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Interactive
CK-12 Foundation

Newton's Method

For Students 11th - Higher Ed
Does the accuracy of the first guess make a difference down the line? Learners investigate the effects of the iterative process of finding roots, using Newton's Method. By moving the initial guess of a root on a graph, pupils observe the...
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Interactive
CK-12 Foundation

Absolute Extrema and Optimization: Building the Biggest Box

For Students 11th - Higher Ed
Optimally, you want the largest box. Given a square piece of box material, pupils determine the size of congruent squares to cut out of the corners to create a box with the greatest volume. Learners determine the equation of the volume...
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Interactive
CK-12 Foundation

Derivatives of Trigonometric Functions: Derivative of sin(x)

For Students 11th - Higher Ed
Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...
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Interactive
CK-12 Foundation

Tangent Line Approximation: Estimating Square Roots

For Students 11th - Higher Ed
Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...
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Interactive
CK-12 Foundation

Newton's Method

For Students 11th - Higher Ed
Use an iterative process to find an approximation of a square root. Pupils use the interactive to find an approximation to find the positive root of a quadratic function with Newton's method. With the graphs, learners position the...
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Interactive
CK-12 Foundation

Slope of a Tangent Line: Slope of the Tangent and Secant Lines

For Students 11th - Higher Ed
Learn to find the slope through a single point. The interactive provides a visualization of how to find the slope of a tangent line. With the aid of the visualization, pupils see the definition of the derivative in action. Class members...
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Interactive
CK-12 Foundation

Average and Instantaneous Rates of Change

For Students 11th - Higher Ed
How can you determine the rate of change on a curve? Pupils use the interactive to discover what happens with the average rate of change as the point move closer to the other. Using the definition of the derivative, learners find that it...
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Interactive
CK-12 Foundation

Intermediate Value Theorem, Existence of Solutions: Function Exploration

For Students 11th - Higher Ed
Does the value exist? The interactive allows pupils to visualize the Intermediate Value Theorem. Using the visualization, individuals respond to questions using specific values and general values. The class comes to the conclusion what...
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Interactive
CK-12 Foundation

Blood Types

For Students 6th - 12th Standards
Does your blood type matter? The video explains the four main blood types and the importance of knowing blood types when performing transfusions. The interactive reviews the information with a quick graphic organizer and questions.
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Interactive
CK-12 Foundation

Natural Selection: Of Seasons and Species

For Students 6th - 12th Standards
Do predators look for different things in different seasons? The quick interactive shows how some species survive longer in one season than another based on the conditions. The challenge questions encourage pupils to demonstrate that...
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Interactive
CK-12 Foundation

Natural Selection: Natural Disasters

For Students 6th - 12th Standards
Can natural disasters alter natural selection? The interactive explores this concept with mice living through a forest fire. As the environment changes, the camouflage also changes. How does this one disaster impact future generations?
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Interactive
CK-12 Foundation

Passive Transport

For Students 6th - 12th Standards
Some molecules move through a membrane with diffusion while others require protein channels. The video and interactive discuss both types of passive transport. Challenge questions allow scholars to demonstrate their understanding.
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Interactive
CK-12 Foundation

Cellular Respiration: Can Photosynthesis Be Reversed?

For Students 6th - 12th Standards
Cellular respiration and photosynthesis relate closely, but many don't realize how. Scholars drag and drop the reactants and products to the chemical reactions for both processes. Then they answer three multiple-choice questions.
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Interactive
CK-12 Foundation

Electric Analogies

For Students 9th - 12th Standards
We can see the result of electricity  but not the process itself. The simulation compares electric circuits to a water tower and water wheel cycle. Young scientists adjust the height of the tower, the amount of resistance, and if...
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Interactive
CK-12 Foundation

Relative Velocity Simulation

For Students 6th - 12th Standards
If your pupils think relative velocity is the velocity at which you can run away from your relatives, they need this simulation. Two bikers want to meet at a specific time. Scholars alter the velocity of one rider to arrange the...
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Interactive
CK-12 Foundation

Radiocarbon Dating

For Students 9th - 12th Standards
How do we know how long ago a dinosaur lived or an ancient fire pit was used? Scholars learn about the application of carbon dating and half lives to discover things about the past. They adjust the amount of radioactive carbon in the...
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Interactive
CK-12 Foundation

Subatomic Particle Zoo

For Students 9th - 12th Standards
Everything is made up of atoms, but what are atoms made up of? The simulation explores subatomic particles. It focuses on hadron, boson, and lepton groupings as scholars learn about quarks, neutrinos, gluons, and more.
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Interactive
CK-12 Foundation

Doorbell

For Students 9th - 12th Standards
What are some simple uses for an electromagnet? Scholars explore the electromagnetic circuitry in a doorbell through an interesting simulation. They control the core material, number of loops, amount of current, and strength in a spring....
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Interactive
CK-12 Foundation

Vertical Translations: Vertical Shift of Sinusoidal Functions

For Students 10th - 12th Standards
Create a shift in TV viewing habits. The interactive presents a cosine model of an individual's TV viewing habits during a year. Class members move the model to reflect given conditions. Finally, they determine key features from the...
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Interactive
CK-12 Foundation

Unit Circle: Medieval Castle Defense

For Students 10th - 12th Standards
Who needs a plan — let trigonometry protect you! Pupils determine the angle of an approaching enemy to a village wall. The scholars determine the exact value of trigonometric functions for the angle. Class members use trigonometry to...
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Interactive
CK-12 Foundation

Vertical Translations

For Students 10th - 12th Standards
Change the y-intercept by adding a constant to the function. Individuals move three functions vertically along the y-axis. As they observe how the equation of the functions change with the vertical movement, learners determine how...
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Interactive
CK-12 Foundation

Exponential Decay: Cool Sunglasses

For Students 10th - 12th Standards
Who wouldn't want to wear four pairs of sunglasses? Each pair of sunglasses reduces the percent of incoming light by one-half. An interactive tutorial helps young mathematicians build a graph that models this scenario. They...
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Interactive
CK-12 Foundation

Geometric Sequences and Exponential Functions: Bouncing Ball

For Students 9th - 12th Standards
Explore a geometric sequence model through a simulation. Learners change the starting drop height of a ball and watch how the heights of following bounces change. They consider the ratio of the consecutive bounces as they analyze...
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Interactive
CK-12 Foundation

Logarithms: Logarithm Triangle

For Students 10th - 12th Standards
Study logarithmic properties using a triangle. A clever manipulative shows how a triangle can represent the three parts of a logarithmic or exponential equation. Pupils review the concept and then answer guiding questions to further...