You need to warm up. Period.
A proper warm-up can increase the blood flow to the working muscle which results in decreased muscle stiffness, less risk of injury and improved performance. Additional benefits of warming up include physiological and psychological preparation.
Physically, the increased blood flow, vascular dilation and increased core temperature allows muscles to become more elastic and responsive. It allows for more efficient transfer of oxygen to the muscles and allows your body to work more efficiently.
Mentally, a warm-up clears your mind and increases your focus for the workout ahead. You need to get focused to lift heavy, run fast or do an intense workout. Your warm-up is also a time for you to strategize, plan, and prepare your mental game. Practice visualization and positive self-talk as you go through the motions in your warm up.
Come in early. Get your warm-up done early so you are ready to go when class starts.
Things you should work on.
Mobilize your restrictions. If you know you are tight in the hips or the shoulders or any place else, then you must mobilize that particular area. That means get it warm, stretch it and loosen it up prior to your workout. If you know you have tight hips and are going to be squatting, then your warm up should focus on heating, stretching and loosening up your hips in preparation.
Practice new skills. When you come into the gym you should be fresh and alert and ready to practice. You should always be working on a new skill to improve your athletic base. A skill should be both physically and neurologically demanding for you — that might mean double unders, snatches, handstands, muscle ups, etc., or it might mean focusing on mastery of a simpler skill like the squat. You should put in time every day (or at least every workout day) towards developing your skills.
Routines are good.
Having a routine is excellent because it allows you to get to work immediately and it allows you to get right into your mental preparation without having to spend energy figuring out what to do next. It also allows you to improve with repetition. However, you should be careful that your routine doesn’t turn into a rut. If you are not improving in your warm-up, then you should consider changing some elements of it so that you see improvement. If your warm-up includes 10 pull-ups with a thick band for assistance and you never progress to a lighter band, then there is a problem. If your warm-up includes a hip stretch and your hips never get more flexible, then you need to change the stretch or work harder. If your skill practice includes working on handstands but your handstands are not improving then you have to consider changing it up somewhat and finding a progression that lets you progress.
In short, a good warm-up sets you up for success, so be sure to get in early and warm up.