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Professional Development: Deep Dive into the Math Shifts

Grades K–High School

Overview: The Deep Dive into the Math Shifts Module is a 1–3 hour module for those who are already familiar with the shifts required by the Common Core State Standards for Mathematics (CCSSM). It provides you with a deeper understanding of these shifts. Using this module, you will take a deep dive into the major work of grades K–8, build a deeper understanding of the coherence of the Standards, and have an opportunity to work through sample problems that reflect the rigor that is expected by the Standards. If you are looking for an introduction to the shifts, please click here.

How to Get Started: You are encouraged to customize any or all portions of this module to meet your needs, or the needs of your audience if you are facilitating this module for professional development. Be sure to read the User's Guide first! You can find it below the PowerPoint presentation.

What's in this Module?

  1. User's Guide
  2. PowerPoint Presentation 
  3. Three Activities: Focus, Coherence, and Rigor
  4. Extension Activity: Creating Problems
  5. Related Research and Readings

You can download all components of this module by clicking the "Download All" option on the left. You can also scroll down to learn more about the different approaches to using this professional development, and to preview the components of individual activities.

After completing this module, you are encouraged to engage with the key shifts required by the CCSSM through the iTunes U Courses, created by teachers for teachers.

 

PowerPoint Presentation

The PowerPoint presentation provides you with a closer look at the focus, coherence, and rigor required by the CCSSM. It highlights the two levels of focus in the Standards, the two levels of coherence in the Standards, and delves deeper into the concept of rigor. To view the notes that go with each slide, download the full PowerPoint.

User's Guide: Be Sure To Read This First!

The User's Guide is a detailed guide for you, the self-learner and/or facilitator. The guide includes a summary of the contents of the module, followed by suggestions for using the module—whether you have 1 hour or a full 3 hours. There is a summary of each of the activities and full references/links for all papers, videos, and other web resources.

If you have 1 hour...
  • View the PowerPoint presentation (15 min.)
  • Complete the Coherence Activity: Uncovering Progressions and Themes (45 min.)
  • Use the remaining module components (Engaging with the Content, Analyzing Sample Problems, Extension Activity, Related Readings & Discussion Questions, Additional Videos & Web Resources) as time permits throughout the year (e.g., for future self-learning, in PLCs, during common planning times)
If you have 2 hours...
  • View the PowerPoint presentation (15 min.)
  • Complete the Focus Activity: Engaging with the Content (30 min.)
  • Complete the Coherence Activity: Uncovering Progressions and Themes (45 min.)
  • Complete the Rigor Activity: Analyzing Sample Problems (30 min.)
  • Use the remaining module components (Extension Activity, Related Readings & Discussion Questions, Additional Videos & Web Resources) as time permits throughout the year (e.g., for future self-learning, in PLCs, during common planning times)
If you have 3 hours...
  • View the PowerPoint presentation (15 min.)
  • Complete the Focus Activity: Engaging with the Content (30 min.)
  • Complete the Coherence Activity: Uncovering Progressions and Themes (45 min.)
  • Complete the Rigor Activity: Analyzing Sample Problems (45 min.)
  • Complete the Extension Activity: Creating Problems to meet the Focus, Coherence, and Rigor of the Standards (45 min.)
  • Use any remaining module components (Related Readings & Discussion Questions, Additional Videos & Web Resources) as time permits throughout the year (e.g., for future self-learning, in PLCs, during common planning times)

 

All times are suggested and can be expanded to incorporate more discussion as needed. Any portions of this module may be modified, reproduced, and disseminated without prior permission.

Three Activities: Focus, Coherence, and Rigor

There are three embedded activities that will strengthen your understanding of the shifts. Allow for time after each activity for reflection. Materials for the three activities are below. The answer key for the Coherence Activity is available using the "Download All" option above.

Focus Activity: Engaging with the Content

Focus strongly where the Standards focus

You may choose to engage in the K–2 and 3–5 grade band activities or the 3–5 and 6–8 grade band activities, depending on your preference. Each activity allows you to consider the topics that require focus in each grade band (K–2, 3–5,and 6–8) and think about how this focus will impact your work. This activity includes opportunities for discussion with colleagues.

Coherence Activity: Uncovering Progressions and Themes

Think across grades; link to major topics within grades

This activity gets you involved in uncovering some of the thoughtful progressions and themes woven into the Standards. This activity makes vivid the concept of coherence across grades and within grades.

Activity Directions

Printing Instructions

Application Cards (Forest Green)

Decompose Cards (Yellow)

Equations Cards (Yellow)

Fluency Cards (Red)

Place Value Cards (Pink)

Number Line Cards (Blue)

Operations Cards (Lime Green)

 
Rigor Activity: Analyzing Sample Problems

In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity

You will solve problems specifically developed to illustrate the key shifts required by the CCSSM. You will also analyze and evaluate sample problems for their alignment to the Standards and their illustration of the shift of rigor. The sample problems provided will encourage discussion about conceptual understanding, procedural skill and fluency, and application.

Extension Activity

 Creating problems that meet the focus, coherence, and rigor required by the CCSSM

You will use your understanding of focus, coherence, and rigor to create a set of CCSSM-aligned problems in one domain over a particular grade band. You may need additional time to finish this extension activity.

Directions Samples

The five articles below can be used in professional learning communities (PLCs) or as post-reading for this professional development session. These readings are shared to support teachers' understandings of the intellectual and academic implications of the Standards. You will find discussion questions on each of the articles by following the provided link on the right. The articles recommended for this module are:

K–8 Publishers' Criteria for the Common Core State Standards for Mathematics.

This document is meant to guide purchasing and reviewing decisions, and establish quality criteria for materials used in the classroom. In addition, the Publishers' Criteria can be a guide to review current text books, pacing guides, and curriculum maps for alignment to the CCSSM.

High School Publishers' Criteria for the Common Core State Standards for Mathematics.

This document is meant to guide purchasing and reviewing decisions, and establish quality criteria for materials used in the classroom. In addition, the Publishers' Criteria can be a guide to review current text books, pacing guides, and curriculum maps for alignment to the CCSSM.

 

The Structure is the Standards.

This essay, (also referred to as "The Grecian Urn Essay" found in the Appendix of the Publishers' Criteria for Mathematics, artfully captures the importance of seeing and understanding the structure in the Standards in order to maintain focus and coherence.

 

Progressions Documents for the Common Core State Standards for Mathematics.

The Progression Documents are a narrative of the Standards and "can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of mathematics."

Thinking About Place Value in Grade 2.

This packet describes the fundamental concepts of the place value standards and offers annotated examples of place value tasks that assess conceptual understanding.

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