Uncomplicating Algebra to Meet Common Core Standards in Math K 8

Author: Marian Small
Publisher: Teachers College Press
ISBN: 0807755176
Format: PDF, Docs
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In the second book in the Uncomplicating Mathematics Series, professional developer Marian Small shows teachers how to uncomplicate the teaching of algebra by focusing on the most important ideas that students need to grasp. Organized by grade level around the Common Core State Standards for Mathematics, Small shares approaches that will lead to a deeper and richer understanding of algebra for both teachers and students. The book opens with a clear discussion of algebraic thinking and current requirements for algebraic understanding within standards-based learning environments. The book then launches with Kindergarten, where the first relevant standard is found in the operations and algebraic thinking domain, and ends with Grade 8, where the focus is on working with linear equations and functions. In each section the relevant standard is presented, followed by a discussion of important underlying ideas associated with that standard, as well as thoughtful, concept-based questions that can be used for classroom instruction, practice, or assessment. 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.

Building Proportional Reasoning Across Grades and Math Strands K 8

Author: Marian Small
Publisher: Teachers College Press
ISBN: 0807756601
Format: PDF, Mobi
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Although proportional reasoning is not formally introduced as a topic in the Common Core and other mathematics curricula until 6th grade, introducing its fundamental ideas in the early grades helps students develop essential skills in ratios, percentages, and other proportional representations when they reach the upper grades. The author takes this complex subject and crafts examples and questions that help teachers see the larger purpose in teaching concepts, such as unitizing, and how that understanding is essential for more complex ideas, such as ratios. Teachers and vertical teams can see how the concepts can build year after year. This new resource by well-known professional developer Marian Small suggests questions that are both interesting for students and useful for providing diagnostic information to teachers. Chapters are organized by grade level (K-8) around the Common Core State Standards for Mathematics to help teachers use the resource more easily.

Teaching Mathematical Thinking

Author: Marian Small
Publisher: Teachers College Press
ISBN: 0807758566
Format: PDF, ePub, Docs
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This new resource by math education expert Marian Small helps schools and districts to refine their teaching of standards-based mathematical practices. Small devotes a chapter to each of the eight standards of practice and includes a discussion of what each standard looks like in grades K-2, 3-5, and 6-8. Specific attention is given to helping students make sense of problems and persevere in solving them (Standard 1) and encouraging students to create viable mathematical arguments and to effectively and respectfully critique the reasoning of others (Standard 3). The author also discusses how to formatively assess student performance for each practice standard. To provide additional support to U.S. teachers in their instructional planning, this resource includes attention to the Canadian math processes of visualization and mental math and estimation.

Good Questions

Author: Marian Small
Publisher: Teachers College Press
ISBN: 080775854X
Format: PDF, Docs
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This bestselling resource provides tools to help experienced and novice teachers effectively and efficiently differentiate mathematics instruction in grades K-8. This third edition includes key changes that will make it easier for teachers to use the tools in all quality state standards environments, as well as with many new classroom examples for each grade band.

More Good Questions

Author: Marian Small
Publisher: Teachers College Press
ISBN: 0807773026
Format: PDF, Docs
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We know that Differentiated Instruction helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open questions and Parallel tasks. Showing teachers how to get started and become expert with these strategies, this book also demonstrates how to use more inclusive learning conversations to promote broader student participation. Strategies and examples are organized around Big Ideas within the National Council of Teachers of Mathematics (NCTM) content strands. With particular emphasis on Algebra, chapters also address Number and Operations, Geometry, Measurement, and Data Analysis and Probability, with examples included for Pre-Calculus.

Common Core Standards for Elementary Grades K 2 Math English Language Arts

Author: Amber Evenson
Publisher: ASCD
ISBN: 1416615644
Format: PDF
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Smart implementation of the Common Core State Standards requires both an overall understanding of the standards and a grasp of their implications for planning, teaching, and learning. This Quick-Start Guide provides a succinct, all-in-one look at * The content, structure, terminology, and emphases of the Common Core standards for mathematics and English language arts and literacy in the lower elementary grades. * The meaning of the individual standards within each of the four ELA/literacy strands and five math domains, with an emphasis on areas that represent the most significant changes to business as usual. * How the standards connect across and within strands, domains, and grade levels to develop the foundational language arts, literacy, and mathematics understanding that will support a lifetime of successful learning. Here, teachers of grades K-2 and elementary school leaders will find information they need to begin adapting their practices to help all students master the new and challenging material contained in the standards. A practical lesson planning process to use with the Common Core, based on Classroom Instruction That Works, 2nd Ed., is included, along with six sample lessons. LEARN THE ESSENTIALS OF THE COMMON CORE The grade-level and subject-specific Quick-Start Guides in the Understanding the Common Core Standards series, edited by John Kendall, are designed to help school leaders and school staffs turn Common Core standards into coherent, content-rich curriculum and effective, classroom-level lessons.

Uncomplicating Fractions to Meet Common Core Standards in Math K 7

Author: Marian Small
Publisher: Teachers College Press
ISBN: 0807773034
Format: PDF, ePub, Mobi
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The Common Core State Standards for Mathematics challenges students to become mathematical thinkers, not just mathematical “doers.” In her new resource, professional developer Marian Small shows teachers how to uncomplicate the teaching of fractions by focusing on the most important fraction ideas that students need to grasp. The book is organized by grade level beginning with Grade 1, where the first relevant standard is found in the geometry domain, and ending with Grade 7, where the focus is on operations with rational numbers and proportional thinking. In each section the relevant standard is presented, followed by a discussion of important underlying ideas associated with that standard, as well as some thoughtful, concept-based questions that can be used for classroom instruction, practice, or assessment. Underlying ideas include: Background for the mathematics of the standard. Suggestions for appropriate representations for those specific mathematical ideas, including equations, drawings, and manipulatives. Suggestions for explaining ideas to students. Cautions about misconceptions or situations to avoid.This accessible book provides math teachers with support for differentiated instruction. Math coaches can use it to assist teachers with their transition to the Common Core State Standards. All teachers will find it helpful to see the mathematical fraction learning that precedes and follows the grades that they teach. It is also an excellent text for preservice teachers as they prepare themselves and their students to understand and teach math with a deep level of understanding. “Uncomplicating Fractions is a great resource that helps us understand how to teach and assess student learning of fractions. Marian Small truly ‘uncomplicates’ fractions by providing a resource that is practical and a must-have for all math coaches andevery K–7 teacher!” —Ruth Harbin Miles, board of directors, National Council of Teachers of Mathematics, Mary Baldwin College instructor “At all levels, this book advocates conceptual as well as procedural understandings such as why rational numbers must have repeating or terminating decimal representations. Every section has good questions to ask and grade-level summaries that provide excellent tools to help teachers recognize new ideas introduced at each grade level. I recommend this book for everyone teaching fractions.” —Carol Findell, Professor Emeritus, Mathematics Education, Boston University Marian Small is the former Dean of Education at the University of New Brunswick and longtime professor of mathematics education.

Algebra Connections

Author: Ira J. Papick
Publisher: Prentice Hall
ISBN: 9780131449282
Format: PDF, ePub
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Strong mathematics performance in the middle grades is more important than ever—and teachers entering the field need to prepare for this endeavor in new and innovative ways. This new approach introduces some basic concepts of number theory and modern algebra that underlie middle grade arithmetic and algebra, with a focus on collaborative learning combined with extensive in-class and out-of-class assignments.Gives both pre-service and in-service teachers a fundamental understanding of the key mathematical ideas that they will be teaching, so that in turn they can help their students learn important mathematics. Directly connects college-level abstract algebra and number theory to standards-based middle grade mathematics curricula. Gives specific examples from middle-grade curricular materials to show readers the direct connections between the mathematics they are learning and the mathematics they will be teaching. Focuses on the mathematics in new reform materials. Offers Classroom Problems and Classroom Discussions that focus on discovery and collaborative learning.A useful reference for teachers of middle-grades mathematics.

Teaching and Learning Algebraic Thinking with 5 to 12 Year Olds

Author: Carolyn Kieran
Publisher: Springer
ISBN: 3319683519
Format: PDF, ePub, Mobi
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This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.