I like the clock explanation.

Take 4/4 like stated above it is four beats/measure and a quarter note= a beat.

Now put that at 60 beats per minute{bpm} (which is quite slow) That is 1 beat every second if we use our second grade math.

Now how many measures or groups of four beats are there?

Well 4 beats = 1 measure so if my third grade teacher was right
60/4= 15 measures in a minute.

Now you can double time the tempo to 120 bpm which is a pretty good pace.

so you get 2 beats every second

30 measures in a minute.

It's a lot easier when you use Multiples of 60 as the tempo at first.

Now if we go to 5/4 the only difference is the number of beats per measure.

So now at 60 bpm we still have a beat every second but we cut the measures in that minute down to 12 and so on.

This is how I learned a long time ago in middle school band.