Number string structure and design

How are number strings designed? Typically, people tend to describe number strings as having the following structure

Entry problem

Helper problems

Challenge problem (or clunker)


This post from Math Coach on Demand (which also has a bunch of addition and subtraction number strings) describes the structure like this:

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Again, the concept of helper problems. But is there just one “formula” for a number string? Continue reading “Number string structure and design”

On the rug with Angela

It’s late in the school year and I’m sitting on the edge of the rug in Angela Fiorito’s 1st grade class at PS 158 in Manhattan. There is no doubt that the kids are excited to begin math, and, in particular, a number string. The class is working on addition, particularly making use of four strategies that were initiated and named after students in the classroom. Continue reading “On the rug with Angela”

True False and Fill in the Blank Number Strings for Second Grade

A teacher recently handed me a second grade interim assessment with some true or false and fill in the blank problems:

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She asked me if I could develop some number strings to help her students prepare for this assessment. It called to mind some equivalency number strings that are developed in the Trades, Jumps and Stops algebra unit (Contexts for Learning Mathematics) as well as some problems in the Thinking Mathematically book by Thomas Carpenter, Megan Franke, and Linda Levi (2003).   Continue reading “True False and Fill in the Blank Number Strings for Second Grade”

Developing Algebra

This string was developed by our colleague Bill Jacob, University of California, Santa Barbara, who is, among other things, an algebraist.  The post is written by our colleague Monica Mendoza, University of California, Santa Barbara who leads a summer algebra institute for teachers as part of her work at The Center for Mathematical Inquiry with Bill. Continue reading “Developing Algebra”

From additive to multiplicative thinking

A few weeks ago our colleague and collaborator Pam Weber Harris led a really interesting numeracy workshop at Math in the City (City College). A former high school teacher and now teacher educator based in Austin, Texas, Pam has expertise in many areas: technology, assessment, K-12 mathematics, and more recently numeracy routines.  Her latest publication, Building Powerful Numeracy for Middle and High School Students, is a direct outgrowth of number strings that extends our work to college level mathematics.  Pam renames number strings as problem strings, but the essence of the routine remains the same.

Continue reading “From additive to multiplicative thinking”