This is a continuation of my previous post, where I use Taffanel/Gaubert's Exercises Journaliers no. 1 to practice polyrhythms. Check that out before trying these! It will give you the correct placement in the measure for 4:3 and 4:5, which I have not notated here.
In these exercises, the metronome stays the same but the player has to change gears. I like to use this as an articulation exercise. You can shift from single tonguing to double tonguing as the tempo changes (but the metronome doesn't). It keeps you on your toes.
Set your metronome to a 3-beat pattern. The suggested tempo is a quarter note=45 but you can start slower if it helps. You'll need to start on the third beat for this to come out right. I love the fact that this pattern gives you an added rest for breathing!
The following variation puts the polyrhythm first. If you are doing this as an articulation exercise, it is good to start with double tonguing and then go to single tonging. I find this shift to slower tonguing more challenging.