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.
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 preservice 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 the following: 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 are supported by math education research Case Studies 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 to help teachers relate concepts from each chapter to their own instructional materials and programs Accompanying online Support Material that 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 preservice 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.
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.
Kumon's research has discovered that children learn more easily when they tackle one skill at a time. That's why Kumon Focus on Workbooks shine a spotlight on one challenging maths topic per book and help children improve these essential skills and gain confidence in their abilities. Each workbook utilises the Kumon Method - a step-by-step, incremental approach that helps children learn at their own pace and without anxiety. By rigorously practising each skill, the child will be proficient in the mathematics that is crucial for future learning.
Do your students suppose that 1/3 is greater than 1/2, since 3 is greater than 2? Do they believe that having “halves” means having two, and only two, congruent “pieces” of a whole? What tasks can you offer—what questions can you ask—to determine what your students know or don’t know—and move them forward in their thinking? This book focuses on the specialised pedagogical content knowledge that you need to teach fractions effectively in grades 3–5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with fractions—not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of fractions. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.
Kumon's research has discovered that children learn more easily when they tackle one skill at a time. That's why Kumon Focus on Workbooks shine a spotlight on one challenging maths topic per book and help children improve these essential skills and gain confidence in their abilities. Each workbook utilises the Kumon Method - a step-by-step, incremental approach that helps children learn at their own pace and without anxiety. By rigorously practising each skill, the child will be proficient in the mathematics that is crucial for future learning.
Kumon's research has discovered that children learn more easily when they tackle one skill at a time. That's why Kumon Focus on Workbooks shine a spotlight on one challenging maths topic per book and help children improve these essential skills and gain confidence in their abilities. Each workbook utilises the Kumon Method - a step-by-step, incremental approach that helps children learn at their own pace and without anxiety. By rigorously practising each skill, the child will be proficient in the mathematics that is crucial for future learning.
The fun, engaging program that will help your child master the addition facts once and for all—without spending hours and hours drilling flash cards! Addition Facts That Stick will guide you, step-by- step, as you teach your child to understand and memorize the addition facts, from 1 + 1 through 9 + 9. Hands-on activities, fun games your child will love, and simple practice pages help young students remember the addition facts for good. In 15 minutes per day (perfect for after school, or as a supplement to a homeschool math curriculum) any child can master the addition facts, gain a greater understanding of how math works, and develop greater confidence, in just six weeks! Mastery of the math facts is the foundation for all future math learning. Lay that foundation now, and make it solid, with Addition Facts That Stick!
Readers will put their multiplication skills to use in this clever math adaptation starring the fairy-tale favorite, Rumpelstiltskin. It's been 10 years since the queen defeated Rumpelstiltskin and now he's back to collect his payment from years before. He causes a stir in the kingdom by making mischief with his multiplying stick and threatens to do far worse if the debt is not repaid. It's up to Peter, the young prince, to take possession of the Rumpelstiltskin’s magical multiplying stick and learn how to use it—and multiply both whole numbers and fractions-- in order to restore peace to the kingdom. A perfect mix of math, fairy-tale, and fun, The Multiplying Menace will get STEM/STEAM readers excited to solve the adventure one number at a time.
You've tried managing your time. You've tried prioritizing your time. Now discover how to multiply it. Do you feel like you're busier than ever - yet never caught up? You're not alone. Many of us are tired, frustrated, and stressed from being overworked at the office and at home, with no concrete plan for getting it all under control without compromising our well-being. In Procrastinate on Purpose, self-discipline strategist Rory Vaden presents a different approach for how to identify and focus on what's important. Instead of one more calendar, checklist, or gadget, he points out that what we really need is an understanding of the emotional reasons we fail to maximize our time - and he then reveals the five 'permissions' we can grant ourselves in order to get better results while creating more margin in our daily lives. In this paradigm-shifting book, you will discover how to- Identify your most significant priorities, in business and in life Create more time to do the things you love without sacrificing results Say no to the things that don't matter, and yes to the things that do Implement systems that give you more time tomorrow than you have today Gain control and inner peace by adopting the 'multiplier mindset' Informed by Southwestern Consulting's work with thousands of busy clients, and interspersed with Vaden's case studies that reveal the 'multiplier mindset' at work, this insightful, practical book will turn everything you thought you knew about time upside-down-and it will change the way you work and live. From the New York Timesbestselling author of Take the Stairs- A bold new way to get things done. 'Managing your time is a lot like managing your money. It's not about the numbers; it's about your behavior. The best time-management tricks in the world won't do you much good if they don't actually make your life better. In Procrastinate on Purpose, Rory builds on what we've all heard about time management and adds the two things that have always been missing- emotion and significance.' Dave Ramsey, New York Timesbestselling author and nationally syndicated radio show host 'If you've ever thought, 'I wish I had more time,' read the great principles of this book. And then I dare you to do what Rory does- live them.' Jon Acuff, New York Timesbestselling author of Start andQuitter 'Procrastinate on Purposewill alter the way the professional world thinks about time - I've never read anything like it. Useful, unique, and relevant . . . this is an absolute must-read for every leader.' Sue Schick, CEO of UnitedHealthcare of Pennsylvania and Delaware 'This book is a game-changer.' Jon Gordon, bestselling author of The Energy Busand The Carpenter 'Every once in a while a book comes along that completely shifts the way an entire generation thinks about a specific topic. When it comes to time management and productivity, Procrastinate on Purposemay be the one!' Andy Andrews, New York Timesbestselling author of The Traveler's Giftand The Noticer
