Connecting Concepts in Color: Patterns and Algebra

Abstract

A mathematical model captures information about the main ideas in a problem situation. The kinds of thinking needed to model with mathematics are central to the Common Core State Standards for Mathematics [CCSSM] (2010). In fact, “model with mathematics” is included in the standards as a valued habit of mind to be cultivated (Standard for Mathematical Practice 4) as well as core content. Modeling includes several kinds of activity: noticing associations among categories and quantities, developing mathematically useful representations of situations, analyzing relationships and representations, taking the risk of starting (and perhaps abandoning) a strategy. Important to modeling are making connections among representations while bringing to mind and choosing strategies for making sense of a scenario (Schifter, Bastable, & Russell, 2009; Seago, Mumme, & Branca, 2004). Clear in the CCSSM and the associated Learning Progression documents is that all of these skills, practices, and habits of mind are sharpened in middle school (Common Core Standards Writing Team, 2015)