Common+Core+Standards

=Common Core Standards= toc

Getting Started
Creation of the Common Core Standards was organized, with a $35 million assist from the Bill and Melinda Gates Foundation, through the collaboration of two organizations: the National Governors Association Center of Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO). Their task was to determine what common knowledge and skills United States youngsters needed to have in order to be well prepared for college and careers. They began with two content areas: mathematics and English/language arts (ELA) from the kindergarten level through high school. Work has begun on developing common standards for science.

The Mathematics Work Team and Mathematics Feedback Group were populated by distinguished professors, members of state department of education offices, math instructional specialists, classroom teachers, and research scientists. The leader for this challenging task was Bill McCallum, head of the Department of Mathematics at the University of Arizona.

These math groups include plenty of professionals with mathematical and research experience. They looked at each other's work. Exploring the systems in countries with strong mathematical scores according to international testing also informed their decisions. The National Council of Teachers of Mathematics (NCTM), the leading authority on math education and policy in the United States, provided some structure for the new standards. Another source was //Adding It Up: Helping Children Learn Mathematics// from the 2001 Mathematics Learning Study Committee of the National Research Council.

Structure and Content
Most state math standards have used the structure put forth by the National Council of Teachers of Mathematics. Math is separated into five goals. These goals are the same for grades K-12 with, of course, increasing levels of complexity.


 * [[image:NCTMlogo.gif align="right" link="@http://www.nctm.org/"]]**Number and Operation**
 * **Measurement**
 * **Algebra**
 * **Geometry**
 * **Data Analysis and Probability**

The designers for the new Common Core standards went with a different plan and broke K-5 and 6-8 mathematics into six domains for each level:



Once the domains were determined the Common Core math standards were built on the idea of progressions. The progressions are narrative documents describing the progression of a topic--a domain--across a number of grade levels. The writers of the progressions carefully considered both research on children's cognitive development and the logical structure of mathematics. For each domain they discussed, “How should the concept progress?” Once they had the progressions in place the Work Team sliced them into grade level standards.

The layout of the standards is relatively straightforward. The overarching domain is seen above in red, Number and Operations in Base Ten. To the right is the shorthand, all math educators will become familiar with this, 3.NBT, which tells that this refers to 3rd grade in the domain of Number and Operations in Base Ten. Each domain contains between three to nine standards. The standard in the example above is "Use place value understanding and properties of operations to perform multi-digit arithmetic." Within each standard are specific skills grouped together in clusters. The Kentucky Association of School Administrators created a three-page overview chart, Common Core State Standards for Math--K-12 Overview, that can help those new to the standards see the big picture.

Now that the standards have been adopted the original team is further refining the Progression Documents. Bill McCallum, continuing his leadership role on the work team, posts drafts of the progressions and asks for feedback at their math team blog Tools for the Common Core. It is obvious that much time and care is going into crafting these documents. It is very open minded of this high-powered group to post their drafts and solicit public feedback. As of 12/2011 drafts for six of the twelve elementary and middle school progressions have been posted.  Progression  5/2011 || Ratios and Proportional Relationships (RP) Progression  9/2011 || Progression  5/2011 || The Number System (NS) || Progression  4/2011 || Expressions and Equations (EE) Progression  4/2011 || Progression  8/2011 || Functions (F) || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Progression-Measurement 6/2012 <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Progression-Data 6/2011 || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Statistics and Probability (SP) <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Progression 12/2011 || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Progression 6/2012 || <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Geometry (G) ||
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Progressions Documents for Math Standards **
 * <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 19px; text-align: center; text-decoration: none; vertical-align: baseline;">K-5 || <span style="background-color: transparent; color: #000000; display: block; font-family: Arial; font-size: 19px; text-align: center; text-decoration: none; vertical-align: baseline;">6-8 ||
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Counting and Cardinality (CC)
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Operations and Algebraic Thinking (OA)
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Number and Operations in Base Ten (NBT)
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Number and Operations--Fractions (NF)
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Measurement and Data (MD)
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Geometry (G) K-6

Dr. McCallum explains the importance of the progressions: //It is important to produce up-to-date versions of the progressions documents. They 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 the mathematics. This would be useful in teacher preparation and professional development, organizing curriculum, and writing textbooks. Progressions documents also provide a transmission mechanism between mathematics education research and standards. Research about learning progressions produces knowledge which can be transmitted through the progressions document to the standards revision process; questions and demands on standards writing can be transmitted back the other way into research questions.//

Common Core standards are new to all educators. Teachers will need to read not only the standards for their own grade level but for a few levels above and below. The Progression Documents are very insightful; they are based on research and experience. Analysis and discussion with colleagues will help math teachers understand the thought process behind the structure of each domain.

Common Core standards are not meant to be a list of skills for each grade level. As important as the nuts and bolts in each domain are the Standards for Mathematical Practice.


 * 1) **[[image:CCart.jpg align="right"]]Make sense of problems and persevere in solving them.**
 * 2) **Reason abstractly and quantitatively.**
 * 3) **Construct viable arguments and critique the reasoning of others.**
 * 4) **Model with mathematics.**
 * 5) **Use appropriate tools strategically.**
 * 6) **Attend to precision.**
 * 7) **Look for and make use of structure.**
 * 8) **Look for and express regularity in repeated reasoning.**

These practices are an amalgam of NCTM's process standards and the strands of mathematical proficiency discussed in //Adding It Up//. The Standards for Mathematical Practice are meant to be at the forefront of all decision making about math curriculum. When creating lessons teachers should plan to include these practices. Occasionally lessons should be designed around these concepts rather than specific skills. Students, and teachers too, will need to be taught HOW to "construct viable arguments and critique the reasoning of others."

What districts and educators really want to know now is "What is going to change? How different will my curriculum be?" After Illinois adopted the Common Core standards in June, 2010 the ISBE convened a group to conduct a gap analysis. The task was to compare the 1997 IL Standards with the Common Core. The group looked for items that were in both documents, items that were in the new document but not the old, and items that were now at a different level. Using a tool from Achieve.org, a major player in the Common Core initiative, the ISBE created a 242-page Excel spreadsheet, Comparison of 1997 Illinois Standards to Common Core Standards for Math. The Gap Analysis is meant to be a jumping off point, a tool for districts to use as they adjust their own curriculum.

The general consensus is that many standards have moved down to a lower grade. Teaching higher level topics, in a new way, with the expectation for deeper conceptual awareness will require some major professional development. It could be particularly challenging for teachers who are not math specialists. Elementary level teachers, who are expected to be expert in all content areas, will have to adapt to new standards in both math and English/language arts.



Extended discussion of the Common Core standards for high school goes beyond the scope of this project. One thing that the creators have suggested but not required is a change in the structure of the high school math courses. Currently high school math classes are segregated by topic: Algebra I, Geometry, Algebra II, Trigonometry, etc. The math Work Group believes that it would be more beneficial if these topics were integrated. They have suggested a sequence of Math I, Math II, Math III.

For more information about the structure of high school courses see Common Core State Standards for Mathematics, Appendix A: Designing High School Mathematics Courses Based on the Common Core Standards.

Most state standards have ended up being used as a checklist of skills that teachers needed to "cover" at each grade level. There is always a rush to get through all of the topics before the ISAT occurs in early March. Taking the time to mull over a topic or actually apply a skill with an engaging project rarely happens. Teachers feel pressured to present lessons in the most efficient way. Direct instruction lectures with a focus on the rule or the algorithm are the quickest way to cover material. This is bad on so many levels. This style of teaching is BORING! Especially with a topic as abstract as mathematics. When this lecture-based teaching technique is the predominant one used students that learn better with different styles tend to tune out and disengage. Rushing through foundational concepts can make a student's entire mathematical understanding shaky. The designers of the new math standards planned, specifically, to address this "inch deep, mile wide" problem.



The work of Richard Lesh and others at The Rational Number Project based at the University of Minnesota touches on the idea of Modes of Representation. When teaching and learning mathematics it is not enough to memorize rules and use algorithms. Asking students to explain a problem or a situation using a different modality often elicits groans. "If I understand it //this// way why should I have to draw a picture or explain it in writing?" Memorizing rules is an epidemic in math. Insisting that students use another modality can be an assessment, proving that conceptual learning has occurred.

//But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student's mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device// (such as FOIL-First, Outer, Inner, Last) //to expand a product such as (a+b)(x+y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a+b+c)(x+y). Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness. (McCallum)//

media type="custom" key="11760070" align="left"Dan Meyer is well known in math circles through his blog dy/dan. Before taking time out to work on his dissertation and do presentations around the country Mr. Meyer taught algebra in California. He took the eternal math student whine, “When are we ever going to use this?” to heart. By creating WCYDWT lessons (What Can You Do With This) he provides modeling, incorporates multimedia, and sparks interest in his students. Let me repeat that. The teacher sparks an interest...in algebra...in his students. The one-line description of his blog is “less helpful.” Mr. Meyer believes that by breaking down problems into subsets for students we do them a disservice. The uncertainty and struggle are important aspects of gaining problem solving skills. Mr. Meyer's TED Talk has been an inspiration to many math teachers and viewed by over a half a million people.

1) **Be less helpful.** This is the tagline on Dan Meyer's blog. a) When solving problems in real life one helpful skill is to be able to determine what information is relevant. In textbook sketches the measurements are frequently and helpfully labelled. However, "less helpful" would produce deeper thought. The process of determining relevant information is vital to successful problem solving. b) A related idea is breaking down a task into logical and orderly steps. Too often a complex math problem is conveniently broken down in a textbook into parts a through d. In reality breaking down the steps is an integral aspect of problem solving.

2) **Use engaging multimedia.** In the example Mr. Meyer gives in his presentation a textbook uses a line drawing to help students visualize filling a tank with water. To make the problem more compelling he took video of a hose filling a clear octagonal tank. The line drawing is static; the video is active. While the video is running the students can contribute ideas and suggestions and collaborate to make sense of the situation.

An April, 2011 article in the New York Times announced that the Pearson Foundation and the Bill and Melinda Gates Foundation, both non-profit organizations, are teaming up to create 24 online math and English/language arts courses aligned to the Common Core. The "courses will use video, interactive software, games, social media and other digital materials to present math lessons for kindergarten through 10th grade." Dan Meyer is involved with this project. Although the Pearson Foundation is designing the courses Pearson Education, the for-profit publishing company, will be marketing 20 of the courses to school districts. The Bill and Melinda Gates Foundation has donated $3 million so that four of the courses can be offered for free. This will give educators an idea what a professionally designed, Common Core-aligned, technologically advanced course could look like. It is also a great marketing scheme to sell the other 20 courses. Most of the courses are scheduled to be completed by January, 2013.

There has been much uncertainty about how, exactly, the new standards will be different. Finally, slowly, some information is trickling out from the Common Core math work group. They have created a website called The Illustrative Mathematics Project.

//The Illustrative Mathematics Project will provide guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.//

//This website is currently under construction. On completion, it will provide a process for submitting, discussing, reviewing, and publishing tasks. It will also display the standards in multiple views and provide easy access to tasks associated with individual standards and tasks associated with higher order structures in the standards.//

As of December, 2011 only a few of the standards have "illustrations." Those that do may also include tips for using multiple modalities, teaching ideas, or common errors.



One aspect of the new standards that differs from the current IL standards is the focus on number sense in earlier grades. Number sense is an intuitive grasp numbers, how they work, how they compare and relate to each other. Without number sense any other mathematical learning is just going through the motions.



Take the old bugaboo fractions for example. Students may be introduced to the idea of fractions in third or fourth grade. Before long the kids are using rules and algorithms to find common denominators and add and subtract fractions. This tends to happen before the students have a firm grasp of the concept of a fractional part--what numerators and denominators really represent. Then, to pile on, multiplication and division are introduced. These operations with fractions are challenging concepts and form the basis of later learning such as proportions and equation solving. Focusing on number and operation early for an extended period of time and in a deeper way should provide a much stronger foundation for later complex mathematical thinking.

Assessment
One aspect of the Race to the Top competition was to choose two organizations to design the assessments for the new Common Core standards. In September, 2010 SMARTER Balanced Assessment Consortium and Partnership for Assessment of Readiness for College and Careers (PARCC) were chosen. Illinois is one of 24 states that comprise PARCC.

These two organizations are now in a race against the clock to design appropriate assessments, choose a test-creation company, and have all of it ready for the start of the 2014-2015 school year. In October, 2011 PARCC posted an Excel spreadsheet, PARCC Major Milestones, that lays out their schedule for the next three years. The tracks include Governance, Transition and Implementation, Educator Engagement and Instructional Models, Technology, and more. Math leaders and administrators have been eagerly awaiting news in many of these areas, especially Model Instructional Units. It looks like development of these units will begin in May, 2012 and the first set are scheduled to be released in October, 2012.

Originally the assessment plan was as shown in the image. Assessments 1, 2, and 3 would occur at the ends of the first three quarters with a comprehensive assessment at the end of the year. Many states had issues with this design. One concern was that end-of-quarter assessments would have the effect of locking in curriculum sequence. Another problem was that such frequent, required testing would be disruptive to the school schedule and the learning process. The biggest concern, though, was that this plan would be too expensive.

A June, 2011 letter to the state chiefs of education from the governing board of PARCC said that it had received this feedback and made adjustments to the assessment schedule. The latest information is that Assessments 1 and 2 will be available but optional while the last two would be mandatory.

//Component 3 (Required, counts toward summative score): Rich Performance‐Based Assessments in grades 3‐8 and high school administered as close to the end of year as possible. Priorities in ELA/literacy will include focusing on writing effectively when analyzing text; in mathematics, priorities will include focusing on application of concepts, skills and understandings. This assessment will be comprised primarily of performance tasks and will be scored in time to be incorporated into the end‐of‐year summative score for each student.//

//Component 4 (Required, counts toward summative score): Grades 3‐8 end‐of‐year assessments comprised of innovative, computer‐based machine‐scorable items focusing on reading and comprehending complex texts in ELA/literacy, and the full range of standards in mathematics. (PARCC)//

On November 29, 2011 it was announced that PARCC awarded a contract worth $1.5 million to the University of Pittsburgh to "develop prototype student assessments as well as exemplary instructional tasks for the Common Core ELA/literacy state standards." Presumably similar news will soon be forthcoming regarding mathematics.

In a change from the current state tests these assessments will all be computerized. Results will be available sooner which means that schools and teachers will be able to use the data to guide instruction. Districts need to begin preparing their technology infrastructure and hardware to ensure that test taking will go smoothly in the 2014-2015 school year.

One thing is known for the short term. There will be no Common Core questions or procedures on the 2012 ISATs. Additionally, for the first time, the ISBE will not be releasing any new test preparation materials. This is an obvious indicator that the state is gearing up to phase out ISAT and prepare for new assessments. Additionally the writing test has been suspended for the 2012 test.

<span style="background-color: #ffffce; color: #000066; font-family: Arial; font-size: 16px; text-decoration: none; vertical-align: baseline;"> There will be no new ISAT Sample Books for the 2011-2012 school year. Please use the existing 2011 Sample Books for test preparation for the spring 2012 ISAT tests.

Another question about the PARCC assessments is "Will they take the place of any current assessments?" Kids these days spend a lot of time taking tests--a beginning of the year diagnostic, MAP tests three times a year, Cog ATs to determine eligibility for gifted programs or special ed, EXPLORE test in 8th grade for high school placement, district-wide end-of-semester common finals, ISATs, not to mention the quizzes and tests from the classroom teachers. According to PARCC's Major Milestone plan they will be field testing through the spring of 2012 and hope to have prototypes for the Instructional Tasks and the Final Assessments complete in July, 2012. In August, 2011 PARCC released a draft form of what they are calling Model Content Framework. The Model Content Frameworks are voluntary resources offered by PARCC to help curriculum developers and teachers as they work to implement the standards in their states and districts. They are designed with the following purposes in mind:
 * Supporting implementation of the Common Core State Standards, and
 * Informing the development of item specifications and blueprints for the PARCC assessments in grades 3–8 and high school.

For a two-week window in August, 2011 PARCC solicited feedback from the public. More than 1,000 people responded and PARCC made some adjustments including making the math framework shorter by a third. In October, 2011 the 78-page, version 1.0 of the Model Content Framework was unveiled.

Professional Development and Implementation
As recently as September, 2011 there were only scraps of information available about how teachers should go about adjusting their teaching and curriculum in order to prepare for Common Core standards. The parties involved have been working feverishly and there has been a flood of information released recently.

Districts need to absorb all of this disparate information and prepare their teachers. Curriculum administrators should be keeping current on the releases from all of the Common Core-related organizations. Having a cadre of regional curriculum leaders will allow for sharing among peers and much needed collaboration. Remember that these standards are "common." This means that at least 47 states are going through exactly the same transition. At least 24 states are members of PARCC and will be preparing for the same assessments. It is not necessary for every district to invent the wheel independently. Illinois seems to be moving slowly in providing implementation resources but other PARCC consortium members are making good progress. Achieve, the organization that is coordinating the efforts of the PARCC consortium, releases helpful information. In September, 2011 they released From Ideas to Reality: A Recap of the Common Core State Standards in 2010-2011. Included are updates on positive strides taken in different areas of implementation. Louisiana, for instance, has done a nice job leveraging "state or regional leadership." Arizona and Washington have created well-designed "cross-walks" comparing current state standards to the Common Core. Sample curriculum maps and frameworks have been designed by Indiana and Ohio. The Tennessee Department of Education has created a digital resource center "to aid educators in their transition to CCSS." Illinois is presumably organizing some "train the trainer" modules in order to provide professional development to districts and regional offices of education. If Illinois state chiefs are not stepping up quickly enough then regional curriculum leaders need to organize on their own.

If a district-wide math committee is not already in place one needs to be created. Including members from all levels--primary, intermediate, middle, and high school will provide the widest input. Curriculum directors should provide an overview of the Common Core State Standards thus far and then delegate. Have smaller groups become expert in different areas and report back.

Outreach to teachers not involved in the math committee is crucial. One or two large-group meetings will not be sufficient or effective. Use technology to disseminate information in digestible chunks. Ask teachers to read something, the Progression Document for Ratio and Proportion for Grades 6-7 for example, then discuss during content area meetings and report back.

In November, 2011 the state of Kentucky was chosen as a demonstration site for a professional development model supporting the Common Core standards. Organized by Leaning Forward (formerly known as the National Staff Development Council) and supported by grants from foundations the group will design and deliver professional development. Six other states, including Illinois, will serve as "critical friends" in supporting this development. Leaning Forward said that professional development cannot be an occasional thing. They "support new school year and daily school schedules that provide substantive time for professional learning for educators." //(Gewertz)//

Self Study of CCSS
By adopting Common Core standards the states have put into motion a paradigm shift. Teachers will teach differently; students will learn differently. The concepts taught will be introduced at new grade levels. Assessments will demand deeper understanding not rote memorization. Implementation of these changes will be messy. Although it is a big task, here are the resources that forward-thinking math educators and all curriculum directors should absorb.


 * Step 1**--Read a comprehensive overview, perhaps this document. In this way you can learn how the Common Core Standards Initiative came to be. Additionally you can get a sense of who all the players and organizations are and what roles they play.


 * Step 2**--Read the Common Core State Standards themselves. If you are, say, a 7th grade teacher it would be a good idea to not only read the standards for your grade level but one grade above and below.


 * Step 3**--Read the Progression Documents. These are narratives that describe the progression of particular domains such as ratio and proportion or geometry. The progression documents are separated into K-5, 6-8, and high school. A well-prepared teacher should read the documents for all six domains for the level they teach.


 * Step 4**--In October, 2011 PARCC released the Model Content Framework. This is an attempt to put some “meat” on the bones of the standards and give some examples and possible curricular structure to the standards. Again, teachers should read the framework for the level they teach as well as the one above and below.


 * Step 5**--In November, 2011 the work group that wrote the math standards and is in process of creating the progression documents is slowly releasing some examples of the standards in action on their website, The Illustrative Mathematics Project. Explore the illustrations that have been released so far.


 * Step 6**--Stay current! Check in to the websites of important organizations such as Common Core Standards Initiative, PARCC, and ISBE on a regular basis. Education Week, a well-regarded information source, has a blog, Curriculum Matters, that provides current news and analysis.

Resources
Common Core State Standards Initiative. Retrieved December 5, 2011. @http://www.corestandards.org/

Common Core State Standards for Mathematics, <span class="wiki_link_ext">Appendix A: Designing High School Mathematics Courses Based on the Common Core Standards. 2010. @http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf

Common Core State Standards Initiative K-12 Standards Development Teams. Common Core State Standards Initiative. Retrieved December 3, 2011. www.corestandards.org/assets/CCSSI_K-12_dev-team.pdf

Curriculum Matters. Education Week blog. Retrieved December 5, 2011. @http://blogs.edweek.org/edweek/curriculum/

Comparison of 1997 Illinois Standards to Common Core Standards for Math. Illinois State Board of Education. July, 2010. @http://www.isbe.net/common_core/excel/Math_gap.xls

Dillon, Sam. //Foundations Join to Offer Online Courses for Schools.// New York Times. April 27, 2011. @http://www.nytimes.com/2011/04/28/education/28gates.html?_r=2&pagewanted=all

Gewertz, Catherine. Kentucky to Model Professional Development for New Standards. Education Week blog Curriculum Matters. November 4, 2011. @http://blogs.edweek.org/edweek/curriculum/2011/11/kentucky_to_model_professional.html

Gulley, Wendy. //Ten Research Findings From "Adding It Up"//. May, 2001. www.pisa.oecd.org/pages/0,2987,en_32252351_32235731_1_1_1_1_1,00.html

Lesh, Richard, et al. //The Rational Number Project-Initial Fraction Ideas//. University of Minnesota, College of Education & Human Development. 2009. @http://www.cehd.umn.edu/rationalnumberproject/rnp1-09.html

Model Content Framework. PARCC. October, 2011. @http://www.parcconline.org/sites/parcc/files/PARCC%20MCF%20for%20Mathematics_Fall%202011%20Release.pdf

The New Illinois Learning Standards Incorporating the Common Core. Illinois State Board of Education. Retrieved December 5, 2011. @http://www.isbe.net/common_core/default.htm

The Illustrative Mathematics Project. Retrieved December 1, 2011. @http://illustrativemathematics.org/standards/k8

PARCC Governing Board Meeting Follow-up to State Chiefs. PARCC. June, 29, 2011. @http://www.parcconline.org/sites/parcc/files/PARCCGoverningBoardMeetingFollow-uptoChiefs_1.pdf

Partnership for Assessment of Readiness for College and Careers. Retrieved December 5, 2011. @http://www.parcconline.org/

Progression Documents for the Common Core Math Standards. Institute for Mathematics and Education. Retrieved December 3, 2011. //http://ime.math.arizona.edu/progressions///

Tools for the Common Core. Retrieved December 1, 2011. @http://commoncoretools.wordpress.com/

Waggoner, Deborah. Common Core State Standards for Math--K-12 Overview. Kentucky Association of School Administrators. July, 2010. @http://www.kasa.org/professional_development/documents/MicrosoftWord-CommonCoreStateStandardsforMathgradesK12overview.pdf

White, Patricia L. //Pitt Awarded $1.5 Million to Develop Prototype Student Assessments and Instructional Tasks for the Common Core State Standards//. University of Pittsburgh News. November 29, 2011. @http://www.news.pitt.edu/Develop_Prototype_Student_Assessment