You're going to have to consider individual backgrounds.. Someone who is technically more competent will manage better.
Personally I don't teach this stuff in a way that is jazz specific, its just improv/composition in general with no stylistic constraint - though we do sometimes work in a specific genre/style/form etc.
Assuming that the student has some traditional classical background, (eg. has come to me from another teacher who focused on exams) first topic of discussion is usually that a scale isn't just a linear run of notes, and that we can have a much deeper understanding of the scale and use it to build music. And this may happen in a short time or over an extended run of lessons where you'll need to incorporate tunes with each step etc. - depends on your student.
To start increasing their understanding of the scale, and their ability to play in and around it we play patterns. These are not written out in notation, they are theoretically constructed based on scale degree numbers. So i give them a number pattern, such as 1,2,3,4,5. and then say "now shift it up so it starts on the number 2 note" (which may require further explaination or a demo so they clearly understand.. so in C major, they will have played CDEFG, then DEFGA - they take this through each scale degree. It comes out a bit like a hanon exercise but instead of reading it they have to create it and know the scale properly.
Then the challenge is increased by using a more complex pattern, so something pretty pretty ballsy (at this stage, and would come much later once we'd done more keys and other things - its just to illustrate where you can go) would be like 1, 3, 5, 7, 6, 4, b3, 3, 1, 1, in swing 8ths, which would sound kind of jazzy.. shifted to the next mode it would be 2,4,6,8,7,5,b4, 4, 2, 2 - but you get them to think of the D as 1, not 2.. so they are thinking modally. You can also use straight rhythms and do something more like a bach motif, or something styled on some other composer.. so that you're demonstrating the scale's function within a variety of musical examples.
Anyway, once you've done a bit of this, with simple patterns like 1324 for example, or the same simple patterns with different rhythms you bring in 135. Putting 135 through each mode will give you all the root triads found within the working key.. add the 7th if the student can handle it.. such as
C major, CEG (B)
D minor, DFA (C)
E minor, EGB (D)
F major, FAC (E)
etc.
In this situation I start asking them to play the "pattern" as a chord. - And I start asking for transitions between modes that are not linear.. more likely just random.. so they'll end up playing something like CEG, FAC, EGB, ACE, DFA, GBD, CEG (notice this includes a 2-5-1).
To get this under control it may mean doing simple improvisations over a 2 chord progression. C major, F major, C major, F major for example.. and then another 2 chord progression.. after this you can start talking about more complex common chord progressions.. tunes that use the 3 primary chords (there are millions of those) and ii-V-I situations.
There are a bunch of tunes that frequently use 2-5-1-6 turnarounds, "I get a kick out of you" is a good example.. it just repeats this through out the verses (though you have to deal with 6 operating as a secondary dominant and being outside the base scale, not a huge problem as its extremely common and allows you to put out that this stuff (using only scale notes) isn't rules its just a guide).
The tune "autumn leaves" is pretty much just awesome for the whole idea because it runs through the entire key in a 4ths progression (251 is a fragment of this). Means you practice all chords, all modes, and the melody itself lends it self to minor improvisational alterations.. the progression in the tune runs like this
Am, D7, G, C, F# half dim, B7, Em.
You can then play things like what I did over the 2-5-1 in the video (simple pentascale improv over each chord/mode) as a solo section between repetitions of the head. Where you have a 6 chord that would have in theory been a m7, but is a dom7 in the tune, a good mode for improv is the phyrgian dominant, based on the 5th degree of the harmonic minor. So where its B7 (such as in autumn leaves) you play the 5th mode of E harmonic minor.
As i said earlier I don't confine myself to jazz.. you can do things like an alberti figure in the LH and very scale like passages in the RH, that uses 1 4 5 progressions and you end up sounding like a clementi sonatina. You can encourage students to observe figurations found in their fully notated scores, be they jazz or otherwise.. and imitate the rhythms or chord progressions now that they can identify them.. look at different transitions between chords.. how other composers use different inversions of chords or voicings to make the same set of notes more interesting.
..you can ofcours prepare lessons like that.. say, find 5 sonatinas in the same key that have a passage with an alberti line. Draw on harmonic elements from all of them.. improvise/compose your own passage.
the rootless jazz LH voicings usually start out as 3rd and 7th only. - you would get to practicing 2-5-1s like this, as LH voicings plus improv, or RH voicings plus walking bass etc. AND as LH voicings of a tune, plus the melody, working from a lead sheet... then you add the 5,9, 6, 13 degrees to the chords, then things like b9s and 13s.. inversions of the voicings.. tritone substitutions.. this is months and months of practice and many tunes though to learn properly and in all keys.
etc, etc ramble ramble.. hope that helps in some way.
..I haven't really touched on arranging a standard tune.. hmm.. whole other topic, save for another post.
Topic: ABRSM Jazz syllabus and other recomendations