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Illustrative Math Probability & Sampling Unit

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Illustrative Math Probability & Sampling Unit

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In this unit, students understand and use the terms "event," "sample space," "outcome," "chance experiment," "probability," "simulation," "random," "sample," "random sample," "representative sample," "overrepresented," "underrepresented," "population," and "proportion." They design and use simulations to estimate probabilities of outcomes of chance experiments and understand the probability of an outcome as its long-run relative frequency. They represent sample spaces (that is, all possible outcomes of a chance experiment) in tables and tree diagrams and as lists. They calculate the number of outcomes in a given sample space to find the probability of a given event. They consider the strengths and weaknesses of different methods for obtaining a representative sample from a given population. They generate samples from a given population, e.g., by drawing numbered papers from a bag and recording the numbers, and examine the distributions of the samples, comparing these to the distribution of the population. They compare two populations by comparing samples from each population.

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Illustrative Mathematics Grade 7, Unit 8 - Teachers | Kendall Hunt

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In this unit, students understand and use the terms “event,” “sample space,” “outcome,” “chance experiment,” “probability,” “simulation,” “random,” “sample,” “random sample,” “representative sample,” “overrepresented,” “underrepresented,” “population,” and “proportion.” They design and use simulations to estimate probabilities of outcomes of chance experiments and understand the probability of an outcome as its long-run relative frequency. They represent sample spaces (that is, all possible outcomes of a chance experiment) in tables and tree diagrams and as lists. They calculate the number of outcomes in a given sample space to find the probability of a given event. They consider the strengths and weaknesses of different methods for obtaining a representative sample from a given population. They generate samples from a given population, e.g., by drawing numbered papers from a bag and recording the numbers, and examine the distributions of the samples, comparing these to the distribution of the population. They compare two populations by comparing samples from each population.

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In this unit, students generate and work with bivariate data sets that has more variability than in previous units. They learn to understand and use the terms "scatter plot" and "association," and describe associations as "positive" or "negative" and "linear" or "non-linear." Students describe scatter plots, using a term previously used to describe univariate data "cluster," and the new term "outlier." They fit lines to scatter plots and informally assess their goodness of fit by judging the closeness of the data points to the lines, and compare predicted and actual values. Students learn to understand and use the terms "two-way table," "bar graph," and "segmented bar graph," using two-way tables to investigate categorical data.

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Illustrative Mathematics Grade 8, Unit 6 - Teachers | Kendall Hunt

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In this unit, students generate and work with bivariate data sets that has more variability than in previous units. They learn to understand and use the terms "scatter plot" and "association," and describe associations as "positive" or "negative" and "linear" or "non-linear."

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In this unit on one-variable statistics, students discuss the difference between statistical and non-statistical questions and classify that data as numerical or categorical. They represent and interpret data using data displays, and describe distributions using the appropriate terminology. They create data displays and calculate summary statistics using technology, then interpret the values in context. They learn that standard deviation is a measure of variability, and they interpret standard deviation in context. They recognize outliers, investigate their source, make decisions about excluding them from the data set, and understand how the presence of outliers impacts measures of center and measures of variability. They compare measures of center and the standard deviation and the interquartile range for different data sets. In the culminating activity, students pose and answer a statistical question by designing an experiment, collecting data, and analyzing data.

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Illustrative Mathematics Algebra 1, Unit 1 - Teachers | Kendall Hunt

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In this unit on one-variable statistics, students discuss the difference between statistical and non-statistical questions and classify that data as numerical or categorical. They represent and interpret data using data displays, and describe distributions using the appropriate terminology. They create data displays and calculate summary statistics using technology, then interpret the values in context. They learn that standard deviation is a measure of variability, and they interpret standard deviation in context. They recognize outliers, investigate their source, make decisions about excluding them from the data set, and understand how the presence of outliers impacts measures of center and measures of variability. They compare measures of center and the standard deviation and the interquartile range for different data sets. In the culminating activity, students pose and answer a statistical question by designing an experiment, collecting data, and analyzing data.

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In grade 8, students informally constructed scatter plots and lines of fit, noticed linear patterns, and observed associations in categorical data using two-way tables. In this unit, students revisit two-way tables to find associations in categorical data using relative frequencies. The unit also builds on previous knowledge of scatter plots by assessing how well a linear model matches the data using residuals as well as the correlation coefficient for best-fit lines (found using technology). It closes with an exploration of the difference between correlation and causal relationships as well as an opportunity to apply this learning to anthropology and sports.

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Illustrative Mathematics Algebra 1, Unit 3 - Teachers | Kendall Hunt

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In grade 8, students informally constructed scatter plots and lines of fit, noticed linear patterns, and observed associations in categorical data using two-way tables. In this unit, students revisit two-way tables to find associations in categorical data using relative frequencies.

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IXL Skill Plan | Arkansas Mathematics Standards (adopted in 2023): Statistics

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IXL’s dynamic math practice skills offer comprehensive coverage of Arkansas Calculus standards. Find a skill to start practicing!

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Websites

What's Going On in This Graph? is a free, weekly online feature of the ASA and New York Times Learning Network. New York Times graphs of different types and context act as a springboard for middle- and high-school students in any course (college also welcome) to think critically about graphs. On most Wednesdays from September to April, graphs are released. Students respond to three questions: What do you notice? What do you wonder? What's going on in this graph? Teachers moderate their responses online from 9 a.m. - 2 p.m. ET. On Friday, the original article, additional questions, and "stat nuggets" -definitions of statistical terms and where they are seen in the graph-are revealed. No statistics background is necessary.

STatistics Education Web (STEW) is a free, online resource for peer-reviewed statistics lesson plans.

Census at School - U.S. is a free international classroom project that engages students in grades 4-12 in statistical problemsolving using their own real data. Students complete an online survey, analyze their class census results, and compare their class with random samples of students in the United States and abroad.

Common Core Statistics and Probability Resources - This document includes resources from the ASA, National Council of Teachers of Mathematics, and others that support the teaching of statistics and probability as covered by the Common Core State Standards. Included are lesson plans, applets, videos, data sources, media, technology, teacher preparation materials, and assessment resources.

The World of Statistics offers free international statistics education resources from around the world.

This is Statistics is aimed at high-school juniors and seniors, as well as their parents, instructors, and counselors. The goal is to interest students in statistics as their future career.

Stats.org is a collaboration between the ASA and Sense About Science USA that aims to provide guidance regarding statistical literacy to journalists and the public.

OpenIntro Statistics provides free resources for high-school and college introductory statistics courses, including textbooks, labs, videos, lecture slides, data sets, and forums.

ARTIST (Assessment Resource Tools for Improving Statistical Thinking) has field-tested assessment inventory scales on specific topics in probability and statistics, as well as a searchable item database that allows teachers to build their own assessments.

LOCUS is an NSF-funded project focused on developing assessments of statistical understanding across levels of development as identified in the Guidelines for Assessment and Instruction in Statistics Education (GAISE). The intent of these assessments is to provide teachers, educational leaders, assessment specialists, and researchers with a valid and reliable assessment of conceptual understanding in statistics consistent with the Common Core State Standards.

FiveThirtyEight covers news, sports, and features from a statistical viewpoint. The head of the group is Nate Silver, who is famous for his 2012 election predictions.

Project-SET is an NSF-funded project focused on developing innovative curricular materials to foster students' statistical learning.

CAUSEweb has helpful resources for teaching an introductory statistics course, including class examples, labs, homework assignments, data sets, cartoons, songs, jokes, and quotes. This site also houses information about the biennial U.S. Conference on Teaching Statistics and the Electronic Conference on Teaching Statistics.

The International Statistical Literacy Project provides resources for elementary and middle-school teachers to expand their knowledge of probability and statistics and to use in the classroom.

National Council of Teachers of Mathematics (NCTM) Illuminations is a repository of lesson plans, online activities, and connections to the NCTM Standards.

Illustrative Mathematics is a site providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers.

Engage NY offers resources to support Common Core Statistics Standards.

MERLOT Statistics Portal provides lessons and resources for teaching introductory statistics.

AIMS Project: Adapting and Implementing Innovative Material in Statistics includes lesson plans and activities based on innovative materials for introductory statistics courses aligned with GAISE recommendations.

Publications

The Journal of Statistics Education is a free online, international journal focusing on statistics teaching and learning. The journal's website also contains links to several statistical education organizations, newsletters, discussion groups, and the JSE data archive.

Statistics Teacher (ST) is an online journal published by the American Statistical Association (ASA) - National Council of Teachers of Mathematics (NCTM) Joint Committee on Curriculum in Statistics and Probability for Grades K-12. ST supports the teaching and learning of statistics through education articles, lesson plans, announcements, professional development opportunities, technology, assessment, and classroom resources.

Bridging the Gap Between Common Core State Standards and Teaching Statistics includes 20 data analysis and probability investigations for teachers to use in their K-8 classrooms. Each investigation is based on the four-step statistical process as defined in the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework.

The Making Sense of Statistical Studies (MSSS) student module consists of 15 hands-on investigations that help students design and analyze statistical studies. It is written for an upper-middle-school or high-school audience having some background in exploratory data analysis and basic probability. The teacher's module includes supporting resources to help teachers use MSSS, as well as all the pages from the student module.

Significance is a magazine that demonstrates the practical use of statistics and shows how statistics benefits society. Back issues of Significance are freely available online.

is a magazine about statistics intended for anyone who has an interest in using data to advance science, education, and society.

The Statistical Significance Series highlights the contributions statisticians make to society.

Teaching Statistics: Resources for Undergraduate Instructors presents a collection of classic and original articles about various aspects of statistical education, along with descriptions of innovative and successful projects.

The Quantitative Literacy Series is a four-part series of books written through a collaborative effort of teachers and statisticians. It is designed for use with middle- and high-school students. The books are part of an ASA project that was funded in part by the National Science Foundation. Though out of print, the books listed below are available through book resale sites.

Exploring Data, by James Landwehr and Ann Watkins

Exploring Probability, by Claire Newman, Thomas Obremski, and Richard Scheaffer

The Art and Techniques of Simulation, by Mrudulla Gnanadesikan, Richard Scheaffer, and Jim Swift

Exploring Surveys: Information from Samples, by James Landwehr, Jim Swift, and Ann Watkins

The Elementary Quantitative Literacy (EQL) Series was written by a team of elementary school teachers and statisticians to introduce the key ideas and lessons in data analysis and probability in the K-6 mathematics curriculum. Though out of print, the books listed below are available through book resale sites.

Exploring Statistics in the Elementary Grades, Book One, by Carolyn Bereska, L. Carey Bolster, Cyrilla H. Bolster, and Richard Scheaffer

Exploring Statistics in the Elementary Grades, Book Two, by Carolyn Bereska, L. Carey Bolster, Cyrilla H. Bolster, and Richard Scheaffer

Data-Driven Mathematics is a series of modules funded by the National Science Foundation and written by statisticians and mathematics teachers. Intended to complement a modern mathematics curriculum in the secondary schools, the modules offer materials that integrate data analysis with topics typically taught in high-school mathematics courses and provide realistic, real-world data situations for developing mathematical knowledge. Scanned copies of these books are freely available to download (PDF) through the following links:

Advanced Modeling and Matrices - Teacher's Edition, by Gail Burrill, Jack Burrill, James Landwehr, and Jeffrey Witmer

Advanced Modeling and Matrices, by by Gail Burrill, Jack Burrill, James Landwehr, and Jeffrey Witmer

Exploring Centers - Teacher's Edition, by Henry Kranendonk and Jeffrey Witmer

Exploring Centers, by Henry Kranendonk and Jeffrey Witmer

Exploring Linear Relations - Teacher's Edition, by Gail Burrill and Patrick Hopfensperger

Exploring Linear Relations, by Henry Kranendonk and Jeffrey Witmer

Exploring Projects - Teacher's Edition, by Emily Errthum, Maria Mastromatteo, Vince O'Connor, and Richard Scheaffer

Exploring Projects, by Emily Errthum, Maria Mastromatteo, Vince O'Connor, and Richard Scheaffer

Exploring Regression - Teacher's Edition, by Gail Burrill, Jack Burrill, Patrick Hopfensperger, and James Landwehr

Exploring Regression, by Gail Burrill, Jack Burrill, Patrick Hopfensperger, and James Landwehr

Exploring Symbols - Teacher's Edition, by Gail Burrill, Miriam Clifford, and Richard Scheaffer

Exploring Symbols, by Gail Burrill, Miriam Clifford, and Richard Scheaffer

Exploring Systems of Inequalities - Teacher's Edition, by Gail Burrill and Patrick Hopfensperger

Exploring Systems of Inequalities, by Gail Burrill and Patrick Hopfensperger

Mathematics in a World of Data - Teacher's Edition, by Jack Burrill, Miriam Clifford, Emily Errthum, Henry Kranendonk, Maria Mastromatteo, and Vince O'Connor

Mathematics in a World of Data, by Jack Burrill, Miriam Clifford, Emily Errthum, Henry Kranendonk, Maria Mastromatteo, and Vince O'Connor

Modeling with Logarithms - Teacher's Edition, by Jack Burrill, Miriam Clifford, and James Landwehr

Modeling with Logarithms, by Jack Burrill, Miriam Clifford, and James Landwehr

Probability Models - Teacher's Edition, by Patrick Hopfensperger, Henry Kranendonk, and Richard Scheaffer

Probability Models, by Patrick Hopfensperger, Henry Kranendonk, and Richard Scheaffer

Probability Through Data - Teacher's Edition, by Patrick Hopfensperger, Henry Kranendonk, and Richard Scheaffer

Probability Through Data, by Patrick Hopfensperger, Henry Kranendonk, and Richard Scheaffer

Statistics: A Guide to the Unknown offers a collection of essays that describe the important applications of statistics and probability. Instead of teaching methods, the essays illustrate past accomplishments and current uses of statistics and probability. Examples of surveys, questionnaires, experiments, and observational studies illustrate the importance and influence of statistics.

Guidelines, Reports, and Statements

Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework provides recommendations and a curriculum framework with examples for teaching statistics in the pre-K-12 years.

The Statistical Education of Teachers (SET) (PDF download) report outlines the content and conceptual understanding teachers need to know in assisting their students develop statistical reasoning skills. SET is intended for everyone involved in the statistical education of teachers, both the initial preparation of prospective teachers and the professional development of practicing teachers.

Preparing K-12 Teachers of Statistics: A Joint Position Statement of the American Statistical Association and National Council of Teachers of Mathematics (PDF download) details the preparation and support teachers need to successfully support students' learning of statistics in the pre-K-12 curriculum.

Videos, Media, and Workshops

K-12 Statistics Education Webinars were developed as part of the follow-up activities for the Meeting Within a Meeting Statistics Workshop for Mathematics and Science Teachers.

The Meeting Within a Meeting (MWM) Statistics Workshop for Mathematics and Science Teachers supports teaching of statistics within the Common Core and Next Generation Science Standards through conceptual understanding, active learning, real-world data applications, and appropriate use of technology.

The Beyond AP Statistics Workshop is offered for AP Statistics teachers and consists of enrichment material just beyond the basic AP syllabus.

Stats + Stories is a collection of podcasts about the statistics behind the stories and the stories behind the statistics.

The Chance Project emphasizes using current news media as motivation for studying issues in probability and statistics. A highlight is the monthly Chance News (which functions as a wiki), abstracting recent articles from newspapers and magazines with suggestions for pedagogical uses.

YouTube Videos on Descriptive Statistical Concepts by Duke University professors and students is a collection of 52 videos that teach basic descriptive statistical concepts. The videos cover core concepts, pedagogy, JMP software, and applet demonstrations.

Data to Insight Videos on YouTube
Chris Wild's Data to Insight: An Introduction to Data Analysis is a free, online, hands-on introduction to statistical data analysis.

Against All Odds: Inside Statistics is a free video series teaching introductory statistics concepts with real-life applications. This is an updated version of the 1980s series and contains videos, a glossary, teacher guides, and student guides.

Data Sources and Archives

Data.Gov
DASL (Dataset and Story Library)
Chance Project Data Sets
U.S. Census Bureau
UCLA Statistics Case Studies
Rice Virtual Lab in Statistics
Gapminder
Census at School - U.S.
Census at School International
Journal of Statistics Education Data Archive
Baseball Prospectus
Advanced Football Analytics
Tuva
ICPSR (Inter-University Consortium for Political and Social Research)
Virtual Laboratories in Probability and Statistics

Applets, Simulation Tools, and Videos

Student Competitions

ASA Poster Competition is for grades K-12.
ASA Project Competition (written report) is for grades 7-12.
Curtis Jacobs Memorial Prize for Outstanding Statistical Project is for Washington, DC, metro-area students.

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Statistics Lecture 1.1:  The Key Words and Definitions For Elementary Statistics

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In grade 7, students examined processes for collecting samples from a population and using information from the samples to estimate characteristics for the population. In this unit, students expand on this idea by exploring the normal distribution and applying their understanding of the distribution to provide estimates with a margin of error. The unit also examines experimental studies, observational studies, and surveys. For experimental studies, it examines methods for analyzing the data using a randomization distribution and modeling the data with normal distributions. The importance of random selection for gathering a sample for surveys and observational studies and the importance of random assignment in experimental studies is emphasized. The unit concludes with ways to analyze the results from the various study types. Data from surveys and observational studies using random samples are used to estimate population means and proportions with a margin of error.

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Illustrative Mathematics Algebra 2, Unit 7 - Teachers | Kendall Hunt

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In grade 7, students examined processes for collecting samples from a population and using information from the samples to estimate characteristics for the population. In this unit, students expand on this idea by exploring the normal distribution and applying their understanding of the distribution to provide estimates with a margin of error.

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In this unit, students extend what they learned about probability in grade 7 by considering events that are combined in various ways including both occurring, at least one occurring, and one event happening under the condition that the other happens as well. This unit introduces the relationship between probabilities of some combinations of events using the Addition Rule, \(P(\text{A or B}) = P(\text{A}) + P(\text{B}) - P(\text{A and B})\). Conditional probability is discussed. In particular, the Multiplication Rule \(P(\text{A and B}) = P(\text{A | B}) \boldcdot P(\text{B})\) is used to determine conditional probabilities as well as independence of events A and B. Independence is further explored using everyday language as well as through the equation \(P(\text{A | B}) = P(\text{A})\) when events A and B are independent.

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Illustrative Mathematics Geometry, Unit 8 - Teachers | Kendall Hunt

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In this unit, students extend what they learned about probability in grade 7 by considering events that are combined in various ways including both occurring, at least one occurring, and one event happening under the condition that the other happens as well.