You do want to include that next beat to lock things in rhythmically and make sure fingerings are right (if you stop before the beat and miss that connection, they don't always realize when they need an alternate).
Dotted rhythms, usually at a slower tempo:
Long short long short (basically turn the first and third 16ths into dotted sixteenths and the second and fourth into 32nds)
Short long short long (the same thing but opposite) (they will struggle to keep the short notes on the beat without pushing them ahead; watch that).
It's important to do it both ways, which makes them practice each connection very quickly but with time between to make sure it was right, and ensures they can control timing of fingers in general
You can also do fancier dotted rhythms if the basics aren't working:
Long short short short
short Long short short
short short Long short
short short short Long.
In any case, sometimes it's good to do the first variation one last time before you play it straight again, as that's usually closer to the feel.
Like musical words, note groupings can give players small reasonable chunks to keep track of in a run. NEVER group after the last sixteenth of a beat unless the music is really demanding it (very rare). Note jumps and articulations can guide note groupings, but if nothing stands out to you, grouping before the second 16th (e+a1) (e+a2) tends to work well.
If you've got groupings planned, you can practice one note grouping at a time, then the whole thing with pauses between groupings (like pausing between words for young readers), then with no pauses at all.
Identify scales, arpeggios, scales in thirds. Mark them. Practice those patterns separately, then in the music.
Make sure players have marked alternate fingerings (left F, forked F, left Eb, etc.), and done so efficiently (one letter or symbol, not multiple words) throughout the piece.
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