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Interactive
CK-12 Foundation

DeMoivre's Theorem and nth Roots: The nth Roots of Unity

For Students 11th - Higher Ed
The nth roots of unity all have a magnitude of one. Scholars use the unit circle and DeMoivre's Theorem to find the complex roots of one and discover that the complex numbers all lie on the unit circle and are equally spaced around it...
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Interactive
CK-12 Foundation

Plots of Polar Coordinates: Submarine Sonar

For Students 11th - Higher Ed Standards
Find the location of enemy submarines with a sonar display that doubles as a polar coordinate system. Pupils find polar coordinates that would be the same location of plotted submarines. They then determine multiple polar coordinates...
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Interactive
CK-12 Foundation

Translation of Vectors and Slope: Rearranging a Classroom

For Students 11th - Higher Ed Standards
Find out if vectors are equal in the classroom. Pupils use the interactive to create vectors showing the movements boys perform in rearranging classroom furniture. The scholars determine which boy moved furniture the farthest, or if they...
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Interactive
CK-12 Foundation

Translation of Vectors and Slope: Identical Vectors

For Students 11th - Higher Ed Standards
Translate vectors to find equivalent ones. An interactive shows 10 randomly displayed vectors. Pupils grab the vectors and move them to group them with similar vectors in magnitude and direction. Scholars find the groups of vectors that...
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Interactive
CK-12 Foundation

Permutations with Repetition: Permutations and Repetition

For Students 9th - 12th Standards
What's in a name? An interactive asks users to find the number of ways to arrange the letters in the word DAD and MOM. Pupils use the interactive to arrange the letters but restrict the permutations to be unique for MOM and answer...
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Interactive
CK-12 Foundation

Combinations: Making the Team

For Students 9th - 12th Standards
Determine how many three-player teams you can make from five players. Pupils drag dots representing players to create a list of teams they can form with a limited number of players. They then find out the number of teams one individual...
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Interactive
CK-12 Foundation

Combination Problems: Friends at a Party

For Students 9th - 12th Standards
Friend or stranger? Can there be less than three in a group? The interactive asks learners to prove that for seven people at a party, at least three of them are either mutual friends or mutual strangers. Pupils determine the number of...
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Interactive
CK-12 Foundation

Pascal's Triangle: Pyramid Blocks

For Students 9th - 12th Standards
Build a pyramid of sums. An interactive presents the first five rows of Pascal's Triangle as a pyramid. Pupils match missing entries in the pyramid and continue the pattern to determine entries of other rows. The learners use the entries...
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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...
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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.
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Interactive
CK-12 Foundation

Mutually Exclusive Events: Lemon Roulette!

For Students 7th - 12th Standards
You first! An interactive sets up a game between two friends who hope they don't find a lemon hidden under a tray. Pupils determine whether there is an advantage of going first. Individuals find the probabilities of each friend finding...
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Interactive
CK-12 Foundation

Mutually Inclusive Events: Flower Beds at the Community Garden

For Students 9th - 12th Standards
What color does your garden grow? Learners manipulate the number of flowers of two colors in two garden plots. They determine the probabilities of choosing a particular color of a flower in a given plot. Scholars find the relationship of...
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Interactive
CK-12 Foundation

Mutually Inclusive Events: Card Game

For Students 9th - 12th Standards
Find probabilities of pulling cards. Using a Venn diagram, individuals sort five cards along the rules of a game. The pupils calculate compound probabilities using the information from the diagram. Initially, the interactive provides the...
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Interactive
CK-12 Foundation

Geometric Probability: Dartboard

For Students 6th - 12th Standards
Get your class on target with probability using an exciting resource. The interactive presents three square dartboards with different target areas, which are combinations of square units. Pupils determine the probabilities of randomly...
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Interactive
CK-12 Foundation

Conditional Probability: Candy Store

For Students 9th - 12th Standards
An interactive uses a candy store to involve the pupils in conditional probabilities. Learners determine probabilities as customers purchase different types of candies and the stock decreases.
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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...
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Interactive
CK-12 Foundation

Dependent Events: Cheryl's Birthday

For Students 9th - 12th Standards
Use dependency to find a birthday. Learners use an interactive to keep track of excluded potential dates of a birthday using information provided to two people about a third's birthday. Scholars then use the dependency between the dates...
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Interactive
CK-12 Foundation

Discrete Random Variables: Roll the Dice!

For Students 9th - 12th Standards
And the winner is ... not always who it appears to be. An interactive gives the directions for a dice game that on the surface gives one player an advantage over the other. Pupils look closer at the possible outcomes and find the...
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Interactive
CK-12 Foundation

Sums and Differences of Independent Random Variables: Traveling Seasickness

For Students 9th - 12th Standards
Use a Punnett square to calculate probabilities. The resource presents a situation in which two patients are randomly selected from a group of patients with a particular illness. Pupils use the interactive to determine the likelihood...
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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...
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Interactive
CK-12 Foundation

Normal Approximation of the Binomials Distribution: When to Approximate

For Students 9th - 12th
Normalizing a binomial distribution — determine when it is all right. Given the rule of thumb of when it is appropriate to use the normal distribution to approximate a binomial distribution, pupils look at different scenarios. Scholars...
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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...
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Interactive
CK-12 Foundation

Expected Value: Game of Chance

For Students 11th - 12th Standards
Determine whether the payoff is worth it. Pupils calculate the expected value of a game with three different payoff levels. Each level has a different probability of winning money. The scholars find the expected payoffs for each level...
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Interactive
CK-12 Foundation

Expected Value: Win a Dollar

For Students 11th - 12th Standards
Spin a wheel, land on a color ... and win. Learners create a graph to display the probabilities of the amount of money they can win by spinning a colored wheel. The pupils use the dollar amounts and their probabilities to calculate the...

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