Big Band
Over the years I have noticed that many school big band charts are virtually unplayable for the guitarists. (Particularly for middle school aged students!) This is largely due to the commonly used keys and the extended chords that are often present in such charts. 
An easy option is to use tritone shapes. These are often the 3rd and 7th of the chord and the extensions are handled by the piano and horns.

The example below shows an easy way for a guitar player to play the chords shown (moving in 4ths). It is easy to play and in a swing style it can be very effective as the entire chord is not required. 



This example plays the same chord voicings. Notice that the chords shapes are exactly the same. The movement is still in 4ths but the chord names are different. This is a very common movement in so many songs and arrangements. This is quite a difficult sequence to play in big barre chord shapes. (Probably around 5th -6th grade standard!)

It's a great way of getting through the chord changes.

Bb7 contains Bb D F Ab
Eb7 contains Eb G Bb Db
Ab7 contains Ab C Eb Gb
Db7 contains Db F Ab Cb (same as B)
Notice that the 3rd and 7th of th chords are used.