With 3 children, they all learn differently. My 14 yo son just reads the verse over and over and over, has me quiz him, then goes back and reads it over and over and over.
My 11yo daughter lays upside down (usually on the stairs) with a white board. She writes the verse and reads it over and over. After a few times, she will erase a word, recite the verse, erase a word, recite the verse...... this goes on until she can do the entire thing from memory.
My youngest walks in circles around me while repeating what I say. It takes her about 15 circles and repeating the passage 2x to have it down well.
Of course none of this starts until we know what the verses mean.
My children work through the Awana book, therefore they are always learning different passages than their siblings. In the summer we review the book or do extra credit. If you don't use the Awana curriculum, require certain basic passages. If you have never tried memorizing before, it's never too late to start for yourself. God wants us to memorize His word. Take baby steps so you don't overwhelm yourself and give up.
If your student is An overachiever, encourage her to learn more and not stop just because the 'requirement' was met. This could be a new passage or the passages surrounding the original.
Example: you ask your 9 yo to memorize John 3:16. He gets it in a day. Instead of waiting a week to five him a new verse have him work on John 3:17. Then 3:18, And so on until you are ready for him to move on to another section.
Remember to be enthusiastic when encouraging anyone to memorize scripture. Your enthusiasm will help them to become enthusiastic themselves.