Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have been some public misunderstandings about the standards and the role that algorithms and representations have in the teaching and learning of mathematics. In this article, I will first look at how algorithms and representations are discussed in the standards, and then examine and unpack some of the public conceptions around algorithms and representations.