This article establishes and addresses opportunities for ethics integration into Machine-learning (ML) courses. Following a survey of the history of computing ethics and the current need for ethical consideration within ML, we consider the current state of ML ethics education via an exploratory analysis of course syllabi in computing programs. The results reveal that though ethics is part of the overall educational landscape in these programs, it is not frequently a part of core technical ML courses. To help address this gap, we offer a preliminary framework, developed via a systematic literature review, of relevant ethics questions that should be addressed within an ML project. A pilot study with 85 students confirms that this framework helped them identify and articulate key ethical considerations within their ML projects. Building from this work, we also provide three example ML course modules that bring ethical thinking directly into learning core ML content. Collectively, this research demonstrates: (1) the need for ethics to be taught as integrated within ML coursework, (2) a structured set of questions useful for identifying and addressing potential issues within an ML project, and (3) novel course models that provide examples for how to practically teach ML ethics without sacrificing core course content. An additional by-product of this research is the collection and integration of recent publications in the emerging field of ML ethics education.