Interactive
CK-12 Foundation

Radical Equations: Geometric Visual of a Square Root

For Students 8th - 11th Standards
How can you draw a number? A set of questions takes learners through the reasoning for why a geometric construction can be drawn to represent the square root of a number. An interactive helps visualize the construction.
Interactive
CK-12 Foundation

Sum and Difference of Cubes: Stacking Blocks

For Students 9th - 11th Standards
Investigate polynomial factoring patterns by finding a connection to volume. As learners build a three-dimensional solid from smaller solids, they convert the visual model to a mathematical expression. Their models represent the sum of...
Interactive
CK-12 Foundation

Scientific Notation Values

For Students 6th - 8th Standards
Scientific notation is the focus of a five-question interactive. A model with movable points offers a visual reference to help solve true or false, multiple-choice, and fill in the blank questions. A discussion question challenges...
Interactive
CK-12 Foundation

Visual Patterns: Building the Queen's Tower

For Students 6th - 8th
A resource fit for a queen. Scholars recognize and continue a pattern in towers people are building for a queen. They write and use an algebraic expression for the number of tiles in the towers.
Interactive
CK-12 Foundation

Visual Patterns: Balloons

For Students 6th - 8th
Balloons aren't just for little kids; they can teach important math concepts, too. Individuals use an interactive to continue a color pattern with balloons. They continue the pattern and write a mathematical expression to represent the...
Interactive
CK-12 Foundation

Basic Visual Patterns: Train Cars

For Students K - 2nd
An interactive comprised of five questions challenges young scholars to complete a simple pattern. After examining a train with colored carts, learners arrange a green, blue, and yellow block into their corresponding space. Questions are...
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...
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...
Interactive
CK-12 Foundation

Properties of Definite Integrals

For Students 11th - Higher Ed
Close your eyes and visualize a definite integral. An interactive provides a visualization of a function and definite integral on a closed interval. Pupils move one point of the interval in either the positive or negative direction....
Interactive
CK-12 Foundation

Matrix Multiplication: Vectors

For Students 10th - 12th Standards
Visualize matrix multiplication on the coordinate plane. Pupils use the interactive to create a matrix multiplication problem using vectors. The scholars see the resulting product of the matrices as a vector.
Interactive
CK-12 Foundation

Completing the Square

For Students 9th - 12th Standards
Determine the area of a square with quadratics. Pupils use the interactive to visualize the process of completing the square. Scholars build a square area model to represent a quadratic expression then determine the amount that...
Interactive
CK-12 Foundation

Trigonometric Functions and Angles of Rotation: The Triangle in the Circle

For Students 10th - 12th Standards
Go around the unit circle and create triangles. Pupils move a point around the unit circles to visualize the triangle associated with the angle in standard position. The three main trigonometric functions are defined in terms of the legs...
Interactive
CK-12 Foundation

Reference Angles and Angles in the Unit Circle: Exploring Reference Angles

For Students 10th - 12th Standards
A steal of a deal — get four angles for the value of one. An interactive resource allows individuals to visualize all four angles that have the same reference angle. Pupils answer questions by using the interactive to create the...
Interactive
CK-12 Foundation

Irwin 2D

For Students 6th - 12th
Learners explore two-dimensional motion through visual modeling with an interactive lesson that allows them to control the path of a robot. Graphs show both the horizontal and vertical motion as the robot continues through its...
Interactive
CK-12 Foundation

Portrait Gallery

For Students 9th - 12th
An interactive lesson explores the effect of force angles on resulting forces. Learners adjust angles of strings supporting hanging portraits and watch the effects on the resultant force. Vector diagrams provide a visual representation...
Interactive
CK-12 Foundation

Galvanometer

For Students 9th - 12th Standards
In 1820, Hans Christian Orstead discovered the link between electricity and magnetism, which allows us to measure current and voltage. The simulation allows scholars to observe the inner workings of an ammeter and voltmeter as they...
Interactive
CK-12 Foundation

Pythagorean Theorem to Determine Distance: Distance Between Friends

For Students 8th - 12th Standards
Pupils use an interactive to help visualize the right triangles needed to calculate distances between friends' houses. Individuals solve five problems on how to determine distances and comparing the distances.
Interactive
CK-12 Foundation

Trigonometric Functions of Negative Angles

For Students 10th - 12th Standards
When is the trigonometric value of a negative angle the same as the positive angle? Pupils compare the values of trigonometric functions for different angles and their negatives. The interactive resource provides a visual display to make...
Interactive
CK-12 Foundation

Mixed Numbers as Improper Fractions: Pineapple Slices

For Students 6th Standards
Practice adding and subtracting improper fractions with pineapple slices. Young mathematicians move whole pineapple slices to visualize the addition of the 2/5s that is on Sally's plate. Pupils also use a combination of mixed numbers and...
Interactive
CK-12 Foundation

Addition and Subtraction of Polynomials: Adding Polynomials

For Students 8th - 10th Standards
Stack the like terms to add vertically. The resource contains a visual aid to help with the addition of polynomials using the vertical method. Pupils use the aid to calculate the sum of two polynomials.
Interactive
CK-12 Foundation

Vector Subtraction

For Students 11th - Higher Ed Standards
Move vectors to determine their difference. Pupils use an interactive to visualize the opposite of a vector. They use the concept of adding vectors to subtract vectors by adding the opposite and, finally, view the differences of the...
Interactive
CK-12 Foundation

Complement Rule for Probability: Changes in an Election

For Students 7th - 12th Standards
Pupils determine the probability of one mayoral candidate winning given the other's chance. The interactive provides a circle graph to help visualize each candidate's percentages of winning.
Interactive
CK-12 Foundation

Conditional Probability: Game Show with Monty

For Students 9th - 12th Standards
The car is behind door one — no wait, it is behind door three. An interactive allows learners to visualize the Monty Hall problem. Pupils work through the probabilities of choosing the car with their first pick. Next, they determine...
Interactive
CK-12 Foundation

Conditional Probability: Colorful Cubes

For Students 9th - 12th Standards
An interactive provides a model to visually represent the formula for the probability of an outcome. Given 10 numbered color cubes, pupils arrange them on the top and bottom shelf to represent the probability fraction. The learners...

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