The first time I've been to the Co-op and not played a tune. Jake worked on I,VI,II,V chord progressions. This is a progression that is used a lot in the harmony to I've Got Rhythm which is a chord progression used in a lot of jazz standards. I will illustrate in C major (which is the key that Bb instruments will play for I've Got Rhythm, more commonly known as Rhythm Changes). This sequence is also common at the end of a section with a I chord at the begining of the next section and is called a turnaround. It joins the sections up harmonically.
The I chord is C major7, VI is A minor7 but Jake changed this to dominant 7 e.g A7, II is Dm7 and V is G7. We then played a third or seventh from each chord over a 4 bar sequence. When alternating between the 3rd and 7th we would get a guide tone, a line of notes that only move up to a tone. We then played 2 notes to the bar, again playing 3rds and 7ths. This is excellent practice for learning chords and sequences. For the A7 the third is C# which is not part of the C major scale. We then improvised but had to play a third or seventh of the chord on beat one of each bar. This is known as leading tones.
The third and seventh are what define the nature of the chord, i.e. is it a major, minor, dominant, half diminished etc. To use those tones in this way really maps the chord progression. Steve Watterman, a couple of weeks ago, said that that is what he looks for when auditioning people for the Trinity jazz degree.
You can move on to playing thirds and sevenths on beats one and three. Plenty to practice there. We also went through the scales to play for each chord. For the I chord just play C major, IV is a dominant 7 so there are a number of scales that you can use to make it sound more jazzy. Jake likes the harmonic minor that starts a fith below. So for A7 you would play the harmonic minor that starts on D. Harmonic minor scales are major scales with a flat 3rd and 6th so you have F natural (not sharp) and Bb rather than B plus C sharp of course. Start that scale on A though. The Bb is a flat 9 and the C# is the third of the chord. Emphasise these notes when playing. For the II chord play the dorian which is C major starting on the D and for the V chord (G7) you can play the harmonic minor that starts a fith below again (C) but work that one out for yourself.
All of this stuff sounds complicated if you are not familiar with it but work on it and it comes more easily.