Interactive
CK-12 Foundation

Displaying Categorical Variables: Spending Habits

For Students 6th - 10th Standards
Bar or circle graph—which is best? Given a circle graph and a total amount of money earned, pupils calculate the amount of money in each category. Learners use the calculated amounts to create a bar graph and compare the two displays.
Interactive
CK-12 Foundation

Displaying Univariate Data: Ordering Leaves

For Students 9th - 12th Standards
Leaf a little time to organize data. Given data displayed in a stem-and-leaf plot, learners organize the data in a list. Pupils use the data to determine the mode, median, and range of the data set. They determine the benefits of using a...
Interactive
CK-12 Foundation

Line Graphs to Display Data Over Time: Strawberry Competition

For Students 6th - 8th Standards
Take the tediousness out of graphing. Using the interactive tool, learners can efficiently create a line graph from a set of data. They then use the graph to answer questions about specific trends in the data.
Interactive
CK-12 Foundation

One-Sided Limit Type: One-Sided Limits

For Students 11th - Higher Ed
Not everything that's one-sided is bad. A slider interactive aids learners in investigating one-sided limits from graphs. A set of challenge questions assesses their understanding of the relationship between one- and two-sided limits.
Interactive
CK-12 Foundation

Least-Squares Regression

For Students 9th - 12th
Residual plots let you find the perfect line of best fit. As users adjust the points on a scatter plot and a possible line of best fit, the interactive automatically changes the residual plot. This change allows them to see connections...
Interactive
CK-12 Foundation

Chain Rule

For Students 11th - Higher Ed
Keep it on the chains. Pupils work through the steps in the chain rule using the interactive as a guide. Learners identify the two composed functions and their associated derivatives from a set of choices. They continue on to build the...
Interactive
CK-12 Foundation

Derivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima

For Students 11th - Higher Ed
Rolle with the mean values and derivatives. Scholars complete the statements of Rolle's Theorem and the Mean Value Theorem. Using the interactive to illustrate scenarios, pupils respond to questions concerning the theorems in terms of...
Interactive
CK-12 Foundation

Sequence: The Sequence Calculator

For Students 11th - Higher Ed Standards
Work through a sequence in discovering number patterns. Using the interactive, pupils explore arithmetic and geometric sequences by setting the initial value and the common difference or ratio. Learners distinguish between the two types...
Interactive
CK-12 Foundation

Proportions and Scale: Problem Solving Plan, Proportions

For Students 6th - 8th Standards
Slide into a lesson on proportions. A slider interactive lets users adjust three of the four values in a proportion and automatically updates the fourth value. Scholars use the interactive to help answer a set of challenge questions on...
Interactive
CK-12 Foundation

Estimation to Check Decimal Multiplication: Watering a Garden

For Students 6th Standards
Mathematicians solve six multiple-choice and true or false questions using their knowledge of estimation and multiplying decimals. The interactive provides a garden-themed tool that creates a visual aid of three watering cans to assist...
Interactive
CK-12 Foundation

Discriminant

For Students 9th - 12th Standards
Discriminate between the types of roots. The interactive root introduces the discriminant and its connection to the types and number of roots. Pupils use a slider to view graphically the effect of the sign of the discriminant on a...
Interactive
CK-12 Foundation

Right Triangles, Bearings, and Other Applications: Sailing Race

For Students 9th - 12th Standards
Help your class get their bearings when it comes to right triangles. Pupils determine distances traveled or components given the bearing of a sailboat using an interactive. The scholars develop a sense of finding the bearings of a given...
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

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

Reciprocal Identities

For Students 10th - 12th Standards
Get a better understanding of the trigonometric functions by taking a look at the flip side. Pupils create angles within a unit circle and compare the values of the standard trigonometric functions to their reciprocal functions. The...
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

Vertical Translations: Translating a Square Root Function

For Students 10th - 12th Standards
How does the equation of a function reflect translations? Scholars manipulate the starting point of the parent square root function before determining the new equations that result from the translations. Class members also determine the...
Interactive
CK-12 Foundation

Double Angle Identities: Ferris Wheel

For Students 10th - 12th
Use a Ferris wheel to soar to new heights of understanding on double angle identities. Here is an interactive that applies an example of a Ferris wheel to show how doubling the angle does not double the value of a trigonometric ratio....
Interactive
CK-12 Foundation

Unit Vectors and Components: Bow and Arrow

For Students 9th - Higher Ed Standards
Aim for a better understanding of vector components. Scholars adjust the angle of release on a bow and determine the horizontal and vertical components of the velocity vector. The pupils finish by determining how the angle affects...
Interactive
CK-12 Foundation

Counting Events: Flipping Unfair Coins

For Students 7th - 12th Standards
Who said life was fair? An interactive uses an area diagram to represent the probabilities of flipping unfair coins. Pupils use the diagram to calculate the probabilities of outcomes of flipping the two coins. The scholars must decide...
Interactive
CK-12 Foundation

Binomial Distributions and Probability: Roll One!

For Students 9th - 12th
It takes exactly one to win. Pupils calculate the probability of rolling five dice and having only a single die come up with a one. Learners calculate the number of expected wins out of a series of games. The interactive provides...
Interactive
CK-12 Foundation

Expected Value: Creating a Discrete Probability Distribution Table

For Students 11th - 12th Standards
Wanna roll the dice? Determine whether it is a good idea to play a dice game. An interactive presents the rules for a game of dice. Pupils find the probabilities of each event and calculate the expected value of the game. They finish...
Interactive
CK-12 Foundation

Numerical Computations: Counting Out Probability

For Students 6th - 8th Standards
Keep your heads up while counting. Pupils use an interactive to create a table with the possible outcomes of flipping three coins and then determine the probabilities of getting certain combinations of heads and tails.
Interactive
CK-12 Foundation

Additive and Multiplicative Rules for Probability: Red Dress? Blue Dress? Both!

For Students 7th - 12th Standards
The sum of the parts is greater than the whole. An interactive uses a Venn-like model to show the percentage of females from a survey that have a blue dress, a red dress, or both. The pupils determine the numbers in each category...