Marian Small

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.

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.

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.

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.

Learn how to provide rich, online mathematics instruction that optimizes the limited time you have with students, while doing it in a way that does not overwhelm parents. This practical resource: highlights the value of open questions for differentiating instruction in the K–8 virtual environment; shows teachers how to adapt the materials that they are already using; illustrates how students can incorporate items from their home environment into math lessons; demonstrates how to build and maintain community with students online; explores the logistics of independent meetings with students and parents; provides samples and directions for creating tools like number lines and manipulatives at home; and much more. Featuring professional developer Marian Small’s special brand of lucid explanation of difficult concepts, engaging teaching examples, troubleshooting tips, and formative assessments, Teaching Math Online is a must-have for anyone teaching math either wholly online or in blended classrooms.Book Features:Provides immediate assistance for teachers with little or no experience teaching math online.Offers specific suggestions for supporting parents in their new role as the link between teacher and student.Addresses both logistical and pedagogical issues important to successful online learning.Provides online problem visuals for teachers to use with students.Includes reproducibles for creating math manipulatives and tools.Discusses distanced formative assessment.Includes access to exemplar videos for communicating with parents, and for providing students with spoken instruction that they can save and replay.

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.

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 provide rich, online mathematics instruction that optimizes the limited time you have with students, while doing it in a way that does not overwhelm parents. This practical resource: highlights the value of open questions for differentiating instruction in the K–8 virtual environment; shows teachers how to adapt the materials that they are already using; illustrates how students can incorporate items from their home environment into math lessons; demonstrates how to build and maintain community with students online; explores the logistics of independent meetings with students and parents; provides samples and directions for creating tools like number lines and manipulatives at home; and much more. Featuring professional developer Marian Small’s special brand of lucid explanation of difficult concepts, engaging teaching examples, troubleshooting tips, and formative assessments, Teaching Math Online is a must-have for anyone teaching math either wholly online or in blended classrooms.Book Features:Provides immediate assistance for teachers with little or no experience teaching math online.Offers specific suggestions for supporting parents in their new role as the link between teacher and student.Addresses both logistical and pedagogical issues important to successful online learning.Provides online problem visuals for teachers to use with students.Includes reproducibles for creating math manipulatives and tools.Discusses distanced formative assessment.Includes access to exemplar videos for communicating with parents, and for providing students with spoken instruction that they can save and replay.

Marian Small has written the kind of book teachers will keep on their closest shelf as they explore and return to the big ideas of mathematics. In her new resource, Understanding the Math We Teach and How to Teach It, Marian brings the support and insight teachers need to teach math with clarity and confidence. With this new resource, new and experienced teachers alike will focus on the big ideas and practices in mathematics, deepening your own understanding and content knowledge, learn how to teach those big ideas using a student-centered, problem-solving approach, and anticipate student thinking and explore effective tools, models, and rich mathematical questions that nudge student thinking forward.This readable and relatable resource will give you a well-founded base of mathematical knowledge, leading to better math instruction that will capture your students' interest. It is sure to become a trusted treasure you return to again and again.

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.

The pressure is on. Principals, expected to improve math performance at their schools, often don't know where to begin as they may be uncomfortable with math themselves—or believe that their schools are already doing all that they can. How can K–12 school leaders recognize and ensure that their school or district is supporting good math instruction?Marian Small and Doug Duff provide the answer to that and other questions in The School Leader's Guide to Building and Sustaining Math Success. Drawing on their vast experience working with administrators, Small and Duff provide practical advice and helpful tools for improving math instruction.They guide you through the initial steps of establishing a strong math culture, developing common tasks, and getting buy-in, and then offer specific suggestions for monitoring, supporting, and sustaining improvement. You'll learn what sort of data to collect, what to look for in the classroom, what to listen for in conversations with teachers and students, and how to deal with reluctant staff or parents.With its real-world examples and insights, this book is essential reading for any principal who wants to bring about positive change and real growth in the teaching and learning of math in their school.

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 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.

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. Organised 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.

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.