Moving up by skips means you are moving higher either from line note to line note or from space note to space note.
Without needing to state the letter names, it is easy to play by skipping. Start on Middle C and play only the line notes.
Now try starting on D and play only the space notes.
Next try skipping downward from Middle C. Your eyes will be reading from left to right, but your hand will be moving to the left heading down into the lower pitches of the piano.
Start on Middle C and play moving lower by skips, striking only the line notes.
The Graph to Staff Approach breaks the beginning stages of reading music on the staff into easy progressive steps and fun activities.