From Pam Harris' Building Powerful Numeracy for Middle & High School Students:
“A problem string is a purposefully designed sequence of related problems that helps students mentally construct numerical relationships and nudges them toward a major, efficient strategy…[P]roblem strings are not intended to be used all at once, handed out as worksheets, or used as independent work for students.
By using models and problem strings in a systematic way, with an eye toward the major, efficient strategies, we can help secondary students construct mental numerical relationships. For those students who come to us with some elementary work in numeracy, we can build on their current understanding and support their continued development, while at the same time helping those who lack that understanding gain the foundation they need. When we give secondary students this numerical power, we also help them engage in learning higher mathematics with more confidence and more success."
Pamela Weber Harrris, Building Powerful Numeracy for Middle and High School Students, p. 10
Problem strings are not only for numeracy. Check out the algebra problems strings on this site.