Interactive
CK-12 Foundation

Comparing Methods for Solving Quadratics: Comparing Methods to Solve a Quadratic

For Students 9th - 12th Standards
Determine the quickest process for solving quadratics. Pupils compare the number of steps in the process of solving quadratics using three different methods. Scholars determine which situations lend themselves to the different solving...
Interactive
CK-12 Foundation

Translating Sine and Cosine Functions: Translating Sine

For Students 10th - 12th Standards
Learn how to slide sine back and forth and up and down. Pupils move the starting point of a graph of sine vertically and horizontally. They investigate the changes to the equation of the graph in relationship to the translation. They...
Interactive
CK-12 Foundation

Sine Graph and Cosine Graph: Changing Amplitude

For Students 10th - 12th Standards
Scholars manipulate the amplitude of the graphs of sine and cosine, notice how the change in amplitude is reflected in their graphs, and answer several questions about the concept they noticed.
Interactive
CK-12 Foundation

Whole Number Subtraction: Penguins Go for a Swim

For Students 6th
As penguins jump off of an iceberg, young mathematicians count the remaining penguins in order to discover the whole number subtraction answer. As they work through the questions, they can manipulate the red dot to add and subtract more...
Interactive
CK-12 Foundation

Equivalent Fractions: Number Line

For Students 3rd Standards
Arrange improper fractions on a number line to determine the equivalency to whole numbers. The number line starts at -4 and ends at 4, while users must turn the improper fraction into a proper fraction in order to place it on the number...
Interactive
CK-12 Foundation

Special Triangle Ratios: Special Right Triangle Ratios

For Students 9th - 12th Standards
Go from one side length to any other side length with special right triangles. Individuals use the interactive to investigate the ratio of sides in 45-45 and 30-60 right triangles. Scholars make generalizations about the types of special...
Interactive
CK-12 Foundation

Six Trigonometric Functions and Radians: Degrees to Radians and Back Again!

For Students 10th - 12th Standards
How do degrees relate to radians? The interactive allows pupils to manipulate the size of an angle in a unit circle to help see that relationship. Users determine the radian measure for given degree measures of angles, realizing the...
Interactive
CK-12 Foundation

Conversion between Degrees and Radians: Arc and Radians Relationship

For Students 10th - 12th Standards
How are arc lengths and radians related? An interactive resource demonstrates the relationship as pupils create arc lengths in a unit circle and compare them to the angle measurements. Questions ask individuals to build upon this...
Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Horizontal Translations

For Students 10th - 12th Standards
Find out what causes a function to slide. Pupils move a function along the x-axis and see the resulting change in its equation. Scholars determine the effects that the translation has on the intercepts, domain, and range of the function.
Interactive
CK-12 Foundation

Evaluation of Perfect Square Roots: Neighborhood Park

For Students 7th - 9th Standards
Walking in the park can be good for the body and for mathematics skills. Young scholars use an interactive app to investigate the relationship between squares and square roots using a square with adjustable length. The program also...
Interactive
CK-12 Foundation

Joint and Combined Variation: Variable Sliders

For Students 8th - 10th
Learners use a pair of sliders to investigate how changes in a variable affects other variables in joint variation. A set of five challenge questions tests understanding.
Interactive
CK-12 Foundation

Solving Equations Using the Pythagorean Theorem: Cryptography

For Students 8th - 10th Standards
Don't keep this resource a secret. Individuals learn to use the Pythagorean Theorem to find Pythagorean triples. They also see how Pythagorean triples can be useful in the field of cryptography to encrypt secret messages.
Interactive
CK-12 Foundation

Pythagorean Theorem and Its Converse

For Students 8th - 10th
To be a right triangle, or not to be — that is the question. Scholars drag line segments in an Internet application to see if they form right triangles. Once they get the results of the activity, they connect them to the converse of the...
Interactive
CK-12 Foundation

Completing the Square

For Students 8th - 10th Standards
An interactive aids in understanding of how to complete the square for a quadratic equation. A set of five challenge questions tests this understanding.
Interactive
CK-12 Foundation

Inverses by Mapping: Inverse Functions

For Students 10th - 12th Standards
Map your way to successfully understanding inverse functions. Pupils use an interactive map to investigate how changes in the graph of a function affect the graph of its inverse. The results of the activity lead to the conclusion that...
Interactive
CK-12 Foundation

Ambiguous Case: Furniture Store Problems

For Students 10th - 12th
Remove any ambiguity about using a helpful resource. Individuals use an interactive to find the number of triangles that fit given conditions. They find that some conditions can result in more than one triangle in the ambiguous case.
Interactive
CK-12 Foundation

Determination of Unknown Triangle Measures Given Area: Jib Sheets

For Students 10th - 12th Standards
Solving triangles is a breeze. Young boat enthusiasts solve problems involving triangles in the context of sails on a boat. They must apply different strategies, including the Law of Cosines and area formulas.
Interactive
CK-12 Foundation

Multiplying Polynomials

For Students 9th - 11th Standards
Help your class find patterns in polynomial multiplication. Pupils multiply a trinomial by a binomial using a graphic organizer. They respond to questions about patterns observed in polynomial multiplication before a discussion question...
Interactive
CK-12 Foundation

Monomial Factors of Polynomials: Mystery Boxes

For Students 8th - 10th Standards
Shortcut the work in finding total volumes. Pupils determine a polynomial expression that would represent the combined volume of three boxes. Each box has the same height, and the scholars rewrite the expression by factoring out the...
Interactive
CK-12 Foundation

Addition and Subtraction of Polynomials: Sliders

For Students 8th - 10th Standards
Slide the coefficients to determine sums of polynomials. The interactive contains sliders to change the coefficients of an addend in a polynomial addition problem. Pupils determine the coefficients of the addend to arrive at particular...
Interactive
CK-12 Foundation

Multiplication of Polynomials by Binomials: Rainbows

For Students 8th - 10th Standards
Is it possible to use the distributive property with several terms? Learners multiply a polynomial by a binomial using the same method as with a monomial. The scholars distribute each term of the binomial to each term in the polynomial...
Interactive
CK-12 Foundation

Linear Programming: Bakers' Dilemma

For Students 9th - 12th Standards
Place the pies in a line. Pupils create a graph of a system of linear inequalities to represent the number of pies a bakery can make. Learners analyze the vertices on the graph to determine the number of pies they can bake without...
Interactive
CK-12 Foundation

Linear Systems with Addition and Subtraction: XYZ Tiles

For Students 8th - 10th Standards
Cover it up to reveal the values of variables. Using arrangements of colored tiles representing algebraic expressions, pupils layer them over each other to determine the values of variables. The procedure models the elimination method in...
Interactive
CK-12 Foundation

Trigonometric Form of Complex Numbers

For Students 11th - Higher Ed Standards
Represent complex numbers in two ways. Pupils use the interactive to convert polar and rectangular representations of complex numbers. The learners drag an overlay back and forth over the coordinate plane to reveal the polar coordinates...