1. K–8 Session 1: Exploring the Critical Areas
Module 1: A Closer Look at the Common Core State Standards for Mathematics
K–8 Session 1:
Exploring the Critical Areas
Title slide [Welcome participants. They should be able to work alone as well as in small groups.]
Introduction: “In this session we are going to begin exploring critical areas for your grade which represent e key mathematical ideas in the Common Core State Standards (CCSS) for your grade level.”

2. Expected Outcomes
Understand that the critical areas describe key mathematical concepts for students to learn at each grade level.
Identify that the critical areas are designed to bring focus to the standards at each grade level.
Consider how the critical areas can be used to inform curriculum and guide instruction.
Review the expected outcomes for this session.
Understand that the critical areas describe key mathematical concepts for students to learn at each grade level.
Identify that the critical areas are designed to bring focus to the standards at each grade level.
Consider how the critical areas can be used to inform curriculum and guide instruction.

3. Introduce the Common Core State Standards (CCSS) for Mathematics.
Say, “The Common Core State Standards Initiative is a state-led effort coordinated by the National Governors Association Center for Best Practices and the Council of Chief State School Officers. The standards were developed in collaboration with teachers, school administrators, and experts, to provide a clear and consistent framework to prepare our children for college and the workforce.”
“The standards are informed by the highest, most effective models from states across the country and countries around the world, and provide teachers and parents with a common understanding of what students are expected to learn. Consistent standards will provide appropriate benchmarks for all students, regardless of where they live.
These standards define the knowledge and skills students should have within their K–12 education careers so that they will graduate high school able to succeed in entry-level, credit-bearing academic college courses and in workforce training programs. The standards:
Are aligned with college and work expectations;
Are clear, understandable, and consistent;
Include rigorous content and application of knowledge through high-order skills;
Build upon strengths and lessons of current state standards;
Are informed by other top performing countries, so that all students are prepared to succeed in our global economy and society; and
Are evidence-based.
Ask, “How is the implementation of the Common Core State Standards different than past standards implementations?”
Say, “In Oregon, implementation of these standards will be different in three ways:
Nationally developed resources and assessments will be shared
Both English Language Arts and Mathematics will be implemented simultaneously
Focus will be on attending to the Instructional Core”

4. The Instructional Core
Principle #1: Increases in student learning occur only as a consequence of improvements in the level of content, teachers’ knowledge and skill, and student engagement.
Principle #2: If you change one element of the instructional core, you have to change the other two.
Introduce the Instructional Core.
Say, “The instructional core includes three interdependent components: teachers’ knowledge and skill, students’ engagement in their own learning, and academically challenging content. Richard Elmore identifies a number of core principals as we consider implementing the instructional core, but for this introduction we’ll just identify two principles:
Principle #1: Increases in student learning occur only as a consequence of improvements in the level of content, teachers’ knowledge and skill, and student engagement. These three components need to be thought of as interdependent rather than isolated and independent of each other.
Principle #2: If you change one element of the instructional core, you have to change the other two. We cannot think of implementing the CCSS as just swapping out one set of standards for another. As we increase the rigor of the content, we must focus on using recent educational research to improve teacher content knowledge and practice and student engagement and ownership of their learning.” (Such as How People Learn, National Research Council; Looking Inside the Classroom, Horizon Research; Improving Instruction through Schoolwide Professional Development: Effects of the Data-on-Enacted-Curriculum Model, Rolf Blank)
Richard Elmore, Ph.D., Harvard Graduate School of Education 4

5. Organizational Elements
POLICIES, PROCESSES & PROCEDURES
STRUCTURES
RESOURCES
HUMAN, MATERIAL, MONEY
STAKEHOLDERS
CULTURE
Introduce the Organizational Elements
Say, “It is important to remember that the organizational elements that surround the instructional core are critical to the successful implementation of a districtwide improvement strategy.”
“The instructional core does not occur in isolation of these organizational elements, so any implementation strategy would need to take into consideration how these elements impact successful implementation.”
“In time, more information on implementation of the CCSS through an instructional core focus will be developed.”
“The purpose of this session is to give an overview of the Common Core State Standards for Mathematics, which is intended to help attend to the Teacher-Content interaction described in the instructional core. Future sessions will help deepen a teacher’s understanding of the new content, as well as help teachers understand the new Student-Content interaction (CCSS Standards for Mathematical Practices) and eventually Teacher-Student interactions.”
Adapted from the Public Education Leadership Project at Harvard University 5

6. Show the “Table of Contents.”
Highlight the different sections of the CCSS document:
Introduction
Provides a rationale for focus and coherence
Describes purpose of standards
Illustrates how to read the standards
Standards for Mathematical Practice
Outlines eight standards for all students to develop proficiency
Standards for Mathematical Content
Organized by grade level from kindergarten through grade 8
Organized by conceptual categories at the high school level
Glossary
Includes definitions
Sample of Works Consulted
Lists references

7. outline the essential mathematical ideas for each grade level.
For each grade level from kindergarten through grade 8, the Critical Areas
outline the essential mathematical ideas for each grade level.
Say, “During this session we are going to begin exploring the grade level standards for mathematical content. Here is a slide of the first page of the grade 2 mathematical content standards.
Read the top section of the slide:
In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.
Say, “The critical areas are designed to bring focus to the standards at each grade level by describing the big ideas that educators can use to build their curriculum and to guide instruction. For each grade, kindergarten through grade 8, there are two, three, or four critical areas. Notice that the critical areas at the top of this slide are described in more detail in the next paragraphs.”
Highlight that the one sentence descriptions at the top of the page correspond with the paragraphs below.

8. Exploring the Critical Areas
Identify at least one or two important mathematical concepts within this critical area. What do students need to learn prior to these concepts? How do these concepts support learning in later grades?
What evidence would convince you that a student understands these concepts?
What common misconceptions do students have when studying this critical area? What challenges have you had in teaching these critical area concepts?
Distribute Critical Areas Handouts [see materials section on page 1]
Note that teachers should examine the grades they teach. Suggest that groups form by grade level or grade bands. This activity can be repeated if a teacher teaches more than one grade level. Allow 35–60 minutes to study each grade.
Say, “In grade level groups (3–4 people in each group) you will analyze the critical areas and discuss the following questions.”
Identify at least one or two important mathematical concepts within this critical area. What do students need to learn prior to these concepts? How do these concepts support learning in later grades?
What evidence would convince you that a student understands these concepts?
What common misconceptions do students have when studying this critical area? What challenges have you had in teaching these critical area concepts?
As participants are working, keep track of their pacing to ensure that they have enough time to discuss all of the critical areas for their grade.
Encourage groups to spend no more than 10 minutes per critical area.

9. Whole Group Discussion
How do the mathematical concepts build from grade to grade?
What are the similarities in the types of evidence that would convince you that a student understands these ideas?
Are there common themes in student misconceptions and in challenges to teaching?
Compare the concepts in the critical areas with those that you are currently teaching. How are they similar? How are they different?
Discussion: (15 minutes)
Facilitate the whole group discussion. Starting with kindergarten or the lowest grade-level explored, ask each group to share highlights from their discussion.
Slide 9
Ask participants to consider the following questions as each group is sharing:
How do the mathematical concepts build from grade to grade?
What are the similarities in the types of evidence that would convince you that a student understands these ideas?
Are there common themes in student misconceptions and in challenges to teaching?
Compare the concepts in the critical areas with those that you are currently teaching. How are they similar? How are they different?

10. Expected Outcomes
Understand that the critical areas describe key mathematical concepts for students to learn at each grade level.
Identify that the critical areas are designed to bring focus to the standards at each grade level.
Consider how the critical areas can be used to inform curriculum and guide instruction.
Revisit the expected outcomes:
Understand that the critical areas describe key mathematical concepts for students to learn at each grade level.
Identify that the critical areas are designed to bring focus to the standards at each grade level.
Consider how the critical areas can be used to inform curriculum and guide instruction.

11. Reflection
How do the critical areas help to bring focus to the standards at your grade level?
How will you use the critical areas to inform your curriculum and guide your instruction?
What questions do you still have about the critical areas?
How has this activity increased your understanding of the instructional core?
Distribute Critical Areas Handout B (reflection worksheet)
Ask participants to answer the following questions on the handout:
How do the critical areas help to bring focus to the standards at your grade level?
How will you use the critical areas to inform your curriculum and guide your instruction?
What questions do you still have about the critical areas?
How has this activity increased your understanding of the instructional core?
Ask participants to share reflections (optional).