You could try something along these lines ...
Tell your student that there are animals hiding on the piano and that you're going to find them together. Play a group of 2 black keys (one after the other, not the 2 notes together) as you say, "Gir-affe" (one syllable for each note). Then find another 'Giraffe' on the piano, and then another.
Then say, "Look, here's an 'El-e-phant'" as you play a group of 3 black keys. Find another 'Elephant', and then another.
You could then play a 2 or 3 group of black keys without saying anything and ask your student if it's a giraffe or an elephant. If he/she gets the hang of this, you could extend it to getting your student to find the giraffes and elephants.
It's possible that your student is struggling with the concept of dividing up the many black keys they can see into 'groups' and 'numbers'. Removing these concepts from the process of differentiation may provide the intermediate step they need.
HTH