Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1118835522
Total Pages : 304 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5 by : Judith A. Muschla

Download or read book Teaching the Common Core Math Standards with Hands-On Activities, Grades 3-5 written by Judith A. Muschla and published by John Wiley & Sons. This book was released on 2014-02-12 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helping teachers prepare elementary students to master the common core math standards 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 3-5 Teaching 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.

Principles and Standards for School Mathematics

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Author :
Publisher :
ISBN 13 : 9780873534840
Total Pages : 20 pages
Book Rating : 4.5/5 (348 download)

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Book Synopsis Principles and Standards for School Mathematics by :

Download or read book Principles and Standards for School Mathematics written by and published by . This book was released on 2000 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easy-to-read summary is an excellent tool for introducing others to the messages contained in Principles and Standards.

Mathematics Learning in Early Childhood

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Publisher : National Academies Press
ISBN 13 : 0309147433
Total Pages : 399 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematics Learning in Early Childhood by : National Research Council

Download or read book Mathematics Learning in Early Childhood written by National Research Council and published by National Academies Press. This book was released on 2009-11-13 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.

The Common Core Mathematics Standards

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Author :
Publisher : Corwin Press
ISBN 13 : 1452284148
Total Pages : 160 pages
Book Rating : 4.4/5 (522 download)

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Book Synopsis The Common Core Mathematics Standards by : Ted H. Hull

Download or read book The Common Core Mathematics Standards written by Ted H. Hull and published by Corwin Press. This book was released on 2012-04-17 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transform math instruction with effective CCSS leadership The Common Core State Standards (CCSS) for mathematics describe the "habits of mind" that teachers should develop in their students without which the content standards cannot be successfully implemented. This professional development resource helps principals and math leaders grapple with the changes that must be addressed so that teachers can implement the practices required by the CCSS. Features include: A clear explanation of the CCSS for Mathematical Practice Techniques to help leadership teams collaboratively implement and maintain the new standards A proficiency matrix with examples of instructional strategies for helping students reach competency in each standard An example of how a fourth-grade classroom might implement the CCSS Readers will find reproducible, pullout tools to help with the change process, including an instructional sequence chart. A comprehensive and easy-to-use resource for teachers, district and school leaders, and mathematics curriculum coordinators, The Common Core Mathematics Standards provides the definitive road map for leading the change necessary to align math instruction with best practices.

Implementing the Common Core State Standards Through Mathematical Problem Solving

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Author :
Publisher : Lawrence Erlbaum Associates
ISBN 13 : 9780873537100
Total Pages : 90 pages
Book Rating : 4.5/5 (371 download)

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Book Synopsis Implementing the Common Core State Standards Through Mathematical Problem Solving by : Theresa J. Gurl

Download or read book Implementing the Common Core State Standards Through Mathematical Problem Solving written by Theresa J. Gurl and published by Lawrence Erlbaum Associates. This book was released on 2012 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Kindergarten

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Author :
Publisher : McGraw-Hill Education
ISBN 13 : 9780021198948
Total Pages : 31 pages
Book Rating : 4.1/5 (989 download)

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Book Synopsis AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Kindergarten by : Access Align, Achieve LLC

Download or read book AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Kindergarten written by Access Align, Achieve LLC and published by McGraw-Hill Education. This book was released on 2011-10-03 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: McGraw-Hill has proudly partnered with Align, Assess, Achieve LLC to distribute The Common Core: Clarifying Expectations for Teachers and Students. These easy-to-read flips books are an indispensable resource for educators seeking to isolate and understand the grade level expectations of the standards. Because each guide's focus is on a single grade (or select range of grades), the roles of classroom teachers are clearly defined, ensuring a more seamless transition to the Common Core. Ten flipbooks unpack the grade appropriate standards for Math content for each grade K-8 and for grades 9-12. The flipbooks also connects the Enduring Understands and Essential Questions for Mathematical Practices to each standards. Each page unpacks the Cluster and grade level specific standards into clear teacher friendly text

The Common Core Mathematics Companion: The Standards Decoded, Grades 6-8

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Author :
Publisher : Corwin Press
ISBN 13 : 1506341659
Total Pages : 463 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis The Common Core Mathematics Companion: The Standards Decoded, Grades 6-8 by : Ruth Harbin Miles

Download or read book The Common Core Mathematics Companion: The Standards Decoded, Grades 6-8 written by Ruth Harbin Miles and published by Corwin Press. This book was released on 2016-03-23 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Common Core Mathematics Companion 6-8 offers a practical guide for implementing the CCSS Math Standards. Teachers will appreciate the misconception alerts and ideas for differentiation." — Jay McTighe, Author and Consultant When it comes to math, standards-aligned is achievement-aligned… In the short time since The Common Core Mathematics Companions, Grades K-2 and 3-5 burst on the scene, they have been lauded as the best resources for making critical math ideas easy to teach. With this brand-new 6-8 volume, middle school math success is at your fingertips. Page by page, the authors lay out the pieces to a cutting-edge curriculum, helping you to: Get the inside scoop on which standards connect, what key vocabulary means, and time-saving tables showing where to focus instruction for each grade Write curriculum for: ratios and proportional relationships, the number system, expressions and equations, functions, geometry, and statistics & probability Use the What to Teach pages to deliver powerful standards-based lessons Learn effective techniques to create an environment where all students can experience math break-throughs Incorporate the Standards for Mathematical Practice to improve students’ ability to problem solve, construct viable arguments, use tools strategically, attend to precision, and more The Common Core Mathematics Companion, Grades 6–8 has what every middle school needs to provide students with the foundation for the concepts and skills they will be expected to know in grade 9–12. Ruth Harbin Miles is a mathematics coach, with special expertise in developing teachers’ content knowledge and strategies for engaging students to achieve high mathematics standards. A serving member on the Board of Directors for the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics, Ruth is a co-author with Linda Gojak of The Common Core Mathematics Companions, K–2 and 3–5 (Corwin). Lois Williams, Ed.D., who taught mathematics in grades K–8 for 20 years, is currently an adjunct professor at Mary Baldwin College and an International Fellow with the Charles A. Dana Center, training teachers in the College and Career Readiness Standards She has been honored with a Fulbright Teacher Exchange and the Virginia Middle School Mathematics Teacher of the Year award.

Helping Children Learn Mathematics

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Author :
Publisher : National Academies Press
ISBN 13 : 0309131987
Total Pages : 53 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Helping Children Learn Mathematics by : National Research Council

Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

Your Mathematics Standards Companion, Grades 3-5

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Author :
Publisher : Corwin Press
ISBN 13 : 1544302339
Total Pages : 360 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Your Mathematics Standards Companion, Grades 3-5 by : Linda M. Gojak

Download or read book Your Mathematics Standards Companion, Grades 3-5 written by Linda M. Gojak and published by Corwin Press. This book was released on 2017-05-17 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transforming the standards into learning outcomes just got a lot easier In this expansion of the original popular Common Core Mathematics Companions, you can see in an instant how teaching to your state standards should look and sound in the classroom. Under the premise that math is math, the authors provide a Cross-Referencing Index for states implementing their own specific mathematics standards, showing which of your standards are the same as CCSS-M, which differ and how—and which page number to turn to for standards-based teaching ideas. It’s all here, page by page: The mathematics embedded in each standard for a deeper understanding of the content Examples of what effective teaching and learning look like in the classroom Connected standards within each domain so teachers can better appreciate how they relate Priorities within clusters so teachers know where to focus their time The three components of rigor: conceptual understanding, procedural skills, and applications Vocabulary and suggested materials for each grade-level band with explicit connections to the standards Common student misconceptions around key mathematical ideas with ways to address them Sample lesson plans and lesson planning templates Cross-referenced index listing the standards in the following states, explaining what is unique to the standards of each state Your Mathematics Standards Companion is your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.

Common Core Mathematics Standards and Implementing Digital Technologies

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Author :
Publisher : IGI Global
ISBN 13 : 1466640871
Total Pages : 448 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Common Core Mathematics Standards and Implementing Digital Technologies by : Polly, Drew

Download or read book Common Core Mathematics Standards and Implementing Digital Technologies written by Polly, Drew and published by IGI Global. This book was released on 2013-05-31 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Standards in the American education system are traditionally handled on a state-by-state basis, which can differ significantly from one region of the country to the next. Recently, initiatives proposed at the federal level have attempted to bridge this gap. Common Core Mathematics Standards and Implementing Digital Technologies provides a critical discussion of educational standards in mathematics and how communication technologies can support the implementation of common practices across state lines. Leaders in the fields of mathematics education and educational technology will find an examination of the Common Core State Standards in Mathematics through concrete examples, current research, and best practices for teaching all students regardless of grade level or regional location. This book is part of the Advances in Educational Technologies and Instructional Design series collection.

Your Mathematics Standards Companion, Grades 6-8

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Author :
Publisher : Corwin Press
ISBN 13 : 1544304870
Total Pages : 336 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Your Mathematics Standards Companion, Grades 6-8 by : Ruth Harbin Miles

Download or read book Your Mathematics Standards Companion, Grades 6-8 written by Ruth Harbin Miles and published by Corwin Press. This book was released on 2017-05-25 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transforming the standards into learning outcomes just got a lot easier In this resource, you can see in an instant how teaching to your state standards should look and sound in the classroom. Under the premise that math is math, the authors provide a Cross-Referencing Index for states implementing their own specific mathematics standards, allowing you to see and understand which page number to turn to for standards-based teaching ideas. It’s all here, page by page: Get the inside scoop on which standards connect, what key vocabulary means, and time-saving tables showing where to focus instruction for each grade Write curriculum for: ratios and proportional relationships, the number system, expressions and equations, functions, geometry, and statistics & probability Use the What to Teach pages to deliver powerful standards-based lessons Learn effective techniques to create an environment where all students can experience math break-throughs Incorporate the Standards for Mathematical Practice to improve students’ ability to problem solve, construct viable arguments, use tools strategically, attend to precision, and more Cross-referenced index listing the standards in the following states, explaining what is unique to the standards of each state Your Mathematics Standards Companion is your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.

Using the Common Core State Standards for Mathematics with Gifted and Advanced Learners

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Author :
Publisher : Using the Common Core State St
ISBN 13 : 9781593639945
Total Pages : 0 pages
Book Rating : 4.6/5 (399 download)

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Book Synopsis Using the Common Core State Standards for Mathematics with Gifted and Advanced Learners by : Susan K. Johnsen

Download or read book Using the Common Core State Standards for Mathematics with Gifted and Advanced Learners written by Susan K. Johnsen and published by Using the Common Core State St. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the Common Core State Standards for Mathematics With Gifted and Advanced Learners provides teachers and administrators examples and strategies to implement the new Common Core State Standards (CCSS) with advanced learners at all stages of development in K-12 schools. The book describes--and demonstrates with specific examples from the CCSS--what effective differentiated activities in mathematics look like for top learners. It shares how educators can provide rigor within the new standards to allow students to demonstrate higher level thinking, reasoning, problem solving, passion, and inventiveness in mathematics. By doing so, students will develop the skills, habits of mind, and attitudes toward learning needed to reach high levels of competency and creative production in mathematics fields.

AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Grade 4

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Author :
Publisher : McGraw-Hill Education
ISBN 13 : 9780021198986
Total Pages : 37 pages
Book Rating : 4.1/5 (989 download)

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Book Synopsis AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Grade 4 by : Access Align, Achieve LLC

Download or read book AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Grade 4 written by Access Align, Achieve LLC and published by McGraw-Hill Education. This book was released on 2011-10-04 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: McGraw-Hill has proudly partnered with Align, Assess, Achieve LLC to distribute The Common Core: Clarifying Expectations for Teachers and Students. These easy-to-read flips books are an indispensable resource for educators seeking to isolate and understand the grade level expectations of the standards. Because each guide's focus is on a single grade (or select range of grades), the roles of classroom teachers are clearly defined, ensuring a more seamless transition to the Common Core. Ten flipbooks unpack the grade appropriate standards for Math content for each grade K-8 and for grades 9-12. The flipbooks also connects the Enduring Understands and Essential Questions for Mathematical Practices to each standards. Each page unpacks the Cluster and grade level specific standards into clear teacher friendly text

AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Grade 5

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Author :
Publisher : McGraw-Hill Education
ISBN 13 : 9780021198993
Total Pages : 38 pages
Book Rating : 4.1/5 (989 download)

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Book Synopsis AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Grade 5 by : Access Align, Achieve LLC

Download or read book AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Grade 5 written by Access Align, Achieve LLC and published by McGraw-Hill Education. This book was released on 2011-10-04 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: McGraw-Hill has proudly partnered with Align, Assess, Achieve LLC to distribute The Common Core: Clarifying Expectations for Teachers and Students. These easy-to-read flips books are an indispensable resource for educators seeking to isolate and understand the grade level expectations of the standards. Because each guide's focus is on a single grade (or select range of grades), the roles of classroom teachers are clearly defined, ensuring a more seamless transition to the Common Core. Ten flipbooks unpack the grade appropriate standards for Math content for each grade K-8 and for grades 9-12. The flipbooks also connects the Enduring Understands and Essential Questions for Mathematical Practices to each standards. Each page unpacks the Cluster and grade level specific standards into clear teacher friendly text

AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Grade 6

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Author :
Publisher : McGraw-Hill Education
ISBN 13 : 9780076628988
Total Pages : 45 pages
Book Rating : 4.6/5 (289 download)

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Book Synopsis AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Grade 6 by : Access Align, Achieve LLC

Download or read book AAA The Common Core: Clarifying Expectations for Teachers and Students. Math, Grade 6 written by Access Align, Achieve LLC and published by McGraw-Hill Education. This book was released on 2011-10-11 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: McGraw-Hill has proudly partnered with Align, Assess, Achieve LLC to distribute The Common Core: Clarifying Expectations for Teachers and Students. These easy-to-read flips books are an indispensable resource for educators seeking to isolate and understand the grade level expectations of the standards. Because each guide's focus is on a single grade (or select range of grades), the roles of classroom teachers are clearly defined, ensuring a more seamless transition to the Common Core. Ten flipbooks unpack the grade appropriate standards for Math content for each grade K-8 and for grades 9-12. The flipbooks also connects the Enduring Understands and Essential Questions for Mathematical Practices to each standards. Each page unpacks the Cluster and grade level specific standards into clear teacher friendly text

Teaching to the Math Common Core State Standards

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Author :
Publisher :
ISBN 13 : 9789462099616
Total Pages : 234 pages
Book Rating : 4.0/5 (996 download)

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Book Synopsis Teaching to the Math Common Core State Standards by : F. D. Rivera

Download or read book Teaching to the Math Common Core State Standards written by F. D. Rivera and published by . This book was released on 2015 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a methods book for preservice middle level majors and beginning middle school teachers. It takes a very practical approach to learning to teach middle school mathematics in an emerging Age of the Common Core State Standards. The Common Core State Standards in Mathematics (CCSSM) is not meant to be "the" official mathematics curriculum; it was purposefully developed primarily to provide clear learning expectations of mathematics content that are appropriate at every grade level and to help prepare all students to be ready for college and the workplace. A quick glance at the Table of Contents in this book indicates a serious engagement with the recommended mathematics underlying the Grade 5 through Grade 8 and (traditional pathway) Algebra I portions of the CCSSM first, with issues in content-practice assessment, learning, teaching, and classroom management pursued next and in that order. In this book we explore what it means to teach to the CCSSM within an alignment mindset involving content-practice learning, teaching, and assessment. The Common Core state content standards, which pertain to mathematical knowledge, skills, and applications, have been carefully crafted so that they are teachable, learnable, coherent, fewer, clearer, and higher. The practice standards, which refer to institutionally valued mathematical actions, processes, and habits, have been conceptualized in ways that will hopefully encourage all middle school students to engage with the content standards more deeply than merely acquiring mathematical knowledge by rote and imitation. Thus, in the CCSSM, proficiency in content alone is not sufficient, and so does practice without content, which is limited. Content and practice are both equally important and, thus, must come together in teaching, learning, and assessment in order to support authentic mathematical understanding. This blended multisourced text is a "getting smart" book. It prepares preservice middle level majors and beginning middle school teachers to work within the realities of accountable pedagogy and to develop a proactive disposition that is capable of supporting all middle school students in order for them to experience growth in mathematical understanding that is necessary for high school and beyond, including future careers.

The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5

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Author :
Publisher : Corwin Press
ISBN 13 : 1483381595
Total Pages : 321 pages
Book Rating : 4.4/5 (833 download)

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Book Synopsis The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5 by : Linda M. Gojak

Download or read book The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5 written by Linda M. Gojak and published by Corwin Press. This book was released on 2015-05-28 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Your user’s guide to the mathematics standards In the 12 short months since the ELA versions of The Common Core Companions, Grades K-2 and 3-5, burst on the scene, they’ve already assisted tens of thousands of teachers with the day-to-day "what you do." Teachers’ one big criticism: what about mathematics? Luckily NCTM past-president Linda Gojak and mathematics coach Ruth Harbin Miles stepped up to the task. The result? That version of the mathematics standards you wish you had. Page by page, The Common Core Mathematics Companions clearly lay out: The mathematics embedded in each standard for a deeper understanding of the content Examples of what effective teaching and learning look like in the classroom Connected standards within each domain so teachers can better appreciate how they relate Priorities within clusters so teachers know where to focus their time The three components of rigor: conceptual understanding, procedural skills, and applications Vocabulary and suggested materials for each grade-level band with explicit connections to the standards Common student misconceptions around key mathematical ideas with ways to address them Don’t spend another minute poring over the mathematics standards. Gojak and Miles have already done the heavy-lifting for you. Focus instead on how to teach them, using The Common Core Mathematics Companion as your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.