Principles to Actions Professional Learning Toolkit

These grade-band specific professional learning modules are focused on the Effective Teaching Practices and Guiding Principles from Principles to Actions: Ensuring Mathematical Success for All.

Presentation, presenter notes, and required materials are provided in each module to support professional learning with teachers through analyzing artifacts of teaching (e.g., mathematical tasks, narrative and video cases, student work samples, vignettes) and abstracting from the specific examples general ideas about how to effectively support student learning.

The Teaching and Learning Modules were developed in collaboration with the Institute for Learning (IFL) at the University of Pittsburgh.

Principles to Actions Reflection Guide »

Learning modules are available exclusively to NCTM members. Limited open examples are provided for each grade level (denoted with *).

Effective Teaching Practices

To access module materials, use links on left column of table below.

Primary emphasis

Secondary emphasis

	Establish math goals to focus learning	Implement tasks that promote reasoning and problem solving	Use and connect math representations representa- tions	Facilitate meaningful math discourse	Pose purposeful Questions	Build procedural fluency from conceptual understanding under- standing	Support productive struggle in learning math	Elicit and use evidence of student thinking
Elementary School
Band Concert*	Band Concert module has moderate degree of emphasis for principle Establish math goals to focus learning	Band Concert module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Band Concert module has moderate degree of emphasis for principle Use and connect math representations	Band Concert module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Band Concert module has moderate degree of emphasis for principle Pose purposeful Questions	Band Concert module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Band Concert module has moderate degree of emphasis for principle Support productive struggle in learning math	Band Concert module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
Addition Strings	Addition Strings module has moderate degree of emphasis for principle Establish math goals to focus learning	Addition Strings module has high degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Addition Strings module has no degree of emphasis for principle Use and connect math representations	Addition Strings module has no degree of emphasis for principle Facilitate meaningful math discourse	Addition Strings module has no degree of emphasis for principle Pose purposeful Questions	Addition Strings module has high degree of emphasis for principle Build procedural fluency from conceptual understanding	Addition Strings module has no degree of emphasis for principle Support productive struggle in learning math	Addition Strings module has no degree of emphasis for principle Elicit and use evidence of student thinking
Donuts	Donuts module has moderate degree of emphasis for principle Establish math goals to focus learning	Donuts module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Donuts module has high degree of emphasis for principle Use and connect math representations	Donuts module has no degree of emphasis for principle Facilitate meaningful math discourse	Donuts module has high degree of emphasis for principle Pose purposeful Questions	Donuts module has high degree of emphasis for principle Build procedural fluency from conceptual understanding	Donuts module has no degree of emphasis for principle Support productive struggle in learning math	Donuts module has no degree of emphasis for principle Elicit and use evidence of student thinking
Half of a whole*	Half of a whole module has moderate degree of emphasis for principle Establish math goals to focus learning	Half of a whole module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Half of a whole module has no degree of emphasis for principle Use and connect math representations	Half of a whole module has high degree of emphasis for principle Facilitate meaningful math discourse	Half of a whole module has high degree of emphasis for principle Pose purposeful Questions	Half of a whole module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Half of a whole module has no degree of emphasis for principle Support productive struggle in learning math	Half of a whole module has no degree of emphasis for principle Elicit and use evidence of student thinking
Bubble Gum	Bubble Gum module has moderate degree of emphasis for principle Establish math goals to focus learning	Bubble Gum module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Bubble Gum module has high degree of emphasis for principle Use and connect math representations	Bubble Gum module has no degree of emphasis for principle Facilitate meaningful math discourse	Bubble Gum module has high degree of emphasis for principle Pose purposeful Questions	Bubble Gum module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Bubble Gum module has no degree of emphasis for principle Support productive struggle in learning math	Bubble Gum module has no degree of emphasis for principle Elicit and use evidence of student thinking
Multiplication String	Multiplication String module has moderate degree of emphasis for principle Establish math goals to focus learning	Multiplication String module has high degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Multiplication String module has no degree of emphasis for principle Use and connect math representations	Multiplication String module has no degree of emphasis for principle Facilitate meaningful math discourse	Multiplication String module has no degree of emphasis for principle Pose purposeful Questions	Multiplication String module has high degree of emphasis for principle Build procedural fluency from conceptual understanding	Multiplication String module has no degree of emphasis for principle Support productive struggle in learning math	Multiplication String module has no degree of emphasis for principle Elicit and use evidence of student thinking
Hungry Caterpillar	Hungry Caterpillar module has moderate degree of emphasis for principle Establish math goals to focus learning	Hungry Caterpillar module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Hungry Caterpillar module has moderate degree of emphasis for principle Use and connect math representations	Hungry Caterpillar module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Hungry Caterpillar module has moderate degree of emphasis for principle Pose purposeful Questions	Hungry Caterpillar module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Hungry Caterpillar module has moderate degree of emphasis for principle Support productive struggle in learning math	Hungry Caterpillar module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
Middle School
Candy Jar*	Candy Jar module has moderate degree of emphasis for principle Establish math goals to focus learning	Candy Jar module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Candy Jar module has moderate degree of emphasis for principle Use and connect math representations	Candy Jar module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Candy Jar module has moderate degree of emphasis for principle Pose purposeful Questions	Candy Jar module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Candy Jar module has moderate degree of emphasis for principle Support productive struggle in learning math	Candy Jar module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
Calling Plans 2	Calling Plans 2 module has moderate degree of emphasis for principle Establish math goals to focus learning	Calling Plans 2 module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Calling Plans 2 module has no degree of emphasis for principle Use and connect math representations	Calling Plans 2 module has no degree of emphasis for principle Facilitate meaningful math discourse	Calling Plans 2 module has high degree of emphasis for principle Pose purposeful Questions	Calling Plans 2 module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Calling Plans 2 module has no degree of emphasis for principle Support productive struggle in learning math	Calling Plans 2 module has no degree of emphasis for principle Elicit and use evidence of student thinking
Hexagon	Hexagon module has moderate degree of emphasis for principle Establish math goals to focus learning	Hexagon module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Hexagon module has moderate degree of emphasis for principle Use and connect math representations	Hexagon module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Hexagon module has moderate degree of emphasis for principle Pose purposeful Questions	Hexagon module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Hexagon module has high degree of emphasis for principle Support productive struggle in learning math	Hexagon module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
Counting Cubes*	Counting Cubes module has moderate degree of emphasis for principle Establish math goals to focus learning	Counting Cubes module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Counting Cubes module has high degree of emphasis for principle Use and connect math representations	Counting Cubes module has high degree of emphasis for principle Facilitate meaningful math discourse	Counting Cubes module has no degree of emphasis for principle Pose purposeful Questions	Counting Cubes module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Counting Cubes module has no degree of emphasis for principle Support productive struggle in learning math	Counting Cubes module has no degree of emphasis for principle Elicit and use evidence of student thinking
Two Tanks	Two Storage Tanks module has moderate degree of emphasis for principle Establish math goals to focus learning	Two Storage Tanks module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Two Storage Tanks module has high degree of emphasis for principle Use and connect math representations	Two Storage Tanks module has no degree of emphasis for principle Facilitate meaningful math discourse	Two Storage Tanks module has high degree of emphasis for principle Pose purposeful Questions	Two Storage Tanks module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Two Storage Tanks module has no degree of emphasis for principle Support productive struggle in learning math	Two Storage Tanks module has high degree of emphasis for principle Elicit and use evidence of student thinking
Triangle	Triangle module has moderate degree of emphasis for principle Establish math goals to focus learning	Triangle module has high degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Triangle module has no degree of emphasis for principle Use and connect math representations	Triangle module has no degree of emphasis for principle Facilitate meaningful math discourse	Triangle module has no degree of emphasis for principle Pose purposeful Questions	Triangle module has high degree of emphasis for principle Build procedural fluency from conceptual understanding	Triangle module has no degree of emphasis for principle Support productive struggle in learning math	Triangle module has no degree of emphasis for principle Elicit and use evidence of student thinking
High School
Pay It Forward*	Pay It Forward module has moderate degree of emphasis for principle Establish math goals to focus learning	Pay It Forward module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Pay It Forward module has moderate degree of emphasis for principle Use and connect math representations	Pay It Forward module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Pay It Forward module has moderate degree of emphasis for principle Pose purposeful Questions	Pay It Forward module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Pay It Forward module has moderate degree of emphasis for principle Support productive struggle in learning math	Pay It Forward module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
S-Pattern*	S - Pattern module has moderate degree of emphasis for principle Establish math goals to focus learning	S - Pattern module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	S - Pattern module has moderate degree of emphasis for principle Use and connect math representations	S - Pattern module has no degree of emphasis for principle Facilitate meaningful math discourse	S - Pattern module has moderate degree of emphasis for principle Pose purposeful Questions	S - Pattern module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	S - Pattern module has high degree of emphasis for principle Support productive struggle in learning math	S - Pattern module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
Playground	Playground module has moderate degree of emphasis for principle Establish math goals to focus learning	Playground module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Playground module has no degree of emphasis for principle Use and connect math representations	Playground module has no degree of emphasis for principle Facilitate meaningful math discourse	Playground module has high degree of emphasis for principle Pose purposeful Questions	Playground module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Playground module has high degree of emphasis for principle Support productive struggle in learning math	Playground module has no degree of emphasis for principle Elicit and use evidence of student thinking
Bike and Truck	Bike and Truck module has moderate degree of emphasis for principle Establish math goals to focus learning	Bike and Truck module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Bike and Truck module has no degree of emphasis for principle Use and connect math representations	Bike and Truck module has high degree of emphasis for principle Facilitate meaningful math discourse	Bike and Truck module has high degree of emphasis for principle Pose purposeful Questions	Bike and Truck module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Bike and Truck module has no degree of emphasis for principle Support productive struggle in learning math	Bike and Truck module has no degree of emphasis for principle Elicit and use evidence of student thinking
Calling Plans 1	Calling Plans 1 module has moderate degree of emphasis for principle Establish math goals to focus learning	Calling Plans 1 module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Calling Plans 1 module has high degree of emphasis for principle Use and connect math representations	Calling Plans 1 module has no degree of emphasis for principle Facilitate meaningful math discourse	Calling Plans 1 module has high degree of emphasis for principle Pose purposeful Questions	Calling Plans 1 module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Calling Plans 1 module has no degree of emphasis for principle Support productive struggle in learning math	Calling Plans 1 module has no degree of emphasis for principle Elicit and use evidence of student thinking
Sine Waves	Sine Waves module has moderate degree of emphasis for principle Establish math goals to focus learning	Sine Waves module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Sine Waves module has no degree of emphasis for principle Use and connect math representations	Sine Waves module has no degree of emphasis for principle Facilitate meaningful math discourse	Sine Waves module has high degree of emphasis for principle Pose purposeful Questions	Sine Waves module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Sine Waves module has high degree of emphasis for principle Support productive struggle in learning math	Sine Waves module has no degree of emphasis for principle Elicit and use evidence of student thinking

Effective Teaching Practices

To access module materials, use links on left column of table below.

Primary emphasis

Secondary emphasis

	Establish math goals to focus learning	Implement tasks that promote reasoning and problem solving	Use and connect math representations representa- tions	Facilitate meaningful math discourse	Pose purposeful Questions	Build procedural fluency from conceptual understanding under- standing	Support productive struggle in learning math	Elicit and use evidence of student thinking
Elementary School
Band Concert*	Band Concert module has moderate degree of emphasis for principle Establish math goals to focus learning	Band Concert module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Band Concert module has moderate degree of emphasis for principle Use and connect math representations	Band Concert module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Band Concert module has moderate degree of emphasis for principle Pose purposeful Questions	Band Concert module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Band Concert module has moderate degree of emphasis for principle Support productive struggle in learning math	Band Concert module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
Addition Strings	Addition Strings module has moderate degree of emphasis for principle Establish math goals to focus learning	Addition Strings module has high degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Addition Strings module has no degree of emphasis for principle Use and connect math representations	Addition Strings module has no degree of emphasis for principle Facilitate meaningful math discourse	Addition Strings module has no degree of emphasis for principle Pose purposeful Questions	Addition Strings module has high degree of emphasis for principle Build procedural fluency from conceptual understanding	Addition Strings module has no degree of emphasis for principle Support productive struggle in learning math	Addition Strings module has no degree of emphasis for principle Elicit and use evidence of student thinking
Donuts	Donuts module has moderate degree of emphasis for principle Establish math goals to focus learning	Donuts module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Donuts module has high degree of emphasis for principle Use and connect math representations	Donuts module has no degree of emphasis for principle Facilitate meaningful math discourse	Donuts module has high degree of emphasis for principle Pose purposeful Questions	Donuts module has high degree of emphasis for principle Build procedural fluency from conceptual understanding	Donuts module has no degree of emphasis for principle Support productive struggle in learning math	Donuts module has no degree of emphasis for principle Elicit and use evidence of student thinking
Half of a whole*	Half of a whole module has moderate degree of emphasis for principle Establish math goals to focus learning	Half of a whole module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Half of a whole module has no degree of emphasis for principle Use and connect math representations	Half of a whole module has high degree of emphasis for principle Facilitate meaningful math discourse	Half of a whole module has high degree of emphasis for principle Pose purposeful Questions	Half of a whole module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Half of a whole module has no degree of emphasis for principle Support productive struggle in learning math	Half of a whole module has no degree of emphasis for principle Elicit and use evidence of student thinking
Bubble Gum	Bubble Gum module has moderate degree of emphasis for principle Establish math goals to focus learning	Bubble Gum module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Bubble Gum module has high degree of emphasis for principle Use and connect math representations	Bubble Gum module has no degree of emphasis for principle Facilitate meaningful math discourse	Bubble Gum module has high degree of emphasis for principle Pose purposeful Questions	Bubble Gum module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Bubble Gum module has no degree of emphasis for principle Support productive struggle in learning math	Bubble Gum module has no degree of emphasis for principle Elicit and use evidence of student thinking
Multiplication String	Multiplication String module has moderate degree of emphasis for principle Establish math goals to focus learning	Multiplication String module has high degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Multiplication String module has no degree of emphasis for principle Use and connect math representations	Multiplication String module has no degree of emphasis for principle Facilitate meaningful math discourse	Multiplication String module has no degree of emphasis for principle Pose purposeful Questions	Multiplication String module has high degree of emphasis for principle Build procedural fluency from conceptual understanding	Multiplication String module has no degree of emphasis for principle Support productive struggle in learning math	Multiplication String module has no degree of emphasis for principle Elicit and use evidence of student thinking
Hungry Caterpillar	Hungry Caterpillar module has moderate degree of emphasis for principle Establish math goals to focus learning	Hungry Caterpillar module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Hungry Caterpillar module has moderate degree of emphasis for principle Use and connect math representations	Hungry Caterpillar module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Hungry Caterpillar module has moderate degree of emphasis for principle Pose purposeful Questions	Hungry Caterpillar module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Hungry Caterpillar module has moderate degree of emphasis for principle Support productive struggle in learning math	Hungry Caterpillar module has moderate degree of emphasis for principle Elicit and use evidence of student thinking

	Establish math goals to focus learning	Implement tasks that promote reasoning and problem solving	Use and connect math representations representa- tions	Facilitate meaningful math discourse	Pose purposeful Questions	Build procedural fluency from conceptual understanding under- standing	Support productive struggle in learning math	Elicit and use evidence of student thinking
Middle School
Candy Jar*	Candy Jar module has moderate degree of emphasis for principle Establish math goals to focus learning	Candy Jar module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Candy Jar module has moderate degree of emphasis for principle Use and connect math representations	Candy Jar module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Candy Jar module has moderate degree of emphasis for principle Pose purposeful Questions	Candy Jar module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Candy Jar module has moderate degree of emphasis for principle Support productive struggle in learning math	Candy Jar module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
Calling Plans 2	Calling Plans 2 module has moderate degree of emphasis for principle Establish math goals to focus learning	Calling Plans 2 module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Calling Plans 2 module has no degree of emphasis for principle Use and connect math representations	Calling Plans 2 module has no degree of emphasis for principle Facilitate meaningful math discourse	Calling Plans 2 module has high degree of emphasis for principle Pose purposeful Questions	Calling Plans 2 module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Calling Plans 2 module has no degree of emphasis for principle Support productive struggle in learning math	Calling Plans 2 module has no degree of emphasis for principle Elicit and use evidence of student thinking
Hexagon	Hexagon module has moderate degree of emphasis for principle Establish math goals to focus learning	Hexagon module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Hexagon module has moderate degree of emphasis for principle Use and connect math representations	Hexagon module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Hexagon module has moderate degree of emphasis for principle Pose purposeful Questions	Hexagon module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Hexagon module has high degree of emphasis for principle Support productive struggle in learning math	Hexagon module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
Counting Cubes*	Counting Cubes module has moderate degree of emphasis for principle Establish math goals to focus learning	Counting Cubes module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Counting Cubes module has high degree of emphasis for principle Use and connect math representations	Counting Cubes module has high degree of emphasis for principle Facilitate meaningful math discourse	Counting Cubes module has no degree of emphasis for principle Pose purposeful Questions	Counting Cubes module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Counting Cubes module has no degree of emphasis for principle Support productive struggle in learning math	Counting Cubes module has no degree of emphasis for principle Elicit and use evidence of student thinking
Two Tanks	Two Storage Tanks module has moderate degree of emphasis for principle Establish math goals to focus learning	Two Storage Tanks module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Two Storage Tanks module has high degree of emphasis for principle Use and connect math representations	Two Storage Tanks module has no degree of emphasis for principle Facilitate meaningful math discourse	Two Storage Tanks module has high degree of emphasis for principle Pose purposeful Questions	Two Storage Tanks module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Two Storage Tanks module has no degree of emphasis for principle Support productive struggle in learning math	Two Storage Tanks module has high degree of emphasis for principle Elicit and use evidence of student thinking
Triangle	Triangle module has moderate degree of emphasis for principle Establish math goals to focus learning	Triangle module has high degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Triangle module has no degree of emphasis for principle Use and connect math representations	Triangle module has no degree of emphasis for principle Facilitate meaningful math discourse	Triangle module has no degree of emphasis for principle Pose purposeful Questions	Triangle module has high degree of emphasis for principle Build procedural fluency from conceptual understanding	Triangle module has no degree of emphasis for principle Support productive struggle in learning math	Triangle module has no degree of emphasis for principle Elicit and use evidence of student thinking

	Establish math goals to focus learning	Implement tasks that promote reasoning and problem solving	Use and connect math representations representa- tions	Facilitate meaningful math discourse	Pose purposeful Questions	Build procedural fluency from conceptual understanding under- standing	Support productive struggle in learning math	Elicit and use evidence of student thinking
High School
Pay It Forward*	Pay It Forward module has moderate degree of emphasis for principle Establish math goals to focus learning	Pay It Forward module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Pay It Forward module has moderate degree of emphasis for principle Use and connect math representations	Pay It Forward module has moderate degree of emphasis for principle Facilitate meaningful math discourse	Pay It Forward module has moderate degree of emphasis for principle Pose purposeful Questions	Pay It Forward module has moderate degree of emphasis for principle Build procedural fluency from conceptual understanding	Pay It Forward module has moderate degree of emphasis for principle Support productive struggle in learning math	Pay It Forward module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
S-Pattern*	S - Pattern module has moderate degree of emphasis for principle Establish math goals to focus learning	S - Pattern module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	S - Pattern module has moderate degree of emphasis for principle Use and connect math representations	S - Pattern module has no degree of emphasis for principle Facilitate meaningful math discourse	S - Pattern module has moderate degree of emphasis for principle Pose purposeful Questions	S - Pattern module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	S - Pattern module has high degree of emphasis for principle Support productive struggle in learning math	S - Pattern module has moderate degree of emphasis for principle Elicit and use evidence of student thinking
Playground	Playground module has moderate degree of emphasis for principle Establish math goals to focus learning	Playground module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Playground module has no degree of emphasis for principle Use and connect math representations	Playground module has no degree of emphasis for principle Facilitate meaningful math discourse	Playground module has high degree of emphasis for principle Pose purposeful Questions	Playground module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Playground module has high degree of emphasis for principle Support productive struggle in learning math	Playground module has no degree of emphasis for principle Elicit and use evidence of student thinking
Bike and Truck	Bike and Truck module has moderate degree of emphasis for principle Establish math goals to focus learning	Bike and Truck module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Bike and Truck module has no degree of emphasis for principle Use and connect math representations	Bike and Truck module has high degree of emphasis for principle Facilitate meaningful math discourse	Bike and Truck module has high degree of emphasis for principle Pose purposeful Questions	Bike and Truck module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Bike and Truck module has no degree of emphasis for principle Support productive struggle in learning math	Bike and Truck module has no degree of emphasis for principle Elicit and use evidence of student thinking
Calling Plans 1	Calling Plans 1 module has moderate degree of emphasis for principle Establish math goals to focus learning	Calling Plans 1 module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Calling Plans 1 module has high degree of emphasis for principle Use and connect math representations	Calling Plans 1 module has no degree of emphasis for principle Facilitate meaningful math discourse	Calling Plans 1 module has high degree of emphasis for principle Pose purposeful Questions	Calling Plans 1 module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Calling Plans 1 module has no degree of emphasis for principle Support productive struggle in learning math	Calling Plans 1 module has no degree of emphasis for principle Elicit and use evidence of student thinking
Sine Waves	Sine Waves module has moderate degree of emphasis for principle Establish math goals to focus learning	Sine Waves module has moderate degree of emphasis for principle Implement tasks that promote reasoning and problem solving	Sine Waves module has no degree of emphasis for principle Use and connect math representations	Sine Waves module has no degree of emphasis for principle Facilitate meaningful math discourse	Sine Waves module has high degree of emphasis for principle Pose purposeful Questions	Sine Waves module has no degree of emphasis for principle Build procedural fluency from conceptual understanding	Sine Waves module has high degree of emphasis for principle Support productive struggle in learning math	Sine Waves module has no degree of emphasis for principle Elicit and use evidence of student thinking

Effective Teaching Practices

Elementary Grade Band

The Case of Mr. Harris and the Band Concert*

During this session you will discuss NCTM's publication, Principles to Actions: Ensuring Mathematical Success for All, read and analyze a short case of a teacher, and discuss the eight teaching practices and relate them to the case.

Relates to all 8 principles

The Case of Jennifer DiBrienza and the Addition Strings Task

During this session you will watch a video clip of a class engaged in a whole class discussion on an addition string, discuss what the teacher does to support the students' learning of mathematics, and relate teacher actions in the video to the effective mathematics teaching practices.

Related principles:

Build procedural fluency from conceptual understanding
Implement tasks that promote reasoning and problem solving

The Case of Amanda Smith and the Donuts Task

During this session you will solve and discuss the Donuts Task and then watch video clips of a class working on the task. After viewing the video you will relate the teacher and student actions to the effective mathematics teaching practices and consider how you might apply specific mathematics teaching practices to your work.

Related principles:

Use and connect mathematical representations
Pose purposeful questions

The Case of Millie Brooks and the Half of a Whole Task*

During this session you will solve and discuss the Half of a Whole Task and watch a video clip of a teacher facilitating small group work using this task. You will then, discuss ways the teacher supports her students' learning of mathematics and connect specific teacher actions seen in the video to the Effective Mathematics Teaching Practices.

Related principles:

Facilitate meaningful mathematics discourse
Pose purposeful questions

The Case of Victoria Bill and the Bubble Gum Task

During this session you will solve and discuss the Bubble Gum Task, watch a video clip of a third grade class engaged in a whole discussion of a fraction task, discuss ways the teacher supports her students' learning of mathematics, and relate teacher actions in the video to the Effective Mathematics Teaching Practices.

Related principles:

Use and connect mathematical representations
Pose purposeful questions

The Case of Katherine Casey and the Multiplication Strings Task

During this session you will watch a video clip of a fourth grade class engaged in a whole discussion of a series of related multiplication equations, discuss what the teacher does to support the students' learning of mathematics, and relate teacher actions in the video to the Effective Mathematics Teaching Practices.

Related principles:

Implement tasks that promote reasoning and problem solving
Build procedural fluency from conceptual understanding

The Case of Ms. Bouchard and the Hungry Caterpillar Task

During this session you will examine the purpose and key messages of NCTM's publication, Principles to Actions: Ensuring Mathematical Success for All, read a case of a first-grade teacher using the Very Hungry Caterpillar Task with her students, discuss the eight mathematics teaching practices and relate them to the case, and reflect on next steps in strengthening these teaching practices in your own instruction .

Relates to all 8 principles

Middle School Grade Band

The Case of Mr. Donnelly and the Candy Jar Task*

Relates to all 8 principles

The Case of Elizabeth Brovey and the Calling Plans 2 Task

During this session you will solve and discuss the calling plans task parts 1 and 2, watch two video clips and discuss what the teacher does to support her students engagement in and understanding of mathematics, and discuss the effective mathematics teaching practice of Pose purposeful Questions.

Relates to the principle of:

Pose purposeful questions

The Case of Barbara Peterson, Patrica Rossman and the Hexagon Task

During this session you will solve and discuss the hexagon task, watch a video clip and discuss what the teacher does to support her students' engagement in and understanding mathematics, and discuss how the effective mathematics teaching practice of promote productive struggle connects to other effective mathematics teaching practices through comparing the video clip and a narrative case.

Relates to the principle of:

Supporting productive struggle in learning mathematics

The Case of Peter Dubno and the Counting Cubes Task*

During this session you will solve and discuss counting cubes task, watch the video clip and discuss what the teacher does to support his students' engagement in and understanding of mathematics, and discuss the effective mathematics teaching practices of use and connect mathematical representations and facilitate meaningful mathematical discourse.

Related principles:

Use and connect mathematical representations
Facilitate meaningful mathematics discourse

The Case of Elizabeth Brovey and the Two Storage Tanks Task

During this session you will solve and discuss the Two Storage Tanks Task, watch the video clip of a teacher facilitating small groupwork using this task, discuss ways the teacher supports her students' learning of mathematics, and connect specific teacher actions seen in the video clip to to the Effective Mathematics Teaching Practices.

Related principles:

Use and connect mathematical representations
Pose purposeful questions
Elicit and use evidence of student thinking

The Case of Kelly Polosky and the Triangle Task

During this session you will solve and discuss the Triangle Task, watch video clips and discuss what the teacher does to support her students' engagement in and understanding of mathematics, and discuss the effective mathematics teaching practice procedural fluency from conceptual understanding.

Relates to the principle of:

Build procedural fluency from conceptual understanding

High School Grade Band

The Case of Ms. Culver and the Pay it Forward Task*

Relates to all 8 principles

The Case of Jeffrey Ziegler and the S-Pattern Task*

During this session you will solve and discuss the S-Pattern Task, watch video clips and discuss what the teacher does to support his students' engagement in and understanding of mathematics. You will then discuss the effective mathematics teaching practice of support productive struggle.

Relates to the principle of:

Support productive struggle in learning mathematics

The Case of Debra Campbell and the Building a New Playground Task

During this session you will solve and discuss two versions of the Building a New Playground Task, watch the video clip and discuss what the teacher does to support her students' engagement in and understanding of mathematics, discussing the effective mathematics teaching practices of support productive struggle and Pose purposeful Questions.

Related principles:

Support productive struggle in learning mathematics
Pose purposeful questions

The Case of Shalunda Shackelford and the Bike and Truck Task

During this session you will solve and discuss the Bike and Truck Task, watch video clips and discuss what the teacher does to support her students' engagement in and understanding of mathematics. Using the same video clips, you will also talk through the effective mathematics teaching practice of facilitate meaningful mathematical discourse.

Related principles:

Facilitate meaningful mathematics discourse
Pose purposeful questions

The Case of Wobberson Torchon and the Calling Plans 1 Task

During this session you will solve and discuss the Calling Plans Task, watch the video clip and discuss what the teacher does to support her students' engagement in and understanding of mathematics, and discuss the effective mathematics teaching practices of Pose purposeful Questions and use and connect mathematical representations.

Related principles:

Use and connect mathematical representations
Pose purposeful questions

The Case of Barbara Lynch and the Investigate the Graphs of Sine Waves Task

During this session you will solve and discuss the homework of Sine Waves task, read the case study and discuss what the teacher does to support her students engagement and understanding of mathematics, and discuss the effective mathematics teaching practice elicit and use evidence of student thinking.

Related principles:

Pose purposeful questions
Support productive struggle in learning mathematics
Elicit and use evidence of student thinking

Guiding Principles

Equitable Pedagogy

Equity and Access - All grades
Participants will consider productive and unproductive beliefs with an emphasis on facilitating all students' development of mathematical processes and practices. Participants will be challenged to consider beliefs that hinder students' mathematical growth. The mathematics teaching practices from Principles to Actions will be discussed as a strategy for promoting growth mindsets in students and teachers.

Using Identity and Agency to Frame Access and Equity

Equity and Access - All grades
Vignettes and the voices of students, teachers, and other school personnel are used to develop identity (beliefs about oneself, mathematics, etc.) and agency (the presentation of one's identity) as a framework for defining and addressing obstacles. Effective Teaching Practices support the cultivation of a positive identity and agency.