Park City Mathematics Institute
Reasoning from Data and Chance
Drafts of Project Files (password required)
- Ideas for Grade 8 Data and Statistics: Your GPS on the Highway of Common Core Standards
- Sandra Corbacioglu
- The Common Core State Standards for Grade 8 contain a domain entitled Statistics and Probability which is made up of five standards. This document is intended to aid teachers in understanding these standards, as well as to provide starting points for possible class activities. Neither the standards nor this document will tell teachers how to teach, but will provide a roadmap for interpreting the standards in order to help teachers set and reach appropriate goals for the students in their classroom.
- The Common Cure for Common Core Fever
- Jessica Abarca, Jemal Graham* & Arden Nguyen
- Different states are in different stages of adoption of the Common Core mathematics standards, but many teachers, regardless of where they live, are unsure of how to incorporate the Common Core standards into their daily instruction. This project, developed by the three middle school teachers in the Reasoning from Data and Chance group, is designed to serve as a resource for 7th grade teachers in the classroom as they approach the Statistics and Probability section of the Common Core Standards. For each of the 7th grade standards in the Statistics and Probability section, the handbook highlights key vocabulary and puts each word in language that is easily accessible to both students and teachers. The handbook also provides illustrative examples with pictures, screenshots from Fathom and detailed descriptions that make the standards come alive for students. Finally, the handbook provides teachers with a series of probing questions that they can use in class to check for student understanding.
- Evaluating "Extraordinary" Events in Sports
- Sam Critchlow* and Jason Lang
- What it is: a 2-class period module introducing Bernoulli Trials and binomial probability distributions. Students will make predictions about the outcomes and probability distributions based on calculations and simulations of Bernoulli Trials and evaluate statements about the likelihood of "extraordinary" events. Sports scenarios such as basketball freethrows and soccer penalty kicks are used throughout the lesson to illustrate the principles studies and provide real-world context to evaluate likelihood. Support for Fathom dynamic data software and TI-nspire calculators is included, but neither is required for the lesson.
- Proving that Perseverance Works: Using Stats to Illustrate Improvement in Mastermind Scores
- James Dunseith* and Debbie Seidell
- The first Common Core Standard for Mathematical Practice is for students to "Make sense of problems and persevere in solving them." The purpose of this investigation is to help students make a connection between perseverance and achievement by playing a code-breaking game and measuring their progress over time. Students will learn to play Mastermind and keep track of their results (as measured in turns taken to win). They will learn how to represent their results with measures of center and spread, and as prompted by the Common Core Standards, they will "summarize, represent, and interpret" this data using dot plots and box plots. They will watch these representations change over time, and be asked to draw conclusions about their progress.
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IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
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