I may have missed what you're asking about, but the ta/ti/tika quarter/eighth/sixteenth syllable system is a rhythm counting system to teach music, the Kodály Method[1]. This was coincidentally also what my first music teacher used but I didn't know the name until I was reminded of it even existing here and did a little digging.
I might still just be totally misreading things but I don't see how the assignment above is a valid, let alone a normal application of the Kodály Method?
Seems like the teacher really misunderstood what it was/meant for. I could totally be wrong here.
Translating sentences on paper (and again, how? why? by what metrics?) seems like the exact opposite of what the Kodály Method utilizes and its underpinning principles?
I understand the confusion and it's why I wasn't quite sure if I'd correctly identified what was happening. I took sentence and word as the music theory terms sentence[1] and motive[2]. Then translating the beats of an example into Kodály syllables seemed like a reasonable exercise that could be objectively evaluated.
[1] https://musictheory.pugetsound.edu/mt21c/SentenceStructure.h...
[2] https://musictheory.pugetsound.edu/mt21c/MotiveSection.html
I mean just saying that out loud I can exactly see how it works, pretty interesting. Like why do I naturally say Tika faster than ti and ti faster than ta?
The /t/ consonant in the method requires you to have your tongue touch the roof of your mouth, and the /a/ vowel requires you to have your jaw hang low. The /ti/ sound in the method has your jaw fixed in place whereas it has to move to produce the /ta:/ sound.