A Focus on Multiplication and Division is a groundbreaking effort to make mathematics education research readily accessible and understandable to pre- and in-service K-6 mathematics educators. Revealing students' thought processes with extensive annotated samples of student work and vignettes characteristic of teachers' experiences, this book is sure to equip educators with the knowledge and tools needed to modify their lessons and to improve student learning of multiplication and division. Special Features: Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students. Instructional Links help teachers relate concepts from each chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division. Answer Key posted online offers extensive explanations of in-chapter questions. Each chapter includes sections on the Common Core State Standards for Mathematics and integrates the Ongoing Assessment Project (OGAP) Multiplicative Reasoning Progression for formative assessment purposes. Centered on the question of how students develop their understanding of mathematical concepts, this innovative book places math teachers in the mode of ongoing action researchers.

-Makes mathematics education research on multiplication and division accessible and understandable to pre-service and in-service teachers of grades K-6, allowing teachers to understand evidence in student work and make better instructional decisions. -Uses extensive annotated samples of student work, helping teachers improve their ability to recognize and assess student errors and misconceptions, as well as their understanding, learning, and fluency of multiplicative reasoning. -Built off the wide-scale research gathered in the Ongoing Assessment Project (OGAP), drawn from hundreds of teachers and thousands of examples of student work. -Each chapter includes student work samples and vignettes to illuminate the research, guidance on CCSSM standards, end of chapter questions, professional development activities, and instructional links that help teachers relate concepts back to their own instructional materials and programs. -This edition has been updated throughout with the latest research, CCSSM standards, additional examples and vignettes, and more.

If our eyes were radio rather than optical wide-band detectors it is well known that for us the brightest object in the sky would still be the Sun; that planets, stars and the Milky Way would still shine feebly (and that we would still occasionally be blinded by man-made sources). What is less well known is that quite a different earthbound overcast would hover about us, with its climatic zones, its seasonal changes, its unpredictable storms and scintillating transparence. To be sure, we can get a sort of glimpse of this peculiar type of weather when we tune our receiver to radio broad casting from some remote spot, or photograph the Earth from space at certain specific wavelengths. Nevertheless no one has ever looked at the ionized shroud of the Earth without the help of sophisticated apparatus, and this is one of the reasons why in this domain the phenomena are not easily abstracted from the use of specific techniques. For generations, the study of the ionosphere has been deeply interwoven with the practice of radio communication and detection. Today however, ionospheric physics is best thought of as a branch of space physics; that part of physics which deals with processes at work in the solar system and methods developed for its exploration."

-Makes mathematics education research on fraction concepts accessible and understandable to pre-service and in-service teachers of grades K-8, allowing teachers to understand evidence in student work and make better instructional decisions. -Uses extensive annotated samples of student work, helping teachers improve their ability to recognize and assess student errors and misconceptions, as well as their understanding, learning, and fluency of fraction concepts. -Built off the wide-scale research gathered in the Ongoing Assessment Project (OGAP), drawn from hundreds of teachers and thousands of examples of student work. -Each chapter includes student work samples and vignettes to illuminate the research, guidance on CCSSM standards, end of chapter questions, professional development activities, and instructional links that help teachers relate concepts back to their own instructional materials and programs. -This edition has been updated throughout with the latest research, CCSSM standards, additional examples and vignettes, and more.

The second edition of this book offers a unique approach to making mathematics education research on the teaching and learning of multiplication and division concepts readily accessible and understandable to pre-service and in-service K-6 mathematics teachers. Revealing students' thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers' experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP), and updated throughout, this engaging and easy-to-use resource also features: New chapters on the OGAP Multiplicative Reasoning Framework and Learning Progressions and Using the OGAP Multiplicative Progression to inform instruction and support student learning In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research Case Studies are presented, focusing on a core mathematical idea and different types of instructional responses, to illustrate how teachers can elicit evidence of student thinking and use that information to inform instruction Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students Instructional Links help teachers relate concepts from each chapter to their own instructional materials and programs Accompanying online Support Material includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression A Focus on Multiplication and Division is part of the popular A Focus on . . . collection, designed to aid the professional development of pre-service and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and fractions, this updated new edition bridges the gap between what math education researchers know and what teachers need to know to better understand evidence in student work and make effective instructional decisions.

-Makes mathematics education research on fraction concepts accessible and understandable to pre-service and in-service teachers of grades K-8, allowing teachers to understand evidence in student work and make better instructional decisions. -Uses extensive annotated samples of student work, helping teachers improve their ability to recognize and assess student errors and misconceptions, as well as their understanding, learning, and fluency of fraction concepts. -Built off the wide-scale research gathered in the Ongoing Assessment Project (OGAP), drawn from hundreds of teachers and thousands of examples of student work. -Each chapter includes student work samples and vignettes to illuminate the research, guidance on CCSSM standards, end of chapter questions, professional development activities, and instructional links that help teachers relate concepts back to their own instructional materials and programs. -This edition has been updated throughout with the latest research, CCSSM standards, additional examples and vignettes, and more.

This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts. Special features include: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess and monitor their students' errors and misconceptions, as well as their developing conceptual understanding. A focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work. Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research. Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses. An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions. Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.

This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts. Special features include: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess and monitor their students' errors and misconceptions, as well as their developing conceptual understanding. A focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work. Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research. Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses. An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions. Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.

If our eyes were radio rather than optical wide-band detectors it is well known that for us the brightest object in the sky would still be the Sun; that planets, stars and the Milky Way would still shine feebly (and that we would still occasionally be blinded by man-made sources). What is less well known is that quite a different earthbound overcast would hover about us, with its climatic zones, its seasonal changes, its unpredictable storms and scintillating transparence. To be sure, we can get a sort of glimpse of this peculiar type of weather when we tune our receiver to radio broad casting from some remote spot, or photograph the Earth from space at certain specific wavelengths. Nevertheless no one has ever looked at the ionized shroud of the Earth without the help of sophisticated apparatus, and this is one of the reasons why in this domain the phenomena are not easily abstracted from the use of specific techniques. For generations, the study of the ionosphere has been deeply interwoven with the practice of radio communication and detection. Today however, ionospheric physics is best thought of as a branch of space physics; that part of physics which deals with processes at work in the solar system and methods developed for its exploration."

Combating corruption is a key U.S. value and goal, due to its corrosive effects on the rule of law, economic development, and democratic principles. This book examines how politically powerful foreign officials, their relatives, and close associates have used the services of U.S. professionals and financial institutions to bring large amounts of suspect funds into the U.S. to advance their interests. Using four cases studies, this book shows how some PEPs have used U.S. lawyers, real estate and escrow agents, lobbyists, bankers, and even university officials, to circumvent U.S. anti-money laundering and anti-corruption safeguards, and offers recommendations on how to stop the abuse.

In 1939 Siegel City only had one superhero, the world's first. When he discovered his powers, Gabriel Ruston thought he would be the second, but died on his first excursion in costume. After Gabriel's death, his brother David is drawn into an investigation. What if Gabriel wasn't the second? What if there were others? What if something tragic happened to all of them? In Siegel City, nothing is ever what it seems... even in a Golden Age.

The Climax Studios Festival of Fear is a Halloween tradition, but with monsters roaming the theme park and a monster movie filming on the adjacent film lot, what hell will break loose when a real zombie surfaces and starts biting? When you can't tell who's alive and who's undead, can a stuntman, a makeup artist, a sleaze-slinging blogger and a pair of former cops stop the end of the world from sneaking off the studio lot and infecting all of California?

Josh Corwood has spent his life admiring the superheroes that protect Siegel City. He's wanted to join them, wanted to be like them... but eventually, had to settle for reporting on them from the sidelines. When an undiscovered talent reignites his hope to join the world's protectors, he suddenly discovers that their world isn't everything he'd been led to believe. Surrounded by false idols, Josh decides to turn the tables on them and reveal the greatest con game in history... and hopefully, in the process, find the real heroes that have long been gone. This cult favorite superhero comedy returns in a revised and expanded edition. Check out the book for the first time, or revisit it to see new scenes, plus two additional short stories (not included in the original edition) set in the world of Siegel City

Filmmaker Curtis Dupre seems to have everything he could want on the set of his second film: studio backing, a professional crew, and an actress he's admired for years in the starring role. But people begin to vanish from the set, and from the memories of everybody except Curtis. A strange visitor is eliminating those close to the young director, and there's no telling who is next. To save his friends, to save himself, Curtis Dupre will have to look into himself and discover what it truly means to be The Beginner.