When teaching a green horse:
To slow the stride I use posting trot. I slow my posting and horse naturally doesn't like the fact that I'm at one tempo and they are at another - so they naturally slow the temp. It does take a while but helps to lessen confusion since green beans may not yet understand Half Halts.
To teach lengthened strides - coming off short side of the arena take horse DEEP into the corner asking (with inside leg) horse to step deeply underneath their body in the corner - then head towards "X".
As soon as horse turns toward "X" and their entire body is STRAIGHT then HH (engine should already be revved) and SOFTEN - do NOT throw away reins or horse will fall on forehand and rush. Soften means allow elbows to come forward about an inch (to start). As soon as you feel horse start to rush (posting trot) then HH back to a working trot.
Continue across the diagonal - if you can do so try a second time to push horse forward, HH then soften elbows and allow horse forward until they start rushing or you reach letter on far side of the diagonal.
Dressage is for Trainers!