**Free Reproducibles**

# Mathematics Instruction and Tasks in a PLC at Work, Second Edition

Gain lesson-design strategies and instructional methods of teaching mathematics in a professional learning community (PLC). This results-oriented book presents an approach for teaching math that supports student perseverance and learning through standards-based activities and lessons.

**Benefits**

- Identify essential mathematics content standards students learn during a unit.
- Understand the importance of communicating the why of the essential mathematics learning standards to students.
- Plan for the use of balanced rigor and mathematical routines to teach each content standard during instruction.
- Use a balance of appropriate mathematics activities and tasks needed to develop conceptual understanding, procedural fluency, and application of mathematical concepts and skills.
- Implement instructional math routines that ensure the formative learning of all students during lessons.

## TABLE OF CONTENTS

Chapter 1: Essential Learning Standards: The Why of the Lesson

Chapter 2: Prior-Knowledge Routines

Chapter 3: Mathematical Language Routines

Chapter 4: A Balance of Mathematical Tasks

Chapter 5: Mathematical Discourse Routines

Chapter 6: Lesson-Closure Routines

Chapter 7: High-Quality Tier 1 Mathematics Intervention

Chapter 8: Analysis of the Effectiveness of Mathematics Instruction

Appendix

## STUDY GUIDE

## REPRODUCIBLES

### Introduction

- Figure I.2: Mathematics in a PLC at Work Framework
- Figure I.3: Teacher Team Discussion Tool—Collaborative Lesson-Design Elements
- Figure I.4: Mathematics in a PLC at Work Instructional Framework and Lesson-Design Evaluation Rubric

### Chapter 2

- Figure 2.5: Prior-Knowledge Routine-Planning Tool
- Figure 2.6: Teacher Team Discussion Tool—Prior-Knowledge Routine Process

### Chapter 3

- Figure 3.1: Teacher Team Discussion Tool—Categories of Vocabulary Challenges for Students
- Table 3.1: Vocabulary Challenges and Focused Strategies
- Figure 3.2: Mathematical Language Routines
- Figure 3.3: Mathematical Language Graphic Organizers
- Figure 3.4: Teacher Team Discussion Tool—Planning for Mathematical Language Routine

### Chapter 4

- Figure 4.2: Teacher Team Discussion Tool—Choosing Mathematical Tasks for Lesson Design During the Unit
- Figure 4.3: Planning for the Formative Assessment Process—Kindergarten
- Figure 4.4: Planning for the Formative Assessment Process—Grade 2
- Figure 4.5: Planning for the Formative Assessment Process—Grade 4
- Figure 4.6: Planning for the Formative Assessment Process—Grade 7
- Figure 4.7: Planning for the Formative Assessment Process—High School Geometry

### Chapter 5

- Figure 5.1: Teacher Team Discussion Tool—Student Discourse During the Lesson
- Figure 5.2: Teacher Team Discussion Tool—Self-Evaluation Checklist on Whole-Group Questioning
- Figure 5.3: Teacher Team Discussion Tool—Whole-Group Discourse Teacher Prompts and Student Sentence Starters
- Figure 5.4: Teacher Team Discussion Tool—Checking for Understanding as Part of the In-Class Formative Assessment Process
- Figure 5.5: Teacher Team Discussion Tool—Assessing and Advancing Questions to Ask Students
- Figure 5.6: Team Discussion Tool—Walk-Around Formative Assessment
- Figure 5.7: Sample Classroom Discourse Rights and Responsibilities
- Figure 5.8: Sample Classroom Norms
- Figure 5.10: Teacher Team Discussion Tool—Management of Student Teams
- Figure 5.12: Student Team Processing and Evaluation Tool

### Chapter 6

- Figure 6.1: Teacher Team Discussion Tool—Lesson-Closure Reflection
- Figure 6.2: Teacher Team Discussion Tool—Sample Lesson-Closure Activities

### Chapter 7

### Chapter 8

- Figure 8.1: Teacher Team Discussion Tool—Connecting In-Class Tier 1 Intervention to the End-of-Unit Assessment
- Figure 8.2: Teacher Team Discussion Tool—Lesson-Plan Analysis
- Figure 8.3: Teacher Team Discussion Tool—Protocol for Team Analysis of the Mathematics in a PLC at Work Lesson-Design Tool

### Appendix

- Mathematics in a PLC at Work Lesson-Design Tool
- Mathematics Instruction and Tasks in a PLC at Work Protocols and Tools

### Additional Materials

- Online Resources Reference Guide for Mathematics Support
- Additional Grade-Level Sample Tasks
- Planning for the Formative Assessment Process

### Instructional Rounds Materials

### Lesson-Design Samples

- Grade 5 Lesson-Design Sample: Geometry
- Grade 8 Lesson-Design Sample: Systems of Linear Equations
- Lesson-Design Sample: Algebra 2 Polynomial Functions

### Lesson Study Materials

- Sample Norms for Lesson Study
- Lesson-Study Protocol Instructions
- Lesson-Study Student Evidence Form
- Time Expectations of a Lesson Study
- Lesson-Study Team Reflection

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