The short answer on Supplemental Instruction
The phrase Supplemental Instruction gets used loosely enough that it is worth pinning down before going any further.
Two words, two jobs: Supplemental names the approach and Instruction names who or what it is for. Most confusion comes from treating them as one idea.
Where this usually goes wrong is that a finished worksheet means the work was understood — a mistake that is invisible until something unfamiliar turns up.
Why instruction is the part that matters
Among students and the families supporting them, this is one of those ideas that seems abstract until the moment it is not — typically at the kitchen table on a school night.
Once you separate the supplemental framing from the instruction practice, the idea gets considerably more useful and considerably less quotable.
Two questions to work with
Open with What part of this already makes sense to you? — a diagnostic, not a test.
Follow with What would have to be true for your answer to be wrong?, which is where the actual thinking happens.
Making it routine
In practice this means working a problem aloud, then explaining the reasoning to someone else without notes.
The signal to watch for is the student starts asking their own next question before being prompted.
Next steps
The natural continuation from here is the beginner guide, then a first guided session on a topic that is currently frustrating.