This book is a result of many influences. They include these books below, all of which are available used online:
Richard Feldman, Reason and Argument (Prentice Hall, 1999)
This book is, in many ways, an ethics-focused and condensed version of Feldman’s book, especially his discussion of “simple moral arguments.”
James (and Stuart) Rachels, The Elements of Moral Philosophy (McGraw Hill, many editions, 1986-2014, current 8th edition)
Rachels emphasizes that the morally correct thing to do is always determined by the reasons. From this we develop the strategy of, after identifying some conclusions about the topic, asking what reasons there are to believe that those various conclusions, for example, doing such and such is wrong and doing such and such is not wrong, making a list of these reasons, and then formulating these arguments in logically valid form and evaluating them as sound or not.
Fred Feldman, Introductory Ethics (Prentice Hall, 1978)
This book emphases stating arguments and theories in utterly clear and understandable ways and evaluating these using arguments explicitly stated in logically valid form.
Making Moral Progress focuses mostly on controversial issues. These are many in print collections of readings on controversial moral issues to use with this book, and there are many appropriate readings available online. An exceptionally good collection of readings is edited by David Boonin and Graham Oddie, What’s Wrong? Applied Ethicists and Their Critics, 2nd edition (Oxford University Press, 2009). A collection with very short, less than one page, readings on both ethics and philosophy, edited by Peg Title, is What If . . .: Collected Thought Experiments in Philosophy (Longman, 2005). 1000WordPhilosophy.com is also an excellent source for concise readings on ethical topics.
This book can be also used with no readings at all: the arguments discussed can come from your own thoughts and experiences, from brainstorming in a group, from asking other people, from the internet, from anywhere! On the theme of courses that involve evaluating arguments, but not relying on readings for the arguments, see William B. Irvine, “Teaching without Books,” Teaching Philosophy 16.1 (1993): 35-46.
For an interesting set of readings on “everyday” moral issues, as opposed to moral issues that are more “social issues,” many of which we do not address, see David Benatar’s (out of print) Ethics for Everyday (McGraw Hill, 2002).