Playing a piece all the way through from the start to the finish is the way to perform a piece.
To practise a piece involves working on each section of the piece - each bar, each phrase, each line, beginning middle ending - and working on each layer of the piece - the notes, the rests, the rhythm, the dynamics, the articulation, the fingering, the coordination of the hands.
Think Piano Posture. When learning piano is a new skill for you, make sure you pay a lot of attention to your posture (how you are sitting, and how your body is balancing and moving) move yourself closer or further away if necessary, and add a foot stool if your feet are not able to be flat on the floor when your arms are at the correct playing angle. Arms should be able to 'drop' from the shoulder. Check you are playing with relaxed arms and wrists.
Next pay special attention to your hand shape. Remember the ladybug from your lessons? Are you playing with a curved hand and playing on your fingertips and finger pads...Check your thumbs are playing on their 'corners' and that little fingers are not 'karate chopping'. Your hand and arm shape should be exactly as it is if you are standing and your arms are just resting at your sides from shoulder to fingers. (Gorilla arms) Another way to check is to place your hands on your knees when sitting on the piano bench. The way your hands curve over your knees is their correct shape for playing piano. No stress or strain. You need to be comfortable to make beautiful music.
Now you are ready to look at how to learn what is on the page.
Let's start with learning the notes. Start with a line if it looks easy enough, a bar or two if it looks tricky. One hand at a time is often helpful if the music is challenging.
Did it flow? Did it sound musical? Did it tell the story of what the piece is about?
How does the melody go? The first line...did it go well? Did you miss anything? All the notes the right length? Did it sound like you expected? Go over it another couple of times looking closely at the page as you go to check you didn't miss anything. Then add the second hand. Bass line - any notes you need to hold for a long time?
Put both hands together and check everything goes smoothly - as slow as you need to go to keep it moving and keep it correct. Coming up to speed comes easily when everything is in the correct place at the correct time in the music.
Any staccato? Phrase lines? Did it go smoothly? Did the fingering you chose work? Did you find it easy?
When a small section is working it is time to start a next line or next section. And repeat the above process working through to the end.
When 30 minutes is up take a break. You can always go straight back to it if you like, or come back to it later in the day...or the next day.