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Understanding Common Core Math

Understanding Common Core Math

Author: Jody Waltman

In this lesson, students learn the origin and purpose of the CCSS math standards. Students connect the content and practice standards. Students also evaluate the major instructional shifts required by the math CCSS.

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In this tutorial, we'll take an in depth look at the Common Core math standards. We'll begin by discussing the history of the Common Core math standards. We'll talk about the notable shifts in mathematics education that have been called for by the Common Core math standards, including more depth and fewer topics, coherence, and rigor. Finally, we'll share some considerations that you may want to keep in mind as you work with the Common Core math standards. Let's get started.

Work on the Common Core math standards started in 2009 when state leaders from 48 states and the District of Columbia, along with two territories, began work that was supported by Achieve, which is an independent nonprofit organization that focuses on educational reform, and the National Governors Association Center for Best Practices, or the NDA Center. The Council of Chief State School Officers, or CCSSO, also supported this work.

This group divided the standards into two categories, college and career readiness, and K-12 standards. The College and Career Readiness Standards outline what students should know and understand by the time that they graduate from high school. The K-12 standards, in contrast, outline what students should know and be able to do at each grade level, from elementary school all the way through high school. These content standards are labeled by grade level and content area.

One of the fundamental features of the Common Core math standards is that they call for some pretty major key shifts in mathematics education. As a result of the Common Core standards focus on skills and knowledge that students need for college and careers, and for life in general, they call for three major changes.

First, more depth and greater focus on fewer topics. In other words, instead of listing potentially hundreds of topics that each grade level, the Common Core math standards call for greater focus on the major work that needs to be accomplished at each grade level. In kindergarten through second grade, the focus is on addition and subtraction. In grades three through five, multiplication and division of whole numbers and fractions is the focus. In grade six, the focus shifts to ratios and proportions, algebraic expressions, and equations. In grade seven, ratios and proportions continue to be studied along with arithmetic with rational numbers. And, in grade eight, linear algebra and linear functions are the focus.

The idea here is that we want to put an emphasis on building some solid foundational knowledge and comprehension in these skills. We want to help students establish and practice fluency in mathematical processes and skills, and we want students to be able to apply those mathematical skills to real world problem solving contexts.

The next fundamental shift is coherence, defined as linking topics and thinking across the standards. The Common Core math standards aim to provide a coherent progression between grade levels that fosters connections among the standards at those different grade levels. In this organization, the major topics are scaffolded or reinforced by complimentary topics throughout the varying grade levels.

Here's an example, in grade one students are asked to order three objects by length and then compare the lengths of two objects indirectly by using a third object. In grade two, students build on this scale they measure to determine how much longer one object is than another, and they express that length difference in terms of the standard unit of length. In grade four you can see the progression of these skills as students are now expected to know relative sizes of measurement units within one system of units. We can definitely see coherence here among these various grade level standards and the scaffolded skill levels that are built in.

The third major shift in mathematics education called for by the Common Core math standards is rigor. Defined as pursuing conceptual understanding, procedural skills and fluency, and application with equal intensity. Rigor does not necessarily mean just introducing tougher skills at younger grade levels. Instead, it means helping students to attain deep levels of understanding at every grade level. Within each set of grade level standards, we want to help students build conceptual understanding, procedural skills and fluency, and application.

Conceptual understanding refers to the ability to understand key concepts in mathematics from a variety of perspectives. In other words, we want students to understand the why of mathematics. Procedural skills and fluency refers to the speed and accuracy with which students can perform mathematical calculations. Finally, application means applying mathematical practices and concepts across a wide variety of situations, settings, and real world problems.

Here are some things to consider as you study and perhaps implement the Common Core math standards. First, although the Common Core math standards are used by the majority of states in the United States, they are not nationally adopted standards. Each state can choose whether or not they adopt Common Core math.

Also, there is no standardized assessment that is used with Common Core math. Some states will use the PARCC assessment, some states will assess using the Smarter Balanced assessment, and still others will develop their own statewide assessments. Because there's such a wide variety of assessment types, it may not be possible to make national or state comparisons of student achievement. It is worth noting that several standardized assessments, including the SAT, the AP exam, and be ACT exam are begin to incorporate Common Core standards into their assessments.

In this tutorial we took an in depth look at the Common Core mathematics standards. We discussed the history of Common Core math standards and identified the three notable shifts in mathematics education that are called for by these standards; more in depth coverage in fewer topics, coherence, and rigor. Finally, we shared some considerations that you should keep in mind as you study and, perhaps, implement the Common Core math standards.

Now it's time for you to stop and reflect. Has your state adopted the Common Core mathematics standards? Are you comfortable with implementing the three key shifts into your curriculum planning?

As you reflect on how this new information can be applied, you may want to explore the additional resources section that accompanies this video presentation. This is where you'll find links to resources chosen to help you deepen your learning and explore ways to apply your newly acquired skill set.

Thanks for watching. Have a great day.

Notes on "Understanding Common Core Math"

(00:00 - 00:30) Introduction

(00:31 - 01:28) History

(01:29 - 04:57) Shifts in Math Education

(04:58 - 05:51) Considerations

(05:52 - 06:16) Review

(06:17 - 06:47) Stop and Reflect

Additional Resources

Common Core State Standards for Mathematics Flip Book 

This is a terrific tool from the National Council of Teachers of Mathematics in Kansas that helps in implementing the mathematical standards. The flip book provides teachers with instructions on how to apply the standards at their grade level, and offers examples and embedded professional learning within the document. Here is a link to the kindergarten flip book as an example.


This is a great portal of online lessons aligned to the ELA and Math CCSS by grade level. Teachers can create playlists and track data within this free resource. Also included are handouts and communication components for parents.