# Advanced Common Core Math Explorations: Probability and Statistics

The Advanced Common Core Math Explorations series creates and nurtures mathematical adventurers! This new book in the ACCME series uses a new format inspired by Ian Byrd of byrdseed.tv. The problems have been separated onto individual pages with simplified, bulleted directions. Each problem is introduced with a "teaser" that encourages students to come up with their own questions and observations before receiving the directions. The discussion guides have been rewritten as "I notice" statements and "I wonder" questions. The look and feel of the pages is open and inviting, and the writing is less formal with some of the "messy" details removed. (Some of these details will be available on this page for those who would still like them!) The new format enhances the open-ended, inquiry-based nature of the problems. Incidentally, Ian has created wonderful videos for a few of the activities in the ACCME series. Please check them out at his website!

Exploration 1: Playing with Data

Learn more about familiar measures of central tendency (mean and median) and variability (range), and explore some that may not be familiar (mean absolute deviation) by solving challenging problems that help you to explore relationships between them.

Exploration 2: A Day at the Races

Experience the entire process of carrying out a statistical investigation by testing toy cars for entrance in a race. Collect, display, and analyze data; and interpret your results. Use what you learn to reach conclusions about which is the best car to enter.

Exploration 3: Simulation Station

Begin to explore probability by learning how to design and carry out hands-on experiments called simulations for a variety of real-world situations related to sports, weather, games, and more!

Exploration 4: Comparing Populations

By studying the lengths of the sentences in two popular books, learn how to make inferences about large populations of people or things by gathering data from just a small number of members of the population.

Exploration 5: One More Time!

Things can get pretty complicated when probability experiments are repeated many times, but mathematicians have discovered ways to manage these situations. In this exploration, you are the mathematician who makes the discoveries. When your are ready, apply your new knowledge to design a spinner for a contest at a Math Family Fun Night.

Exploration 6: What are the Chances?

Basic probability problems involve outcomes that do not affect each other and events that have no outcomes in common. In this exploration, you deal with more complex probability situations by inventing and testing your own strategies to handle situations that go beyond the basics.

Exploration 7: Paths and Pascal

You might think that counting outcomes would be one of the easier parts of calculating probabilities. However, when there are a huge number of outcomes, things can get pretty tricky! Fortunately, the branch of mathematics known as combinatorics offers strategies and tools for dealing with these situations. Some of the techniques that mathematicians have discovered involve beautiful number patterns that you will explore in this activity.

Exploration 8: Sports Correlations

Investigate and analyze relationships between statistical variables from the Women's National Basketball Association's 2015 season. Or if you prefer, collect your own data from a sport or other topic that interests you! Learn about the concept of correlation, and apply your algebraic knowledge of slopes and intercepts to interpret what you see and make predictions. Finish by creating and testing your own metric that combines different statistics into a formula that predicts a team's level of success!

Exploration 9: Triangle Trials

In the Triangle Trials exploration, you show how to create triangles by cutting up line segments into three pieces and putting them together. Unfortunately, some ways of cutting the segments won't work. Your job is to figure out the probability that segments will make a triangle as the number of places you are allowed to cut the segment gets larger and larger. Eventually, you discover that you can calculate probabilities even when there are an infinite number of outcomes!