jupiter to determine the effect of gravity.
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.
Percents and Proportions
Measure the temperature on wet and dry bulb thermometers to determine relative humidity. Measure the dew point by cooling a bucket of water until condensation forms on the surface. See how the relative humidity and dew point change over the course of a day.
Approximate the area under a curve in an interval using rectangles. Compare the results of left-hand summation to the results of right-hand summation. Vary the interval and the number of rectangles and explore how the graph of the rectangles and curve change in response.
Try to classify a dozen different rock samples based on their appearance. Common characteristics of each major rock type are described. Rocks also can be classified by where they formed.
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
Roots of a Quadratic
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
Rotations, Reflections, and Translations
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!
Simplifying Algebraic Expressions II
Explore our solar system and learn the characteristics of each planet. Compare the sizes of planets and their distances from the Sun. Observe the speeds of planetary orbits and measure how long each planet takes to go around the Sun.
Analyze the spectra of a variety of stars. Determine the elements that are represented in each spectrum, and use this information to infer the temperature and classification of the star. Look for unusual features such as redshifted stars, nebulae, and stars with large planets.
Observe the movement of particles of an ideal gas at a variety of temperatures. A histogram showing the Maxwell-Boltzmann velocity distribution is shown, and the most probable velocity, mean velocity, and root mean square velocity can be calculated. Molecules of different gases can be compared.
Temperature and Particle Motion
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. Plot your find on a zoomable number line map. Can you become a master Treasure Hunter?
Treasure Hunter (Decimals on the Number Line)
Release a lytic virus in a group of cells and observe how cells are infected over time and eventually destroyed. Data related to the number of healthy cells, infected cells, and viruses can be recorded over time to determine the time required for the virus to mature within a cell.
Virus Lytic Cycle
Shine white light or a single-color beam through a prism. Explore how a prism refracts light and investigate the factors that affect the amount of refraction. The index of refraction of the prism, width of the prism, prism angle, light angle, and light wavelength can be adjusted.
Explore the processes of photosynthesis and respiration that occur within plant and animal cells. The cyclical nature of the two processes can be constructed visually, and the simplified photosynthesis and respiration formulae can be balanced.
Cell Energy Cycle
Select sample cells from a plant or animal and place the cells on a microscope to look inside the cells. Information about their common structures is provided (and the structures are highlighted), but you will need to move your microscope slide to find all the different structures.
Chemical changes result in the formation of new substances. But how can you tell if a chemical change has occurred? Explore this question by observing and measuring a variety of chemical reactions. Along the way you will learn about chemical equations, acids and bases, exothermic and endothermic reactions, and conservation of matter.
Trace the path of blood through a beating heart and the network of blood vessels that supplies blood to the body. Take blood samples from different blood vessels to observe blood cells and measure the levels of oxygen, carbon dioxide, sugar, and urea.
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.
Build a glucose molecule, atom-by-atom, to learn about chemical bonds and the structure of glucose. Explore the processes of dehydration synthesis and hydrolysis in carbohydrate molecules.
Measure the mass and volume of a variety of objects, then place them into a beaker of liquid to see if they float or sink. Learn to predict whether objects will float or sink in water based on their mass and volume. Compare how objects float or sink in a variety of liquids, including gasoline, oil, seawater, and corn syrup.
Drop a chunk of material in a beaker of water and observe whether it sinks or floats. Cut the chunk into smaller pieces of any size, and observe what happens as they are dropped in the beaker. The mass and volume of each chunk can be measured to gain a clear understanding of density and buoyancy.
Density Experiment: Slice and Dice
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.
Investigate the motion of an object as it falls to the ground. A variety of objects can be compared, and their motion can be observed in a vacuum, in normal air, and in denser air. The position, velocity, and acceleration are measured over time, and the forces on the object can be displayed. Using the manual settings, the mass, radius, height, and initial velocity of the object can be adjusted, as can the air density and wind.
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 3 (Functions and Problem Solving)
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.
General Form of a Rational Function
Test your hearing range by listening to low-, medium-, and high-frequency sounds. Compare the relative loudness of sounds at each frequency to create an equal-loudness curve. In a quiet room, measure your threshold of audibility for each frequency, and compare your results to others. The volume of each sound can be adjusted.
Hearing: Frequency and Volume
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!
Sort and pair the images of human chromosomes obtained in a scan. Find differences in the scans of the various patients to find out specific things that can cause disease, as well as the gender of the person.
Use data from up to three weather stations to predict the motion of a hurricane. The wind speed, wind direction, cloud cover and air pressure are provided for each station using standard weather symbols.
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.
Introduction to Functions
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit.
Least-Squares Best Fit Lines
Drag bar magnets and a variety of other objects onto a piece of paper. Click Play to release the objects to see if they are attracted together, repelled apart, or unaffected. You can also sprinkle iron filings over the magnets and other objects to view the magnetic field lines that are produced.
Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes.
Modeling the Factorization of x2+bx+c
Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product.
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 is a nice illustration of division with remainders.
No Alien Left Behind (Division with Remainders)
Observe the five main types of nuclear decay: alpha decay, beta decay, gamma decay, positron emission, and electron capture. Write nuclear equations by determining the mass numbers and atomic numbers of daughter products and emitted particles.
How do scientists measure and describe the weather? In this introductory lesson, students will practice using a thermometer, anemometer, rain gauge, and hygrometer to record weather conditions in a variety of locations and dates. This lesson uses U.S. customary units.
Observing Weather (Customary)
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.
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 the polygon to see that the sum is unchanged.
Polygon Angle Sum
Observe the populations of grass, prairie dogs, ferrets and foxes in a prairie ecosystem. Investigate feeding relationships and determine the food chain. Bar graphs and line graphs show changes in populations over time.
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, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
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).
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.
Quadratics in Polynomial Form
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 displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median.
Reaction Time 1 (Graphs and Statistics)
Explore how river erosion affects landscapes in the short term and over long periods of time. Describe the features of mountain streams and meandering rivers, and use a floating barrel to estimate current speed. Witness the changes that occur as mountain streams erode downward and meandering rivers erode from side to side.
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 vehicle, and discover the shortest path between two cities.
Road Trip (Problem Solving)
Gain an understanding of the causes of seasons by observing Earth as it orbits the Sun in three dimensions. Observe the path of the Sun across the sky on any date and from any location. Create graphs of solar intensity and day length, and use collected data to describe and explain seasonal changes.
Seasons in 3D
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.
Simplifying Algebraic Expressions I
Solve systems of linear equations, written in standard form. Explore what it means to solve systems algebraically (with substitution or elimination) and graphically. Also, use a draggable green point to see what it means when (x, y) values are solutions of an equation, or of a system of equations.
Solving Linear Systems (Standard Form)
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.
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.
Toy Factory (Set Models of Fractions)