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 organised 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.

This book focuses on the most important concepts and skills needed to provide early learners (preK–2) with a strong foundation in mathematics, in ways that are fun for both children and educators! Professional developer Marian Small provides sample activities and lessons, troubleshooting tips, and formative assessments, and much more.

This resource by popular professional developer Marian Small comprehensively addresses different mathematical domains for grades 3–8. Small shows new and veteran teachers how to do three fundamental things well: identify the most important math to assess, construct formative and summative assessments, and provide students with clear and timely feedback.

This resource by popular professional developer Marian Small comprehensively addresses different mathematical domains for grades 3–8. Small shows new and veteran teachers how to do three fundamental things well: identify the most important math to assess, construct formative and summative assessments, and provide students with clear and timely feedback.

Now in its Fourth Edition?with more than 50 new questions and a new chapter on financial literacy?this bestselling resource helps experienced and novice teachers effectively and efficiently differentiate mathematics instruction in grades K–8. Math education expert Marian Small shows teachers how to get started and become expert at using two powerful and universal strategies: Open Questions and Parallel Tasks. This edition is even easier for teachers to use in all quality state standards environments, including direct links to content standards and standards for mathematical practice. Parallel tasks and question examples are provided at each grade band: K–2, 3–5, and 6–8. Along with each example, the text describes how teachers can evoke productive conversations that meet the needs of a broad range of learners.Book Features:New tasks and questions to develop financial literacy.Connection of tasks and questions to standards and mathematical big ideas.About 500 tasks and questions that teachers can adapt or use as-is.Teaching tips and task variations.A template to help teachers build new tasks.“Look-fors” to see student thinking and diagnose difficulties.Guidance for using follow-up questions and math conversations to create a rich math classroom.

Learn how to differentiate math instruction to help all students be successful learners in the secondary mathematics classroom. Featuring 89 new questions, this revised edition uses two powerful and universally applicable strategies—Open Questions and Parallel Tasks—to help teachers differentiate instruction with less difficulty and greater success. This popular book shows teachers how to get started and become expert with these strategies, demonstrating how to use more inclusive learning conversations to promote broader student participation and how to formatively assess understanding. Strategies and examples are organized around Big Ideas and reference common standards. With particular emphasis on algebra, chapters also address number and operations, geometry, measurement including trigonometry, and data analysis and probability. Updated with many new examples and expanded guidelines for teachers to create their own open tasks and questions, More Good Questions, Second Edition is designed to allow students to respond from their own expertise level and to also come together as a math community for the conceptual conversation around a math problem.Book Features:Underscores the rationale for differentiating instruction (DI) with nearly 300 specific examples for grades 6–12 math.Describes easy-to-implement strategies designed to overcome the most common DI problems that teachers encounter.Offers questions and tasks that teachers and coaches can adopt immediately or use as models to create their own, along with scaffolding and consolidating questions.Includes Teaching Tips sidebars and an organizing template at the end of each chapter to help teachers build new tasks and open questions.Shows how to create a more inclusive classroom learning community with mathematical talk that engages participants from all levels.PROFESSIONAL DEVELOPMENT: Visit Marian Small's website onetwoinfinity.ca for in-person and online professional development.

How can teachers move beyond surface-level coverage of math standards to focus on what truly matters for student understanding?This book, co-published with the National Council of Teachers of Mathematics (NCTM), provides a transformative approach to K–8 mathematics instruction. Rather than treating standards as a fixed checklist of skills to be executed, internationally recognized expert Marian Small demonstrates how to treat them as professional texts that require thoughtful interpretation. By uncovering the "big ideas" behind the standards, educators can move beyond surface-level coverage to foster deeper mathematical thinking and lasting student understanding.Drawing on decades of classroom experience, this resource helps teachers translate teacher-facing standards into student-centered learning experiences. Small introduces a framework that shifts the focus from micro-level procedures to macro-level concepts, ensuring that students prioritize reasoning and connections over rote alignment. With examples spanning across grades K–8, the book illustrates how the same standard can be interpreted in multiple ways to shape how students learn and demonstrate their knowledge.This guide also reimagines the role of evaluation through asset-driven assessment. By framing tasks and questions that emphasize what students do know and can explain, teachers can provide more meaningful opportunities for student voice in the math classroom. Whether you are a classroom teacher, coach, or instructional leader, this book offers the tools necessary to design powerful instruction that surfaces conceptual understanding for every learner.Key Features:A Proven Framework: Learn a systematic way to look at math standards in terms of broader educational goals and the foundational ideas upon which they are based.Asset-Driven Assessment: Gain strategies for designing assessments that prioritize student voice and focus on what students understand and can explain.Conceptual Task Design: Access practical guidance on creating questions and tasks that surface deep reasoning rather than just procedural fluency.K–8 Grade Span Support: Explore numerous examples across many domains and grade levels that show how big ideas develop as students progress.Alignment With Mathematical Practices: Discover how to naturally attend to mathematical practices while teaching core content standards.

How can teachers move beyond surface-level coverage of math standards to focus on what truly matters for student understanding?This book, co-published with the National Council of Teachers of Mathematics (NCTM), provides a transformative approach to K–8 mathematics instruction. Rather than treating standards as a fixed checklist of skills to be executed, internationally recognized expert Marian Small demonstrates how to treat them as professional texts that require thoughtful interpretation. By uncovering the "big ideas" behind the standards, educators can move beyond surface-level coverage to foster deeper mathematical thinking and lasting student understanding.Drawing on decades of classroom experience, this resource helps teachers translate teacher-facing standards into student-centered learning experiences. Small introduces a framework that shifts the focus from micro-level procedures to macro-level concepts, ensuring that students prioritize reasoning and connections over rote alignment. With examples spanning across grades K–8, the book illustrates how the same standard can be interpreted in multiple ways to shape how students learn and demonstrate their knowledge.This guide also reimagines the role of evaluation through asset-driven assessment. By framing tasks and questions that emphasize what students do know and can explain, teachers can provide more meaningful opportunities for student voice in the math classroom. Whether you are a classroom teacher, coach, or instructional leader, this book offers the tools necessary to design powerful instruction that surfaces conceptual understanding for every learner.Key Features:A Proven Framework: Learn a systematic way to look at math standards in terms of broader educational goals and the foundational ideas upon which they are based.Asset-Driven Assessment: Gain strategies for designing assessments that prioritize student voice and focus on what students understand and can explain.Conceptual Task Design: Access practical guidance on creating questions and tasks that surface deep reasoning rather than just procedural fluency.K–8 Grade Span Support: Explore numerous examples across many domains and grade levels that show how big ideas develop as students progress.Alignment With Mathematical Practices: Discover how to naturally attend to mathematical practices while teaching core content standards.

This full-color resource will help K–8 teachers find new ways to clarify concepts that students find difficult. This extensively updated teaching resource provides over engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K–8. Readers are provided with a strong mathematical background, downloadable copies of the visuals they can use directly, and helpful questions to raise with their students. Expected answers for each question and follow-up extensions are also provided. This expanded second edition includes 5 new Notice and Wonder activities to get mathematical conversations started and 5 new Student Assessment activities with suggestions for visuals that students can create to help teachers assess comprehension. This user-friendly book will help teachers find new ways to clarify concepts that students find difficult. It will also help teachers working with students with low reading ability, including English language learners and special education students.Book Features: 3 visuals, including color artwork and graphics.Questions and tasks to use with students in leading the instructional conversation.Expected answers and explanations of why each question is important.Prompts for students to show their understanding of a concept by using visuals.Vital mathematical background and context.

This full-color resource will help K–8 teachers find new ways to clarify concepts that students find difficult. This extensively updated teaching resource provides over engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K–8. Readers are provided with a strong mathematical background, downloadable copies of the visuals they can use directly, and helpful questions to raise with their students. Expected answers for each question and follow-up extensions are also provided. This expanded second edition includes 5 new Notice and Wonder activities to get mathematical conversations started and 5 new Student Assessment activities with suggestions for visuals that students can create to help teachers assess comprehension. This user-friendly book will help teachers find new ways to clarify concepts that students find difficult. It will also help teachers working with students with low reading ability, including English language learners and special education students.Book Features: 3 visuals, including color artwork and graphics.Questions and tasks to use with students in leading the instructional conversation.Expected answers and explanations of why each question is important.Prompts for students to show their understanding of a concept by using visuals.Vital mathematical background and context.

Dr. Marian Small has written a landmark book for a wide range of educational settings and audiences, from pre-service math methods courses to ongoing professional learning for experienced teachers. Understanding the Math We Teach and How to Teach It, K-8 focuses on the big mathematical ideas in elementary and middle school grade levels and shows how to teach those concepts using a student-centered, problem-solving approach.

Comprehensive and Readable: Dr. Small helps all teachers deepen their content knowledge by illustrating core mathematical themes with sample problems, clear visuals, and plain language Big Focus on Student Thinking: The book''s tools, models. and discussion questions are designed to understand student thinking and nudge it forward. Particularly popular features include charts listing common student misconceptions and ways to address them, a table of suggested manipulatives for each topic, and a list of related children''s book Implementing Standards That Make Sense: By focusing on key mathematics principles, Understanding the Math We Teach and How to Teach It, K-8 helps to explain the "whys" of state standards and provides teachers with a deeper understanding of number sense, operations, algebraic thinking, geometry, and other critical topics

Dr. Small, a former dean with more than 40 years in the field, conceived the book as an essential guide for teachers throughout their career: "Many teachers who teach at the K-8 level have not had the luxury of specialist training in mathematics, yet they are expected to teach an increasingly sophisticated curriculum to an increasingly diverse student population in a climate where there are heightened public expectations. They deserve help."

Dr. Marian Small has written a landmark book for a wide range of educational settings and audiences, from pre-service math methods courses to ongoing professional learning for experienced teachers. Understanding the Math We Teach and How to Teach It, K-8 focuses on the big mathematical ideas in elementary and middle school grade levels and shows how to teach those concepts using a student-centered, problem-solving approach.

Comprehensive and Readable: Dr. Small helps all teachers deepen their content knowledge by illustrating core mathematical themes with sample problems, clear visuals, and plain language Big Focus on Student Thinking: The book''s tools, models. and discussion questions are designed to understand student thinking and nudge it forward. Particularly popular features include charts listing common student misconceptions and ways to address them, a table of suggested manipulatives for each topic, and a list of related children''s book Implementing Standards That Make Sense: By focusing on key mathematics principles, Understanding the Math We Teach and How to Teach It, K-8 helps to explain the "whys" of state standards and provides teachers with a deeper understanding of number sense, operations, algebraic thinking, geometry, and other critical topics

Dr. Small, a former dean with more than 40 years in the field, conceived the book as an essential guide for teachers throughout their career: "Many teachers who teach at the K-8 level have not had the luxury of specialist training in mathematics, yet they are expected to teach an increasingly sophisticated curriculum to an increasingly diverse student population in a climate where there are heightened public expectations. They deserve help."

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 organised 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.

This book focuses on the most important concepts and skills needed to provide early learners (preK–2) with a strong foundation in mathematics, in ways that are fun for both children and educators! Professional developer Marian Small provides sample activities and lessons, troubleshooting tips, and formative assessments, and much more.

This resource by popular professional developer Marian Small comprehensively addresses different mathematical domains for grades 3–8. Small shows new and veteran teachers how to do three fundamental things well: identify the most important math to assess, construct formative and summative assessments, and provide students with clear and timely feedback.

This resource by popular professional developer Marian Small comprehensively addresses different mathematical domains for grades 3–8. Small shows new and veteran teachers how to do three fundamental things well: identify the most important math to assess, construct formative and summative assessments, and provide students with clear and timely feedback.

Now in its Fourth Edition?with more than 50 new questions and a new chapter on financial literacy?this bestselling resource helps experienced and novice teachers effectively and efficiently differentiate mathematics instruction in grades K–8. Math education expert Marian Small shows teachers how to get started and become expert at using two powerful and universal strategies: Open Questions and Parallel Tasks. This edition is even easier for teachers to use in all quality state standards environments, including direct links to content standards and standards for mathematical practice. Parallel tasks and question examples are provided at each grade band: K–2, 3–5, and 6–8. Along with each example, the text describes how teachers can evoke productive conversations that meet the needs of a broad range of learners.Book Features:New tasks and questions to develop financial literacy.Connection of tasks and questions to standards and mathematical big ideas.About 500 tasks and questions that teachers can adapt or use as-is.Teaching tips and task variations.A template to help teachers build new tasks.“Look-fors” to see student thinking and diagnose difficulties.Guidance for using follow-up questions and math conversations to create a rich math classroom.

Learn how to differentiate math instruction to help all students be successful learners in the secondary mathematics classroom. Featuring 89 new questions, this revised edition uses two powerful and universally applicable strategies—Open Questions and Parallel Tasks—to help teachers differentiate instruction with less difficulty and greater success. This popular book shows teachers how to get started and become expert with these strategies, demonstrating how to use more inclusive learning conversations to promote broader student participation and how to formatively assess understanding. Strategies and examples are organized around Big Ideas and reference common standards. With particular emphasis on algebra, chapters also address number and operations, geometry, measurement including trigonometry, and data analysis and probability. Updated with many new examples and expanded guidelines for teachers to create their own open tasks and questions, More Good Questions, Second Edition is designed to allow students to respond from their own expertise level and to also come together as a math community for the conceptual conversation around a math problem.Book Features:Underscores the rationale for differentiating instruction (DI) with nearly 300 specific examples for grades 6–12 math.Describes easy-to-implement strategies designed to overcome the most common DI problems that teachers encounter.Offers questions and tasks that teachers and coaches can adopt immediately or use as models to create their own, along with scaffolding and consolidating questions.Includes Teaching Tips sidebars and an organizing template at the end of each chapter to help teachers build new tasks and open questions.Shows how to create a more inclusive classroom learning community with mathematical talk that engages participants from all levels.PROFESSIONAL DEVELOPMENT: Visit Marian Small's website onetwoinfinity.ca for in-person and online professional development.

How can teachers move beyond surface-level coverage of math standards to focus on what truly matters for student understanding?This book, co-published with the National Council of Teachers of Mathematics (NCTM), provides a transformative approach to K–8 mathematics instruction. Rather than treating standards as a fixed checklist of skills to be executed, internationally recognized expert Marian Small demonstrates how to treat them as professional texts that require thoughtful interpretation. By uncovering the "big ideas" behind the standards, educators can move beyond surface-level coverage to foster deeper mathematical thinking and lasting student understanding.Drawing on decades of classroom experience, this resource helps teachers translate teacher-facing standards into student-centered learning experiences. Small introduces a framework that shifts the focus from micro-level procedures to macro-level concepts, ensuring that students prioritize reasoning and connections over rote alignment. With examples spanning across grades K–8, the book illustrates how the same standard can be interpreted in multiple ways to shape how students learn and demonstrate their knowledge.This guide also reimagines the role of evaluation through asset-driven assessment. By framing tasks and questions that emphasize what students do know and can explain, teachers can provide more meaningful opportunities for student voice in the math classroom. Whether you are a classroom teacher, coach, or instructional leader, this book offers the tools necessary to design powerful instruction that surfaces conceptual understanding for every learner.Key Features:A Proven Framework: Learn a systematic way to look at math standards in terms of broader educational goals and the foundational ideas upon which they are based.Asset-Driven Assessment: Gain strategies for designing assessments that prioritize student voice and focus on what students understand and can explain.Conceptual Task Design: Access practical guidance on creating questions and tasks that surface deep reasoning rather than just procedural fluency.K–8 Grade Span Support: Explore numerous examples across many domains and grade levels that show how big ideas develop as students progress.Alignment With Mathematical Practices: Discover how to naturally attend to mathematical practices while teaching core content standards.

How can teachers move beyond surface-level coverage of math standards to focus on what truly matters for student understanding?This book, co-published with the National Council of Teachers of Mathematics (NCTM), provides a transformative approach to K–8 mathematics instruction. Rather than treating standards as a fixed checklist of skills to be executed, internationally recognized expert Marian Small demonstrates how to treat them as professional texts that require thoughtful interpretation. By uncovering the "big ideas" behind the standards, educators can move beyond surface-level coverage to foster deeper mathematical thinking and lasting student understanding.Drawing on decades of classroom experience, this resource helps teachers translate teacher-facing standards into student-centered learning experiences. Small introduces a framework that shifts the focus from micro-level procedures to macro-level concepts, ensuring that students prioritize reasoning and connections over rote alignment. With examples spanning across grades K–8, the book illustrates how the same standard can be interpreted in multiple ways to shape how students learn and demonstrate their knowledge.This guide also reimagines the role of evaluation through asset-driven assessment. By framing tasks and questions that emphasize what students do know and can explain, teachers can provide more meaningful opportunities for student voice in the math classroom. Whether you are a classroom teacher, coach, or instructional leader, this book offers the tools necessary to design powerful instruction that surfaces conceptual understanding for every learner.Key Features:A Proven Framework: Learn a systematic way to look at math standards in terms of broader educational goals and the foundational ideas upon which they are based.Asset-Driven Assessment: Gain strategies for designing assessments that prioritize student voice and focus on what students understand and can explain.Conceptual Task Design: Access practical guidance on creating questions and tasks that surface deep reasoning rather than just procedural fluency.K–8 Grade Span Support: Explore numerous examples across many domains and grade levels that show how big ideas develop as students progress.Alignment With Mathematical Practices: Discover how to naturally attend to mathematical practices while teaching core content standards.

This full-color resource will help K–8 teachers find new ways to clarify concepts that students find difficult. This extensively updated teaching resource provides over engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K–8. Readers are provided with a strong mathematical background, downloadable copies of the visuals they can use directly, and helpful questions to raise with their students. Expected answers for each question and follow-up extensions are also provided. This expanded second edition includes 5 new Notice and Wonder activities to get mathematical conversations started and 5 new Student Assessment activities with suggestions for visuals that students can create to help teachers assess comprehension. This user-friendly book will help teachers find new ways to clarify concepts that students find difficult. It will also help teachers working with students with low reading ability, including English language learners and special education students.Book Features: 3 visuals, including color artwork and graphics.Questions and tasks to use with students in leading the instructional conversation.Expected answers and explanations of why each question is important.Prompts for students to show their understanding of a concept by using visuals.Vital mathematical background and context.

This full-color resource will help K–8 teachers find new ways to clarify concepts that students find difficult. This extensively updated teaching resource provides over engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K–8. Readers are provided with a strong mathematical background, downloadable copies of the visuals they can use directly, and helpful questions to raise with their students. Expected answers for each question and follow-up extensions are also provided. This expanded second edition includes 5 new Notice and Wonder activities to get mathematical conversations started and 5 new Student Assessment activities with suggestions for visuals that students can create to help teachers assess comprehension. This user-friendly book will help teachers find new ways to clarify concepts that students find difficult. It will also help teachers working with students with low reading ability, including English language learners and special education students.Book Features: 3 visuals, including color artwork and graphics.Questions and tasks to use with students in leading the instructional conversation.Expected answers and explanations of why each question is important.Prompts for students to show their understanding of a concept by using visuals.Vital mathematical background and context.

Dr. Marian Small has written a landmark book for a wide range of educational settings and audiences, from pre-service math methods courses to ongoing professional learning for experienced teachers. Understanding the Math We Teach and How to Teach It, K-8 focuses on the big mathematical ideas in elementary and middle school grade levels and shows how to teach those concepts using a student-centered, problem-solving approach.

Comprehensive and Readable: Dr. Small helps all teachers deepen their content knowledge by illustrating core mathematical themes with sample problems, clear visuals, and plain language Big Focus on Student Thinking: The book''s tools, models. and discussion questions are designed to understand student thinking and nudge it forward. Particularly popular features include charts listing common student misconceptions and ways to address them, a table of suggested manipulatives for each topic, and a list of related children''s book Implementing Standards That Make Sense: By focusing on key mathematics principles, Understanding the Math We Teach and How to Teach It, K-8 helps to explain the "whys" of state standards and provides teachers with a deeper understanding of number sense, operations, algebraic thinking, geometry, and other critical topics

Dr. Small, a former dean with more than 40 years in the field, conceived the book as an essential guide for teachers throughout their career: "Many teachers who teach at the K-8 level have not had the luxury of specialist training in mathematics, yet they are expected to teach an increasingly sophisticated curriculum to an increasingly diverse student population in a climate where there are heightened public expectations. They deserve help."

Dr. Marian Small has written a landmark book for a wide range of educational settings and audiences, from pre-service math methods courses to ongoing professional learning for experienced teachers. Understanding the Math We Teach and How to Teach It, K-8 focuses on the big mathematical ideas in elementary and middle school grade levels and shows how to teach those concepts using a student-centered, problem-solving approach.

Comprehensive and Readable: Dr. Small helps all teachers deepen their content knowledge by illustrating core mathematical themes with sample problems, clear visuals, and plain language Big Focus on Student Thinking: The book''s tools, models. and discussion questions are designed to understand student thinking and nudge it forward. Particularly popular features include charts listing common student misconceptions and ways to address them, a table of suggested manipulatives for each topic, and a list of related children''s book Implementing Standards That Make Sense: By focusing on key mathematics principles, Understanding the Math We Teach and How to Teach It, K-8 helps to explain the "whys" of state standards and provides teachers with a deeper understanding of number sense, operations, algebraic thinking, geometry, and other critical topics

Dr. Small, a former dean with more than 40 years in the field, conceived the book as an essential guide for teachers throughout their career: "Many teachers who teach at the K-8 level have not had the luxury of specialist training in mathematics, yet they are expected to teach an increasingly sophisticated curriculum to an increasingly diverse student population in a climate where there are heightened public expectations. They deserve help."