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Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.

Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.

The PWN the SAT Math Guide was created to help ambitious, highly motivated kids maximize their SAT math scores. Do you crave a higher score? Are you willing to do a little hard work to achieve it? Good. I knew I liked you.

Read this book from beginning to end, with a pencil in hand and a calculator and an Official SAT Study Guide by your side. When you’re done, you’ll be able to approach the SAT with confidence—very few questions will surprise you, and even fewer will be able to withstand your withering attacks.

Stand tall, intrepid student. Destiny awaits.

Updated for the New SAT

This new edition of the Math Guide has been updated, rather painstakingly, to reflect the realities of the new SAT coming March 2016. This book was not rushed to market to take advantage of interest in the new exam. I took my time, and hopefully I got it right.

Chapters are broken into five major sections: Techniques, Heart of Algebra, Passport to Advanced Math, Problem Solving and Data Analysis, and Additional Topics in Math. Each chapter concludes with a reference list of similar questions from official practice tests.

Practice questions are designated as either “Calculator” or “No calculator.” Students will be forbidden from using their calculators for one whole section of the new SAT.

Emphasis is placed on nimbleness—the ability to approach problems in multiple ways to find the one that works best. Calculator solutions and shortcuts are provided where appropriate.

Join me online

Readers of this book are encouraged to register as Math Guide Owners at the PWN the SAT website. There will be video solutions and other bonus content there. Signing up there will also give me a way to get in touch with you if I make book updates. See details at http://mathguide.pwnthesat.com.

Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.

There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets:

Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understandingScores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.

There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets:

Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understandingScores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. Hands-on Activities for Teaching the Common Core Math Standards is designed to help teachers instruct their students so that they will better understand and apply the skills outlined in the Standards.

This important resource also gives teachers a wealth of tools and activities that can encourage students to think critically, use mathematical reasoning, and employ various problem-solving strategies.

Filled with activities that will help students gain an understanding of math concepts and skills correlated to the Common Core State Math Standards Offers guidance for helping students apply their understanding of math concepts and skills, develop proficiency in calculations, and learn to think abstractly Describes ways to get students to collaborate with other students, utilize technology, communicate ideas about math both orally and in writing, and gain an appreciation of the significance of mathematics to real lifeThis practical and easy-to-use resource will help teachers give students the foundation they need for success in higher mathematics.

Hollywood actress and math whiz Danica McKellar has completely shattered the “math nerd” stereotype. For years, she’s been showing girls how to feel confident and ace their math classes – with style! With Girls Get Curves, she applies her winning techniques to high school geometry, giving readers the tools they need to feel great and totally “get” everything from congruent triangles to theorems, and more. Inside you’ll find:

· Time-saving tips and tricks for homework and tests

· Illuminating practice problems (and proofs!) with detailed solutions

· Totally relatable real-world examples

· True stories from Danica’s own life as an actress and math student

· A Troubleshooting Guide, for getting unstuck during even the trickiest proofs!

With Danica as a coach, girls everywhere can stop hiding from their homework and watch their scores rise!

The Common Core Connections series provides teachers with a skill assessment and analysis to help determine individualized instruction needs. Focused, comprehensive practice pages and self-assessments guide students to reflection and exploration for deeper learning! Standards correlations are printed on each page to make planning and documentation simple. This series is an ideal resource for differentiation and remediation. Each 96-page book includes a skill assessment, assessment analysis, Common Core State Standards Alignment Matrix, and answer key.

A critical read for teachers and parents who want to improve children’s mathematics learning, What’s Math Got to Do with It? is “an inspiring resource” (Publishers Weekly). Featuring all the important advice and suggestions in the original edition of What’s Math Got to Do with It?, this revised edition is now updated with new research on the brain and mathematics that is revolutionizing scientists’ understanding of learning and potential.

As always Jo Boaler presents research findings through practical ideas that can be used in classrooms and homes. The new What’s Math Got to Do with It? prepares teachers and parents for the Common Core, shares Boaler’s work on ways to teach mathematics for a “growth mindset,” and includes a range of advice to inspire teachers and parents to give their students the best mathematical experience possible.

A pioneering educator, Mighton realized several years ago that children were failing math because they had come to believe they were not good at it. Once students lost confidence in their math skills and fell behind, it was very difficult for them to catch up, particularly in the classroom. He knew this from experience, because he had once failed math himself.

Using the premise that anyone can learn math and anyone can teach it, Mighton's unique teaching method isolates and describes concepts so clearly that students of all skill levels can understand them. Rather than fearing failure, students learn from and build on their own successes and gain the confidence and self-esteem they need to be inspired to learn. Mighton's methods, set forth in The Myth of Ability and implemented in hundreds of Canadian schools, have had astonishing results: Not only have they helped children overcome their fear of math, but the resulting confidence has led to improved reading and motor skills as well.

The Myth of Ability will transform the way teachers and parents look at the teaching of mathematics and, by extension, the entire process of education.

SHE’LL TRY TO SOLVE FIVE QUESTIONS IN THREE HOURS, FOR ONE IMPROBABLE DREAM.

THE DREAM OF REPRESENTING HER COUNTRY, AND BECOMING A MATH OLYMPIAN.

As a small-town girl in Nova Scotia bullied for liking numbers more than boys, and lacking the encouragement of her unsupportive single mother who frowns at her daughter’s unrealistic ambition, Bethany's road to the International Math Olympiad has been marked by numerous challenges.

Through persistence, perseverance, and the support of innovative mentors who inspire her with a love of learning, Bethany confronts these challenges and develops the creativity and confidence to reach her potential.

In training to become a world-champion "mathlete", Bethany discovers the heart of mathematics – a subject that’s not about memorizing formulas, but rather about problem-solving and detecting patterns to uncover truth, as well as learning how to apply the deep and unexpected connections of mathematics to every aspect of her life, including athletics, spirituality, and environmental sustainability.

As Bethany reflects on her long journey and envisions her exciting future, she realizes that she has shattered the misguided stereotype that only boys can excel in math, and discovers a sense of purpose that through mathematics, she can and she will make an extraordinary contribution to society.

This book is an essential resource that will guide you through setting up, creating, and maintaining interactive notebooks for skill retention in the classroom. High-interest and hands-on, interactive notebooks effectively engage students in learning new concepts. Students are encouraged to personalize interactive notebooks to fit their specific learning needs by creating fun, colorful pages for each topic. With this note-taking process, students will learn organization, color coding, summarizing, and other important skills while creating personalized portfolios of their individual learning that they can reference throughout the year.

Spanning grades kindergarten to grade 8, the Interactive Notebooks series focuses on grade-specific math, language arts, or science skills. Aligned to meet current state standards, every 96-page book in this series offers lesson plans to keep the process focused. Reproducibles are included to create notebook pages on a variety of topics, making this series a fun, one-of-a-kind learning experience.

Is it possible that the answer to becoming a more efficient and effective thinker is learning how to forget? Yes! Mike Byster will show you how mastering this extraordinary technique—forgetting unnecessary information, sifting through brain clutter, and focusing on only important nuggets of data—will change the quality of your work and life balance forever.

Using the six tools in The Power of Forgetting, you’ll learn how to be a more agile thinker and productive individual. You will overcome the staggering volume of daily distractions that lead to to brain fog, an inability to concentrate, lack of creativity, stress, anxiety, nervousness, angst, worry, dread, and even depression. By training your brain with Byster’s exclusive quizzes and games, you’ll develop the critical skills to become more successful in all that you do, each and every day.

Lawrence Weinstein and John Adam present an eclectic array of estimation problems that range from devilishly simple to quite sophisticated and from serious real-world concerns to downright silly ones. How long would it take a running faucet to fill the inverted dome of the Capitol? What is the total length of all the pickles consumed in the US in one year? What are the relative merits of internal-combustion and electric cars, of coal and nuclear energy? The problems are marvelously diverse, yet the skills to solve them are the same. The authors show how easy it is to derive useful ballpark estimates by breaking complex problems into simpler, more manageable ones--and how there can be many paths to the right answer. The book is written in a question-and-answer format with lots of hints along the way. It includes a handy appendix summarizing the few formulas and basic science concepts needed, and its small size and French-fold design make it conveniently portable. Illustrated with humorous pen-and-ink sketches, Guesstimation will delight popular-math enthusiasts and is ideal for the classroom.

Sally Moomaw, EdD, has spent much of her career researching and teaching STEM education. She is an assistant professor at the University of Cincinnati and the author of several early education books.

Math is a difficult and abstract subject for many students, yet teachers need to make sure their students comprehend basic math concepts. This engaging activity book is a resource teachers can use to give students concrete understanding of the math behind the questions on most standardized tests, and includes information that will give students a firm grounding to work with more advanced math concepts.

Contains over 100 activities that address topics like number sense, geometry, computation, problem solving, and logical thinking. Includes projects and activities that are correlated to National Math Education Standards Activities are presented in order of difficulty and address different learning stylesMath Wise! is a key resource for teachers who want to teach their students the fundamentals that drive math problems.

These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math.

This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.

Each play includes speakers for three different grade levels of readability: 4th grade and lower, 5th-6th grade, and 7th-8th grade. Concepts are presented so that they are fluid among these grade levels. Taking a cross-curricular approach, the scripts reinforce key math concepts and standards-based math skills taught in the middle grades, such as order of operations, fractions, inequalities, positive and negative numbers, and graphing on a coordinate plane. Each play includes extended activities that will help the teacher incorporate the math concept into the classroom.

The Common Core State Standards for Mathematics challenges students to become mathematical thinkers, not just mathematical “doers.” This resource will be invaluable for pre- and inservice teachers as they prepare themselves to understand and teach algebra with a deep level of understanding.

“Uncomplicating Algebra is an excellent resource for teachers responsible for the mathematical education of K–8 students. It is also a valuable tool for the training of preservice teachers of elementary and middle school mathematics.”

—Carole Greenes, associate vice provost for STEM education, director of the Practice Research and Innovation in Mathematics Education (PRIME) Center, professor of mathematics education, Arizona State University

“The current climate in North America places a major emphasis on standards, including the Common Core State Standards for Mathematics in the U.S. In many cases, teachers are being asked to teach content with which they themselves struggle. In this book, Dr. Small masterfully breaks down the big ideas of algebraic thinking to assist teachers, math coaches, and preservice teachers—helping them to deepen their own understanding of the mathematics they teach. She describes common error patterns and examines algebraic reasoning from a developmental viewpoint, connecting the dots from kindergarten through grade 8. The book is clearly written, loaded with specific examples, and very timely. I recommend it strongly as a ‘must-read’ for all who are seeking to broaden their understanding of algebra and how to effectively teach this important content area to children.”

—Daniel J. Brahier, director, Science and Math Education in ACTION, professor of mathematics education, School of Teaching and Learning, Bowling Green State University

You know you love your child. But how can you make sure your child knows it?

The #1 New York Times bestselling The 5 Love Languages® has helped millions of couples learn the secret to building a love that lasts. Now discover how to speak your child’s love language in a way that he or she understands. Dr. Gary Chapman and Dr. Ross Campbell help you:

Discover your child’s love languageAssist your child in successful learningUse the love languages to correct and discipline more effectivelyBuild a foundation of unconditional love for your childPlus: Find dozens of tips for practical ways to speak your child’s love language.

Discover your child's primary language—then speak it—and you will be well on your way to a stronger relationship with your flourishing child.

For a free online study guide, visit 5lovelanguages.com.

Improve students’ math skills in the classroom while also providing a way to continue the learning process at home. Weekly Practice: Math for grade 4 allows you to reinforce math topics at school and at home by offering 40 weeks of standards-based activities and skill review. The unique layout and engaging exercises keep students interested as they build concept knowledge and essential skills. Reproducible at-home activities and flash cards are also included to encourage the home-to-school connection that’s essential for student success.

Weekly Practice is the perfect time-saving resource for creating standards-aligned homework packets and keeping students’ skills sharp all year long. The Weekly Practice series for kindergarten to grade 5 provides 40 weeks of comprehensive skill review. Each 192-page supplemental workbook focuses on critical skills and concepts that meet the standards for language arts or math. Designed to help students achieve subject mastery, each book includes four days of practice activities, weekly off-the-page activities, Common Core State Standards alignment matrix, flash cards, and an answer key. Weekly Practice offers an effortless way to integrate language arts or math practice into daily classroom instruction.

Now published as a portable, learning, reference and subject revision guide, students, teachers and hobbyists can have their own low-cost portable version as an eBook.

For easy reading, a comprehensive list of hundreds of topics each with a graphic image and explanatory text act as a useful exam revision reminder or reference tool for professionals.

The accompanying software which brings all these images to life can be downloaded at no extra charge thereby providing an additional computer based interactive learning resource as an easy and enjoyable way to study.

Unlock the accompanying software with your eBook receipt.

Chapters (250 topics): - Mathematics Tools, Number Systems, Number Conversion, Number Types, Compound Measures, Roots, Angles and Parallels, Triangle Ratios, Triangle Angles, Percentages, Ratios, Fractions, Vectors, Geometry, Circle Angles, Area, Surface Area and Symmetry, Volume, Laws, Algebra 0., Algebra 1., Algebra 2., Mathematical Rules, Powers and Indices, Simplifying, Linear Equations, Graphing, Slope and Translation, Curves and Angle Conversion, Personal Finance, Data Analysis, Binary Numbers, Binary Arithmetic, Additional Notes.

With the common core math curriculum being adopted by forty-three states, it is imperative that students learn to master those key math standards. Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5 is the only book currently available that provides activities directly correlated to the new core curriculum for math. This text assists teachers with instructing the material and allows students to practice the concepts through use of the grade-appropriate activities included.

Students learn in different ways, and Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5 acknowledges that fact through the inclusion of suggestions for variations and extensions of each concept to be used for students with different abilities and learning styles. The activities and lessons are as diverse as the students in your classroom. Inside Teaching with Common Core Math Standards With Hands-On Activities Grades 3-5, you will find:

Clear instructions to help you cover the skills and concepts for the new math core curriculum Engaging activities that enforce each core math standard for your students Various suggestions for ways to instruct the concepts to reach the diverse learning styles of your students Complete coverage of mathematical calculations, mathematical reasoning, and problem-solving strategies appropriate for grades 3-5Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5 prepares students to achieve success in the important area of mathematics. As your students gain an understanding of the common core standards, they will build confidence in their ability to grasp and manipulate mathematical concepts as they move forward to the next level.

Solving Word Problems is one of the biggest hurdle that kids face in Algebra. A bit of imagination is required to understand and solve these type of problems along with the calculations.

This book breaks simple word problems using graphics thus helping the kids to visualize and understand the word problems. It develops the imaginative thinking required to solve these problems from an early level. This will help the kids to solve difficult problems as they will learn to imagine, analyze and break the problem into small parts which gives a better understanding on how to solve these type of problems.It explains which areas of maths dyslexics tend to have particular difficulty with, assesses current teaching philosophies and methods, describes a framework of general learning principles that allow dyslexics to make progress in maths, and outlines a number of specific and effective teaching recommendations.

The book helps teachers at primary and secondary levels to better understand the maths performance of dyslexics and gives them an overview of the ways in which dyslexics can best be supported in all aspects of maths learning.

• First to provide the complete guide to lead one through this highly demanding knowledge requirement with full past-years’ exam questions support

• Exact exam−compatibility to answers

• Exact and accurate definitions

• most efficient method of learning, hence saves time

• very advanced trade book

• Complete edition and concise edition eBooks available

This volume contains the proceedings of Work Group 4: Theories of Mathematics, a subgroup of the Seventh International Congress on Mathematical Education held at Université Laval in Québec. Bringing together multiple perspectives on mathematical thinking, this volume presents elaborations on principles reflecting the progress made in the field over the past 20 years and represents starting points for understanding mathematical learning today. This volume will be of importance to educational researchers, math educators, graduate students of mathematical learning, and anyone interested in the enterprise of improving mathematical learning worldwide.

Many students struggle with fractions and must understand them before learning higher-level math. Veteran educator David B. Spangler describes powerful diagnostic methods for error analysis that pinpoint specific student misconceptions and supplies specific intervention strategies and activities for each error pattern. Aligned with NCTM and Common Core State Standards, the research-based, targeted interventions for each error pattern promoted teaching for conceptual understanding. Practical materials include:

Reproducibles for diagnostic tests Practice pages for exercises keyed to the diagnostic tests and error patterns Teacher resources for hands-on activities, game sheets and pieces, and more• enable accurate, complete and independent self education

• holistic question answering techniques

• exact definitions

• latest mark schemes

• most updated exam reports

• complete edition and concise edition eBooks available

The Common Core Connections series provides teachers with a skill assessment and analysis to help determine individualized instruction needs. Focused, comprehensive practice pages and self-assessments guide students to reflection and exploration for deeper learning! Standards correlations are printed on each page to make planning and documentation simple. This series is an ideal resource for differentiation and remediation. Each 96-page book includes a skill assessment, assessment analysis, Common Core State Standards Alignment Matrix, and answer key.

The imperfect numerical notation and scarcity of suitable writing materials in ancient times are presumed to have given rise to need for devices of mechanical calculation. While the definite origin of the abacus is obscure, there is some reason for believing that its earliest form reckoning table covered with sand or fine dust, in which figures were drawn with a stylus, to be erased with the figure when necessary. Though the Abacus is an older tool for calculation it still is used today in Japan taking on a different name called Soroban.

Though the Japanese Abacus or Soroban may appear mysterious or even primitive to those raised in the age of pocket calculators and desktop computers, this intriguing tool is capable of amazing speed and accuracy. It is still widely used throughout the shops and markets of Asia, and its popularity shows no sign of decline. Here for the first time in English is a complete explanation of how to use the abacus.

Rigor: The Common Core has made it policy—and this first-of-its-kind guide takes math teachers and leaders through the process of making it reality. Using the Proficiency Matrix as a framework, the authors offer proven strategies and practical tools for successful implementation of the CCSS mathematical practices—with rigor as a central objective. You’ll learn how to

Define rigor in the context of each mathematical practice Identify and overcome potential issues, including differentiating instruction and using data Relate specific roles and goals for all stakeholders Use assessment tools to guide work and monitor progressFor each of more than 120 visuals, the text identifies the key math concept and the Common Core State Standard being addressed and then provides teachers with:

Mathematical background and context.Questions to use with students to lead the instructional conversation.Expected answers and explanations of why each question is important.Follow-up extensions to solidify and assess student understanding.This book will be useful to a broad range of teachers who will find new ways to clarify concepts that students find difficult. It can be used as a resource to prepare teachers for the higher mathematical thinking requirements of the CCSS Mathematical Practices. It will also be an invaluable resource for teachers working with students with low reading ability, including English language learners and special education students.

“This book provides a way for both teachers and students to get used to talking about mathematics in nonthreatening, open-ended ways. The author’s friendly explanations of the mathematical ideas the pictures are intended to surface give teachers who are less confident about the conceptual aspects of mathematics the support they need to facilitate less-scripted mathematical discourse with their students.”

—Lucy West, education consultant

“A must for any educator who is serious about reaching more students more often and achieving more positive results.”

—Resources for the Mathematics Educator

“A valuable book for mathematics teachers, teacher educators, and faculty involved in differentiated instruction.”

—Choice

“A great resource.”

—Mathematics Teaching in the Middle School

“I highly recommend this user-friendly resource for all mathematics teachers.”

—Teaching Children Mathematics

Content is grouped into 13 broad topics:Manipulatives, Aids, and Concrete Materials Attitudes, Beliefs, and Culture Chance and Data Assessment and Learning Theory Early Number Leading to Place Value Geometry Measurement Number facts and Basic Operations Whole Number Computation Fractions, Decimals, Ratio, and Proportion Number Systems, Principles, and Number Sense Pattern Problem Solving

The core audience for this book includes practicing elementary teachers, teachers-in-training, and mathematics teacher educators. Parents and carers interested in detailed explanations for methods of mathematics teaching used in modern elementary classrooms would also benefit from having access to this resource.

Early Numeracy is admirably grounded in international research and well-established theory, characteristics that are much sought after in the current data driven educational environment.

Like many others, I was drawn to Math Recovery after reading the first edition of Early Numeracy. This second edition is a treasure - it is exciting to consider the impact it will have on children and teachers, and to the growth of the Math Recovery program' - Audrey Murray, Lead Teacher, Midwest Math Recovery Training Center, Minneapolis

This text has been fully updated to include developments and refinements brought about by widespread international application of the assessment tools in the Mathematics Recovery Programme. The book will help practitioners to identify and provide detailed analyses of all children but especially those who are able and those who underachieve in early numeracy. It will enable teachers, learning support personnel, numeracy consultants and educational psychologists to advise colleagues and parents on children's number knowledge and strategies for early numeracy.

The Mathematics Recovery Programme has been successfully applied in Australia, the United Kingdom and Ireland, the United States and Canada, both in specialist interventions and classroom settings. The revised version shows how familiarisation with, and understanding of, the diagnostic assessment tools has allowed teachers to become more knowledgeable in understanding children's difficulties and misconceptions, and more skilled and confident in planning programmes of intervention and monitoring the children's progress.

This new edition includes:

- Integrated frameworks of useful tasks for assessing children's number knowledge and strategies;

- Four separate and revised diagnostic assessment interviews;

- Assessments for addition and subtraction strategies, Base Ten Arithmetical strategies, Early Grouping strategies, and Advanced Grouping strategies in the four operations;

- How the assessment process has impacted significantly on teachers' professional development and contributed to the raising of standards in early numeracy.