As I come from a performing arts background with a degree in Music Theatre I had fun performing this arts challenge.
I began the challenge by looking at and clapping the example sequence that uses the words Ta to symbolise a crotchet (a quarter note) and the word Ti-Ti to represent a quaver (an eighth note). This draws on from what is known as the kodaly method.
The example sequence went as seen below

After clapping out the sequence I began to look at forming my own clapping sequence using Ta (quarter note), and Ti-Ti (eighth note), as well as using Tika-Tika which symbolises a semi-quaver (sixteenth note).
The sequence uses 16 different boxes which repeat after the first 8. Using repetition within the clapping sequence gives students a sense of familiarity within the rhythm that assists in remembering the pattern.

I then used this same patterning to create a melody from the pentatonic scale (C D E G A in C Major). The notes played were above the middle C and ascended up to the A3 on a piano.

As you will note, while there is a clear pattern within the notes, the eighth and sixteenth box contain two different notes. The reasoning behind this was to leave the melody unresolved until the last note in the melody line.
I had a lot of fun creating these patterns and going back to my theory of music, I hope you enjoy clapping out the patterns or playing the melody of my sequence.