Math
Principles and Standards for School Mathematics, published in 2000 by the National Council of Teachers of Mathematics (NCTM), outlines the essential components of a highquality school mathematics program. It calls for and presents a common foundation of mathematics to be learned by all students. It emphasizes the need for wellprepared and wellsupported teachers and administrators. It acknowledges the importance of a carefully organized system for assessing students’ learning and a program’s effectiveness. It also underscores the need for all partners— students, teachers, administrators, community leaders, and parents—to contribute to building a highquality program for all students.
Educational decisions made by teachers, school administrators, and other professionals have important consequences for students and for society. The Principles for school mathematics provide guidance in making these decisions.
The Principles
The six Principles address overarching themes:

Equity. Excellence in mathematics education requires equity—high expectations and strong support for all students.

Curriculum. A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades

Teaching. Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.

Learning. Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

Assessment. Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.
The Standards
The Standards for school mathematics describe the mathematical understanding, knowledge, and skills that students should acquire from prekindergarten through grade 12. Each Standard consists of two to four specific goals that apply across all the grades.
The five Content Standards each encompass specific expectations, organized by grade bands:
The five Process Standards are described through examples that demonstrate what each standard looks like and what the teacher's role is in achieving it:

Problem Solving

Reasoning & Proof

Communication

Connections

Representation
Resources
This is the article that Shannon shared in her math PD about Inquirybased teaching.
https://mathteachingstrategies.wordpress.com/2008/11/24/inquirybasedteaching/
Also, please see the attached pdf article Never Say Anything a Kid Can Say. This article speaks to our philosophy of productive struggle for students and not just telling them how to solve.