In their highly recommended book "Outstanding Teaching: Engaging Learners", Mark Burns and Andy Griffith set out a number of techniques for tapping into the holy grail of engagement: intrinsic motivation.
Using foam dice (they do need to be foam or the activity quickly becomes too noisy) and a 6 x 6 grid of stimuli, a random element is introduced to the way learners interact with content. It can be particularly helpful with writing / creativity.
This example (encouraging learners to explore writing in the Gothic Horror genre) is fairly typical. Learners use dice to land on squares in the grid such as "Lost!" or an image of an egg timer, then attempt to write a sentence inspired by / including the content of the grid square. Learners work in pairs and swapping the pen after each sentence.
An Art example: You are trying to encourage your learners to practice using a range of techniques. You are less concerned about the final product, rather you want them to focus on the range of processes they can employ to create different effects. Supply an outline drawing, a 6 x 6 grid up on the board with different target techniques (oils, tone pencil, pastel, cross-hatching, etc.) and a foam die. Each pair rolls the die twice for an X and Y coordinate, identifies the target technique, e.g. tone pencil, and chooses an area of the outline drawing to fill, then repeats the process.
This has a number of advantages: it's fun and different; it seems to get past the "don't know where to start" / blank page syndrome; "cheating" (e.g. a learner rolling again to get a square they are particularly keen on incorporating into their work) is OK and might even be encouraged; it also has the potential to "depersonalise" interaction with creative content in a way that may be beneficial for some learners who are reticent about revealing their creative output.
Some thought needs to be given to where to go next once the "raw" content has been created - perhaps editing / amending for structure / narrative / coherence, and also to whether to work in pairs, small groups, etc.