Each CD-booklet pair from the Associated Board has a set of 15 tunes broken down into 3 sets of 5: blues & ‘roots’, ‘standards’ and ‘contemporary’. The songs are played by a jazz quartet where you can join in on the ‘head’ or main theme, and where there is space for you to improvise as you respond personally to what you’re hearing. The score is there to help you, if you can interpret it at this stage, and there are ‘guide tones’ in the right places to help you start improvising. Then the set of songs is repeated without the main instrument so you can play the ‘head’ and your own improvisation against a ‘rhythm section' of piano, bass and drums. Plus there are some useful exercises on scales & rhythm appropriate to that level or grade.
One way of understanding improvisation is to see it as a new or additional melody set against the song's original framework; many great jazz solos are simple but moving melodic variations. It's essential however that improvisations sit rhythmically with the song; It's better to concentrate on just a couple of note pitches that are rhythmically right - less is more. Get with the song's 'groove'. Listen to the single-note 'head' or 'A section' of One Note Samba for example (along with its lyrics) and then listen to how its 'B section' cleverly complements it. Think about how the use of space and pauses give meaning to the notes that are played, just like comments in thoughtful conversations.
And for vocalists, get the lyrics to your favourite songs and sing against your favourite lyrical artists. Check out people like Ella Fitzgerald, Norma Winstone or Rene Marie, picking up their inflections, tonality, groove, articulation and timefeel in the process.