This is the most simple question in the world, but it is surprisingly difficult to explain to a student. The heart rate is measured in bpm, beats per minute. Minutes are a true unit. Beats are not a true unit. However, we are using beats as if it where a unit. I'm not sure how to explain this to a student, and I'm confusing myself. Please help.
BPM means "beats per minute" but that doesn't mean that "beats" is a "unit." Otherwise we could have an infinite number of "units" based on counting other things.
For instance: How many red two-door cars with sagging taillights and broken headlights with expired license plates pass by a point on this road in a minute? Oh, $7$, you say? Well I suppose the rate is 7 RTDCSTBHELPPM."
So now "RTDCSTBHELP" is a "unit"?!?!
@Stork led me to the answer, but he didn't quite get there. A "beat" is a "counting unit". This is the term I've been looking for! A "dozen" is also a counting unit. If you google "counting unit", you will find it is a fairly common term. So, if a "beat" is a counting unit, then what kind of unit is a "second". A "second" is a "measuring unit". This implies that counting and measuring should be treated as distinct activities, which makes sense. I had never really stopped to realize that counting and measuring are distinct.
I do apologize for dwelling on this, but I think this terminology will clarify matters for students.
ps. This ancient paper appears to discuss the distinctions.