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:

Screen Shot 2016-03-29 at 5.27.20 PM

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”

30 ways to make number strings more inclusive

Image of teacher-made classroom sign which says Alisha's strategy for multiplication, break up the numbers, 8 times 12, 8 times 10 equals 80, 8 times 2 equals 16, 80 plus 16 equals 96, then shows an array model of that equation.

As a teacher in inclusive settings, number strings were a critical part of my daily mathematical work.  Routines are highly effective in inclusive classrooms, particularly routines like number strings which externalize complex cognitive processes.  By that delicious turn of phrase, I mean that a number string is not the kind of routine that teaches low-level thinking like memorization.  Instead, it allows kids to participate in the strategic thinking of other kids, giving them access to complex processes that too often only go on in individual minds. Continue reading “30 ways to make number strings more inclusive”

Why Conjectures Matter

This post is from our colleague and friend William Deadwyler, a 6th grade math teacher and strings enthusiast who works at MS 22 (South Bronx).


This summer I met Sylvia Glauster, a 5th Grade teacher at The Ancona School in Chicago.  Sylvia led a summer institute for 5th – 8th grade teachers at Math in the City on geometry, based on a new unit she co-wrote The Architects’ Project. My work with Sylvia inspired me to start gathering and publishing students’ conjectures. Outside of my classroom is a bulletin board where conjectures are published. Some of the conjectures are right, some are wrong. All were generated in class, based on investigations and number strings that we discussed together.  Investigating these conjectures will help students develop the curiosity and persistence that all successful mathematicians share.

Continue reading “Why Conjectures Matter”

Encouraging Strings Discussions

Defining the Problem:

In a recent workshop, a third grade teacher shared the following: “I think I’m doing it right, I ask a lot of questions like, ‘How did you solve?’ and ‘Can you explain your strategy?’ or ‘What do you think about _______’s approach?’ But the kids often just stare at me blankly. Only a handful will jump into the conversation. What am I doing wrong?”

Continue reading “Encouraging Strings Discussions”