# Guide to the Common Core State Standards for Math (CCSSM)

## What are the Common Core State Standards?

The Common Core State Standards are guidelines—not a set curriculum—to help teachers ensure their students have the 21st century skills and knowledge they need to be successful by providing clear student learning goals for Math and Language Arts. Forty-five states have adopted the new voluntary Standards that promote equity by ensuring all students, no matter where they live, are well prepared with the skills and knowledge necessary to collaborate and compete with their peers in the United States and abroad.

### The Common Core State Standards for Math (CCSSM) and the Standards of Mathematical Practice

Like the Common Core Language Arts standards, the CCSSM define what students should understand and be able to do. The Common Core State Standards for Mathematics call for student understanding on a conceptual level, to grasp the foundational concepts behind math procedures and to continually engage in critical mathematical practices.

• Standards define what students should understand and be able to do.
• Clusters summarize groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.
• Domains are larger groups of related standards. Standards from different domains may sometimes be closely related.

The Standards for Mathematical Practice describe the attributes of mathematically proficient students, and how they engage with and learn mathematics. The Standards for Mathematical Practice stay the same from the earliest grades through high school:  1) Counting and Cardinality, 2) Comparing, Operations and Algebraic Thinking, 3) Number and Operations in Base Ten, and 4) Number and Operations in Fractions.

### What are the major goals of the CCSSM?

• Focus. Narrowing the scope of content covered in each grade allows students to more deeply understand material, and build a solid foundation for future work.
• Coherence. Standards, educational materials and teachers’ instructions are consistent to form a unified message that makes sense to students. For math, it is about make connections between mathematical topics so there is a smooth progression across grade levels.
• Rigor. ‘Rigor ‘means three things: conceptual understanding, procedural skill and fluency, and applications.

### Transitioning and implementing the Common Core State Standards

Watch a webinar about transitioning and implementing the Common Core.

The Common Core State Standards for Mathematics call for student understanding on a conceptual level, to grasp the foundational concepts behind math procedures and to continually engage in critical mathematical practices. Transitioning to teaching this mathematical way of thinking requires new tools and methods. One way to make the transition smoother is to formulate an overall plan and provide an online portal or wikispace for feedback, as well as a support system, online tools, and resources for teachers and administrators.

Read a white paper about how to successfully plan for CCSS for math.

### A Common Core math standard example

An example of how a Common Core math standard is structured can be seen in the very first one set for kindergarten:  CCSS.math.Coten. K.C.C.A. 1) Count to 1000 by ones and by tens. It is alignment and is a building block for the Standards for Mathematical Practice 1) Counting and Cardinality.

As the student advances through the curriculum, what changes is the way the Standards look as students engage with and master new and more advanced mathematical ideas that build upon and integrate with each other. So, standards and practice must be taught in tandem for the highest level of effectiveness.

### Aligning with the new standards

Because the CCSSM are guidelines and not a national curriculum, the task of ensuring proper alignment is up to teachers and school administrators. While this gives educators freedom to implement the standards in a way that will be most beneficial for their own students, it also means that they need to develop or find new CCSS aligned educational materials. The Partnership for 21st Century Skills has suggestions to help educators, with sample math lessons, and a framework for aligning curricula and assessments:

• Use backward-design principles (such as Understanding by Design, 1) to design curriculum that encourages inquiry-based learning and enables embedded, performance-based assessments.
• Develop interdisciplinary performance tasks and or project-based learning units that integrate the full P21 Framework in alignment with CCSS, consider capstone performance such as senior portfolios.
• Create curricula-embedded assessment to enable assessment as and for learning.
• Collect and share exemplary student work that demonstrates mastery of college and career ready knowledge and skills.
• Provide meaningful opportunities for educators to collaboratively review curricula, student work and student performance data in order to refine the curricula and assessments over time.

Take advantage of the Partnership for 21st Century Skills free Common Core toolkit.

The Common Core is designed to build understanding and to help the student realize that conceptual learning is a way of thinking and a skill. That means that the teacher acts as a guide, and creates an experiential environment to help students approach procedurally and conceptually, rather than teaching by rote. This means that the teacher or parents need to rethink their own approach to support re-engagement with math.

Stanford University offers online courses for educators, including free Common Core classes. Here are some additional resources from DreamBox that cover Common Core-aligned lesson plans and lessons by grade.

How technology helps implement the Common Core

Technology—both devices and software—can be invaluable tools in teaching to new math standards and to support blended learning. Lessons can available 24/7 to students so work can continue in and out of school. Online lessons step students through material, allow for review of challenging material, and for the teacher to access progress reporting. One of the most valuable technologies to teach Common Core subjects is adaptive learning technology. It is software that learns and alters itself based on the student’s responses. Adaptive technology, particularly intelligent adaptive learning technology, supports competency based learning because it adjusts the student’s learning path and pace within and between lessons, and advances the student based on comprehension. It also provides formative and summative data in Common Core-aligned progress reports to the student’s teacher, so instruction can be tailored to individual needs, understandings, and interest.