First of all, a friend of mine directed to me a great resource on the common core which had math vocabulary lists for all grade levels. This site is from a school district in Utah. I had some concerns about one or two of the terms used on the third grade list because I couldn't find them in the standards documents. The elementary math coordinator from their district told me that the majority of the words are common core. Actually, she believes they all are, but some did come from their math series Houghton Mifflin Go Math. Honestly though, the site was great. Here is the

link. While looking through that site, I stumbled across a blog titled

Tools for the Common Core State Standards. It's author is Bill McCallum. He wrote the article

The Structure is the Standards. This article is a must read for Common Core. So much great information, so little time! Okay, now the reason I started this post in the first place. On that same vocabulary search I found a site from the University of Arizona that published some draft papers that describe the progression of the mathematics through each of the strands. The papers are labeled by grade level are very easy to read. What I loved most about the papers though is the one or two paragraphs at the end of each one that explains how the math at the lower grades is setting the foundation for the math in the grades beyond. It is very specific too. Want to know why it's important to compose and decompose shapes? Read the Geometry paper. Want to know why it's important to know algebra at the lower grades? Read the K-5 Operations and Algebraic Thinking page. Here is an example excerpt from the geometry:

Where the Geometry Progression is Heading

Composition and decomposition of shapes is used throughout geometry from Grade 6 to high school and beyond. Compositions and decompositions of regions continues to be important for solving a wide variety of area problems, including justiﬁcations of formulas and solving real world problems that involve complex shapes. Decompositions are often indicated in geometric diagrams by an auxiliary line, and using the strategy of drawing an auxiliary line to solve a problem are part of looking for and making use of structure

(MP7). Recognizing the signiﬁcance of an existing line in a ﬁgure is also part of looking for and making use of structure. This may involve identifying the length of an associated line segment, which in turn may rely on students’ abilities to identify relationships of line segments and angles in the ﬁgure. These abilities become more sophisticated as students gain more experience in geometry. In Grade 7, this experience includes making scale drawings of geometric ﬁgures and solving problems involving angle measure, surface area,

and volume (which builds on understandings described in the Geometric Measurement Progression as well as the ability to compose and decompose ﬁgures) 6/23/2012, comment at commoncoretools.wordpress.com.

Just for those teachers who sometimes ask, "Why do I need to teach this?" These papers answer the question.