Assignment 1
Applet Collections
| Title | Description |
|---|---|
| PHET Interactive Simulations | PhET is a collection of free, interactive, research-based mathematics and science simulations. The mathematics and statistics section includes simulations for topics such as number sense, ratios, sampling distributions, variability, curve fitting, and other mathematical concepts. The simulations are designed to let students manipulate variables and explore mathematical relationships through immediate visual feedback, making them useful for developing conceptual understanding through experimentation. |
| Stats Kingdom Basic Statistics Applets | Stats Kingdom provides a collection of online statistics calculators and tools covering descriptive statistics, measures of center and variability, percentiles, outliers, probability, combinatorics, odds, and Markov chains. Many of the tools provide step-by-step calculations, allowing students to compare their own work with a computational approach. This resource can be useful for helping students explore statistical calculations while also connecting numerical results to concepts such as variation, distribution, and probability. |
| Rossman/Chance Applets | The Rossman/Chance Applet Collection contains interactive tools covering a wide range of statistics topics. The collection includes descriptive statistics, correlation, regression, sampling distributions, confidence intervals, ANOVA, randomization tests, probability, and statistical inference. Many of the applets allow students to simulate repeated samples or experiments, making them particularly useful for understanding sampling variability and the reasoning behind statistical inference. |
| Statsmedic Applets | Stats Medic provides easy-to-use interactive applets designed to help teachers bring statistics concepts to life. The collection includes tools for creating graphs, exploring statistical concepts, and performing formal statistical inference. The applets are intended to supplement statistics instruction and provide alternatives to relying solely on traditional calculators. |
| Geogebra Probability Applets | This GeoGebra collection contains interactive probability activities, including coin-flipping simulations, repeated trials, Pascal's Triangle, binomial random variables, binomial distributions, dice experiments, expected value, normal curves, and probability games. Because students can manipulate and observe the simulations, the collection can help connect theoretical probability with experimental results and visual representations. |
Probability Applets For Binomial distribution
| Title | Description |
|---|---|
| PHET Interactive Plinko Probability | The PhET Plinko Probability simulation provides a visual way to explore probability through repeated trials. As objects move through a branching structure, students can observe how individual random outcomes accumulate into a distribution. This makes the simulation useful for discussing randomness, repeated trials, probability distributions, and the relationship between individual outcomes and larger patterns. PhET's simulations are designed around interactive exploration and immediate feedback. |
| Rossman/Chance Binomial Simulation (One Proportion Applet) | The Rossman/Chance collection includes simulations that allow students to investigate probability and sampling through repeated random processes. Within the broader collection are probability tools and simulations involving random numbers, sampling, and repeated trials. These activities can help students investigate how theoretical probability relates to simulated outcomes and how distributions emerge from repeated experiments. |
| Stats Medic Binomial Applet | To get to the Binomial applet, scroll down to the probability section and click on the binomial applet. You or your students will be able to explore the relationship between with success versus failure with multiple trials. |
| Geogebra Binomial Probability Distribution | One of the included activities simulates repeated coin-toss experiments and displays the frequencies of possible outcomes. Students can use these simulations to compare experimental results with the theoretical binomial distribution and explore how changing the probability or number of trials affects the distribution. |
| Random Services Binomial Coin Experiment | Random Services provides interactive probability experiments covering several probability models. Its collection specifically includes a Binomial Coin Experiment along with other Bernoulli-trial and binomial experiments. The applets allow students to investigate repeated trials and observe how the number of successes varies from experiment to experiment, providing a visual way to connect individual Bernoulli trials to the binomial distribution. |
Additional Resources
| Title | Type | Description |
|---|---|---|
|
"The Organic Chemistry Tutor"
Intro To Probability |
Video | The Organic Chemistry Tutor's probability materials provide video-based explanations of fundamental probability concepts and problem-solving techniques. Its probability resources cover topics such as basic probability, independent and dependent events, conditional probability, addition and multiplication rules, compound probability, expected value, tree diagrams, Bayes' theorem, and probability distributions. The videos can serve as supplemental instruction or review because they demonstrate how probability concepts are applied to worked examples. |
| Probability texts, videos and example prompts | Text | ProbabilityCourse.com is an online probability resource intended to provide instructional material related to probability and random processes. It can be used as a supplemental source for reading and studying probability concepts. Because the site contains instructional materials and examples, it can provide students with additional explanations and practice beyond what is covered during class. |
| KhanAcademy Probability Practice Prompts | Practice Prompts | Khan Academy's probability section provides lessons, practice problems, quizzes, and assessments covering a broad range of probability topics. Topics include simple probability, sample spaces, set notation, experimental probability, simulations, addition and multiplication rules, independent and dependent events, and conditional probability. This makes the resource useful for both introducing probability concepts and providing students with additional opportunities to practice and receive feedback. |
| A Cartoon Guide to Statistics | Book | The Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith is an introductory statistics book that uses cartoons and visual explanations to present statistical concepts. It covers topics including data description, probability, random variables, binomial and normal distributions, sampling, confidence intervals, hypothesis testing, comparing populations, experimental design, and regression. The visual format makes it a potential supplemental resource for students who benefit from explanations that are less formal or text-heavy than a traditional statistics textbook. |
| What is Probability and Randomness? | How to be Rational | Video | This video is intended as a conceptual introduction to probability and randomness. It can be used as a supplementary resource for students who are beginning to think about probability beyond simply calculating answers. In particular, it can help introduce the ideas of uncertainty, random outcomes, and the reasoning involved in making decisions when outcomes are not certain. |
Assignment 2
Liars Dice
Roll your dice privately. Keep your screen hidden from other players until a bid is challenged.
Keep your dice private. When a challenge happens, reveal your dice along with everyone else. The group counts all matching faces, including ones as wild dice.
How to Play Liars Dice
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Set Up and Roll Your Dice
Each player opens this page on their own phone or computer. Position your device so that no other player can see your screen. Roll your dice and keep the results private. Do not show your dice to the other players until a challenge is made.
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Make the First Bid
The starting player looks at their own dice and predicts the minimum number of times a particular face appears across everyone's dice. For example, saying "seven 3s" means you predict that there are at least seven dice showing 3 across all players' dice. You do not need to know the exact total, only what you believe is present.
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Raise the Bid or Challenge
Play proceeds clockwise. On your turn, you must either raise the previous bid or challenge it. To raise a bid, you may increase the quantity of the same number, such as raising "seven 3s" to "eight 3s," or choose a higher number with any quantity, such as raising "seven 3s" to "four 4s." The bid must follow these rules, and you should consider your own dice when deciding whether the prediction is believable.
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Remember That Ones Are Wild
Dice showing 1 count as wild dice. When checking a bid for another number, every die showing that number and every die showing 1 counts toward the predicted total. For example, a bid of "seven 3s" is correct if the players have at least seven dice showing either 3 or 1 combined. Ones do not need to be bid directly to count toward a prediction.
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Challenge a Bid
If you believe the current bid is too high, challenge it instead of raising it. Once a challenge is made, all players reveal their dice. Count every die showing the predicted number, including all wild 1s, to determine whether the bid was correct.
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Determine the Winner of the Challenge
If the total number of matching dice, including wild 1s, is at least the quantity that was bid, the prediction was correct and the bidder wins the challenge. If the total is less than the quantity that was bid, the prediction was incorrect and the challenger wins. The player who loses the challenge loses one die.
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Start the Next Round
After the challenge is resolved, the losing player removes one die from their collection on their device. Everyone rolls their remaining dice for the next round. The player who lost the challenge opens the next round by making the first bid.
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Elimination and Winning the Game
A player who loses all their dice is eliminated from the game and no longer participates in bidding. Continue playing rounds until only one player has dice remaining. That player is the winner.
Want help estimating the odds of a bid? Use this calculator to assist with your decisions.
Open Liars Dice Calculator ↗Assignment 3
This is where the description and information for Assignment 3 will go.