In every classroom, you are going to have students who finish their work quickly. Even with modifying my lessons so kids are working at their own level, some kids are just quick!
There are a couple things I have done in the past to help with this.
In third grade I have two folders. One is unfinished work-that is where their work that they haven't finished goes. They have until the end of the week to get this work turned in to me.
My other folder is their "busy work" folder. I had this in kindergarten as well. These folders are leveled. Not everyone has the same work inside. The work that goes inside includes materials the children need to practice or material to "push" the student ahead. And it's not all worksheets. I have webquest directions, scavenger hunt materials, and things to make/build.
We check these once a week, on a day that we don't have a lot of specials (art, music, PE, etc). I record the names of the students who need more work and go from there.
In third grade I have a white board. After each lesson, I write the assignment on that board. It stays up there and I keep adding. If I give a multiplication worksheet, I write it on the board. When I have everyone's sheet, I erase it. The children know, but need lots of reminders, to check this board and their unfinished work folder first. Then they can work on their busy work folder.
One other thing I do is have a SWAT team. This stands for Students Working Alongside the Teacher. This is a couple of students who I use to help me around the room. They might help organize supplies for me, put labels on things, file mail away, cut things out, help put up bulletin boards... These students are picked based on the previous weeks behavior. I try my best to pick a boy and a girl; however this past year I had way more girls than boys so it wasn't as easy.