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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

PRINTABLE REPRODUCIBLES

Introduction

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

Chapter 1

• End-of-Unit Test for Second Grade on Two-Digit Addition and Subtraction With Balanced Cognitive Demand
• Figure 1.2: Discussion Tool for Making Sense of the Agreed-On Essential Learning Standards for the Unit
• Figure 1.3: Sample Unit Progression for Eighth-Grade Geometry
• Figure 1.4: Four Categories of Cognitive Demand
• Figure 1.5: Sample Higher-Level-Cognitive-Demand Task Discussion Tool
• Figure 1.6: Tool for Sorting Unit Tasks by Cognitive-Demand Level
• Figure 1.7: Strategies for Increasing the Cognitive Demand of Tasks
• Figure 1.8: Team Discussion Tool for Identifying Higher-Level-Cognitive-Demand Tasks for a Unit
• Figure 1.9: Task-Analysis Discussion Tool
• Figure 1.10: Assessment Instrument Quality-Evaluation Tool
• Figure 1.11: High-Quality Assessment Diagnostic and Discussion Tool
• Figure 1.12: Tool for Planning and Preparing for Common Assessment Instrument Task Development
• Figure 1.13: Checking for Cognitive-Demand Balance on the Common Unit Assessment Instrument
• Figure 1.14: Collaborative Team Task-Scoring Discussion Prompts
• Figure 1.16: Assessment Instrument Alignment and Scoring Rubric Tool
• Figure 1.17: Collaborative Homework Assignment Protocol Discussion Tool
• Figure 1.18: Homework Quality Diagnostic Tool
• Figure 1.19: Setting Your Collaborative Team’s Before-the-Unit Priorities
• Mathematical Task Questions
• Revised Sample Assessment Questions for End-of-Unit Test on Expressions
• Table 1.1: Before-the-Unit-Begins Status Check Tool for HLTA 1–Making Sense of the Agreed-On Essential Learning Standards (Content and Practices) and Pacing
• Table 1.2: Before-the-Unit-Begins 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 HLTA 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 2.2: Identifying Proficiency With the Standards for Mathematical Practice
• Figure 2.3: Mathematics Instruction and Higher-Level-Cognitive-Demand Mathematical Task Development Tool
• Figure 2.4: Teacher Actions That Provide Targeted and Differentiated Support
• Figure 2.5: Prompts for Differentiated In-Class Support and Student Perseverance
• Figure 2.6: Sample Transformations Using the Coordinate Grid
• Figure 2.7: Strategies for Maintaining Higher-Level-Cognitive-Demand Tasks During Instruction
• Figure 2.8: Checking for Understanding Versus Using the Formative Assessment Process Tool
• Figure 2.9: Grade 8 Higher-Level-Cognitive-Demand Reasoning Task
• Figure 2.10: Walkthrough Formative Assessment Observation Tool
• Figure 2.12: Small-Group Discourse Peer-to-Peer Engagement Tool
• Figure 2.13: Mathematical Practices Lesson-Planning Tool
• Figure 2.14: Learning About the Mathematical Practices Lesson-Planning Tool
• Figure 2.15: Mathematical Practices Lesson-Study Planning and Analysis Tool
• Figure 2.16: Lesson-Study Student Data Observation Tool
• Figure 2.17: Reflection and Debriefing Prompts to Follow Implementation of the Mathematical Practices Lesson-Planning Tool
• Figure 2.18: Setting Your Collaborative Team’s During-the-Unit Priorities
• Table 2.1: During-the-Unit Status Check Tool for HLTA 6–Using Higher-Level-Cognitive-Demand Mathematical Tasks Effectively
• Table 2.2: During-the-Unit Status Check Tool for HLTA 7–Using In-Class Formative Assessment Processes Effectively
• Table 2.3: 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: Collaborative Team Student Feedback Discussion Tool
• Figure 3.4: Student Action Plan Template for Response to an End-of-Unit Assessment
• Figure 3.5: Tool for Student Self-Assessment and Feedback
• Figure 3.6: Collaborative Team Data-Analysis Protocol
• Figure 3.7: Collaborative Team Scoring and Analysis Activity
• Figure 3.8: Sample Unit 1 Learning Standard Tracking Tool
• Figure 3.9: Collaborative Team SMART Goal-Setting Reflections
• Figure 3.10: Setting Your Collaborative Team’s After-the-Unit Priorities
• Sample Student Self-Assessment–End-of-Unit Test Cover Page
• Student Action Plan Template for Response to an End-of-Unit Assessment
• Sample Student Self-Assessment, Goal Setting, and Action Plan
• 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-Ends Status Check Tool for HLTA 10–Ensuring Evidence-Based Adult Goal Setting and Action for the Next Unit of Study
• Tool for Student Self-Assessment and Feedback

Epilogue

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

• All Things PLC
• Common Core Conversation, “Math Resources”
• EngageNY, “New York State Math Curriculum”
• Howard County Public Schools Secondary Mathematics Common Core Wiki
• Illustrative Mathematics
• Inside Mathematics, “Common Core State Standards for Mathematical Practice”
• 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, “PARCC Task Prototypes and New Sample Items for Mathematics”
• Smarter Balanced Assessment Consortium, “Sample Items and Performance Tasks”
• Virgina Department of Education, “Mathematics”