Do you want to make common moves harder? One way to do this is to engage your core muscles - abdominal muscles and back muscles. Some gyms have mats that are especially slippery! Do forward and side lunges on these mats. Try some push ups too.
Do you want to make this harder? Grab a ball or other weight with a handle. You will see them at your gym, most likely. Did you ever wonder what their use is? Here is one use. Grab two of these balls with handles, for instance, and do push ups while holding them to the mat. A slippery mat will be harder than a regular mat. You will use intercostal and chest muscle fibers to keep the weights from slipping out from under you. Core muscles will be engaged. This is much harder than regular push ups. Try doing them with one arm if you can.
Be creative and see for yourself what other exercise variations you can do on a slippery mat with or without handle weights.
My third book, Pocket Guide to Fitness, is available on http://www.authorhouse.com and http://www.amazon.com. If you look up my name on those Web sites, you will find my other books The Boy in a Wheelchair and Life, Work and Play: Poems and Short Stories. These two books are on my Web site http://www.louizapatsis.com.