Humans rely on step-by-step reasoning to solve new problems, each step guided by the feedback of its effect on a potential solution. For complicated problems, such a sequence of step-by-step interactions might take place between the human and some sort of software system, like a Python interpreter, and the sequence of operations so obtained would then constitute an algorithm to solve a particular class of problems. Based on these ideas, this work proposes a general and scalable method to generate synthetic training data, which we in turn use to teach a Large Language Model to carry out new and previously unseen tasks. By tracing the execution of an algorithm, through careful transformations of the control flow elements, we can produce ``code traces'' containing step-by-step solutions for a range of problems. We empirically verify the usefulness of training on such data, and its superiority to tracing the state changes directly.