CK-12 Foundation
Slope of a Tangent Line: Slope of the Tangent and Secant Lines
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...
CK-12 Foundation
Average and Instantaneous Rates of Change
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...
CK-12 Foundation
Inverse Functions
Provide a graphical view of inverses. Pupils manipulate points on a line and see the relationship of the graph with the graph of its inverse. Using the relationship between the graphs, scholars respond to questions concerning inverses...
CK-12 Foundation
Vector Sum and Difference: The Country of Dreams
Find your way around using vectors. Scholars use an interactive to learn about vector addition. They answer a set of questions about modeling a route on a map using vectors.
CK-12 Foundation
Vector Projection
Two words summarize the interactive: vector projector. An easy-to-use resource lets users investigate vector projections on the coordinate plane. Given the components of two vectors, they determine the projection of one vector onto the...
CK-12 Foundation
Arithmetic Series Sums: Adding Arithmetic Sums
Sum up the shortcuts. The interactive allows pupils to discover a shortcut in finding a partial sum of an arithmetic series. Learners use the shortcut to find other sums and to verify the process.
CK-12 Foundation
Sequence of Partial Sums: Partial Sums
Have some fun building squares out of triangles. Pupils investigate the partial sums of odd numbers. Using the sum of the first four odd numbers, learners see that it can be rewritten as a sum containing a triangular number. Simplifying...
CK-12 Foundation
Ellipses Centered at the Origin: Lithotripsy
Investigate ellipses through the lens of medical applications. Pupils use a medical scenario to determine the equation of an ellipse. By using the interactive, learners determine the foci and major and minor axes of the ellipse that...
CK-12 Foundation
Parabolas: Invisible Graph
Envision the function as the point swings. Given a point connected to another point and a line, pupils trace through an invisible graph. Learners identify the name of the given point and the line and determine the type of conic section...
CK-12 Foundation
Hyperbolas
Hyperbolas—practice thinking outside of the box. Pupils alter the end behavior box to create various graphs of hyperbolas. They determine formulas to find the distance from the origin to the foci. Using that information, scholars...
CK-12 Foundation
Equations of Circles: The Sea of Happiness
Map this! Help your young mathematicians draw a circular island on a map. Given specifics of the location and size of an island on a map, pupils transform a circle to meet the given requirements. They then determine the location of the...
CK-12 Foundation
Two-Dimensional Vectors: River Ferry and Current Vectors
Fight against the current. Pupils explore the resulting path when they are crossing a river while being pushed downstream by the current. Using vector notation, learners express the speed and direction of a ferry. They finish by...
CK-12 Foundation
Definition of Inverse Functions
Investigate the definition of inverse functions graphically. Using the interactive, scholars create a graph of a function and view its resulting inverse. They then determine whether a group of functions have inverses that are also...
CK-12 Foundation
Existence: One-to-One Functions and Inverses
One-to-one means the answer is simple, right? Given four graphs, pupils use a vertical line to test each graph to find out if they are one-to-one. By using the resource, learners realize that not all one-to-one relations are functions....
CK-12 Foundation
Solving Logarithmic Equations
Pupils follow a chain of reasoning in deconstructing a logarithmic equation step by step. Using their knowledge of logarithms, learners compare the solutions of logarithmic equations when the bases are changed.
CK-12 Foundation
Recursive Formulas: Fibonacci Sequence
Explore the building blocks of the Fibonacci Sequence. Given the lengths of sides of squares, pupils deduce the pattern to determine the lengths of two more squares. Learners continue to work with recursive formulas to generate numerical...
CK-12 Foundation
Equations of Circles: Finding the Equation of a Circle
It's all about location and size. With the aid of the interactive, pupils explore the relationship between the location and size of a circle and its equation. The learners use that relationship to determine the equation of a circle given...
Shodor Education Foundation
Linear Function Machine
What goes in must come out! Learners play with a function machine to determine the correct function. They enter input values and watch as the machine produces the output.
CK-12 Foundation
Prime and Composite Numbers
Nine true or false, multiple-choice, and discussion questions make up an interactive designed to reinforce scholars' knowledge of prime and composite numbers. A number chart reveals every prime number through 100.
CK-12 Foundation
Values Written as Powers: Binary Numbers 25 to 31
A five-question interactive boosts proficiency in working with binary numbers. Multiple-choice, short answer, and discussion questions challenge mathematicians to write numbers 25 through 31in exponential and binary form. An adjustable...
CK-12 Foundation
Prime Factorization: Chocolate Chip Factoring
An interactive resource challenges mathematicians to show what they know about prime factorization. Five multiple-choice, true or false, and discussion questions use chocolate chip cookies to set a real-world application of the...
CK-12 Foundation
Addition of Integers: Number Blocks
A five-question interactive provides a horizontal number line where integers are stacked on top of one another to find solutions of addition problems. Mathematicians move numbers to the numbers line, as numbers build higher, the sum of...
CK-12 Foundation
Integer Division: Dropping Anchor
An interactive made up of five questions challenges mathematicians to divide integers and reflect on division properties. A moveable anchor aids in problem-solving. Question types include multiple-choice, true or false, and...
CK-12 Foundation
Percents as Decimals
In some cases, decimals are just easier to work with. An easy-to-use interactive shows how to convert percents to decimals. It then challenges learners to answer a set of questions, some of which include percents that are greater than...