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Tennessee - Science: Physics
State Performance Indicators | Adopted: 2008
SPI.3231.1.3: : Given Newton?s laws of motion, analyze scenarios related to inertia, force, and action-reaction.
SPI.3231.1.3: : Given Newton?s laws of motion, analyze scenarios related to inertia, force, and action-reaction.
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Atwood Machine
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. 5 Minute Preview
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Fan Cart Physics
Gain an understanding of Newton's Laws by experimenting with a cart (on which up to three fans are placed) on a linear track. The cart has a mass, as does each fan. The fans exert a constant force when switched on, and the direction of the fans can be altered as the position, velocity, and acceleration of the cart are measured. 5 Minute Preview
SPI.3231.1.4: : Solve motion and conceptual problems regarding velocity, acceleration, and displacement using displacement-time graphs and velocity-time graphs.
SPI.3231.1.4: : Solve motion and conceptual problems regarding velocity, acceleration, and displacement using displacement-time graphs and velocity-time graphs.
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Distance-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 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. 5 Minute Preview

Distance-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 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. 5 Minute Preview

Free-Fall Laboratory
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. 5 Minute Preview
SPI.3231.1.5: : Evaluate and describe the phenomena related to Archimedes? Principle, Pascal?s Principle, and Bernoulli?s Principle.
SPI.3231.1.5: : Evaluate and describe the phenomena related to Archimedes? Principle, Pascal?s Principle, and Bernoulli?s Principle.

Archimedes' Principle
Place weights into a boat and see how far the boat sinks into a tank of liquid. The depth of the boat can be measured, as well as the amount of liquid displaced. The dimensions of the boat and the density of the liquid can be adjusted. See how much weight the boat can hold before it sinks to the bottom! 5 Minute Preview

Determining Density via Water Displacement
Drop objects in a beaker that is filled with water, and measure the water that flows over the edge. Using Archimedes' principle, determine the density of objects based on the amount of displaced water. 5 Minute Preview
SPI.3231.1.9: : Given the mass, velocity and time it takes to stop an object in an inelastic collision, determine the momentum and impulse of the collision.
SPI.3231.1.9: : Given the mass, velocity and time it takes to stop an object in an inelastic collision, determine the momentum and impulse of the collision.
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2D Collisions
Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios. 5 Minute Preview
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Air Track
Adjust the mass and velocity of two gliders on a frictionless air track. Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic. 5 Minute Preview
SPI.3231.1.10: : Analyze and solve problems related to elastic and inelastic collisions related to change in momentum.
SPI.3231.1.10: : Analyze and solve problems related to elastic and inelastic collisions related to change in momentum.
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2D Collisions
Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios. 5 Minute Preview

Air Track
Adjust the mass and velocity of two gliders on a frictionless air track. Measure the velocity, momentum, and kinetic energy of each glider as they approach each other and collide. Collisions can be elastic or inelastic. 5 Minute Preview
SPI.3231.1.11: : Given a projectile launched at an angle, select the correct equation from a list for calculating: the maximum height of travel, time of flight and/or the maximum horizontal distance covered.
SPI.3231.1.11: : Given a projectile launched at an angle, select the correct equation from a list for calculating: the maximum height of travel, time of flight and/or the maximum horizontal distance covered.
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Feed the Monkey (Projectile Motion)
Fire a banana cannon at a monkey in a tree. The monkey drops from the tree at the moment the banana is fired from the cannon. Determine where to aim the cannon so the monkey catches the banana. The position of the cannon, launch angle and initial velocity of the banana can be varied. Students can observe the velocity vectors and the paths of the monkey and banana. 5 Minute Preview
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Golf Range
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. 5 Minute Preview
SPI.3231.1.12: : Given a scenario where a projectile is being launched at an angle, answer the following conceptual questions.
SPI.3231.1.12.a: : What is the velocity in the y direction when the projectile is at maximum height?

Feed the Monkey (Projectile Motion)
Fire a banana cannon at a monkey in a tree. The monkey drops from the tree at the moment the banana is fired from the cannon. Determine where to aim the cannon so the monkey catches the banana. The position of the cannon, launch angle and initial velocity of the banana can be varied. Students can observe the velocity vectors and the paths of the monkey and banana. 5 Minute Preview
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Golf Range
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. 5 Minute Preview
SPI.3231.1.12.b: : What acceleration does the projectile have in the x direction after launched.

Feed the Monkey (Projectile Motion)
Fire a banana cannon at a monkey in a tree. The monkey drops from the tree at the moment the banana is fired from the cannon. Determine where to aim the cannon so the monkey catches the banana. The position of the cannon, launch angle and initial velocity of the banana can be varied. Students can observe the velocity vectors and the paths of the monkey and banana. 5 Minute Preview

Golf Range
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. 5 Minute Preview
SPI.3231.1.12.a: : What is the velocity in the y direction when the projectile is at maximum height?
SPI.3231.1.12.a: : What is the velocity in the y direction when the projectile is at maximum height?

Feed the Monkey (Projectile Motion)
Fire a banana cannon at a monkey in a tree. The monkey drops from the tree at the moment the banana is fired from the cannon. Determine where to aim the cannon so the monkey catches the banana. The position of the cannon, launch angle and initial velocity of the banana can be varied. Students can observe the velocity vectors and the paths of the monkey and banana. 5 Minute Preview

Golf Range
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. 5 Minute Preview
SPI.3231.1.12.b: : What acceleration does the projectile have in the x direction after launched.
SPI.3231.1.12.b: : What acceleration does the projectile have in the x direction after launched.

Feed the Monkey (Projectile Motion)
Fire a banana cannon at a monkey in a tree. The monkey drops from the tree at the moment the banana is fired from the cannon. Determine where to aim the cannon so the monkey catches the banana. The position of the cannon, launch angle and initial velocity of the banana can be varied. Students can observe the velocity vectors and the paths of the monkey and banana. 5 Minute Preview

Golf Range
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. 5 Minute Preview
SPI.3231.1.13: : Analyze and solve pendulum problems using the pendulum period formula: [T = 2pi (square root of (L/g)]
SPI.3231.1.13: : Analyze and solve pendulum problems using the pendulum period formula: [T = 2pi (square root of (L/g)]
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Pendulum Clock
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. 5 Minute Preview
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Period of Mass on a Spring
Measure the period of a mass on the end of a spring. Determine the effects of gravitational acceleration, mass, and the spring constant on the period of the spring. Create an equation for the period of a spring given its mass and spring constant. 5 Minute Preview
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Period of a Pendulum
Practice measuring the period of a pendulum. Perform experiments to determine how mass, length, gravitational acceleration, and angle affect the period of a pendulum. 5 Minute Preview
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Simple Harmonic Motion
Observe two different forms of simple harmonic motion: a pendulum and a spring supporting a mass. Use a stopwatch to measure the period of each device as you adjust the mass hanging from the spring, the spring constant, the mass of the pendulum, the length of the pendulum, and the gravitational acceleration. 5 Minute Preview
SPI.3231.1.14: : Relate the variables of work, power, kinetic energy, and potential energy to mechanical situations and solve for these variables.
SPI.3231.1.14: : Relate the variables of work, power, kinetic energy, and potential energy to mechanical situations and solve for these variables.
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Pulley Lab
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. 5 Minute Preview
SPI.3231.1.15: : Calculate the gravitational attraction between two objects.
SPI.3231.1.15: : Calculate the gravitational attraction between two objects.
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Pith Ball Lab
Pith balls with positive, negative, or no electrical charge are suspended from strings. The charge and mass of the pith balls can be adjusted, along with the length of the string, which will cause the pith balls to change position. Distances can be measured as variables are adjusted, and the forces (Coulomb and gravitational) acting on the balls can be displayed. 5 Minute Preview
SPI.3231.1.17: : Solve problems for centripetal force, and angular acceleration.
SPI.3231.1.17: : Solve problems for centripetal force, and angular acceleration.
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Torque and Moment of Inertia
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. 5 Minute Preview
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Uniform Circular Motion
Measure the position, velocity, and acceleration (both components and magnitude) of an object undergoing circular motion. The radius and velocity of the object can be controlled, along with the mass of the object. The forces acting on the object also can be recorded. 5 Minute Preview
SPI.3231.1.18: : Analyze and solve problems related to rotational motion and torque.
SPI.3231.1.18: : Analyze and solve problems related to rotational motion and torque.

Torque and Moment of Inertia
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. 5 Minute Preview
SPI.3231.2.2: : Solve an applied problem of heat exchange with respect to specific heat.
SPI.3231.2.2: : Solve an applied problem of heat exchange with respect to specific heat.
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Calorimetry Lab
Investigate how calorimetry can be used to find relative specific heat values when different substances are mixed with water. Modify initial mass and temperature values to see effects on the system. One or any combination of the substances can be mixed with water. A dynamic graph (temperature vs. time) shows temperatures of the individual substances after mixing. 5 Minute Preview
SPI.3231.2.4: : Describe all forms of heat exchange.
SPI.3231.2.4: : Describe all forms of heat exchange.
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Calorimetry Lab
Investigate how calorimetry can be used to find relative specific heat values when different substances are mixed with water. Modify initial mass and temperature values to see effects on the system. One or any combination of the substances can be mixed with water. A dynamic graph (temperature vs. time) shows temperatures of the individual substances after mixing. 5 Minute Preview
SPI.3231.3.1: : Identify the components of standing waves; including nodes, antinodes, fundamental, numeric harmonics, and overtones.
SPI.3231.3.1: : Identify the components of standing waves; including nodes, antinodes, fundamental, numeric harmonics, and overtones.
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Ripple Tank
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. 5 Minute Preview
SPI.3231.3.2: : Distinguish between longitudinal and transverse waves and identify components of all mechanical waves including wavelength, frequency, period, crest, trough, and amplitude.
SPI.3231.3.2: : Distinguish between longitudinal and transverse waves and identify components of all mechanical waves including wavelength, frequency, period, crest, trough, and amplitude.
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Longitudinal Waves
Observe the propagation of longitudinal (compression) waves in a closed or open tube with evenly-spaced dividers. The strength and frequency of the waves can be manipulated, or waves can be observed as individual pulses. Compare the movement of dividers to graphs of displacement, velocity, acceleration and pressure. 5 Minute Preview
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Ripple Tank
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. 5 Minute Preview
SPI.3231.3.3: : Select the type of mechanical waves that apply to natural wave phenomena such as sound, water or earthquake.
SPI.3231.3.3: : Select the type of mechanical waves that apply to natural wave phenomena such as sound, water or earthquake.
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Earthquakes 1 - Recording Station
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. 5 Minute Preview

Longitudinal Waves
Observe the propagation of longitudinal (compression) waves in a closed or open tube with evenly-spaced dividers. The strength and frequency of the waves can be manipulated, or waves can be observed as individual pulses. Compare the movement of dividers to graphs of displacement, velocity, acceleration and pressure. 5 Minute Preview
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Ripple Tank
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. 5 Minute Preview
SPI.3231.3.4: : Differentiate among the wave interactions of reflection, refraction, diffraction, or interference (constructive and destructive interferences).
SPI.3231.3.4: : Differentiate among the wave interactions of reflection, refraction, diffraction, or interference (constructive and destructive interferences).
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Ray Tracing (Lenses)
Observe light rays that pass through a convex or concave lens. Manipulate the position of an object and the focal length of the lens and measure the distance and size of the resulting image. 5 Minute Preview
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Ray Tracing (Mirrors)
Observe light rays that reflect from a convex or concave mirror. Manipulate the position of an object and the focal length of the mirror and measure the distance and size of the resulting image. 5 Minute Preview
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Refraction
Determine the angle of refraction for a light beam moving from one medium to another. The angle of incidence and each index of refraction can be varied. Using the tools provided, the angle of refraction can be measured, and the wavelength and frequency of the waves in each substance can be compared as well. 5 Minute Preview
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Ripple Tank
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. 5 Minute Preview
SPI.3231.3.6: : Demonstrate a proficiency in solving problems related to wavelength, frequency, period, and speed of mechanical waves.
SPI.3231.3.6: : Demonstrate a proficiency in solving problems related to wavelength, frequency, period, and speed of mechanical waves.

Ripple Tank
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. 5 Minute Preview
SPI.3231.4.3: : Solve problems related to Snell?s law.
SPI.3231.4.3: : Solve problems related to Snell?s law.
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Refraction
Determine the angle of refraction for a light beam moving from one medium to another. The angle of incidence and each index of refraction can be varied. Using the tools provided, the angle of refraction can be measured, and the wavelength and frequency of the waves in each substance can be compared as well. 5 Minute Preview
SPI.3231.4.4: : Given a drawing of a laboratory optics bench with a singular lens; choose the measurements that will enable the calculation of focal length.
SPI.3231.4.4: : Given a drawing of a laboratory optics bench with a singular lens; choose the measurements that will enable the calculation of focal length.
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Ray Tracing (Lenses)
Observe light rays that pass through a convex or concave lens. Manipulate the position of an object and the focal length of the lens and measure the distance and size of the resulting image. 5 Minute Preview
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Ray Tracing (Mirrors)
Observe light rays that reflect from a convex or concave mirror. Manipulate the position of an object and the focal length of the mirror and measure the distance and size of the resulting image. 5 Minute Preview
SPI.3231.4.5: : Identify the properties of light related to reflection, refraction, diffraction, and interference of light waves.
SPI.3231.4.5: : Identify the properties of light related to reflection, refraction, diffraction, and interference of light waves.
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Basic Prism
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. 5 Minute Preview
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Refraction
Determine the angle of refraction for a light beam moving from one medium to another. The angle of incidence and each index of refraction can be varied. Using the tools provided, the angle of refraction can be measured, and the wavelength and frequency of the waves in each substance can be compared as well. 5 Minute Preview
SPI.3231.4.6: : Using light ray diagrams, identify the path of light using a convex lens, a concave lens, a plane mirror, a concave mirror and a convex mirror.
SPI.3231.4.6: : Using light ray diagrams, identify the path of light using a convex lens, a concave lens, a plane mirror, a concave mirror and a convex mirror.
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Ray Tracing (Lenses)
Observe light rays that pass through a convex or concave lens. Manipulate the position of an object and the focal length of the lens and measure the distance and size of the resulting image. 5 Minute Preview
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Ray Tracing (Mirrors)
Observe light rays that reflect from a convex or concave mirror. Manipulate the position of an object and the focal length of the mirror and measure the distance and size of the resulting image. 5 Minute Preview
SPI.3231.5.3: : Explain the relationship between magnetism and current.
SPI.3231.5.3: : Explain the relationship between magnetism and current.
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Electromagnetic Induction
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. 5 Minute Preview
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Magnetic Induction
Measure the strength and direction of the magnetic field at different locations in a laboratory. Compare the strength of the induced magnetic field to Earth's magnetic field. The direction and magnitude of the inducting current can be adjusted. 5 Minute Preview
SPI.3231.5.4: : Identify the equilibrium point between two spheres of differing charges.
SPI.3231.5.4: : Identify the equilibrium point between two spheres of differing charges.
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Pith Ball Lab
Pith balls with positive, negative, or no electrical charge are suspended from strings. The charge and mass of the pith balls can be adjusted, along with the length of the string, which will cause the pith balls to change position. Distances can be measured as variables are adjusted, and the forces (Coulomb and gravitational) acting on the balls can be displayed. 5 Minute Preview
SPI.3231.5.5: : Find the equivalent resistance for a combination series and parallel circuit.
SPI.3231.5.5: : Find the equivalent resistance for a combination series and parallel circuit.
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Advanced Circuits
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. 5 Minute Preview
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Circuit Builder
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. 5 Minute Preview
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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. 5 Minute Preview
SPI.3231.5.6: : Solve electricity problems related to voltage, current, and resistance using Ohm?s law.
SPI.3231.5.6: : Solve electricity problems related to voltage, current, and resistance using Ohm?s law.
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Advanced Circuits
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. 5 Minute Preview
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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. 5 Minute Preview
SPI.3231.6.1: : Solve half-life problems.
SPI.3231.6.1: : Solve half-life problems.
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Half-life
Investigate the decay of a radioactive substance. The half-life and the number of radioactive atoms can be adjusted, and theoretical or random decay can be observed. Data can be interpreted visually using a dynamic graph, a bar chart, and a table. Determine the half-lives of two sample isotopes as well as samples with randomly generated half-lives. 5 Minute Preview
SPI.3231.6.2: : Identify parts of an atom (protons, electrons, neutrons, nucleus, and electron cloud).
SPI.3231.6.2: : Identify parts of an atom (protons, electrons, neutrons, nucleus, and electron cloud).
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Element Builder
Use protons, neutrons, and electrons to build elements. As the number of protons, neutrons, and electrons changes, information such as the name and symbol of the element, the Z, N, and A numbers, the electron dot diagram, and the group and period from the periodic table are shown. Each element is classified as a metal, metalloid, or nonmetal, and its state at room temperature is also given. 5 Minute Preview
SPI.3231.6.3: : Describe and identify the three basic forms of radioactivity (alpha particles, beta particles, and gamma rays).
SPI.3231.6.3: : Describe and identify the three basic forms of radioactivity (alpha particles, beta particles, and gamma rays).
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Nuclear Decay
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. 5 Minute Preview
SPI.3231.6.4: : Identify nuclear reactions given descriptions of the reactions.
SPI.3231.6.4: : Identify nuclear reactions given descriptions of the reactions.
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Nuclear Decay
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. 5 Minute Preview
Correlation last revised: 9/16/2020
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.
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Introduction to the Heatmap
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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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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