Proportional Reasoning linked to Common Core Standards and other helpful Tools

Just recently a colleague – Roland O’Daniel – sent me a link to an incredible source, Tools for the Common Core Standards, for accessing instructional prototypes/information regarding the Common Core Standards (CCS) . The CommonCoreTools blog is by far one of the best, most useful and current that I have seen thus far. Each of these blog posts is authored by Bill McCallum. Some of these CCS tools are authored by the same, while others have appropriate references and sources.

The posted CCS Tools are: Progression of Ratios and Proportional Reasoning, Videos about the Standards, Choosing Curriculum Aligned with the Practices, Fractions Progression, Curriculum Analysis Tools, Examples of Structure in the CCS, Data within Measurement and Data Progression, Massachusetts Resources to help Teachers Engage with the CCS. Some of these are in draft form, but each provides an opportunity to comment on the Tool and to get reactions from other teachers. Other CTL blogs written in the past about the CCS, Response to Intervention, and Multiple Representations connect to this most recent CCS Tool.

Regarding Progression on Ratios and Proportional Relationships, 6-7 Ratio and Proportional Relationships, the connections to fractions, modeling, vocabulary, precision of measurement, multiple representations, and other CCS domain links are especially important and provide prototypes of where a teacher might start in linking instruction to the CCS. There are excellent models for developing conceptual understandings of equivalent ratios versus equivalent fractions, the double number line, and multiple representations; how structure is used for conceptual understanding; and connections to the CCS Domains of geometry, statistics and probability.

This entire article/tool forced me to think deeply about the mathematics in proportional reasoning in ways that I had not considered and will provide a critical instructional source for teachers to look at the conceptual understanding rather than procedural/algorithmic approaches to ratios and proportions.

The Kentucky Department of Education (KDE), in “A Closer Look at the Mathematics Progression of the Kentucky Core Academic Standards, grades K – HS”  has done a nice job in connecting the progression of ratios and proportional reasoning against appropriate CCS Domains. The Bill McCallum blog can be seen throughout as the G5 – G8 student progresses in their understanding and application of number to ratios to proportional reasoning. See below for that progression.

progression table 5th

rp table 2

rp table 3

rp table 4

Check out Bill McCallum’s blog and send comments as you react to, and use, these important and useful CCS Tools.

Additionally, a comprehensive listing of the most current Progression Documents for the Common Core Standards in Mathematics can be found at Progressions Project by ASU’s Institute for Mathematics and Education.

Products to date, as listed on the website are:

Draft 3–5 progression on Number and Operations—Fractions

Data part of the K–5 progression on Measurement and Data

Draft K–5 Progression on Number and Operations in Base Ten

Draft K–5 Progression on Counting and Cardinality and Operations and Algebraic Thinking

Draft 6–8 Progression on Expressions and Equations

Draft 6–7 Progression on Ratios and Proportional Relationships

There will be more CCS Tools to come and thanks to the writing committees for these instructional connections.


  1. I found your blog posts to be particularly helpful regarding instructional suggestions and interpretations of the CCS. For a number like 60 having the student to think of it as being 6 groups of 10’s through counting by tens, holding manipulatives, and counting it off on the number line (the CCS stress the use of the number line for conceptual understanding of numbers) will assist with giving meaning to the number.
    Elementary teachers are especially eager for this kind of assistance. I am anxious to read your other posts.

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