"Polypad is a collection of interactive digital manipulatives for teachers and students. The unique tools and features on Polypad enable exploration, creativity, and problem solving. Students can quickly visualize their ideas and experiment with mathematical objects, while teachers can author and share complex and highly customized activities – the possibilities are endless."

Copy and paste this url to get started and find tutorials - https://polypad.amplify.com/help

This is an amazing math tool!

The addition rule for probability is explained using Venn Diagrams. [Probability playlist: Lesson 3 of 29]

Today we’re going to begin our discussion of probability. We’ll talk about how the addition (OR) rule, the multiplication (AND) rule, and conditional probabilities help us figure out the likelihood of sequences of events happening - from optimizing your chances of having a great night out with friends to seeing Cole Sprouse at IHop!

Today we're going to introduce bayesian statistics and discuss how this new approach to statistics has revolutionized the field from artificial intelligence and clinical trials to how your computer filters spam! We'll also discuss the Law of Large Numbers and how we can use simulations to help us better understand the "rules" of our data, even if we don't know the equations that define those rules.

Sixth grade math teacher Ana Posada shares a lesson on probability. Students do simulations of dependent and independent events using a goody bag of objects where they can document the differences between them.

There are a lot of events in life that we just can’t predict, but just because something is random doesn’t mean we don’t know or can’t learn anything about it. Today, we’re going to talk about how we can extract information from seemingly random events starting with the expected value or mean of a distribution and walking through the first four “moments” - the mean, variance, skewness, and kurtosis.

Today we're going to introduce one of the most flexible statistical tools - the General Linear Model (or GLM). GLMs allow us to create many different models to help describe the world - you see them a lot in science, economics, and politics. Today we're going to build a hypothetical model to look at the relationship between likes and comments on a trending YouTube video using the Regression Model. We'll be introducing other popular models over the next few episodes.

Replication (re-running studies to confirm results) and reproducibility (the ability to repeat an analyses on data) have come under fire over the past few years. The foundation of science itself is built upon statistical analysis and yet there has been more and more evidence that suggests possibly even the majority of studies cannot be replicated. This "replication crisis" is likely being caused by a number of factors which we'll discuss as well as some of the proposed solutions to ensure that the results we're drawing from scientific studies are reliable.

These activities introduce students to the use of sampling for advertising purposes. They also generates a discussion about how advertisers use gimmicks to get people to buy more of their product. Even young students will admit that they have been induced to buy fast food meals in order to collect all of the toys.

Today we’re going to talk about good and bad surveys. From user feedback surveys, telephone polls, and those questionnaires at your doctors office, surveys are everywhere, but with their ease to create and distribute, they're also susceptible to bias and error. So today we’re going to talk about how to identify good and bad survey questions, and how groups (or samples) are selected to represent the entire population since it's often just not feasible to ask everyone.

We’ve talked a lot in this series about how often you see data and statistics in the news and on social media - which is ALL THE TIME! But how do you know who and what you can trust? Today, we’re going to talk about how we, as consumers, can spot flawed studies, sensationalized articles, and just plain poor reporting. And this isn’t to say that all science articles you read on facebook or in magazines are wrong, but that it's valuable to read those catchy headlines with some skepticism.

When collecting data to make observations about the world it usually just isn't possible to collect ALL THE DATA. So instead of asking every single person about student loan debt for instance we take a sample of the population, and then use the shape of our samples to make inferences about the true underlying distribution our data. It turns out we can learn a lot about how something occurs, even if we don't know the underlying process that causes it. Today, we’ll also introduce the normal (or bell) curve and talk about how we can learn some really useful things from a sample's shape - like if an exam was particularly difficult, how often old faithful erupts, or if there are two types of runners that participate in marathons!

Students are introduced to the technology of flexible circuits, some applications and the photolithography fabrication process. They are challenged to determine if the fabrication process results in a change in the circuit dimensions since, as circuits get smaller and smaller (nano-circuits), this could become very problematic. The lesson prepares students to conduct the associated activity in which they perform statistical analysis (using Excel® and GeoGebra) to determine if the circuit dimension sizes before and after fabrication are in fact statistically different. A PowerPoint® presentation and post-quiz are provided. This lesson and its associated activity are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.

Students apply pre-requisite statistics knowledge and concepts learned in an associated lesson to a real-world state-of-the-art research problem that asks them to quantitatively analyze the effectiveness of different cracked steel repair methods. As if they are civil engineers, students statistically analyze and compare 12 sets of experimental data from seven research centers around the world using measurements of central tendency, five-number summaries, box-and-whisker plots and bar graphs. The data consists of the results from carbon-fiber-reinforced polymer patched and unpatched cracked steel specimens tested under the same stress conditions. Based on their findings, students determine the most effective cracked steel repair method, create a report, and present their results, conclusions and recommended methods to the class as if they were presenting to the mayor and city council. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.

This 8-minute video lesson provides analysis of variance 1: Calculating SST (Total Sum of Squares). [Statistics playlist: Lesson 75 of 85]

This 13-minute video lesson provides analysis of variance 2: Calculating SSW and SSB (total sum of squares within and between). [Statistics playlist: Lesson 76 of 85]

This 12-minute video lesson plays with the formula for variance of a population. And looks at alternate variance formulas. [Statistics playlist: Lesson 16 of 85]

This 7-minute video lesson gives formulas for the Bernoulli Distribution Mean and Variance. [Statistics playlist: Lesson 42 of 85]

This 10-minute video lesson explains box and whisker plots. [Statistics playlist: Lesson 9 of 85]

This 8-minute video lesson takes problems from CK12.org to discuss using the Empirical Rule with a standard normal distribution. [Statistics playlist: Lesson 33 of 85]