Here the almost final draft of the Progression on Number and Operations in Base Ten, K–5. It incorporates many changes in response to comments here on this blog and elsewhere.

In addition to numerous small edits and corrections, and some redrawn figures, here are some of the more significant changes:

- The sidenote with glossary entry for algorithm was moved to first instance of “algorithm” together with some text on notation for standard algorithm (this piece is a revision of a paragraph that was in the main body of the previous version).
- Section on Strategies and Algorithm: The 2 old paragraphs were deleted and 3 new paragraphs were inserted. Reason: the new paragraphs give an overview of the organization of the NBT standards for strategies and algorithms explaining that students see efficient, accurate, and generalizable methods from the beginning of their work with calculation and that there is a progression from strategies to algorithms: for addition and subtraction (with whole numbers in K to Grade 4; and generalization to decimals in Grades 4 to 6), for multiplication (Grades 3 to 5) and division (Grades 3 to 6) with whole numbers, then decimals.
- The balance of emphasis on “special strategy” vs “general method” in the earlier progression has been shifted in this draft in the direction of general methods..
- Mathematical practices section was revised to focus more on the centrality of the SMPs, illustrating progression from strategy to algorithm and following the structure of the sections on computations, and strategy and algorithm.

As usual, please comment in NBT thread in the Forums.

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## About Bill McCallum

I was born in Australia and came to the United States to pursue a Ph. D. in mathematics at Harvard University, met my wife, and never went back. I am a professor at the University of Arizona, working in number theory and mathematics education.

I have been using a link

http://ime.math.arizona.edu/progressions/

to get to these progressions. I noticed that the document for NBT is not this latest version. Is there a better link to find the most updated versions of the progressions?

It took me a while, but this link should now be giving the most up to date version. You might need to refresh your browser to get it to update.