Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Grades 3-5, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics.

Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library.

Reasoning and Sense Making in the Mathematics Classroom, Grades 6-8, based on extensive research conducted by the authors, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in middle school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how instruction can support students in their development of these competencies. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without this base of conceptual understanding, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making look like in learning and teaching? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Grades 6-8 explores a different topic that children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication," or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how students attempt to make sense of the concepts of fractions and geometric properties of shapes. Chapter 2 discusses how reasoning about ratios and proportional relationships involves deep understanding of the multiplicative relationships embedded in the comparisons of two quantities. Chapter 3 focuses on what it means to call algebra a "style of mathematical thinking" and illustrates how students can view it as a reasoning and sense-making activity rather than as an isolated set of concepts to be memorized without understanding and quickly forgotten. Reasoning and sense making are inextricably linked in statistics and probability. Discussion and examples are used in chapter 4 to illustrate pedagogical practices that recognize and address students' development of statistical understanding, including some of the misunderstandings that students display along the way. Chapter 5 examines how students make sense of and reason about decomposing shapes, and discusses the mental processes underlying this reasoning in the context of area, surface area, and volume. Not just a theoretical treatise, the book provides specific suggestions for related instructional activities for each topic. Reasoning and Sense Making in the Mathematics Classroom, Grades 6-8 will be a valuable and practical addition to your professional library.

Detailed plans for helping elementary students experience deep mathematical learning Do you work tirelessly to make your math lessons meaningful, challenging, accessible, and engaging? Do you spend hours you don’t have searching for, adapting, and creating tasks to provide rich experiences for your students that supplement your mathematics curriculum? Help has arrived! Classroom Ready-Rich Math Tasks for Grades 4-5 details more than 50 research- and standards-aligned, high-cognitive-demand tasks that will have your students doing deep-problem-based learning. These ready-to-implement, engaging tasks connect skills, concepts and practices, while encouraging students to reason, problem-solve, discuss, explore multiple solution pathways, connect multiple representations, and justify their thinking. They help students monitor their own thinking and connect the mathematics they know to new situations. In other words, these tasks allow students to truly do mathematics! Written with a strengths-based lens and an attentiveness to all students, this guide includes: • Complete task-based lessons, referencing mathematics standards and practices, vocabulary, and materials • Downloadable planning tools, student resource pages, and thoughtful questions, and formative assessment prompts • Guidance on preparing, launching, facilitating, and reflecting on each task • Notes on access and equity, focusing on students’ strengths, productive struggle, and distance or alternative learning environments. With concluding guidance on adapting or creating additional rich tasks for your students, this guide will help you give all of your students the deepest, most enriching and engaging mathematics learning experience possible.

Develop a deep understanding of mathematics. This user-friendly resource presents grades 3–5 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Focus on an understanding of and procedural fluency with multiplication and division. Address how to learn and teach fraction concepts and operations with depth. Thoroughly teach plane and solid geometry. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, and modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Use charts and diagrams for classifying shapes, which can engage students in important mathematical practices. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Place Value, Addition, and Subtraction 2 Multiplication and Division 3 Fraction Concepts 4 Fraction Operations 5 Geometry 6 Measurement Epilogue Next Steps Appendix A Completed Classification of Triangles Chart Appendix B Completed Diagram for Classifying Quadrilaterals

Develop a deep understanding of mathematics by grasping the context and purpose behind various strategies. This user-friendly resource presents high school teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Combine student understanding of functions and algebraic concepts so that they can better decipher the world. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, or modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Gain clarity about the most productive progression of mathematical teaching and learning for high school. Watch short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction Equations and Functions Structure of Equations Geometry Types of Functions Function Modeling Statistics and Probability Epilogue: Next Steps Appendix: Weight Loss Study Data References Index