Question: I am an assistant professor preparing a 5 lecture series 'introduction to programming'. The target audience are first year engineering undergrads - from a mix of mechanical, electrical, electronic, telecomms and civil engineering majors. Some of these students will never have programmed before. We will use Matlab.

I am expecting that many of these students will never have coded before and almost all will not have seen Matlab before. They will need Matlab in all subsequent years of their degree.

Given the extremely limited time for this course, how can I give best bang for their buck, without it being too dry?

Is there something cool we could work towards creating over the 5 weeks?

More info: There are 5 x 4 hours sessions. Classroom cannot be flipped as there will be 50+ students.

Editing here to thank everyone who has taken the time and effort to give extremely helpful detailed replies. I appreciate it guys.

Answer: 
With only 5 sessions, I would abandon the idea of building something cool, and focus with laser-like precision on whatever they *need to know* going forward in their coursework. There is such a small amount of time to learn the basics of any programming language.

MatLab supports lambdas, objects, and GUI design, but unless they are going to get into rather serious programming, I imagine that you would steer clear of these. (I don't know how you would cover any of them in 5 days with novices in any case.)

The danger in heading towards UI and a game is that they will come out without being able to do what they presumably need in the next class, such as matrix multiplication, or graphing an integral multiplication. You may be better using your five sessions to delve into five areas of greatest need, as determined by the future required coursework of your students.
I don't know Matlab, so this answer is mostly about generic programming concepts.

The core of programming is problem solving, so I would think the best use of the limited time you have available would be to focus on computational thinking and providing them with the techniques they will need to be able to think their way around a problem sufficiently to be able to express a solution in code.

Matlab is of course designed specifically for solving problems rooted in various Scientific, Mathematical and Engineering domains, so ideally, any example programs you use for demonstration and explaining the concepts should be as close as possible to the types of problems that the students will be solving by themselves. 

One of the pre-requisites for being able to write the code to solve a problem is to have gained a clear understanding of the problem being solved, so it would be useful to stick to problems which the learners would already be able to understand on-paper.

It could be useful to look at the Harvard CS50 syllabus as a starting point, it places a heavy emphasis on developing computational thinking skills by challenging learners to solve typical programming problems: <https://cs50.harvard.edu/ap/syllabus/>

Many of the concepts covered in the first 3-4 lessons of the CS50 syllabus are universally applicable to programming in any language, and David J Malan's delivery of these concepts in his lectures seems to go down very well with his students. 

A number of other specific techniques which I believe would be useful:

* Problem decomposition, illustrated by describing a complex problem, analysing it and dividing into sub-problems.
* Steps to solving a problem by starting with example/test inputs, describing the steps, and reaching a result 'by-hand'.
* Pattern recognition and using generalisation to describe a solution using pseudocode, then translation into a runnable program
* Using the debugger to set breakpoints, inspect variables and step through code to find/fix errors.

Terminology, as well as the 'grammar' of the language is of course important too - there's a lot of jargon to to absorb in a very limited space of time. 

Newcomers frequently find themselves spending a great deal of time attempting to decypher syntax errors, so some of the most important terminology for them to understand will be the words/phrases which frequently appear in the Matlab error frame - for example, misuse of particular symbols/operators, or incorrect use of particular data types. 

Perhaps finally, make sure to include frequent reminders that they can (and should) be making extensive use of Google and StackOverflow to find out what the syntax errors and other jargon means as well.