At my school, we are required to learn how to do these skills:
-Foward roll
-Backword roll
-Cartwheel
-Round off
-Headstand
-Headstand foward roll
-Split Leap
-Scale/arabesque
-Handstand
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Pre-competitive gymnastics is basically working on technique and conditioning, and getting you ready if you decide to take up competitive gymnastics. Many places let you compete in competitions. After some time if the coaches think you are doing well, they will recommend you to join the competitive group.
On an intermediate level of gymnastics you may lean harder level skills. Like on level 5 you tipically learn a glide kip on bars and perfect your front hand spring on vault. Usually intermediate gymnaists do competitive but some still do rec. and rock at it! One thing you must do on intermediate is stretch and condition every day and eat the right foods