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TABLE OF CONTENTS

Part 1: A Culture of Learning
Chapter 1: Work as a Collaborative Mathematics Team Focused on Student Learning
Chapter 2: Build a Community of Learners
Part 2: Mathematics Foundations
Chapter 3: Teach Grade- or Course-Level Content
Chapter 4: Connect to Prior Knowledge
Chapter 5: Develop Number Sense
Chapter 6: Focus on Problem Solving
Chapter 7: Develop Procedural Fluency
Part 3: Student Engagement
Chapter 8: Communicate Using Mathematical Language
Chapter 9: Grow Learning Through Student Discourse
Chapter 10: Use Meaningful Feedback for Learning
Chapter 11: Empower Learners Through Student Investment
Appendix A: Data Analysis Protocols
Appendix B: Cognitive-Demand-Level Task Analysis Guide
Appendix C: Team Actions to Avoid and Consider for Tier 1 and Tier 2

PRINTABLE REPRODUCIBLES

Introduction

• Figure I.2: Tier 1 and Tier 2 Mathematics Instruction in a PLC at Work

Chapter 1: Work as a Collaborative Mathematics Team Focused on Student Learning

• Figure 1.1: High-Quality Tier 1 and Tier 2 Mathematics Strategies Rubric
• Table 1.1: Work of Collaborative Mathematics Teams Focused on Student Learning in Tier 1 and Tier 2
• Figure 1.4: Example of Rigorous Mathematics
• Figure 1.9: Essential Standard Intervention Planning Tool
• Essential Standards Intervention Planning Tool: Algebra 1 Systems of Linear Equations Example
• Choose and Solve
• Leveled Tasks: Systems of Linear Equations A
• Leveled Tasks: Systems of Linear Equations B
• How Many?
• Same Answer Different Ways A
• Same Answer Different Ways B
• Three Reads Protocol: Systems of Linear Equations
• Which Is Better?
• Error Analysis Task A
• Error Analysis Task B
• Essential Standards Intervention Planning Tool: Seventh-Grade Unit Rate and Proportional Relationships Example
• Which Rate Doesn’t Belong
• Find the Unit Rate Relay Game
• Unit Rate Card Sort
• Is Bigger Better?
• Three Reads Protocol: What’s One?
• Keep Running!
• Figure 1.9: Essential Standard Intervention Planning Tool: Fourth-Grade Multidigit Addition and Subtraction Example
• Addition and Subtraction Number Talks Within 20
• Tic-Tac-Toe: Addition and Subtraction Mental Strategies
• Tic-Tac-Toe: Addition and Subtraction Over or Under Estimating
• Tic-Tac-Toe: Addition and Subtraction Standard Algorithm
• Picture This A
• Picture This B
• Three Ways A
• Three Ways B
• Three Ways C
• How Much?
• Leveled Tasks: Addition and Subtraction A
• Leveled Tasks: Addition and Subtraction B
• Known Tens Interactive Number Talks
• Hundred, Tens, and Ones Organizer
• Base Ten Models: Set A
• Base Ten Models: Set B
• Base Ten Models: Set C
• Base Ten Models: Set D
• Base Ten Models: Set E
• Base Ten Models: Set F
• Base Ten Models: Template

Chapter 2: Build a Community of Learners

• Figure 2.1: Reflection Tool on Characteristics of Belonging
• Figure 2.7: Desk Arrangement Reflection
• Figure 2.8: Physical Environment Considerations in a Learning Community
• Figure 2.9: Error Analysis Task

Chapter 3: Teach Grade- or Course-Level Content

• Figure 3.2: Protocol to Determine How to Reach Grade- or Course-Level Learning in Tier 1 Lessons
• Figure 3.3: Differentiation Plan for a High-Level-Cognitive-Demand Task
• Figure 3.8: Leveled Tasks

Chapter 4: Connect to Prior Knowledge

• Figure 4.3: Prior Knowledge Routine

Chapter 5: Develop Number Sense

• Table 5.1: Number Sense by Grade Band
• Figure 5.2: Give Me a Quantity
• Figure 5.8: Examples of Number Lines Across Grade Levels

Chapter 6: Focus on Problem Solving

• Figure 6.1: Examples of Problem-Solving Tasks
• Figure 6.2: Problem-Solving Graphic Organizer (Elementary Example)
• Figure 6.4: Problem-Solving Graphic Organizer (Middle School Example)
• Figure 6.8: Sample Problems Without Numbers

Chapter 7: Develop Procedural Fluency

• Table 7.1: Key Fact and Procedural Fluency Expectations by Grade Level
• Figure 7.3: Multidigit Subtraction Progression of Strategies
• Figure 7.7: Sample Guiding Questions to Facilitate Connecting and Comparing Strategies
• Figure 7.14: Examples of Mathematical Concepts by Grade Band for Card Sorts
• Multiplication by 3 Card Sort
• Multiplication by 4 Card Sort
• Multiplication by 5 Card Sort
• Multiplication by 6 Card Sort
• Multiplication by 7 Card Sort
• Multiplication by 8 Card Sort
• Multiplication by 9 Card Sort

Chapter 8: Communicate Using Mathematical Language

• Table 8.2: Comparison of Teacher and Student Actions
• Figure 8.5: Would You Rather? Prompts
• Figure 8.6: Graphic Organizer for Meaningful Notes
• Figure 8.7: Sample Mathematics Journal Prompts
• Figure 8.9: Mathematics Graphic Organizer Examples

Chapter 9: Grow Learning Through Student Discourse

• Table 9.2: Sample Mathematics Questions to Deepen Student Thinking
• Figure 9.1: Sample Sentence Frames to Build Discourse Routines
• Figure 9.2: Sample Content-Specific Sentence Frames

Chapter 10: Use Meaningful Feedback for Learning

• Figure 10.1: Examples of Incorrect Student Verbal Explanations and Written Work Needing Feedback
• Figure 10.7: Examples of Student Questions Across Grade Levels

Chapter 11: Empower Learners Through Student Investment

• Figure 11.1: Feedback for Student Reflection Scenario and Discussion
• Figure 11.5: Common Assessment Reflection
• Figure 11.9: Analytic Rubric for Problem Solving
• Figure 11.10: Single-Point Rubric
• Figure 11.12: Learning Targets and Success Criteria for Essential Standard
• Figure 11.14: Proficiency Scale for Essential Standard
• Figure 11.17: Example Weekly Grade 2 Student Tracker

Epilogue

• Figure E.1: Sample Questions to Answer as a Team When Planning for Tier 1 and Tier 2 Instruction

Appendix A: Data Analysis Protocols

• Student Work Protocol
• Essential Learning Standard Analysis Protocol: Grade 4 Sample

Appendix B: Cognitive-Demand-Level Task Analysis Guide

• Cognitive-Demand Levels of Mathematical Tasks

Appendix C: Team Actions to Avoid and Consider for Tier 1 and Tier 2

• Team Actions to Avoid and Consider for Tier 1 and Tier 2

SUGGESTED RESOURCES

Books

• Brown, T., & Ferriter, W. M. (2021). You can learn! Building student ownership, motivation, and efficacy with the PLC at Work process. Bloomington, IN: Solution Tree Press.
• Dimich, N. (2014). Design in five: Essential phases to create engaging assessment practice. Bloomington, IN: Solution Tree Press.
• Dimich, N. (2024). Design in five: Essential phases to create engaging assessment practice (2nd ed.). Bloomington, IN: Solution Tree Press.
• Dixon, J. K., Nolan, E. C., Lott Adams, T., Brooks, L. A., & Howse, T. D. (2016). Making sense of mathematics for teaching grades K–2. Bloomington, IN: Solution Tree Press.
• DuFour, R., DuFour, R., Eaker, R., Many, T. W., Mattos, M., & Muhammad, A. (2024). Learning by doing: A handbook for Professional Learning Communities at Work (4th ed.). Bloomington, IN: Solution Tree Press.
• Erkens, C., Schimmer, T., & Dimich, N. (2017). Essential assessment: Six tenets for bringing hope, efficacy, and achievement to the classroom. Bloomington, IN: Solution Tree Press.
• Guskey, T. R. (2015). On your mark: Challenging the conventions of grading and reporting. Bloomington, IN: Solution Tree Press.
• Hierck, T. (2017). Seven keys to a positive learning environment in your classroom. Bloomington, IN: Solution Tree Press.
• Hoegh, J. K. (2020). A handbook for developing and using proficiency scales in the classroom. Bloomington, IN: Marzano Resources.
• Kramer, S. V., & Schuhl, S. (2017). School improvement for all: A how-to guide for doing the right work. Bloomington, IN: Solution Tree Press.
• Kramer, S. V., & Schuhl, S. (2023). Acceleration for all: A how-to guide for overcoming learning gaps. Bloomington, IN: Solution Tree Press.
• Lang-Raad, N. D., & Marzano, R. J. (2019). The new art and science of teaching mathematics. Bloomington, IN: Solution Tree Press.
• Many, T. W., Maffoni, M. J., Sparks, S. K., & Thomas, T. F. (2022). Energize your teams: Powerful tools for coaching collaborative teams in PLCs at Work. Bloomington, IN: Solution Tree Press.
• Marzano, R. J. (2010). Formative assessment and standards-based grading. Bloomington, IN: Marzano Resources.
• Marzano, R. J. (2017). The new art and science of teaching. Bloomington, IN: Solution Tree Press.
• Marzano, R. J. (2023). Step into student goal setting: A path to growth, motivation, and achievement. Bloomington, IN: Solution Tree Press.
• Marzano, R. J., Warrick, P. B., Rains, C. L., & DuFour, R. (2018). Leading a high reliability school. Bloomington, IN: Solution Tree Press.
• Mattos, M., Buffum, A., Malone, J., Cruz, L. F., Dimich, N., & Schuhl, S. (2025). Taking action: A handbook for RTI at Work™ (2nd ed.). Bloomington, IN: Solution Tree Press.
• Norris, K., & Schuhl, S. (2016). Engage in the mathematical practices: Strategies to build numeracy and literacy with K–5 learners. Bloomington, IN: Solution Tree Press.
• Reeves, D. (2011). Elements of grading: A guide to effective practice. Bloomington, IN: Solution Tree Press.
• Reeves, D. (2016). Elements of grading: A guide to effective practice (2nd ed.). Bloomington, IN: Solution Tree Press.
• Schuhl, S. (2021). Working together to ensure all students learn mathematics. In S. V. Kramer (Ed.), Charting the course for collaborative teams: Lessons from priority schools in a PLC at Work® (pp. 131–147). Bloomington, IN: Solution Tree Press.
• Schuhl, S., Kanold, T. D., Barnes, B., Jain, D. M., Larson, M. R., & Mozingo, B. (2021). Mathematics unit planning in a PLC at Work, high school. Bloomington, IN: Solution Tree Press.
• Schuhl, S., Kanold, T. D., Deinhart, J., Lang-Raad, N. D., Larson, M. R., & Smith, N. N. (2021). Mathematics unit planning in a PLC at Work, preK–2. Bloomington, IN: Solution Tree Press.
• Schuhl, S., Kanold, T. D., Deinhart, J., Larson, M. R., & Toncheff, M. (2020). Mathematics unit planning in a PLC at Work, grades 3–5. Bloomington, IN: Solution Tree Press.
• Schuhl, S., Kanold, T. D., Kanold-McIntyre, J., Chuang, S., Larson, M. R., & Smith, M. (2021). Mathematics unit planning in a PLC at Work, grades 6–8. Bloomington, IN: Solution Tree Press.
• Schuhl, S., Kanold, T. D., Toncheff, M., Barnes, B., Kanold-McIntyre, J., Larson, M. R., et al. (2024). Mathematics assessment and intervention in a PLC at Work (2nd ed.). Bloomington, IN: Solution Tree Press.
• Toncheff, M., Kanold, T. D., Schuhl, S., Barnes, B., Deinhart, J., Kanold-McIntyre, J., et al. (2024). Mathematics instruction and tasks in a PLC at Work (2nd ed.). Bloomington, IN: Solution Tree Press.

Websites

Chapter 1

• Teacher Team Rubric: Tier 2 Mathematics Intervention Program (Reproducible) in Mathematics Assessment and Intervention in a PLC at Work, Second Edition (Schuhl et al., 2024)

Chapter 3

• Mathematics Unit Planning in a PLC at Work Series Reproducibles
• Achieve the Core
• Achieve the Core

Chapter 4

• Achieve the Core, Coherence Map
• Achieve the Core

Chapter 5

• Steve Wyborney’s Blog
• Number Line
• Zoomable Number Line

Chapter 8

• Which One Doesn’t Belong?
• Building Thinking Classrooms (Facebook Group)

Chapter 9

• Flippity

Chapter 11

• Coherence Map