If you want to save your projects each week and work on them from home then you have to create a Scratch account.

Use the "Join Scratch" button at the top of the page.

Pick a username and password that your child will remember! It is advised not to use their real names so pick something fun like PotatoBoy55 or ilovechips21. Use an email address that you have access to as you will need this to reset the password when they forget it.