I really like bisecting music in all sorts of ways in discussion with my students, but the fact of the matter is that before I can talk this way about music really concrete ideas have to be formed.
Below is a conglomeration of ideas that I use to teach students how to read rhythm and how to understand time signatures. I think it works because it allows students to use rhythm like lego blocks and yet it also allows them to think about the sound of the rhythms when they are played. They can construct their own musical sentences using these tools rather than just thinking about the fractional relationships of rhythm. I hope this explanation can be useful for you too!