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TABLE OF CONTENTS

Chapter 1: Before the Unit
Chapter 2: During the Unit
Chapter 3: After the Unit
Epilogue: Taking Your Next Steps
Appendix A: Standards for Mathematical Practice
Appendix B: Standards for Mathematical Practice Evidence Tool
Appendix C: Cognitive-Demand-Level Task-Analysis Guide
Appendix D: Sources for Higher-Level-Cognitive-Demand Tasks
Appendix E: How the Mathematics at Work High-Leverage Team Actions Support the NCTM Principles to Actions: Ensuring Mathematical Success for All

REPRODUCIBLES

Introduction

• Figure I.1: High-Leverage Team Actions Aligned to the Four Critical Questions of a PLC

Chapter 1

• End-of-Unit Sample Assessment, Grade 6
• End-of-Unit Sample Assessment, Grade 7
• End-of-Unit Sample Assessment, Grade 8
• Figure 1.3: Discussion Tool on Essential Learning Standards for a Congruence and Similarity Unit in Grade 8
• Figure 1.4: Discussion Tool for Making Sense of the Agreed-On Essential Learning Standards for the Unit
• Figure 1.6: Sample Unit Progression for Geometry Across Standards
• Figure 1.8: Four Categories of Cognitive Demand
• Figure 1.9: Tool for Sorting Unit Tasks by Cognitive-Demand Level
• Figure 1.10: Sample Higher-Level-Cognitive-Demand-Task Discussion Tool
• Figure 1.11: Strategies for Increasing the Cognitive Demand of Tasks
• Figure 1.12: Team Discussion Tool for Identifying Higher-Level-Cognitive-Demand Mathematical Tasks for the Unit
• Figure 1.13: Task-Analysis Discussion Tool
• Figure 1.14: Grade 7 Higher-Level-Cognitive-Demand Task
• Figure 1.15: Assessment Instrument Quality-Evaluation Tool
• Figure 1.16: High-Quality Assessment Diagnostic and Discussion Tool
• Figure 1.17: Tool for Planning and Preparing for Common Assessment Instrument Task Development
• Figure 1.18: Sample Assessment Questions for End-of-Unit Test on Expressions (Lower-Level Cognitive Demand Only)
• Figure 1.19: Checking for Cognitive-Demand Balance of Common Unit Assessment Instruments Tool
• Figure 1.24: Collaborative Team Task Scoring Discussion Prompts
• Figure 1.25: Sample Grade 8 Functions Unit Exam
• Figure 1.26: Assessment Instrument Alignment and Scoring Rubric Tool
• Figure 1.27: Collaborative Homework Assignment Protocol Discussion Tool
• Figure 1.28: Homework Quality Diagnostic Tool
• Figure 1.30: Setting Your Collaborative Team’s Before-the-Unit Priorities
• Grade 8 Functions Unit Exam Rubric
• Homework Guidelines
• Mathematical Task Questions
• Table 1.1: Before-the-Unit Status Check Tool–HLTA 1: Making Sense of the Agreed-On Essential Learning Standards (Content and Practices) and Pacing
• Table 1.2: Before-the-Unit Status Check Tool for HLTA 2–Identifying Higher-Level-Cognitive-Demand Mathematical Tasks
• Table 1.3: Before-the-Unit-Begins Status Check Tool for HLTA 3–Developing Common Assessment Instruments
• Table 1.4: Before-the-Unit-Begins Status Check Tool for HTLA 4–Developing Scoring Rubrics and Proficiency Expectations for the Common Assessment Instruments
• Table 1.5: Before-the-Unit-Begins Status Check Tool for HLTA 5–Planning and Using Common Homework Assignments

Chapter 2

• Figure 2.3: Identifying Proficiency With the Standards for Mathematical Practice
• Figure 2.4: Mathematics Instruction and Higher-Level-Cognitive-Demand Task Scenario
• Figure 2.6: Mathematics Instruction and Higher-Level-Cognitive-Demand Task Development Tool
• Figure 2.7: Simultaneous Linear Equations Task
• Figure 2.8: Providing Differentiated In-Class Support for Higher-Level-Cognitive-Demand Tasks
• Figure 2.10: Strategies for Maintaining Higher-Level Cognitive Demand for Tasks During Class
• Figure 2.11: Checking for Understanding Versus Using the Formative Assessment Process Tool
• Figure 2.12: Mathematics Instruction Scenario
• Figure 2.13: Grade-Level Tasks Revisited for Formative Assessment Feedback and Action Considerations
• Figure 2.14: Grade 8 Higher-Level-Cognitive-Demand Reasoning Task
• Figure 2.16: Walk-Around Formative Assessment Tool
• Figure 2.17: Planning for the Formative Assessment Process Example–Grade 6
• Figure 2.18: Planning for the Formative Assessment Process Example–Grade 7
• Figure 2.19: Planning for the Formative Assessment Process Example–Grade 8
• Figure 2.20: Sample Formative Assessment Strategies for Your Classroom
• Figure 2.22: Small-Group Discourse Peer-to-Peer Engagement Tool
• Figure 2.23: Connecting In-Class Formative Assessment Process Work to the End-of-Unit Assessment Tool
• Figure 2.24: Mathematical Practices Lesson-Planning Tool
• Figure 2.25: Learning About the CCSS Mathematical Practices Lesson-Planning Tool
• Figure 2.26: Mathematical Practices Lesson-Study Planning and Analysis Tool
• Figure 2.27: Lesson-Study Student Data Observation Tool
• Figure 2.28: Sample Mathematical Practices Lesson-Planning Tool for Grade 7
• Figure 2.29: Reflection Debriefing Prompts to Follow Implementation of the CCSS Mathematical Practices Lesson-Planning Tool
• Figure 2.30: Setting Your Collaborative Team’s During-the-Unit Priorities
• Planning for the Formative Assessment Process Template
• Sample Lesson-Design Study Model
• End-of-Unit Sample Assessment, Grade 6
• Table 2.1: Common Understandings of Key Terms
• Table 2.2: During-the-Unit Status Check Tool for HLTA 6–Using Higher-Level-Cognitive-Demand Mathematical Tasks Effectively
• Table 2.3: During-the-Unit Status Check Tool for HLTA 7–Using In-Class Formative Assessment Processes Effectively
• Table 2.4: During-the-Unit Status Check Tool for HLTA 8–Using a Lesson-Design Process for Lesson Planning and Collective Team Inquiry

Chapter 3

• Figure 3.2: Sample Grade 6 Task
• Figure 3.3: Collaborative Team Student Feedback Discussion Question Tool
• Figure 3.4: Team Reflection Activity for Group Scoring an Assessment
• Figure 3.9: Collaborative Team Data-Analysis Protocol
• Figure 3.10: Collaborative Team Scoring and Calibration Activity
• Figure 3.11: Analysis of Student Work Tool
• Figure 3.13: Unit 1 Content Standard Cluster Tracker by Teacher
• Figure 3.14: Collaborative Team SMART Goal-Setting Reflections
• Figure 3.16: Setting Your Collaborative Team’s After-the-Unit Priorities
• Sample Mathematical Practices Lesson-Planning Tool for High School Exponential Functions Unit
• Sample Mathematical Practices Lesson-Planning Tool for Third-Grade Plane Geometry
• SMART Goal Worksheet
• SMART Goal Worksheet: American Government
• Student Progress-Tracking Chart
• Student Self-Assessment
• Table 3.1: After-the-Unit-Ends Status Check Tool for HLTA 9–Ensuring Evidence-Based Student Goal Setting and Action for the Next Unit of Study
• Table 3.2: After-the-Unit Status Check Tool for HLTA 10–Ensuring Evidence-Based Adult Goal Setting and Action for the Next Unit of Study

Epilogue

• Figure E.1: Tool for Assessing Your Actions and Setting Your Team Priorities

Appendices

• Appendix D: Sources for Higher-Level-Cognitive-Demand Tasks
• Appendix E: How the Mathematics at Work High-Leverage Team Actions Support the NCTM Principles to Actions: Ensuring Mathematical Success for All

SUGGESTED RESOURCES

• American College Testing Service, Aspire
• College Board, “College Board Tests”
• Common Core Conversation, “Math Resources”
• EngageNY, “New York State Math Curriculum”
• Howard County Public Schools Secondary Mathematics Common Core Wiki
• Illustrative Mathematics
• Infuse Learning
• Inside Mathematics, “Common Core State Standards for Mathematical Practice”
• Institute for Mathematics and Education, “Progressions Documents for the Common Core Math Standards”
• Mathematics Assessment Project
• Mathematics Vision Project
• National Council of Supervisors of Mathematics, “Illustrating the Standards for Mathematical Practice”
• National Council of Teachers of Mathematics
• National Council of Teachers of Mathematics Illuminations
• Partnership for Assessment of Readiness for College and Careers
• Partnership for Assessment of Readiness for College and Careers, “PARCC Task Prototypes and New Sample Items for Mathematics”
• Poll Everywhere
• Smarter Balanced Assessment Consortium
• Smarter Balanced Assessment Consortium, “Sample Items and Performance Tasks”
• Virgina Department of Education, “Mathematics”