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Problem-solving skills are critical to students' success in mathematics, but the techniques can't be caught; they must be taught. Based on the premise that educators must take a deliberate approach to the teaching of problem-solving skills, this book helps teachers engage students in the process. Problem Solving in Mathematics, Grades 3-6 presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. Each chapter demonstrates how teachers can Use the strategies with students at different grade levels Incorporate these strategies into a mathematics program Apply each strategy to real-life situations Make each strategy an integral part of students' thinking processes With helpful teaching notes, sample problems for students that fit into any mathematics curriculum, and step-by-step solutions to sample problems, this book is perfect for teachers who want their students to succeed in mathematics! Book jacket.
Offers practical, classroom-tested ideas for helping students learn mathematics through problem solving.
Mathematics educators have long recognised the importance of helping students to develop problem-solving skills. More recently, they have searched for the best ways to provide their students with the knowledge encompassed in the Common Core State Standards (CCSS). This volume is one in a series from NCTM that equips classroom teachers with targeted, highly effective problems for achieving both goals at once. The 44 problems and tasks for students in this book are organised into the major areas of the high school Common Core: algebra, functions, geometry, statistics and probability, and number and quantity. Examples of modelling, the other main CCSS area, are incorporated throughout. Every domain that is required of all mathematics students is represented. For each task, teachers will find a rich, engaging problem or set of problems to use as a lesson starting point. An accompanying discussion ties these tasks to the specific Common Core domains and clusters they help to explore. Follow-up sections highlight the relevant CCSS Standards for Mathematical Practice that students will engage in as they work on these problems. This book provides high school mathematics teachers with dozens of problems they can use as is, adapt for their classrooms, or be inspired by while creating related problems on other topics. For every mathematics educator, the books in this series will help to illuminate a crucial link between problem solving and the Common Core State Standards.
"Demonstrates problem solving strategies with solutions and teaching notes and allows the teacher to create a collection of problems to fit a particular grade level."-Janice L. Richardson, Associate Professor and Education Coordinator, Department of MathematicsElon UniversityHelp students succeed as problem solvers in and out of the classroom! Problem solving skills are critical to students' success in mathematics, but the techniques can't be caught; they must be taught. Based on the premise that educators must take a deliberate approach to the teaching of problem solving skills, this book helps teachers engage students in the process. Problem Solving in Mathematics, Grades 3-6 stresses the importance of problem solving in mathematics and presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. Each chapter demonstrates how teachers can:Apply the strategies to problems at different grade levels Incorporate these strategies into a mathematics program Understand how each strategy can be applied to real-life situations Make each strategy an integral part of students' thinking processesWith helpful teaching notes, sample problems for students that fit into any mathematics curriculum, and step-by-step solutions to sample problems, this book is perfect for teachers who want their students to succeed in mathematics!
"The authors have provided a unique, strategy-focused resource supported by a wealth of engaging examples that mathematics teachers can readily use to help students develop a more purposeful, systematic, and successful approach to problem solving." —Howard W. Smith, Superintendent Public Schools of the Tarrytowns, Sleepy Hollow, NY "Helps both new and veteran teachers better understand the nature of problem solving as a critical mathematics process. The authors present in very simple terms the strategies that are the backbone of mathematics instruction. This indispensable material is useful at all levels, from basic stages to advanced student work to the development of top problem solvers." —Daniel Jaye, Principal Bergen County Academies, Hackensack, NJ Help students become skilled and confident problem solvers! Demonstrating there is always more than one approach to solving a problem, well-known authors and educators Alfred S. Posamentier and Stephen Krulik present ten basic strategies that are effective for finding solutions to a wide range of mathematics problems. These tried-and-true methods—including working backwards, finding a pattern, adopting a different point of view, solving a simpler analogous problem, and making a visual representation—make problem solving easier, neater, and more understandable for students as well as teachers. Providing numerous sample problems that illustrate how mathematics teachers and specialists can incorporate these techniques into their mathematics curriculum, this updated edition also includes: A variety of new problems that show how to use the strategies References to current NCTM standards Solutions to the problems in each chapter Extensive discussions of the empowering strategies used to solve sample problems The second edition of Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6–12 helps teachers develop students′ creative problem-solving skills for success in and out of school.
NCTM's Process Standards were designed to support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every elementary teacher the opportunity to explore each one of the standards in depth. And with language and examples that don't require prior math training to understand, the series offers friendly, reassuring advice to any teacher preparing to embrace the Process Standards. In the second edition of Introduction to Problem Solving, Susan O'Connell updates her popular and easy-to-use guide. O'Connell eases you into problem solving, giving you an array of entry points for understanding, planning, and teaching; strategies that help students develop mathematical thinking; and a wealth of all-new activities that are modifiable for immediate use with students of all levels. Written by a veteran teacher for teachers of every level of experience, Introduction to Problem Solving fosters a new awareness of the importance of problem solving and highlights ways to implement it without rewriting your curriculum. Best of all, like all the titles in the Math Process Standards Series, Introduction to Problem Solving comes with two powerful tools to help you get started and plan well: online resources with activities customizable to match your lessons and a correlation guide that helps you match mathematical content with the processes it utilizes. If problem solving is a problem you'd like to solve. Or if you're simply looking for new ways to work the problem-solving standards into your curriculum, read, dog-ear, and teach with Introduction to Problem Solving, Second Edition. And if you'd like to learn about any of NCTM's process standards, or if you're looking for new, classroom-tested ways to address them in your math teaching, look no further than Heinemann's Math Process Standards Series. You'll find them explained in the most understandable and practical way: from one teacher to another.
Students get a firm grasp of key problem-solving strategies and meaningful practice in essential number concepts and skills
This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.
Now for grades K-8 with a new kindergarten level and newly revised editions of grades 1 and 2. These new editions of this popular program features: -- lessons that use manipulatives to emphasize hands-on learning at each grade level -- assessment guidelines The program enhances any math text, teaching students to: -- approach problems systematically -- identify various solution strategies -- realize that more than one strategy may be used on a single problem Teacher Sourcebooks feature easy-to-follow strategies, guidelines for multiple uses of the program, extension problems, and evaluation methods. Each Teacher Sourcebook includes blackline masters with problem clusters to reproduce intact or cut into individual problems. Use them as resources for problem-of-the-day, problem-of-the-week, homework activities, or in a problem-solving resource center. Available in Spanish for grades 1-6.
Get ready to take the Math Challenge! Singapore Math Challenge will provide second grade students with skill-building practice based on the leading math program in the world, Singapore Math! Common Core Standards accelerate math expectations for all students, creating a need for challenging supplementary math practice. Singapore Math Challenge is the ideal solution, with problems, puzzles, and brainteasers that strengthen mathematical thinking. Step-by-step strategies are clearly explained for solving problems at varied levels of difficulty. A complete, worked solution is also provided for each problem. -- Singapore Math Challenge includes the tools and practice needed to provide a strong mathematical foundation and ongoing success for your students. The Common Core State Standards cite Singapore math standards as worldwide benchmarks for excellence in mathematics.